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<?xml version="1.0" encoding="UTF-8"?> <!DOCTYPE archimedes SYSTEM "../dtd/archimedes.dtd"> <archimedes xmlns:xlink="http://www.w3.org/1999/xlink"> <info> <author>Guevara, Giovanni di</author> <title>In Aristotelis mechanicas commentarii</title> <date>1627</date> <place>Roma</place> <translator/> <lang>la</lang> <cvs_file>gueva_mecha_005_la_1627.xml</cvs_file> <cvs_version/> <locator>005.xml</locator> </info> <text> <front> </front> <body> <chap id="N10019"> <pb id="p.0001" xlink:href="005/01/001.jpg"/> <p id="N1001E" type="head"> <s id="N10020">IOANNIS <lb/>DE GVEVARA <lb/>CLER. REG. MIN. <lb/>IN ARISTOTELIS MECHANICAS <lb/>Commentarij.</s> </p> <p id="N1002B" type="head"> <s id="N1002D"><emph type="italics"/>VNA CVM ADDITIONIBVS QVIBVSDAM <lb/>Ad eandem materiam pertinentibus.<emph.end type="italics"/></s> </p> <figure id="id.005.01.001.1.jpg" xlink:href="005/01/001/1.jpg"/> <p id="N1003B" type="head"> <s id="N1003D">ROMAE, Apud Iacobum Ma&longs;cardum, MDCXXVII. <lb/>SVPERIORVM PERMISSV.</s> </p> <pb xlink:href="005/01/002.jpg"/> <p id="N10045" type="main"> <s id="N10047">Imprimatur &longs;i videbitur Reuerendi&longs;s. <!-- REMOVE S-->P. Mag. Sac. <!-- REMOVE S-->Pal. <!-- REMOVE S-->Apo&longs;t. <!-- REMOVE S--><emph type="italics"/>A. Epi&longs;c. <!-- REMOVE S-->Hieracen. <!-- REMOVE S-->Vice&longs;g.<emph.end type="italics"/><!-- KEEP S--></s> </p> <p id="N1005B" type="main"> <s id="N1005D"><emph type="italics"/>Imprimatur<emph.end type="italics"/></s> </p> <p id="N10064" type="main"> <s id="N10066">Fr. <!-- KEEP S--></s> <s id="N1006A">Paulus Palumbara Socius Reuerendi&longs;s. <!-- REMOVE S-->P. Fr. <!-- KEEP S--></s> <s id="N10070">Nicolai Ro­<lb/>dulfij Sac. <!-- REMOVE S-->Pal. <!-- REMOVE S-->Apo&longs;t. <!-- REMOVE S-->Mag. Ord. <!-- REMOVE S-->Prædic. <!-- KEEP S--></s> </p> <pb xlink:href="005/01/003.jpg"/> <p id="N10081" type="head"> <s id="N10083">ILLVSTRISS^{MO} PRINCIPI</s> </p> <p id="N10086" type="head"> <s id="N10088">FRANCISCO <lb/>BARBERINO <lb/>S. R. E. CARDINALI <lb/>AMPLISSIMO <lb/><emph type="italics"/>IOANNES DE GVEVARA.<emph.end type="italics"/></s> </p> <p id="N10097" type="main"> <s id="N10099">Q<emph type="italics"/>vod olim opus in Ari­<lb/>&longs;totelis Mechanicas, dum <lb/>Philo&longs;ophiæ, & Mathe­<lb/>maticis vacarem inter­<lb/>mittere coegit nouæ con­<lb/>templationis occa&longs;io, hoc <lb/>ip&longs;um præteritis diebus <lb/>(Illu&longs;tri&longs;sime Princeps) dum publicis nego­<lb/>tijs, <expan abbr="grauioribusq.">grauioribusque</expan> &longs;tudijs implicatus, ægrè <lb/>aut vix, vt decet aggredi potui&longs;&longs;em, breuiter vt­<lb/>cunque perficere, ac prælis mandare, tua me <lb/>compulit ampli&longs;sima gratia. </s> <s id="N100B9">Cum enim te pri­<lb/>mò Magni Patrui, <expan abbr="Summiq.">Summique</expan> Pontificis Lega­<lb/>tum ampli&longs;simum, in Galliam nauigantem, <lb/>ac nuper ex Hi&longs;pania redeuntem ad afferen­<pb xlink:href="005/01/004.jpg"/>dam pacem animis, profligandumque maxi­<lb/>morum Regum auctoritate exortum in Italia <lb/>bellum, quo poteram ob&longs;equio, atque opera eiu&longs;­<lb/>dem Pontificis iu&longs;&longs;u pro&longs;equerer, nobili&longs;simo <lb/>in comitatu innumeræ excitabantur quæ&longs;tio­<lb/>nes, tùm circa rem nauticam, tùm circa ma­<lb/>chinariam, atque vectoriam in vniuer&longs;um<gap/>; <lb/>quarum &longs;olutiones è mechanicis principijs pe­<lb/>tere operæ pretium erat. </s> <s id="N100DC"><expan abbr="Cumq.">Cumque</expan> hinc orta fui&longs;­<lb/>&longs;et mentio de meis hi&longs;ce lucubrationibus eodem <lb/>in genere partis, gratum fore cognoui, &longs;i vlti­<lb/>mam ip&longs;is manum imponens legendas eas ti­<lb/>bi litterarum amanti&longs;simo pro animi refectio­<lb/>ne obtuli&longs;&longs;em. </s> <s id="N100EC">Infatigabiles namque animi eo­<lb/>rum qui in rebus maximis occupantur, non <lb/>ocio, &longs;ed varietate reficiuntur, & oblectantur: <lb/>præ&longs;ertim cum à grauioribus ad leuiora (di­<lb/>gna tamen, & aliquo in genere præ&longs;tantia) vel <lb/>ab agilibus ad &longs;peculabilia, & è contra, oppor­<lb/>tuna quadam vici&longs;situdine conuertuntur. </s> <s id="N100FB">Sed <lb/>nec &longs;emper leuiora, aut minoris ex &longs;e conditio­<lb/>nis dixerim, quæ in contemplationem mecha­<lb/>nicam cadunt, vtpotè quæ non modò ad res per <lb/>magni momenti, ac nece&longs;&longs;arium humanæ vi­<lb/>tæ v&longs;um, &longs;plendoremque ordinantur: quæque <lb/>proinde apud Reges, ac Principes ex quo ge-<pb xlink:href="005/01/005.jpg"/>nus hominum capit, incomparabilem obtinue­<lb/>runt extimationem; verùm quæ &longs;peciali qua­<lb/>dam ratione, in aliam ampliorem, <expan abbr="diuinioremq.">diuinioremque</expan> <lb/>contemplationem, &longs;ummi videlicet rerum ma­<lb/>chinatoris nos conducant. </s> <s id="N1011A">Quippe qui talia hu­<lb/>mano ingenio excogitare dedit molimina, qui­<lb/>bus multaque &longs;upra naturam &longs;unt, naturam ip­<lb/>&longs;am emulando perficeret, arte &longs;uperando ea à <lb/>quibus natur a vincimur, (vt Antipho &longs;cribit <emph.end type="italics"/><arrow.to.target n="marg1"/><lb/><emph type="italics"/>Poeta) & cæle&longs;tem machinam eiu&longs;que mul­<lb/>tiplicem, ac inuariabilem motum, orbi&longs;que to­<lb/>tius molem imitaretur: vt Archimedes alij­<lb/>que permulti in&longs;ignes Mechanici opere præ­<lb/>&longs;titerunt, & Cambray publico in foro li­<lb/>cet videre. </s> <s id="N1013A">Nimirum arte manum dirigente <lb/>tamquam potentiam executiuam, & in&longs;tru­<lb/>mentariam, effectricemque omnium excogi­<lb/>tabilium machinarum. </s> <s id="N10143">Quæ &longs;olis homini­<lb/>bus iccirco data e&longs;t, vt perhibet Philo&longs;ophus,<emph.end type="italics"/><arrow.to.target n="marg2"/><lb/><emph type="italics"/>quia &longs;oli inter omnia animalia &longs;umma pru­<lb/>dentia, in qua ars tota fundatur præditi &longs;unt. <lb/></s> <s id="N10154">Vnde &longs;icut mens ip&longs;a humana imaginem <lb/>diuinæ &longs;apientiæ, ac prouidentiæ refert dum <lb/>cuncta rectè di&longs;ponit; ita, & manus homi­<lb/>nis, omnipotentiam quodammodo exprimit <lb/>Creatoris, dum tam varia, ac mira, Me-<pb xlink:href="005/01/006.jpg"/>chanica cognitione duce patratur. </s> <s id="N10163">Quæ &longs;i <lb/>cunctis ob &longs;ui generis excellentiam maximo <lb/>cum animarum prouentu, atque decore con­<lb/>&longs;ideranda &longs;e offerunt: quàm dignè interdùm <lb/>hac in contemplatione morabitur, quem fru­<lb/>ctum non ex ea iucundè decerpet, qui diuina­<lb/>rum rerum meditationibus a&longs;&longs;uetus, pium­<lb/>que in Deum affectum exercens ip&longs;um &longs;um­<lb/>mum moderatorem veneratur, ac iugiter in <lb/>mundi regimine imitatur; dum non modo <lb/>firmum &longs;e Eccle&longs;iæ Cardinem præbet, in <lb/>quo eius circumuertitur, ac fulcitur machi­<lb/>na gubernationis. </s> <s id="N1017E">Sed ei qui ip&longs;ius vniuer­<lb/>&longs;alis Eccle&longs;iæ nauem &longs;ummo imperio Chri&longs;ti <lb/>vice moderatur, ac regit tanta ob&longs;eruantia, <lb/>atque virtute mini&longs;trat, tali ope atque con&longs;i­<lb/>lio ade&longs;t, vt vnica veluti vtriu&longs;que manu mi­<lb/>&longs;ticæ huius nauis gubernaculum cen&longs;eatur <lb/>inflecti? </s> <s id="N1018D">Tibi igitur Cardinalis Ampli&longs;si­<lb/>me dum talia tuum erga Sancti&longs;simum <lb/>Patruum ter optimum Pontificem agis, mu­<lb/>neraque penè diuina per&longs;oluis, non mediocris <lb/>prouentus &longs;imul, ac iucunditatis offertur <lb/>occa&longs;io in his, quos dicaui præ&longs;tanti&longs;simæ <lb/>&longs;cientiæ Commentarijs. <!-- KEEP S--></s> <s id="N1019D">Nam, & motus <lb/>orbis, vel cuiu&longs;que globi circa cardines, ac <pb xlink:href="005/01/007.jpg"/>circuli circa centrum, admirabile&longs;que eius <lb/>proprietates in ip&longs;is patebunt; & modus quo <lb/>paruo gubernaculo ingentia circumferuntur <lb/>nauigia: quod etiam Iacobus Apo&longs;tolus mi-<emph.end type="italics"/><arrow.to.target n="marg3"/><lb/><emph type="italics"/>ratus e&longs;t, & ad martalia tran&longs;tulit. </s> <s id="N101B5">In&longs;uper <lb/>& quo pacto vela dare liceat, ac remigio vti <lb/>contingat ad nauis progre&longs;&longs;um: Quod Petri <lb/>nauim quam in altum ducere Saluator præ­<lb/>cepit ob oculis ponit: Et qua denique ratione <emph.end type="italics"/><arrow.to.target n="marg4"/><lb/><emph type="italics"/>exiguo pondere ingentia leuentur onera, vt <lb/>vniuer&longs;aliter di&longs;camus; cum Paulo, quan-<emph.end type="italics"/><arrow.to.target n="marg5"/><lb/><emph type="italics"/>tumuis magnum, ac diuturnum in &longs;e &longs;it, <lb/>quod pro Chri&longs;ti nomine patimur in hac vi­<lb/>ta, momentaneum tamen, ac leue in fide­<lb/>lium &longs;tatera inueniri, &longs;olo pondere eius quam <lb/>&longs;peramus futuræ gloriæ, ac retributionis: <lb/>Aliaque permulta id genus licebit &longs;pectare, <lb/>non minus forta&longs;&longs;e ad moralem, ac politi­<lb/>cam in&longs;tructionem, quàm ad vtilem in reli­<lb/>quis, iucundamque Principis exercitatio­<lb/>nem. </s> <s id="N101E6">Quod &longs;i Amplitudini tuæ inter has tem­<lb/>porum angu&longs;tias, non &longs;atis digna obtulerim, <lb/>menti&longs;que propo&longs;itum haud plenè a&longs;&longs;ecutus <lb/>fuerim, ob&longs;equenti&longs;simum, grati&longs;simumque <lb/>&longs;altem in eis a&longs;pice votum, dum vix è Tri­<lb/>remibus po&longs;t longam nauigationem tecum <pb xlink:href="005/01/008.jpg"/>egre&longs;&longs;us, multis, ac varijs honoribus au­<lb/>ctus, vt quo poteram pacto ob&longs;equium erga <lb/>te meum illicò præ&longs;tarem, perpetuoque ani­<lb/>mo in&longs;eruirem, ea detuli prout iacent; morem <lb/>putans gerere tuæ voluntati.<emph.end type="italics"/></s> </p> <p id="N10201" type="margin"> <s id="N10203"><margin.target id="marg1"/>Apud Ari&longs;­<lb/>tot. <!-- REMOVE S-->in <lb/>qu&etail;&longs;t. </s> <s id="N1020E">Mec.<!-- REMOVE S--><margin.target id="marg2"/>Lib. 4. de <lb/>part. </s> </p> <p id="N10217" type="margin"> <s id="N10219">ani­<lb/>mal. </s> <s id="N1021E">cap. <lb/>10.& ma­<lb/>gn. </s> <s id="N10225">Mo­<lb/>ral. <!-- REMOVE S-->c. <!-- REMOVE S-->33.</s> </p> <p id="N1022E" type="margin"> <s id="N10230"><margin.target id="marg3"/>In epi&longs;t. <lb/><!-- REMOVE S-->cap. 3.<!-- KEEP S--></s> </p> <p id="N10239" type="margin"> <s id="N1023B"><margin.target id="marg4"/>Luc. <!-- REMOVE S-->cap. <lb/>5.<!-- KEEP S--></s> </p> <p id="N10245" type="margin"> <s id="N10247"><margin.target id="marg5"/>2. Cor. </s> <s id="N1024C">4.<!-- KEEP S--></s> </p> <figure id="id.005.01.008.1.jpg" xlink:href="005/01/008/1.jpg"/> <pb pagenum="1" xlink:href="005/01/009.jpg"/> <p id="N10259" type="head"> <s id="N1025B">IOANNIS <lb/>DE GVEVARA <lb/>CLER. REG. MIN. <lb/>IN ARISTOTELIS MECHANICAS <lb/>Commentarii: <lb/><emph type="italics"/>VNA CVM ADDITIONIBVS QVIBVSDAM <lb/>Ad eandem materiam pertinentibus.<emph.end type="italics"/></s> </p> <p id="N1026E" type="head"> <s id="N10270">OPERIS ARGVMENTVM.</s> </p> <p id="N10273" type="main"> <s id="N10275">Tota hæc Ari&longs;totelis Mechanica tra­<lb/>ctatio in duas partes diuiditur, in qua­<lb/>rum prima, vniuer&longs;alis quædam do­<lb/>ctrina traditur de natura & obiecto <lb/>ip&longs;ius facultatis Mechanicæ, tum de <lb/>cau&longs;is & principijs earum <expan abbr="operationũ">operationum</expan> <lb/>ad quas facultas ip&longs;a ordinatur in vni­<lb/>uer&longs;um; quæ &longs;anè principia vt præco­<lb/>gnita, &longs;unt etiam &longs;peciales rationes <expan abbr="a&longs;&longs;enti&etilde;di">a&longs;&longs;entiendi</expan> conclu&longs;ionibus <lb/>in &longs;uis demon&longs;trationibus, præter vniuer&longs;aliora illa Geome­<lb/>trica elementa, ac theoremata, quibus pa&longs;&longs;im quoque vtitur <lb/>in ei&longs;dem demon&longs;trationibus. </s> <s id="N10296">Huiu&longs;modi autem cau&longs;æ at­<lb/>que principia, &longs;unt quæ de natura & admirandis proprietati­<lb/>bus circuli ab ip&longs;o Ari&longs;totele afferuntur. </s> <s id="N1029D">Siquidem in re&longs;o­<lb/>lutione, ad ea reducuntur & in ip&longs;is fundantur quæcunque <lb/>de mechanicis in&longs;trumentis, <expan abbr="eorumq.">eorumque</expan> motionibus in progre&longs;­<lb/>&longs;u demon&longs;trantur, vel quæcunque ad artificio&longs;am motionem, <lb/>aut detentionem grauium & leuium hìc o&longs;tenduntur. </s> <s id="N102AC">Proin­<pb pagenum="2" xlink:href="005/01/010.jpg"/><expan abbr="deq.">deque</expan> ex ip&longs;is totam artem mechanicam tanquam ex proprijs <lb/>principijs intelligemus con&longs;urgere. </s> <s id="N102B9">Quamuis huc etiam &longs;pe­<lb/>ctent, & inter eadem principia computari debeant, quæ Ar­<lb/>chimedes, Hero, ac Pappus cum alijs tradiderunt de centro <lb/>grauitatis, in quibus pariter variæ, ac perplures demon&longs;tra­<lb/>tiones mechanicæ fundantur: quæ que propterea à nobis bre­<lb/>ui&longs;&longs;imè colligentur, & ad complementum doctrinæ inferius <lb/>in Additionibus afferentur. </s> </p> <p id="N102C8" type="main"> <s id="N102CA">In &longs;ecunda vero parte huius Mechanicæ tractationis tri­<lb/>gintaquinque Ari&longs;toteles quæ&longs;tiones veluti problemata qu&etail;­<lb/>dam proponit, in quarum &longs;olutionibus, &longs;ingulis experimentis <lb/>ob&longs;eruatis ac ritè per&longs;pectis, <expan abbr="&longs;ingulisq.">&longs;ingulisque</expan> difficultatibus occur­<lb/>rendo, vniuer&longs;am applicat doctrinam in priori parte traditam. </s> </p> <p id="N102D5" type="main"> <s id="N102D7">Rur&longs;us autem primam partem huius libri &longs;eu tractationis <lb/>in duo tantum veluti capita &longs;ub duobus titulis Ari&longs;toteles di­<lb/>&longs;tribuit. </s> <s id="N102DE">In quorum primo agitur de artis mechanicæ obie­<lb/>cto ac facultate. </s> <s id="N102E3">In &longs;ecundo verò de proprietatibus circuli <lb/>in quibus mechanicæ demon&longs;trationes penè omnes fundan­<lb/>tur. </s> <s id="N102EA">Quoniam verò doctrina quæ in ip&longs;o &longs;ecundo capite <expan abbr="cõ-tinetur">con­<lb/>tinetur</expan>, non modò fu&longs;ior e&longs;t, &longs;ed etiam ob&longs;curior, vt commo­<lb/>dius no&longs;tris commentarijs dilucidetur, eam vlteriùs in textus <lb/>diuidendam e&longs;&longs;e cen&longs;uimus, iuxta numerum proprietatum <lb/>circuli, de quibus ip&longs;e philo&longs;ophus tractat; <expan abbr="primumq.">primumque</expan> caput <lb/>prædictum, etiam &longs;ub textus nomine & in&longs;criptione ad vni­<lb/>formitatem &longs;ermonis, ac diui&longs;ionis comprehendere placuit. </s> </p> <p id="N10301" type="main"> <s id="N10303">Tran&longs;lationem denique Leonici elegimus tanquam com­<lb/>muniorem, licet in quibu&longs;dam deficiat, quoniam adhuc gre­<lb/>cus textus mendis e&longs;t plenus. </s> <s id="N1030A">Et quidem mirandum, <expan abbr="dolen-dumq.">dolen­<lb/>dumque</expan> valde e&longs;t, aureum hoc opus Philo&longs;ophi, diuinis propè <lb/>&longs;peculationibus refertum, tot verborum tran&longs;po&longs;itionibus & <lb/>corruptionibus deprauari. </s> <s id="N10317">Qua de cau&longs;a forta&longs;&longs;e permulti il­<lb/>lud exponere neglexerunt, ac difficile iuxtà verum &longs;en&longs;um <lb/>Auctoris intellexerunt. </s> <s id="N1031E">E&longs;t enim in quibu&longs;dam partibus di­<lb/>minutum in alijs verò redundans, ac in multis confu&longs;um. <lb/></s> <s id="N10324">Quapropter nonnullæ nobis permittendæ erunt tran&longs;po&longs;itio­<lb/>num reductiones, <expan abbr="verborumq.">verborumque</expan> re&longs;ecationes, aut additiones <pb pagenum="3" xlink:href="005/01/011.jpg"/>circa litteram ip&longs;ius textus, quam penitus & in rigore &longs;emper <lb/>&longs;ectari nequaquam liceret, ob præfatam corruptionem. <lb/></s> <s id="N10335">Pro viribus tamen eam &longs;ectabimur, &longs;en&longs;um enucleando, ac <lb/>exponendo, nunc per modum parafra&longs;is, nunc vero per mo­<lb/>dum interpretationis & exten&longs;ionis. </s> <s id="N1033C">Multa in quibu&longs;dam lo­<lb/>cis addendo, prout opus fuerit ad complementum doctrinæ, <lb/><expan abbr="multaq.">multaque</expan> pariter &longs;ub Additionum titulo, &longs;eor&longs;um extra com­<lb/>mentarios annectendo, vt &longs;iggillatim quæ &longs;citu digna &longs;unt, & <lb/>ad mechanicam contemplationem pertinent pleniùs eluce­<lb/>&longs;cant. </s> </p> <figure id="id.005.01.011.1.jpg" xlink:href="005/01/011/1.jpg"/> <pb pagenum="4" xlink:href="005/01/012.jpg"/> <p id="N10355" type="head"> <s id="N10357">PRIMA PARS <lb/>MECHANICES <lb/>ARISTOTELIS STAGIRITAE <lb/>IN QVA EA CONTINENTVR, <lb/>quæ ad naturam Mechanicæ facultatis, <lb/>& principia operationum ip&longs;ius <lb/>pertinent.</s> </p> <p id="N10366" type="head"> <s id="N10368"><emph type="italics"/>Quæ &longs;it artis Mechanicæ facultas.<emph.end type="italics"/></s> </p> <p id="N1036F" type="head"> <s id="N10371">Textus Primus.</s> </p> <p id="N10374" type="main"> <s id="N10376">M<emph type="italics"/>iracvlo &longs;unt ea quidem quæ <lb/>natura contingunt, quorum ignoran­<lb/>tur cau&longs;æ: illa verò quæ præter natu­<lb/>ram quæcunque ad hominum vtilita­<lb/>tem arte fiunt. </s> <s id="N10384">In multis enim natu­<lb/>ra ei, quod nobis v&longs;ui e&longs;&longs;e potest, con­<lb/>trarium facit. </s> <s id="N1038B">Natura etenim eun­<lb/>dem &longs;emper habet modum, & &longs;impli­<lb/>citer: vtile autem multifariam commutatur. </s> <s id="N10392">Quando igitur <lb/>quippiam præter naturam oportuerit facere, difficultate &longs;ua <lb/>hæ&longs;itationem præstat, <expan abbr="arteq.">arteque</expan> indiget: quamobrem eam artis <lb/>partem, quæ huiu&longs;modi &longs;uccurrit difficultatibus mechanicam <lb/>appellamus. </s> <s id="N103A1">Quemadmodum enim Antipho &longs;cribit Poeta, &longs;ic <lb/>&longs;e res habet; arte enim &longs;uperamus ea à quibus natura vinci­<lb/>mur. </s> <s id="N103A8">Huiu&longs;modi autem &longs;unt, in quibus & minora &longs;uperant <lb/>maiora: & quæcunque momentum paruum habentia, magna <lb/>movent pondera; & omnia ferè illa, quæ mechanica nuncupa­<lb/>mus & problemata. </s> <s id="N103B1">Sunt autem hæc neque naturalibus om­<lb/>nino quæ&longs;tionibus eadem, neque &longs;eiugata valde: verum ma­<lb/>thematicarum contemplationum, <expan abbr="naturaliumq.">naturaliumque</expan> communia.<emph.end type="italics"/></s> </p> <pb pagenum="5" xlink:href="005/01/013.jpg"/> <p id="N103C2" type="head"> <s id="N103C4">COMMENTARIVS.<!-- KEEP S--></s> </p> <p id="N103C8" type="main"> <s id="N103CA">Ad colligendum quæ nam &longs;it artis mechanicæ facul­<lb/>tas quantauè &longs;it eius dignitas, & excellentia ex ma­<lb/>gnis ac mirabilibus, quæ operatur; illud in primis <lb/>Ari&longs;toteles præmittit, eorum quæ miraculo habentur, alia <lb/>quidem natura contingere, vt in&longs;ueta & peregrina, quorum <lb/>ignorantur cau&longs;æ: alia verò præter naturam, vt quæ artificio <lb/>aliquo adhibito &longs;upra vires patrantur atque ad propriam ho­<lb/>minum vtilitatem ordinantur. </s> <s id="N103DB">Siquidem natura <expan abbr="nõnunquam">nonnunquam</expan> <lb/>deficit in quibu&longs;dam, quæ v&longs;ui nobis e&longs;&longs;e po&longs;&longs;unt, imò con­<lb/>trarium facit, quia eundem &longs;emper, ac &longs;impliciter &longs;eruat mo­<lb/>dum in &longs;uis operationibus; vtile autem ad v&longs;um hominum <lb/>diuer&longs;imodè accommodatur, ac multifariam commutatur, <lb/>iuxtà &longs;cilicet varias exigentias, & opportunitates. </s> <s id="N103EC">Quando <lb/>igitur quippiam præter naturam nos facere oportuerit, ob <lb/>difficultatem quam plerunque in &longs;e id, quod faciendum e&longs;t <lb/>continet, hæ&longs;itare, & cogitare nos cogit quomodo faciamus, <lb/><expan abbr="artemq.">artemque</expan> aliquam propterea quærere quæ difficultati &longs;uccur­<lb/>rat, ae nos ad finem con&longs;equendum opportunis, <expan abbr="aptisq.">aptisque</expan> me­<lb/>dijs dirigat atque perducat. </s> <s id="N10402">Cum verum &longs;it quod Antipho <lb/>&longs;cribit Poeta, arte nos &longs;uperare ea, in quibus vincimur à na­<lb/>tura. </s> <s id="N10409">Quamobrem concludit Ari&longs;toteles, eam artem, &longs;eu <lb/>artis vniuer&longs;æ partem, quæ huiu&longs;modi &longs;uccurrit difficultati­<lb/>bus, <expan abbr="nosq.">nosque</expan> adiuuat ad operandum & <expan abbr="con&longs;equendũ">con&longs;equendum</expan> ea, quæ <lb/>&longs;unt præter naturam, Mechanicam appellamus. </s> <s id="N1041A">Hac enim <lb/>vtimur in his in quibus minora &longs;uperant maiora, & quæcun­<lb/>que paruam vim habentia, magna mouent pondera; in&longs;uper <lb/>& in omnibus ijs, quæ cadunt &longs;ub problemata, quæ commu­<lb/>niter vocantur mechanica. </s> <s id="N10425">Sunt autem (inquit) problema­<lb/>ta mechanica, neque naturalibus quæ&longs;tionibus omnino ea­<lb/>dem, neque &longs;eiuncta valde: verùm <expan abbr="mathematicarũ">mathematicarum</expan> contem­<lb/>plationum, <expan abbr="naturaliumq.">naturaliumque</expan> communia. </s> <s id="N10436">Quia &longs;cilicet non eo­<lb/>dem modo nec eadem ratione procedunt problemata me­<lb/>chanica, ac naturalia &longs;eu phy&longs;ica. </s> <s id="N1043D">Siquidem diuer&longs;is vtun­<pb pagenum="6" xlink:href="005/01/014.jpg"/>tur principijs, vt fu&longs;iùs infra explicabitur; <expan abbr="diuer&longs;asq.">diuer&longs;asque</expan> omnino <lb/>demon&longs;trationes efficiunt. </s> <s id="N1044B">Quoniam verò ea, circa quæ me­<lb/>chanica facultas ver&longs;atur nempe pondus & vis, qua illud mo­<lb/>uetur, &longs;ub obiecto adæquato phy&longs;ices materialiter contine­<lb/>tur, ac non &longs;olùm geometricis, &longs;ed naturalibus quoque ratio­<lb/>nibus nonnulla de ip&longs;is demon&longs;trantur; hinc e&longs;t, vt mechani­<lb/>ca problemata à phy&longs;icis non dicantur valde &longs;eiuncta, nec <lb/>admodum di&longs;tinguantur. </s> <s id="N1045A">Quare concludit Philo&longs;ophus, me­<lb/>chanica problemata e&longs;&longs;e <expan abbr="naturaliũ">naturalium</expan>, <expan abbr="mathematicarumq.">mathematicarumque</expan> con­<lb/>templationum communia, hoc e&longs;t ratione &longs;ubiecti materia­<lb/>lis quod commune e&longs;t phy&longs;icæ ac mathematicæ, & ratione <lb/>quarundam conclu&longs;ionum qu&etail; quidem <expan abbr="vtrarumq.">vtrarumque</expan> &longs;cientia­<lb/>rum principijs demon&longs;trantur. </s> </p> <p id="N10473" type="main"> <s id="N10475">Verùm vt h&etail;c omnia di&longs;tinctiùs eluce&longs;cant, <expan abbr="nihilq.">nihilque</expan> ad hu­<lb/>ius textus Ari&longs;totelis, <expan abbr="naturæq.">naturæque</expan> artis mechanicæ <expan abbr="intelligentiã">intelligentiam</expan> <lb/>in vniuer&longs;um quoad fieri pote&longs;t de&longs;ideretur, nonnullas addi­<lb/>tiones hìc &longs;ubnectere opere pretium putauimus, in quibus ea­<lb/>dem &longs;eor&longs;um, ac luculentiùs, <expan abbr="aliaq.">aliaque</expan> permulta ad comple­<lb/>mentum doctrinæ exponere conabimur. </s> </p> <p id="N10492" type="head"> <s id="N10494"><emph type="italics"/>De Nomine, & Origine facultatis <lb/>Mechanicæ.<emph.end type="italics"/><!-- KEEP S--></s> </p> <p id="N1049E" type="head"> <s id="N104A0">ADDITIO PRIMA.<!-- KEEP S--></s> </p> <p id="N104A4" type="main"> <s id="N104A6">Nomen hoc mechanicæ facultatis, machinalem artem <lb/>aut &longs;cientiam &longs;ignificat; &longs;umpta ethimologia à machi­<lb/>na, &longs;eu inuentione qua aliquid molimur, & quòd adiectiuum <lb/>mechanicus, vel mechanica deriuetur à græca voce <foreign lang="greek">mhkaniko\s</foreign>, <lb/>& hæc <foreign lang="greek">mhkanh</foreign>, vel à <foreign lang="greek">mhka\nhka</foreign>, quæ inuentionem, & machi­<lb/>namentum &longs;ignificat. </s> <s id="N104C1">Vnde etiam apud latinos machina, tam <lb/>animi quoddam inuentum aut molimen, quàm in&longs;trumentum <lb/>aliquod artificio&longs;um quo moles leuantur, aut quocunque <lb/>modo pelluntur denotare vt plurimum con&longs;ueuit, iuxta illud <lb/><arrow.to.target n="marg6"/> Taciti, Nihil tam ignarum barbaris quàm machinamenta, & <lb/>a&longs;tus oppugnationum. </s> <s id="N104D1"><expan abbr="Illudq.">Illudque</expan> Liuij, Turres contabulatas, <pb pagenum="7" xlink:href="005/01/015.jpg"/><expan abbr="machinamentaq.">machinamentaque</expan> alia quatiendis muris portabant. </s> <s id="N104DF">Nam &longs;iue <lb/>loquendo de machinis bellicis, &longs;iue de machinis nauticis aut <lb/>architectonicis, &longs;emper machina vtrumque &longs;ignificatum in­<lb/>uoluit, aut &longs;altem admittit. </s> </p> <p id="N104E8" type="margin"> <s id="N104EA"><margin.target id="marg6"/><emph type="italics"/><gap/>ac. <!-- REMOVE S-->lib.<emph.end type="italics"/> 12. <lb/><emph type="italics"/>ib.<emph.end type="italics"/> 4 <emph type="italics"/>de bel <lb/><gap/> Punico.<emph.end type="italics"/><!-- KEEP S--></s> </p> <p id="N10507" type="main"> <s id="N10509">Ars igitur vel &longs;cientia, quæ ad huiu&longs;modi machinas<arrow.to.target n="marg7"/> &longs;pe­<lb/>ctat à Plinio dicitur machinalis, qua&longs;i machinandi &longs;cientia, <lb/>vel peritia: Ab alijs vero communiter appellatur mechanica. <lb/></s> <s id="N10515">Quo &longs;en&longs;u Archimedes, eo quòd ad debellandos ho&longs;tes plu­<lb/>ra adinuenerit machinamenta, apud Firmicum dicitur<arrow.to.target n="marg8"/> Roma­<lb/>nos exercitus mechanicis artibus &longs;æpe pro&longs;tra&longs;&longs;e. </s> <s id="N10520">V&longs;urpata <lb/>autem vel exten&longs;a &longs;ignificatione, ars quoque mechanica vul­<lb/>go nuncupatur omnis illa quæ circa fabrilia ver&longs;atur, & con­<lb/>di&longs;tinguitur ab arte liberali. </s> <s id="N10529">Nam & mechanicus dicitur qui­<lb/>libet faber vel opifex eorum, quæ ingenio &longs;imul ac manibus <lb/>fiunt. </s> <s id="N10530">Et machinator bellicorum in&longs;trumentorum appella­<lb/>tur non &longs;olum qui bellicas machinas excogitauit, &longs;ed is quo­<lb/>que qui conficit; vt videre e&longs;t apud Liuium, & alios auctores.<arrow.to.target n="marg9"/><lb/>Quamobrem Hero mechanicus, vt apud Pappum Alexandri, <lb/>num lib. 8. &longs;uarum collectionum refertur, mechanicam fa­<lb/>cultatem in rationalem ac manualem di&longs;tinxit, vtpote quæ in <lb/>genere &longs;umpta, vtramque rationem &longs;eu naturam videatur <lb/>amplecti. </s> </p> <p id="N10544" type="margin"> <s id="N10546"><margin.target id="marg7"/><emph type="italics"/>Piin. <!-- REMOVE S-->lib.<emph.end type="italics"/>7. <lb/><emph type="italics"/>cap.<emph.end type="italics"/>37.</s> </p> <p id="N10559" type="margin"> <s id="N1055B"><margin.target id="marg8"/><emph type="italics"/>Firmic. <!-- REMOVE S-->lib.<emph.end type="italics"/><lb/>6.<emph type="italics"/>cap.<emph.end type="italics"/>31.</s> </p> <p id="N1056E" type="margin"> <s id="N10570"><margin.target id="marg9"/><emph type="italics"/>Liu.de bello <lb/>Punico.<emph.end type="italics"/><!-- KEEP S--></s> </p> <p id="N1057C" type="main"> <s id="N1057E">Propriè tamen hìc apud Ari&longs;totelem &longs;icut apud cœteros <lb/>omnes Philo&longs;ophos, ac Geometras, mechanica facultas tan­<lb/>tùm &longs;ignificat artem &longs;iue &longs;cientiam, quæ Geometricis princi­<lb/>pijs circa &longs;tatum & lationem grauium & leuium ver&longs;atur, hoc <lb/>e&longs;t circa grauia & leuia prout artificiosè moueri, aut quie&longs;ce­<lb/>re debent, vt clariùs infra ex Pappo, & ex tradenda<arrow.to.target n="marg10"/> defini­<lb/>tione con&longs;tabit. </s> </p> <p id="N10591" type="margin"> <s id="N10593"><margin.target id="marg10"/><emph type="italics"/>Papp. <!-- REMOVE S-->lib.<emph.end type="italics"/>8. <lb/><emph type="italics"/><expan abbr="collectionũ">collectionum</expan><emph.end type="italics"/></s> </p> <p id="N105A7" type="main"> <s id="N105A9">Iam verò &longs;i originem huius facultatis &longs;ecundum lati&longs;&longs;imam <lb/>eius &longs;ignificationem &longs;pectatæ con&longs;ideremus, eam non ni&longs;i <expan abbr="cũ">cum</expan> <lb/>ip&longs;a natura humana ortum habui&longs;&longs;e comperiemus. </s> <s id="N105B4">Quando­<lb/>quidem nec in ip&longs;is mundi primordijs defuerunt <expan abbr="machinam&etilde;-ta">machinamen­<lb/>ta</expan> quibus arte quadam innata, vel infu&longs;a primis parentibus, <lb/>ip&longs;i &longs;e&longs;e, & à contrarijs defenderent, & commoda con&longs;ecta­<lb/>rentur ad vitam <expan abbr="incolumitatemq.">incolumitatemque</expan> tuendam; Nam & corpora <pb pagenum="8" xlink:href="005/01/016.jpg"/>tegere, & domos con&longs;truere, & agros arare, & commeatus <lb/>vehere, aliaue onera per aquas ac terras longius a&longs;portare; <lb/><expan abbr="aquamq.">aquamque</expan> ip&longs;am ex imis haurire, oleum exprimere, triticum <lb/>terere, ligna cedere, ferrum acuere, <expan abbr="aliaq.">aliaque</expan> huiu&longs;modi perage­<lb/>re ad varios v&longs;us ex nece&longs;&longs;itate, vel ab initio cœperunt; quæ <lb/>cum in&longs;trumenta nonnulla mechanica, tùm artem ip&longs;am ma­<lb/>chinandi &longs;upponunt. </s> </p> <p id="N105DF" type="main"> <s id="N105E1">Quòd &longs;i &longs;ecundum propriam acceptionem loquamur de <lb/>facultate mechanica, quatenus vt diximus ars quædam e&longs;t, <lb/>vel &longs;cientia, quæ geometricis nixa principijs peculiari <expan abbr="quadã">quadam</expan> <lb/>ratione circa &longs;uum obiectum per demon&longs;trationes ver&longs;atur, <lb/>ac præcepta tradit, quibus homo in v&longs;u ac motione grauium, <lb/>& leuium dirigitur ac iuuatur; &longs;ic nullum extat monimentum <lb/>quo ante tempora Eudoxij Architæ, ac Platonis illam c&etail;pi&longs;&longs;e <lb/>a&longs;&longs;ereremus. </s> <s id="N105F6">Eudoxius enim Gnidius, & Archita Tarentinus <lb/>primò geometrica principia ad v&longs;um mechanicum, &longs;eu me­<lb/>chanicam contemplationem tran&longs;tulerunt. </s> <s id="N105FD">Sed Archita eo <lb/>quòd ligneam columbam volantem exhibuerit, <expan abbr="aliaq.">aliaque</expan> præcla­<lb/>ra, & admiranda mechanicæ artis adminiculo patrauerit, ip­<lb/>&longs;iu&longs;met artis inuentor e&longs;t habitus, vt extat apud Eutocium; <lb/>ni&longs;i Democritum Mele&longs;ium qui iam antea opus quoddam fe­<lb/>rè mechanicum Certamen Clep&longs;ydræ in&longs;criptum ediderat, <lb/>inter mechanicæ facultatis Auctores computare velimus. <lb/></s> <s id="N10611">Po&longs;t Architam verò Tarentinum, vnum inuenimus Ari&longs;tote­<lb/>lem Stageritam non modo verioris, ac &longs;olidioris philo&longs;ophiæ <lb/>auctorem maximum, &longs;ed & mathematicarum di&longs;ciplinarum <lb/>in&longs;tructi&longs;&longs;imum qui mechanicæ artis modo &longs;cientifico funda­<lb/>menta iecerit, hunc quem exponimus libellum edens, in quo <lb/>præter &longs;ubtili&longs;&longs;imas quæ&longs;tiones quas acuti&longs;&longs;imè diluit, firmi&longs;­<lb/>&longs;ima, & vniuer&longs;ali&longs;&longs;ima tradit principia quibus mechanici om<lb/>nes tractatus ac demon&longs;trationes eorum nituntur. </s> <s id="N10622">Exinde <lb/>igitur mechanica facultas propagari cœpit, nam Ari&longs;totelem <lb/>&longs;ecuti, vel imitati &longs;unt multi, præ&longs;ertim, qui &longs;equenti &longs;eculo <lb/>maximè claruerunt, vt Archimedes Siracu&longs;anus, cuius do­<lb/>ctrina, ac &longs;ummo ingenio huiu&longs;modi facultas maxima incre­<lb/>menta &longs;u&longs;cepit. </s> <s id="N1062F">Item Cte&longs;ibus machinator præ&longs;tanti&longs;&longs;imus <pb pagenum="9" xlink:href="005/01/017.jpg"/>qui &longs;piritalia & hydraulicas machinas primus inuenit. </s> <s id="N10637">Dein­<lb/>de vero Philo Bizantius, cuius mechanica peritia ab Herone <lb/>commemoratur. </s> <s id="N1063E">Hero ip&longs;e Alexandrinus Philo&longs;ophus Cte­<lb/>&longs;ebij di&longs;cipulus; qui multa ac eruditi&longs;&longs;ima monumenta me­<lb/>chanica protulit. </s> <s id="N10645">Hinc Athenæus, cuius duo extant <expan abbr="fragm&etilde;-ta">fragmen­<lb/>ta</expan> græca de Machinis apud Vitruuium in fine. </s> <s id="N1064E">Vitruuius <expan abbr="etiã">etiam</expan> <lb/>ip&longs;e celeberrimus Architectus. </s> <s id="N10657">Ptolemæus Alexandrinus <lb/>a&longs;tronomorum Princeps, qui libros mechanicos præclari&longs;&longs;i­<lb/>mos edidit. </s> <s id="N1065E">Pappus denique Alexandrinus, mechanicæ fa­<lb/>cultatis propagator egregius, & Hero mechanicus, qui de <lb/>Geodæ&longs;ia ac de machinis bellicis di&longs;&longs;erti&longs;&longs;ime &longs;crip&longs;it. </s> <s id="N10665">Quos <lb/>authores enumera&longs;&longs;e &longs;ufficiat ad exi&longs;tentiam, & originem hu­<lb/>ius facultatis innuendam, cœteris recen&longs;ioribus, breuitatis <lb/>gratia prætermi&longs;&longs;is, qui ad hæc v&longs;que tempora eam magno­<lb/>perè illu&longs;trarunt, <expan abbr="micantq.">micantque</expan> adhuc ip&longs;i, operum ac ingeniorum <lb/>&longs;plendore. </s> </p> <p id="N10676" type="head"> <s id="N10678"><emph type="italics"/>De obiecto circa quod Mechanica facultas <lb/>ver&longs;atur.<emph.end type="italics"/></s> </p> <p id="N10681" type="head"> <s id="N10683">ADDITIO SECVNDA.<!-- KEEP S--></s> </p> <p id="N10687" type="main"> <s id="N10689">Vt <expan abbr="aut&etilde;">autem</expan> Mechanicæ facultatis natura ex proprio obie­<lb/>cto, quemadmodum commune e&longs;t omnibus artibus, <lb/>atque &longs;cientijs in doctrina Ari&longs;totelis 2. de anima text. </s> <s id="N10694">33. <lb/>præcipuè digno&longs;catur, Ob&longs;eruandum in primis e&longs;t, id quod <lb/>per mechanicam facultatem intendimus, & ad quod tanquam <lb/>ad finem con&longs;equendum omnis mechanica contemplatio or­<lb/>dinatur, aliud non e&longs;&longs;e, quàm grauis aut leuis cuiu&longs;que cor­<lb/>poris motionem, vel quietem, quæ parua vt plurimum virtu­<lb/>te, arte ip&longs;a mirabiliter comparatur, &longs;iue motio &longs;it &longs;ecundum <lb/>naturam, &longs;iue &longs;it præter aut contra naturam ip&longs;ius corporis <lb/>grauis aut leuis. </s> <s id="N106A7">Porro inductione con&longs;tat, mechanicum om­<lb/>nem conatum, <expan abbr="omnemq.">omnemque</expan> tractatum in admirabilem lationem, <lb/>aut &longs;tatum corporum ordinari ex ip&longs;ius artis proprio in&longs;titu­<lb/>to, vt ad leuanda, vel detinenda etiam exigua virtute quæ-<pb pagenum="10" xlink:href="005/01/018.jpg"/>cunque pondera, ad aerem vel aquam artificiosè pellendam, <lb/>attrahendam, aut continendam, ad mi&longs;&longs;ilia proijcienda, <expan abbr="aliaq.">aliaque</expan> <lb/>&longs;ecundum varias po&longs;itiones locanda, vel de loco ad locum, <lb/>diuer&longs;imodè transferenda, & &longs;imilia, quæ per &longs;e nota erunt <lb/>mechanicamenta omnia ad id præ&longs;tandum accomodata, ac <lb/>&longs;peculationes mechanicas recen&longs;enti. </s> </p> <p id="N106C7" type="main"> <s id="N106C9">Deinde ob&longs;eruandum e&longs;t, ad prædictam motionem, aut <lb/>quietem arte con&longs;equendam, duo poti&longs;&longs;imum con&longs;iderari à <lb/>Mechanico; nimirum & quantitatem ponderis ex parte cor­<lb/>poris mouendi, & quantitatem virtutis ex parte mouentis, &longs;i­<lb/>ue immediatè ip&longs;e moueat per virtutem intrin&longs;ecam, fiue per <lb/>impre&longs;&longs;ionem impetus, aut per in&longs;trumenta. </s> <s id="N106D6">In hoc enim ars <lb/>ip&longs;a mechanica &longs;ita e&longs;t, vt habita ratione ponderis, aut leui­<lb/>tatis corporis mouendi aut detinendi, proportionalis vis ad id <lb/>præ&longs;tandum adhibeatur, <expan abbr="congruaq.">congruaque</expan> applicentur machina­<lb/>menta, ad &longs;upplendum quod dee&longs;t naturali virtuti. </s> <s id="N106E5">Quod <lb/>nequaquam fieri po&longs;&longs;et &longs;ine con&longs;ideratione quantitatis vtriu&longs;­<lb/>que, nempe ponderis mouendi, & virtutis motiuæ vbi tota <lb/>fundari debet proportio vnius ad alteram. </s> </p> <p id="N106EE" type="main"> <s id="N106F0">Denique ob&longs;eruandum etiam erit, prædictam quantitatem <lb/>ponderis, tum grauitatem, tum leuitatem re&longs;pectu <expan abbr="diuer&longs;orũ">diuer&longs;orum</expan> <lb/>à Mechanicis appellari. </s> <s id="N106FB">Maior enim quantitas ponderis re­<lb/>&longs;pectu minoris, ab ip&longs;is dicitur grauitas; minor vero compa­<lb/>ratione maioris, dicitur leuitas. </s> <s id="N10702">Sicut illud corpus ab ip&longs;is <lb/>dicitur leue, quod minus habet pondus re&longs;pectu alterius; il­<lb/>lud vero graue, quod maius; etiam &longs;i per &longs;e &longs;impliciter lo­<lb/>quendo vtrumque graue &longs;it. </s> <s id="N1070B">Non enim Mechanicus accipit <lb/>graue aut leue &longs;impliciter & &longs;ecundum &longs;e, quemadmodum vt <lb/>plurimum accipit Phy&longs;icus (nempe per graue intelligendo, <lb/>quod nullam habet in &longs;e leuitatem, per leue autem quod nul­<lb/>lam habet in &longs;e grauirtatem;) &longs;ed &longs;emper vtrumque accipit <lb/>re&longs;pectiue; ita vt idem dicatur graue & leue re&longs;pectu diuer&longs;o­<lb/>rum, vt habetur etiam apud Ari&longs;totelem lib. 4. de cœlo tex. <lb/><!-- REMOVE S-->27. vbi aer & aqua re&longs;pectu terræ dicuntur leuia, re&longs;pectu ve­<lb/>ro ignis, grauia. </s> </p> <p id="N1071F" type="main"> <s id="N10721">His ergo præmi&longs;&longs;is facile primo intelligetur, &longs;ubiectum ma-<pb pagenum="11" xlink:href="005/01/019.jpg"/>teriale adæquatum facultatis mechanicæ e&longs;&longs;e grauia & leuia, <lb/>&longs;eu quantitatem ponderis ip&longs;orum, ac virtutis qua moueri <lb/>debent aut detineri. </s> <s id="N1072D">Ratio autem e&longs;t, quia in &longs;cientijs, illud <lb/>dicitur &longs;ubiectum materiale adæquatum, quod complectitur <lb/>omnia de quibus in &longs;cientia tractatur; omne autem de quo in <lb/>hac &longs;cientia tractatur, reducitur ad corpus aliquod graue, aut <lb/>leue mouendum aut detinendum, &longs;iue ad quantitatem virtu­<lb/>tis qua moueri debet aut detineri; <expan abbr="Proindeq.">Proindeque</expan> ip&longs;a grauia & <lb/>leuia vt &longs;ic, <expan abbr="&longs;imulq.">&longs;imulque</expan> virtus motiua ac detentiua illorum, me­<lb/>ritò huius facultatis mechanicæ materiale &longs;ubiectum adæ­<lb/>quatum de&longs;ignatur. </s> </p> <p id="N10748" type="main"> <s id="N1074A">Secundo vero non minus facile con&longs;tabit, obiectum forma­<lb/>le eiu&longs;dem facultatis e&longs;&longs;e admirabilem, & artificio&longs;am mobi­<lb/>litatem, aut quietèm ip&longs;orum grauium, & leuium, ab&longs;trahen­<lb/>do à motione & quiete naturali aut violenta, vt quæ per im­<lb/>petum impre&longs;&longs;um, aut detentionem fieri con&longs;ueuit. </s> <s id="N10755">Con&longs;tat <lb/>autem ex eo quod obiectum formale cuiu&longs;que facultatis, aut <lb/>&longs;cientiæ, e&longs;t ip&longs;a ratio &longs;ub qua de proprio &longs;ubiecto materiali <lb/>agitur in tali &longs;cientia: ratio autem &longs;ub qua in mechanica fa­<lb/>cultate agitur de graui & leui, <expan abbr="virtuteq.">virtuteque</expan> motiua aut detentiua <lb/>eorum, e&longs;t ip&longs;a artificio&longs;a mobilitas &longs;ecundum <expan abbr="locũ">locum</expan>, & quies <lb/>con&longs;equenda ip&longs;orum, mediantibus præceptis tradendis in <lb/>eadem &longs;cientia, vt per &longs;e patet ex fine explicato, ad quem <lb/>tota hæc &longs;cientia dirigitur, & ordinatur. </s> <s id="N10770">Ea ergo admirabi­<lb/>lis, <expan abbr="artificio&longs;aq.">artificio&longs;aque</expan> mobilitas, iure cen&longs;eri debet formale obie­<lb/>ctum huius facultatis mechanicæ. </s> </p> <p id="N1077B" type="main"> <s id="N1077D">Quo tandem fit tertio, vt obiectum totale, & adæquatum <lb/>mechanicæ facultatis in vniuer&longs;um, &longs;int ip&longs;a grauia & leuia <lb/>prout artificiosè mobilia, & vt ita dicam quie&longs;cibilia, <expan abbr="&longs;imulq.">&longs;imulque</expan> <lb/>omnia quæ de ip&longs;is demon&longs;trantur in hac eadem &longs;cientia. <lb/></s> <s id="N1078B">Quod certe non ob&longs;curè &longs;umitur ex Pappo Alexandrino lib. <lb/><!-- REMOVE S-->8. &longs;uarum Collectionum, vbi mechanicam contemplationem <lb/>docet ver&longs;ari circa &longs;tatum & lationem corporum, <expan abbr="motumq.">motumque</expan> <lb/>&longs;ecundum locum in vniuer&longs;o, vt eorum quæ natura fiunt, cau­<lb/>&longs;as reddat; eorum verò quæ à natura &longs;ua di&longs;cedere coguntur <lb/>extra propria loca, in contrarios motus per &longs;ua theoremata <pb pagenum="12" xlink:href="005/01/020.jpg"/>transferat. </s> <s id="N107A2">Ratio vero e&longs;t manife&longs;ta, nam huiu&longs;modi <expan abbr="obiectũ">obiectum</expan> <lb/>totale & adæquatum in qualibet &longs;cientia coale&longs;cere debet <expan abbr="tũ">tum</expan> <lb/>ex &longs;ubiecto materiali etiam adæquato, ac formalitate &longs;ub qua <lb/>de illo agitur; tum etiam ex omnibus ijs quæ de ip&longs;o demon­<lb/>&longs;trantur in &longs;cientia. </s> <s id="N107B5">Explicatum ergo &longs;ubiectum materiale <lb/>&longs;ub illa formalitate cum omnibus quæ de illo demon&longs;trantur <lb/>per theoremata ac problemata mechanica, con&longs;tituetur to­<lb/>tale & adæquatum huius facultatis obiectum, in ordine ad <lb/>quod tota eius e&longs;&longs;entia, ac ratio &longs;pecifica de&longs;umenda e&longs;t, ac <lb/>paulatim inferius explicanda. </s> </p> <p id="N107C2" type="head"> <s id="N107C4"><emph type="italics"/>Qua ratione facultas Mechanica con&longs;tituatur <lb/>Ars & Scientia.<emph.end type="italics"/></s> </p> <p id="N107CD" type="head"> <s id="N107CF">ADDITIO TERTIA.<!-- KEEP S--></s> </p> <p id="N107D3" type="main"> <s id="N107D5">Hviu&longs;que ad &longs;ignificandum habitum intellectualem <expan abbr="cõ-templationis">con­<lb/>templationis</expan> mechanicæ, vt plurimum v&longs;i &longs;umus no­<lb/>mine facultatis mechanicæ, eo quod nomen facultas ab&longs;tra­<lb/>hat à propria &longs;ignificatione artis, aut &longs;cientiæ, <expan abbr="latiusq.">latiusque</expan> pateat <lb/>&longs;ecundum communem omnium conceptionem. </s> <s id="N107E4">Quare de­<lb/>terminandum nunc e&longs;t, vtrum talis habitus vel facultas, &longs;it ve­<lb/>rè in &longs;e, ac propriè vocari po&longs;&longs;it tum ars, tum &longs;cientia. </s> <s id="N107EB">Quod <lb/>&longs;anè au&longs;picari debet à communi ratione artis atque &longs;cientiæ <lb/>ab Ari&longs;totele &longs;æpius explicata, <expan abbr="aptèq.">aptèque</expan> pa&longs;&longs;im licet non &longs;em­<lb/>per di&longs;tincta. </s> <s id="N107F8">Nam 6 Ethicorum cap. 4. artem docet e&longs;&longs;e <lb/>habitum quendam vera cum ratione <expan abbr="effectiuũ">effectiuum</expan> circa id quod <lb/>aliter e&longs;&longs;e atque aliter pote&longs;t; & cuius principium &longs;it in eo <lb/>quod efficitur. </s> <s id="N10805">Vnde eorum quæ ex nece&longs;&longs;itate &longs;unt, vel fiunt <lb/>&longs;ecundum naturam, nullam ait e&longs;&longs;e artem, cum hæc in &longs;e prin­<lb/>cipium habeant. </s> <s id="N1080C">Ac proinde &longs;equenti capite di&longs;tinguit artem <lb/>à &longs;cientia, eo quod &longs;cientia &longs;it de rebus quæ non po&longs;&longs;unt ali­<lb/>ter &longs;e habere. </s> <s id="N10813">Nihilominus 1. Metaphi&longs;ices cap. 1. idem <lb/>Philo&longs;ophus artem videtur confundere cum &longs;cientia &longs;altem <lb/>practica; ait enim, artem e&longs;&longs;e de vniuer&longs;alibus, ac propter <lb/>cau&longs;am ea quæ &longs;fiunt cogno&longs;cere, exemplum adhibens tum <pb pagenum="13" xlink:href="005/01/021.jpg"/>medicinæ, tum architecturæ; imò ip&longs;as mathematicas di&longs;ci­<lb/>plinas indefinitè loquendo, quas con&longs;tat e&longs;&longs;e &longs;cientias, artes <lb/>appellat. </s> </p> <p id="N10825" type="main"> <s id="N10827">Ex quibus primò dicendum erit, mechanicam facultatem <lb/>verè & propriè e&longs;&longs;e artem, prout in hoc libello, & in explica­<lb/>to textu a&longs;&longs;umitur ab Ari&longs;totele. <!-- KEEP S--></s> <s id="N1082F">Nam procul dubio huiu&longs;­<lb/>modi facultas e&longs;t habitus intellectualis vera cum ratione effe­<lb/>ctiuus; qui nimirum pro ratiocinationem ver&longs;atur circa facti­<lb/>bilia, vt &longs;unt grauia & leuia, quæ aliter atque aliter &longs;e po&longs;&longs;unt <lb/>habere &longs;ecundum artificio&longs;am motionem, aut quietem illis <lb/>tribuendam ab eodem principio in quo e&longs;t ip&longs;e habitus intel­<lb/>lectualis, ac directiuus mechanicæ operationis. </s> </p> <p id="N1083E" type="main"> <s id="N10840">Secundò dicendum e&longs;t, eandem facultatem mechanicam <lb/>verè etiam ac propriè e&longs;&longs;e ac vocari po&longs;&longs;e &longs;cientiam. </s> <s id="N10845">Id quod <lb/>implicitè docet Ari&longs;toteles loco citato metaphi&longs;ices, dum <lb/>eodem pacto &longs;ub nomine artis, de hac facultate ac de medi­<lb/>cina loquitur, <expan abbr="eisq.">eisque</expan> competere ait rationem &longs;cientiæ; & in <lb/>&longs;pecie Architectos (qui &longs;anè mechanici &longs;unt) honorabilio­<lb/>res, & doctiores e&longs;&longs;e ait ijs qui manibus propter &longs;olam <expan abbr="cõ&longs;ue-tudinem">con&longs;ue­<lb/>tudinem</expan> & experientiam operantur: quoniam (inquit) cau&longs;as <lb/>eorum quæ fiunt, &longs;ciunt; & &longs;ignum &longs;cientis e&longs;t po&longs;&longs;e docere.<arrow.to.target n="marg11"/><lb/>Vnde Pappus Mechanicam <expan abbr="&longs;cientiã">&longs;cientiam</expan> &longs;imul & artem appellat. </s> </p> <p id="N10867" type="margin"> <s id="N10869"><margin.target id="marg11"/><emph type="italics"/>Paip.Alex, <lb/>lib<emph.end type="italics"/> 8.<emph type="italics"/>math. <lb/></s> <s id="N10879">collat.<emph.end type="italics"/></s> </p> <p id="N1087E" type="main"> <s id="N10880">Ratio autem e&longs;t eadem quam citatis verbis indicauit Ari­<lb/>&longs;toteles; quia nempe &longs;i &longs;cire non e&longs;t aliud ni&longs;i rem per cau­<lb/>&longs;am cogno&longs;cere propter quam res ip&longs;a e&longs;t, & non pote&longs;t ali­<lb/>ter &longs;e habere, vt alibi ip&longs;emet Philo&longs;ophus definit 1. Po&longs;ter. <lb/><!-- REMOVE S-->cap. 2. iure & quidem optimo mechanica facultas &longs;eu noti­<lb/>tia, &longs;cientia e&longs;&longs;e debet, ac dici: quandoquidem hæ omnes <lb/>conditiones illi proprij&longs;&longs;imè conueniunt. </s> <s id="N10890">In primis enim e&longs;t <lb/>intellectualis cognitio eorum quæ circa motionem localem, <lb/>aut quietem grauium ac leuium contingunt, orta ex præexi­<lb/>&longs;tenti alia cognitione principiorum, quæ &longs;iue &longs;int per &longs;e nota, <lb/>&longs;iue demon&longs;trentur in alia &longs;uperiori &longs;cientia, vt infra dicetur, <lb/>omnino tamen &longs;unt cau&longs;a eius quod a&longs;&longs;eritur in conclu&longs;ione. <lb/></s> <s id="N1089E">Ideo <expan abbr="namq.">namque</expan> dicimus in motu circulari, partem diametri, quæ <lb/>magis di&longs;tat à centro circuli, velocius moueri; quia hæc ma-<pb pagenum="14" xlink:href="005/01/022.jpg"/>gis participat de motu recto, ac naturali à quo prouenit ip&longs;a <lb/>maior velocitas tanquam à cau&longs;a intrin&longs;eca, & hoc ita &longs;e ha­<lb/>bere demon&longs;tratur ex principijs geometricis. </s> <s id="N108B0">Similiter non <lb/>ex alio dicimus rotunda corpora &longs;uper planum, facilius mo­<lb/>ueri, ni&longs;i quia parua vel minima &longs;ui parte planum contingám, <lb/>ac minus offen&longs;ant. </s> <s id="N108B9"><expan abbr="Idq.">Idque</expan> probatur eo quòd circulus tangat in <lb/>puncto, ac magis à plano &longs;emotum efficiat angulum. </s> <s id="N108C1">Quæ <lb/>de&longs;umuntur ex geometricis, <expan abbr="&longs;untq.">&longs;untque</expan> veræ cau&longs;æ ip&longs;ius mobili­<lb/>taris facilioris quæ de rotundis corporibus a&longs;&longs;eueratur. </s> <s id="N108CC">Quod <lb/>cum in omnibus conclu&longs;ionibus mechanicis ob&longs;eruetur, vt <lb/>per &longs;e con&longs;tat, palàm conuincitur, eas con&longs;tituere notitiam <lb/>quandam rerum &longs;iue effectuum procedentem ex cognitione <lb/>cau&longs;æ illorum, ac proinde per di&longs;cur&longs;um & illationem virtute <lb/>medij, nempe ip&longs;ius cau&longs;æ præcognitæ, ex notitia <expan abbr="anteced&etilde;-tis">anteceden­<lb/>tis</expan> deueniendo in notitiam con&longs;equentis, quod e&longs;t &longs;ecundum <lb/>hanc conditionem participare propriam rationem &longs;cientiæ. </s> </p> <p id="N108E1" type="main"> <s id="N108E3">Deinde probatur, nam ea quæ per mechanicam notitiam <lb/>ex cau&longs;is proprijs cogno&longs;cuntur, tàm nece&longs;&longs;ario ab ip&longs;is cau­<lb/>&longs;is procedunt, vt non po&longs;&longs;int aliter &longs;e habere, quæ erat altera <lb/>conditio propriæ &longs;cientiæ. </s> <s id="N108EC">Neque enim contingenter pon­<lb/>dus libræ aut vectis magis grauitat in parte remotiori à fulci­<lb/>mento ex eo quòd pars diametri, quæ plus à centro circuli <lb/>di&longs;ce&longs;&longs;erit, magis ab eadem virtute moueri &longs;uapte natura <lb/>præualeat: &longs;ed nece&longs;&longs;ariò ac ineffabiliter, cùm nece&longs;&longs;ariò li­<lb/>bra aut vectis in &longs;uo proprio motu con&longs;tituatur veluti diame­<lb/>ter circuli; & hoc quod e&longs;t pondus in parte di&longs;tantiori à ful­<lb/>cimento quod e&longs;t centrum, magis grauitare &longs;eu efficaciùs de­<lb/>or&longs;um impellere e&longs;&longs;entialiter dependeat ab eo, quod e&longs;t par­<lb/>tem illam di&longs;tantiorem à centro aptiorem e&longs;&longs;e ad motum, vt <lb/>aperti&longs;&longs;imè ex geometricis principijs demon&longs;trabitur. </s> <s id="N10903">Nec <lb/>per accidens e&longs;t, longiùs ferri mi&longs;&longs;ilia funda, quàm manu mi&longs;­<lb/>&longs;a, quia in motu circulari qui fit per emi&longs;&longs;ionem, &longs;eu proie­<lb/>ctionem, magis illa di&longs;tant à centro per fundæ v&longs;um, quàm &longs;i <lb/>&longs;ola manu proijcerentur, vt per &longs;e con&longs;tat; &longs;ed nece&longs;&longs;ariò ex <lb/>tali cau&longs;a talis procedit effectus, qui proinde aliter non pote&longs;t <lb/>&longs;e habere propter eandem rationem, vt in cœteris quoque <pb pagenum="15" xlink:href="005/01/023.jpg"/>facilè erit inductione probare. </s> <s id="N10917">Cumque ip&longs;æ cau&longs;æ ex qui­<lb/>bus mechanica facultas &longs;uas elicit conclu&longs;iones, vel &longs;int per <lb/>&longs;e notæ, vt citius ferri, quod facilius mouetur; Aequalia ab <lb/>æqualibus non moueri, & &longs;imilia; vel fundentur in principijs <lb/>demon&longs;tratis in alia &longs;uperiori &longs;cientia, de quibus habetur ve­<lb/>ra certitudo, & euidentia hinc vlterius fit, vt ip&longs;a pariter co­<lb/>gnitio mechanicarum conclu&longs;ionum, eandem participet, ac <lb/>&longs;ortiatur euidentiam, vt commune e&longs;t omnibus &longs;cientijs, quæ <lb/>nimirum euidentiam non ni&longs;i ex principijs obtinent per re&longs;o­<lb/>lutionem v&longs;que ad elementa, vt &longs;æpè docet Philo&longs;ophus in <lb/>Analiticis. </s> </p> <p id="N1092E" type="main"> <s id="N10930">Quòd &longs;i mechanica facultas &longs;imul à nobis <expan abbr="cõ&longs;tituatur">con&longs;tituatur</expan> ars, <lb/>& hæc iuxta doctrinam allegatam Ari&longs;totelis 6. Ethic. <!-- REMOVE S-->cap. 4. <lb/>&longs;emper ver&longs;etur circa aliquid quod aliter e&longs;&longs;e atque aliter po­<lb/>te&longs;t; Id &longs;anè non ob&longs;tat; nam ibi apud Philo&longs;ophum &longs;ermo <lb/>e&longs;t<gap/> de arte &longs;umpta pro arte &longs;eruili, quæ ver&longs;atur circa &longs;ingu­<lb/>laria, ac varia corporum accidentia, vt circa fabrilia, hoc e&longs;t <lb/>varias corporum formas manibus <expan abbr="effing&etilde;das">effingendas</expan>, & artificiosè in­<lb/>troducendas, quæ certè aliter atque aliter &longs;e po&longs;&longs;unt habere, <lb/>ac proinde de illis dari non pote&longs;t vera &longs;cientia. </s> <s id="N1094F">Alioquin <expan abbr="cũ">cum</expan> <lb/>diximus huiu&longs;modi facultatem e&longs;&longs;e pariter artem, artem &longs;um­<lb/>p&longs;imus cum Ari&longs;totele 1. Metaphi&longs;ices cap. 1. pro habitu in<lb/>tellectuali qui ver&longs;atur circa vniuer&longs;alia factibilia, & ex cau&longs;is <lb/>ea digno&longs;cendo, ac tradendo modum quo fieri debent; quo <lb/>&longs;en&longs;u diximus, artem cum &longs;cientia qua&longs;i confundere, &longs;altem <lb/>loquendo de &longs;cientia practica. </s> <s id="N10962">Quamobrem. <!-- KEEP S--></s> </p> <p id="N10966" type="main"> <s id="N10968">Tertio dicendum e&longs;t, mechanicam facultatem non e&longs;&longs;e <lb/>&longs;cientiam &longs;peculatiuam, &longs;ed practicam. </s> <s id="N1096D">In quo nulla pote&longs;t <lb/>e&longs;&longs;e difficultas præ&longs;ertim in doctrina Ari&longs;totelis, nam vt ip&longs;e <lb/>docet lib. 2. Met. <!-- REMOVE S-->cap. 1. Scientia &longs;peculatiua e&longs;t illa cuius <lb/>finis e&longs;t veritas, <expan abbr="quæq.">quæque</expan> in &longs;e ip&longs;a &longs;i&longs;tit, nullum includens ordi­<lb/>nem ad aliud præter veritatem ip&longs;ius obiecti &longs;cibilis. </s> <s id="N10980">Practi­<lb/>ca verò &longs;cientia e&longs;t, cuius finis e&longs;t opus; nempè quæ ex &longs;e or­<lb/>dinatur ad opus, vel operationem aliquam exercendam præ­<lb/>ter ip&longs;am &longs;cientiam. </s> <s id="N10989">Mechanica autem facultas nullo modo <lb/>ab&longs;trahere pote&longs;t ab ordine quem e&longs;&longs;entialiter dicit ad <expan abbr="motũ">motum</expan> <pb pagenum="16" xlink:href="005/01/024.jpg"/>localem, aut quietem mobilibus impertiendam, & ad <expan abbr="modũ">modum</expan> <lb/>quo moueri debent vel quie&longs;cere. </s> <s id="N1099D">Nam licet nonnullæ pro­<lb/>po&longs;itiones mechanicæ, &longs;i per &longs;e &longs;umantur, &longs;int &longs;peculatiuæ, eo <lb/>quod præci&longs;e &longs;i&longs;tere po&longs;&longs;ent in &longs;ola veritate, nihilominus pro­<lb/>pter connexionem quam habent cum alijs practicis, & ordi­<lb/>nem quem &longs;imul includunt ad praxim, verè con&longs;tituunt <expan abbr="vnã">vnam</expan> <lb/>&longs;cientiam totalem practicam. </s> <s id="N109AE">Quod confirmari etiam pote&longs;t <lb/>ex eo: nam verè ac propriè huiu&longs;modi &longs;cientia cadit &longs;ub illa <lb/>diui&longs;ione generica &longs;cientiæ practicæ, cum Philo&longs;ophus 6. <lb/>Metaph. cap. 1. eam diuidit in actiuam & factiuam. </s> <s id="N109B7"><expan abbr="Quoniã">Quoniam</expan> <lb/>&longs;ub actiua optimè intelligitur contineri &longs;cientias, quæ ver&longs;an­<lb/>tur circa actus immanentes intellectus ac voluntatis, prout <lb/>dirigibiles per ip&longs;as met &longs;cientias; cuiu&longs;modi &longs;unt Logica, & <lb/>Philo&longs;ophia moralis, quarum finis & opus, e&longs;t ip&longs;a rectitudo <lb/>actionis internæ, &longs;eu actuum immanentium intellectus & vo­<lb/>luntatis, &longs;iuè in genere moris in ordine ad hone&longs;tatem, &longs;iuè in <lb/>genere cognitionis in ordine ad veritatem: &longs;ub factiua verò <lb/>contineri omnes illas artes, &longs;iuè &longs;cientias, quæ ver&longs;antur cir­<lb/>ca factionem aliquam &longs;eu opus extrin&longs;ecus faciendum, nem­<lb/>pe genere di&longs;tinctum ab ip&longs;o actu &longs;cientifico per quem opus <lb/>&longs;it aut dirigitur, vt quælibet operatio corporea, vel opus ex <lb/>tali operatione relictum, vt per&longs;picuè docet idem Ari&longs;toteles <lb/><gap/> Met. <!-- REMOVE S-->tex. <!-- REMOVE S-->16. & 1. magn. </s> <s id="N109DC">moral. </s> <s id="N109DF">cap. 33. Et huiu&longs;modi <lb/>dicimus e&longs;&longs;e facultatem mechanicam, cum verè pro fine ha­<lb/>beat opus externum, vt diximus, nempe motum localem & <lb/>artificio&longs;um, vel quietem grauibus & leuibus impertiendam, <lb/>non &longs;ecus ac medicina con&longs;tituitur &longs;cientia practica, <lb/>eo quod eius finis, ad quem ordinatur <lb/>tanquam ad proprium opus <lb/>&longs;it &longs;anitas anima­<lb/>lis ho­<lb/>minibus im­<lb/>pertien­<lb/>da. </s> </p> <pb pagenum="17" xlink:href="005/01/025.jpg"/> <p id="N109FE" type="head"> <s id="N10A00"><emph type="italics"/>Mechanicam facultatem vere ac proprie e&longs;&longs;e <lb/>&longs;cientiam Mathematicam.<emph.end type="italics"/></s> </p> <p id="N10A09" type="head"> <s id="N10A0B">ADDITIO QVARTA.</s> </p> <p id="N10A0E" type="main"> <s id="N10A10">Vtrum autem Mechanica facultás pertineat ad &longs;cien­<lb/>tiam phy&longs;icam, an ad mathematicam, vel potius di­<lb/>cenda &longs;it partim phy&longs;ica, partim mathematica, non leuem <lb/>habet difficultatem. </s> <s id="N10A19">Etenim e&longs;&longs;e &longs;cientia<gap/> phy&longs;icam, illud <lb/>primo loco &longs;uadet, quia nimirum leius &longs;ubiectum e&longs;t phy&longs;i­<lb/>cum, vt graue, & leue, <expan abbr="virtusq.">virtusque</expan> moti<gap/>, ac detentiua, qua &longs;e­<lb/>cundum locum ip&longs;a cientur aut detinenti<gap/>. </s> <s id="N10A2C">Secundo <expan abbr="quoniã">quoniam</expan> <lb/>de huiu&longs;modi &longs;ubiecto agitur &longs;ub ratione phy&longs;ica, prout &longs;cili­<lb/>cet e&longs;t mobile &longs;ecundum locum n<gap/>a &longs;ua aut violentia; quæ <lb/>certè fit per impre&longs;&longs;ionem impetus, eleuationem, vel tractio­<lb/>nem, aut proiectionem, quæ &longs;unt operationes phy&longs;icæ. </s> <s id="N10A3F">Ter­<lb/>tio, quia &longs;i&longs;tendo in puris principijs phy&longs;icis, fatis <expan abbr="vid&etilde;tur">videntur</expan> de­<lb/>mon&longs;trari omnia quæ pertractantur in ip&longs;a mechanica &longs;cien­<lb/>tia quoad propo&longs;itiones vniuer&longs;ales, ac propriè &longs;cientificas. <lb/></s> <s id="N10A4D">Vt exempli gratia, grauia æqualia ex æqualibus <expan abbr="di&longs;tãtijs">di&longs;tantijs</expan> &etail;què <lb/>ponderare, nec vnum po&longs;&longs;e in libra aliud vincere; nam ratio <lb/>huius e&longs;t, quia actio debet e&longs;&longs;e ab inæquali proportione, vt ex <lb/>Ari&longs;t. habetur in phy&longs;icis 1. de Generat. <!-- REMOVE S-->tex. <!-- REMOVE S-->48. Similiter; <lb/>grauia faciliùs tolli beneficio trocleæ, aut vectis, quàm &longs;ola <lb/>manu; & id genus alia, reducuntur ad principium phy&longs;icum <lb/>de maiori facilitate motus circularis, <expan abbr="maioreq.">maioreque</expan> velocitate <lb/>partium, quæ magis di&longs;tant à centro circuli, eo quod maius <lb/>&longs;patium percurrant in æquali tempore ac minus fulciantur. <lb/></s> <s id="N10A6D">Quapropter ip&longs;emet Ari&longs;toteles phy&longs;icè hic videtur tractate <lb/>quidquid ad vniuer&longs;alem doctrinam mechanicam pertinet, <lb/>nec adhibere principia mathematica, ni&longs;i aliquando ad cla­<lb/>riùs & euidentiùs demon&longs;trandum, non &longs;ecus ac in alijs quo­<lb/>que tractationibus phy&longs;icis con&longs;ueuit. </s> <s id="N10A78">Nihil enim prohibet, <lb/>idem diuer&longs;is principijs plurium &longs;cientiarum o&longs;tendi. </s> </p> <p id="N10A7D" type="main"> <s id="N10A7F">Quarto, nam licet mechanica facultas, vt ab alijs traditur, <pb pagenum="18" xlink:href="005/01/026.jpg"/>pa&longs;&longs;im vtatur demon&longs;trationibus mathematicis, id tamen fit, <lb/>vt de&longs;cendat ad particularia, & adaptetur ad praxim, vel vt <lb/>clarius innote&longs;cat veritas ab&longs;tractè con&longs;iderata, cum per figu­<lb/>ras obijcitur &longs;en&longs;ibus, ac metiri po&longs;&longs;umus magnitudinem & <lb/>di&longs;tantiam, vt appareat proportio requi&longs;ita ad motum ip&longs;o­<lb/>rum grauium. </s> </p> <p id="N10A91" type="main"> <s id="N10A93">Quinto, nam e&longs;tò Mechanica &longs;cientia pluries indigeat au­<lb/>xilio mathematico, nec po&longs;&longs;it multa probare, ni&longs;i mutuetur <lb/>aliqua ex principijs geometricis, imò & arithmeticis; non ta­<lb/>men per hoc &longs;equitur, Mathematicis &longs;ubalternari, &longs;icut nec <lb/>Phy&longs;ica, & Theologia &longs;ubalternantur Metaphy&longs;icæ, quamuis <lb/>multa petant ex Metaphy&longs;ica. <!-- KEEP S--></s> </p> <p id="N10AA1" type="main"> <s id="N10AA3">Ex alio verò capite, cum Philo&longs;ophi ac Mathematici om­<lb/>nes, qui de hac facultate &longs;crip&longs;erunt, eam ex Phy&longs;ica, & Geo­<lb/>metria ortam con&longs;tituant, vt videre e&longs;t apud Heronem, Pap­<lb/>pum Alexandrinum, & alios qui eos &longs;equuntur; potius ip&longs;am <lb/>qua&longs;i mixtam ex vtraque, ac tertiam quandam &longs;cientiam per <lb/>&longs;e e&longs;&longs;e videbitur, &longs;icut nonnullis hac tempe&longs;tate vi&longs;um fui&longs;&longs;e <lb/>affirmat Guidus Vbaldus in præfatione &longs;uorum mechanico­<lb/>rum. </s> <s id="N10AB4">Et confirmari po&longs;&longs;et ex verbis illis Ari&longs;totelis iam ex­<lb/>po&longs;itis in fine huius textus, cum loquendo de mechanicis <lb/>problematibus ait: Sunt autem hæc neque naturalibus om­<lb/>ninò quæ&longs;tionibus eadem, neque &longs;eiuncta valde, verùm ma­<lb/>thematicarum contemplationum, <expan abbr="naturaliumq.">naturaliumque</expan> communia. <lb/></s> <s id="N10AC4">Quando quidem quod commune duobus e&longs;t, vtriu&longs;que natu­<lb/>ram participat. </s> </p> <p id="N10AC9" type="main"> <s id="N10ACB">Pro &longs;olutione tamen quæ&longs;tionis, notandum e&longs;t, adhoc vt <lb/>vna &longs;cientia alteri &longs;ubalternetur, duo præcipuè requiri, ad <lb/>quæ reducantur omnia quæ Ari&longs;toteles tradit 2. po&longs;ter. </s> <s id="N10AD2">tex. <lb/><!-- REMOVE S-->58. & &longs;equentibus. </s> </p> <p id="N10AD8" type="main"> <s id="N10ADA">Primum e&longs;t, vt quæ tractantur in &longs;cientia &longs;ubalternata, non <lb/>po&longs;&longs;int <expan abbr="euid&etilde;ter">euidenter</expan> cogno&longs;ci, ni&longs;i ex ijs quæ traduntur ac <expan abbr="demõ-&longs;trantur">demon­<lb/>&longs;trantur</expan> in &longs;cientia &longs;ubalternante, à qua propterea ip&longs;a &longs;cien­<lb/>tia &longs;ubalternata dicitur intrin&longs;ecè & e&longs;&longs;entialiter dependere. <lb/></s> <s id="N10AEC">Ratio autem e&longs;t, quia &longs;cientia &longs;ubalternata cum non habeat <lb/>principia per &longs;e nota, & immediata, &longs;icut illa quæ immediatè <pb pagenum="19" xlink:href="005/01/027.jpg"/>pendet ab habitu principiorum, loco illorum nititur conclu­<lb/>&longs;ionibus demon&longs;tratis in &longs;uperiori &longs;cientia. </s> <s id="N10AF8">Et hac ratione <lb/>nihil demon&longs;tratur in Per&longs;pectiua, quod <expan abbr="nõ">non</expan> inferatur ex con­<lb/>clu&longs;ionibus Geometriæ cui ip&longs;a &longs;ubordinatur; <expan abbr="nihilq.">nihilque</expan> in Mu­<lb/>&longs;ica, quod non nitatur conclu&longs;ionibus ac principijs Arithme­<lb/>ticæ cui &longs;imiliter ip&longs;a &longs;ubalternatur. </s> </p> <p id="N10B0B" type="main"> <s id="N10B0D">Secundum requi&longs;itum e&longs;t, vt idem &longs;it obiectum &longs;ubalter­<lb/>natæ, ac &longs;ubalternantis &longs;ecundum aliquam rationem forma­<lb/>lem. </s> <s id="N10B14">Quandoquidem &longs;i &longs;ubiecta e&longs;&longs;ent e&longs;&longs;entialiter diuer&longs;a <lb/>&longs;ecundum formalitatem qua cadunt &longs;ub &longs;cientiam, non dare­<lb/>tur tran&longs;itus à &longs;cientia &longs;ubalternata ad <expan abbr="&longs;ubalternant&etilde;">&longs;ubalternantem</expan>, vt do­<lb/>cet Ari&longs;toteles; hoc e&longs;t accipiendo ex illa propria principia <lb/>ac media ad probandum &longs;uas conclu&longs;iones; quia tam pa&longs;&longs;io­<lb/>nes demon&longs;trandæ de &longs;ubiecto, quàm principia quæ &longs;unt <lb/>cau&longs;æ intrin&longs;ecæ ip&longs;arum <expan abbr="pa&longs;&longs;ionũ">pa&longs;&longs;ionum</expan>, debent e&longs;&longs;e maximè pro­<lb/>pria & connexa cum ip&longs;o &longs;ubiecto: nihil autem pote&longs;t e&longs;&longs;e <lb/>maximè proprium duobus &longs;ubiectis e&longs;&longs;entialiter diuer&longs;is; ac <lb/>proinde ex connexione cum principijs vnius, inferri non po­<lb/>te&longs;t connexio alterius ad conficiendas demon&longs;trationes. </s> <s id="N10B33">Ea­<lb/>dem ergo e&longs;&longs;entialiter debent e&longs;&longs;e &longs;ubiecta &longs;ubalternantis, ac <lb/>&longs;ubalternatæ, &longs;altem &longs;ecundum aliquam rationem formalem, <lb/>quamuis alia ratione differant inter &longs;e. </s> <s id="N10B3C">Semper enim ratio <lb/>illa formalis &longs;ub qua agitur de aliquo in &longs;cientia, vniuer&longs;aliori <lb/>ac &longs;impliciori modo con&longs;ideratur in &longs;ubalternante, quàm in <lb/>&longs;ubalternata, in qua &longs;emper contrahitur ab aliqua differentia <lb/>accidentali &longs;uperaddita, vt con&longs;tat in Mu&longs;ica re&longs;pectu Arith­<lb/>meticæ, & in Per&longs;pectiua re&longs;pectu Geometriæ. </s> <s id="N10B49">Siquidem in <lb/>Arithmetica &longs;impliciter con&longs;ideratur numerus &longs;ecundum &longs;e, <lb/>in Mu&longs;ica vero con&longs;ideratur numerus in &longs;ono. </s> <s id="N10B50"><expan abbr="Similiterq.">Similiterque</expan> in <lb/>Geometria &longs;olum con&longs;iderantur lineæ, in Per&longs;pectiua vero <lb/>con&longs;iderantur in vi&longs;u, quæ differentiæ putantur accidentales; <lb/>nam vt docet Ari&longs;toteles locis citatis, & 13 metaph. </s> <s id="N10B5C">&longs;um. <!-- REMOVE S-->1. <lb/>cap. 3. Mu&longs;ica & Per&longs;pectiua non ver&longs;antur formaliter circa <lb/>&longs;onum & vi&longs;um &longs;ed circa numerum & lineam de quibus agi­<lb/>tur ab&longs;olutè in Arithmetica, & Geometria. <!-- KEEP S--></s> </p> <p id="N10B68" type="main"> <s id="N10B6A">Quibus po&longs;itis, dicendum e&longs;t, Mechanicam <expan abbr="facultat&etilde;">facultatem</expan> ab­<pb pagenum="20" xlink:href="005/01/028.jpg"/>&longs;olutè ac totaliter non &longs;ubalternari Philo&longs;ophiæ naturali, &longs;ed <lb/>Mathematicæ; Ita &longs;en&longs;it expre&longs;sè Ari&longs;toteles in principio iam <lb/>explicato huius opu&longs;culi, cum ait, &longs;ubiectum quidem huius <lb/>facultatis e&longs;&longs;e Phy&longs;icum, con&longs;iderationem verò e&longs;&longs;e mathe­<lb/>maticam. </s> <s id="N10B7E">Quod po&longs;tea omnes Philo&longs;ophi, ac Mathematici <lb/>vniuer&longs;aliter &longs;upponunt in di&longs;tributione, ac &longs;ub alternatione <lb/>Mathematicarum di&longs;ciplinarum, &longs;ubordinando hanc &longs;cien­<lb/>tiam Geometricæ. <!-- KEEP S--></s> </p> <p id="N10B88" type="main"> <s id="N10B8A">Ratione verò probatur, nam quælibet &longs;cientia &longs;ubalterna, <lb/>illi &longs;cicntiæ dicitur &longs;ubalternari, cuius idem &longs;ubiectum &longs;ecun­<lb/>dum aliquam rationem formalem con&longs;iderat, cuiu&longs;que con­<lb/>clu&longs;ionibus vtitur tanquam principijs ad conficiendas pro­<lb/>prias demon&longs;trationes; &longs;ed &longs;cientia Mechanica circa idem <lb/>&longs;ubiectum &longs;ecundum aliquam rationem formalem ver&longs;atur <lb/>ac Geometria, ex <expan abbr="eaq.">eaque</expan> vt plurimum &longs;umit &longs;ua principia ad <lb/>demon&longs;trandas mechanicas conclu&longs;iones. </s> <s id="N10B9F">Ergo Mechanica <lb/>facultas &longs;ubalternatur Geometriæ & non alteri &longs;cientiæ. </s> <s id="N10BA4">Ma­<lb/>ior pater ex &longs;upra notatis. </s> <s id="N10BA9">Minor in qua e&longs;t difficultas, pro­<lb/>batur quoad priorem partem, ex eo; Nam cettum e&longs;t, ip&longs;um <lb/>corpus mobile graue, aut leue, quod con&longs;tituitur &longs;ubiectum <lb/>huius &longs;cientiæ, non con&longs;iderari ni&longs;i &longs;ecundum quantitatem, <lb/>ponderis quam habet, & prout moueri aut detineri pote&longs;t <lb/>tanta vel tanta virtute, ac mediante aliquo artificio. </s> <s id="N10BB6">Quo <lb/>fit vt proxima ratio &longs;ecundum quam de illo agitur, &longs;it tum <lb/>quantitas ponderis illius, ab&longs;trahendo à materia ponderante, <lb/>tùm quantitas virtutis mouentis aut detinentis, prout &longs;cilicet <lb/>vtraque quantitas coaptari, ac proportionari debet in ordine <lb/>ad motionem aut quietem artificio&longs;am: &longs;eu prout quantitas <lb/>ponderis &longs;ub&longs;tat motioni, aut quieti artificio&longs;æ, quam pro­<lb/>pterea diximus, vltimò complere, & <expan abbr="cõ&longs;tituere">con&longs;tituere</expan> obiectum for­<lb/>male huius &longs;cientiæ. </s> <s id="N10BCD">At huiu&longs;modi ratio formalis &longs;ic expli­<lb/>cata, manife&longs;tè inuoluit quantitatem ab&longs;tractam à materia, <lb/>ac &longs;pecialiter pa&longs;&longs;ionem quandam quantitatis continuæ ac <lb/>permanentis, quæ e&longs;t obiectum Geometriæ; nempe artifi­<lb/>cio&longs;am mobilitatem & quietem; imò talis mobilitas attendi­<lb/>tur iuxta dimen&longs;ionem quantitatiuam ip&longs;ius mobilis, ac pro-<pb pagenum="21" xlink:href="005/01/029.jpg"/>portionem quam habet cum mouente, in tanta propinquita­<lb/>te vel di&longs;tantia; ac per&longs;æpe fundatur in ip&longs;a figura quantitatis <lb/>mobilis aut mouendæ. </s> <s id="N10BE3">Ergo ratio formalis &longs;ub qua Mecha­<lb/>nica facultas circa proprium &longs;ubiectum ver&longs;atur, eandem e&longs;­<lb/>&longs;entialiter rationem &longs;ubiecti Geometriæ participat. </s> </p> <p id="N10BEA" type="main"> <s id="N10BEC">Quod autem Mechanica facultas vtatur principijs. </s> <s id="N10BEF">proba­<lb/>tis in Geometria, palam o&longs;tendunt ip&longs;æ demon&longs;trationes me­<lb/>chanicæ, quæ ferè omnes immediatè nituntur propo&longs;itioni­<lb/>bus, ac theorematibus demon&longs;tratis in illa, deinde re&longs;oluun­<lb/>tur in eadem principia geometrica; <expan abbr="&longs;iquid&etilde;">&longs;iquidem</expan> præcipuè fundan­<lb/>tur in proprietatibus, ac pa&longs;&longs;ionibus circuli quæ &longs;anè demon­<lb/>&longs;trantur principijs geometricis, vt pr&etail;&longs;ertim patet ex tertio ac <lb/>&longs;exto <expan abbr="elementorũ">elementorum</expan> Euclidis. <!-- KEEP S--></s> <s id="N10C09">Rur&longs;us principia Mechanica, quæ <lb/>traduntur ab Archimede, <expan abbr="alijsq.">alijsque</expan> Mechanicis, vel &longs;unt omninò <lb/>geometrica, vel &longs;umuntur ex geometricis. </s> <s id="N10C14">Vt grauia æqua­<lb/>lia ex æqualibus di&longs;tantijs æquè ponderare: Aequalia verò <lb/>grauia ex inæqualibus di&longs;tantijs, non æquè ponderare, &longs;ed <lb/>præponderare ad graue ex maiori di&longs;tantia. </s> <s id="N10C1D">Et æqualibus &longs;i­<lb/>milibusque, figuris planis inter &longs;e coaptatis, centra quoque <lb/>grauitatum inter &longs;e coaptari oportere. </s> <s id="N10C24">Et &longs;imilia vt vi­<lb/>dere e&longs;t apud ip&longs;um Archimedem, Pappum, & alios <lb/>Auctores. </s> </p> <p id="N10C2B" type="main"> <s id="N10C2D">Ad primum igitur argumentum in contrarium Re&longs;ponde­<lb/>tur, &longs;ubiectum Mechanicæ facultatis e&longs;&longs;e quidem phy&longs;icum <lb/>in genere entis, non tamen in genere &longs;cibilis, nempe &longs;ub ra­<lb/>tione qua de illo agitur in hac &longs;cientia. </s> <s id="N10C36">Quare licet <expan abbr="&longs;ubiectũ">&longs;ubiectum</expan> <lb/>materiale huius facultatis, quod e&longs;t graue, & leue, &longs;eu quan­<lb/>titas ponderis cuiu&longs;que corporis mobilis &longs;ecundum locum, <lb/>connotet pa&longs;&longs;ionem quamdam corporis naturalis, quod con<lb/>&longs;tituitur &longs;ubiectum adæquatum Phy&longs;icæ; cum tamen non <expan abbr="cõ-&longs;ideretur">con­<lb/>&longs;ideretur</expan> hic per habitudinem ad illud, pertinere non pote&longs;t <lb/>ad &longs;cientiam phy&longs;icam; &longs;icut nec ip&longs;a quantitas, quæ con&longs;ti­<lb/>tuitur &longs;ubiectum adæquatum totius facultatis mathematicæ, <lb/>quamuis in &longs;e &longs;it affectio corporis naturalis, & pa&longs;&longs;io &longs;ub&longs;tan­<lb/>tiæ corporeæ, de <expan abbr="illaq.">illaque</expan> abundè etiam tractetur in Phy&longs;ica. <lb/></s> <s id="N10C58"><expan abbr="Idemq.">Idemque</expan> exemplificari pote&longs;t in Mu&longs;ica & Per&longs;pectiua, quarum <pb pagenum="22" xlink:href="005/01/030.jpg"/>&longs;ubiecta materialia non minus &longs;unt phy&longs;ica, con&longs;ideratio ve­<lb/>rò mathematica. </s> <s id="N10C65">Ac tandem aperti&longs;&longs;imè con&longs;tare pote&longs;t in­<lb/>ductione partium eiu&longs;dem facultatis Mechanicæ. <!-- KEEP S--></s> <s id="N10C6B">Nam licet <lb/>Centrobarica verbi gratia, vel Machinaria, non agat ni&longs;i de <lb/>&longs;ubiectis phy&longs;icis, tota tamen eorum con&longs;ideratio e&longs;t mathe­<lb/>matica, geometricè procedendo ad <expan abbr="demon&longs;trãdas">demon&longs;trandas</expan> dimen&longs;io­<lb/>nes, &longs;iguras, di&longs;tantias, pondero&longs;itatem, vires, ac motum ip­<lb/>&longs;orum. </s> <s id="N10C7C">Similites &longs;piritalis tractatio quamuis agat de aere, ac <lb/>de coniunctione aeris cum alijs elementis ad multos vitæ no­<lb/>&longs;træ v&longs;us, quæ res phy&longs;icæ in &longs;e &longs;unt, nihilominus ad mathe­<lb/>maticam contemplationem pertinet, & ab Herone mathe­<lb/>maticè cum &longs;uis demon&longs;trationibus traditur, contemplando <lb/>proportionem, numerum, magnitudinem, di&longs;tantiam, ordi­<lb/>nem, figuram, & cau&longs;as effectuum, qui ex inclu&longs;o aere profi­<lb/>ci&longs;cuntur. </s> <s id="N10C8D">Quorum omnium ratio e&longs;t, quia in his non atten­<lb/>ditur &longs;ubiectum materialiter &longs;umptum in e&longs;&longs;e rei, &longs;ed formali­<lb/>tas qua cadit &longs;ub &longs;cientiam, &longs;eu ratio &longs;ub que agitur de ille, <lb/>quæ dicitur &longs;ubiectum, vel obiectum formale; <expan abbr="cumq.">cumque</expan>, hoc in <lb/>propo&longs;ito pertineat ad Mathematicum, &longs;equitur, facultatem <lb/>ip&longs;am &longs;iue &longs;cientiam mechanicam, e&longs;&longs;e verè mathematicam. </s> </p> <p id="N10C9A" type="main"> <s id="N10C9C">Ad &longs;ecundum Re&longs;pondetur, motionem & quietem <expan abbr="grauiũ">grauium</expan> <lb/>& leuium, &longs;iue ex natura &longs;ua, &longs;iue ex aliqua violentia vtraque <lb/>profici&longs;catur, e&longs;&longs;e quidem pa&longs;&longs;iones phy&longs;icas eorum prout <lb/>corpora naturalia &longs;unt, non tamen con&longs;iderari à Mechanicis <lb/>vt tales pa&longs;&longs;iones &longs;unt, &longs;ed prout obtineri po&longs;&longs;um ab illis tan­<lb/>quam finis intentus, mediante aliquo artificio. </s> <s id="N10CAD">Vnde ratio <lb/>formalis &longs;ub qua grauia & leuia con&longs;tituuntur obiecta huius <lb/>&longs;cientiæ, non e&longs;t prout mobilia &longs;unt &longs;ecundum locum, aut <lb/>quie&longs;cere po&longs;&longs;unt, ab&longs;olutè loquendo; &longs;ed prout artificiosè <lb/>moueri aut quie&longs;cere po&longs;&longs;unt, loquendo modum quo mo­<lb/>uenda &longs;unt, vel detinenda, & circa quem formaliter ors ip&longs;a <lb/>ver&longs;atur ad finem intentum. </s> </p> <p id="N10CBE" type="main"> <s id="N10CC0">Ad tertium Re&longs;pondetur, nec omnia, nec &longs;atis demon&longs;tra­<lb/>ri po&longs;&longs;e ex principijs phy&longs;icis in hac &longs;cientia. </s> <s id="N10CC5">Porrò licet non­<lb/>nulla de graui & leui &longs;upponantur, vel etiam probentur ex <lb/><gap/>is, cætera tamen vt plurimum & exactè non <expan abbr="demon&longs;trãtus">demon&longs;tratus</expan> <pb pagenum="23" xlink:href="005/01/031.jpg"/>ni&longs;i ex principijs geométricis, quare ficat de lride multa <lb/>pertractantur in Phy&longs;ica, quod ramen non tollit omnimodam <lb/>eius cognitionem ad Per&longs;pectiuam referri, ita quamuis mul­<lb/>ta de graui & lem &longs;umantur ex phy&longs;icis, hoc non ob&longs;tat quo­<lb/>minus prout artificiosè mobilia &longs;unt, ex pro&longs;e&longs;&longs;o & omnino <lb/>&longs;olum cogno&longs;cantur in hac &longs;cientia ex principijs mathemati­<lb/>cis. </s> <s id="N10CE7">Et &longs;ic, grauia æqualia ex æqualibus di&longs;tantijs æquè pon­<lb/>derare, <expan abbr="vnumq.">vnumque</expan> in libra non po&longs;&longs;e aliud vincere, non &longs;atis <lb/>probatur ex illo principio physico, quod àctio debeat e&longs;&longs;e ab <lb/>inæquali proportione. </s> <s id="N10CF4">Quando quiddem inæqualitas di&longs;&longs;<gap/>­<lb/>tiæ non tollit æqual tatera ponderis, nec proportionem illius <lb/>ad aluerum, &longs;i &longs;ecundum &longs;e ac phy&longs;icis con&longs;ideretur, tollit <lb/>autem &longs;e mathematicè demon&longs;tratur, maiorem di&longs;tantiam a <lb/>centro, vbi grauia falciuntur, grauitatem, vel potiùs effe­<lb/>ctum illius, <expan abbr="actumq.">actumque</expan> ponderandi in ip&longs;is grauibus augere. <lb/></s> <s id="N10D08">Item maior velocitas, ac facilitas quam experimur in motu <lb/>circulari earum partium, quæ magis di&longs;&longs;ant à centro, non <lb/>probatur à priori, nec demon&longs;tratur ex eo quod maius &longs;pa­<lb/>tium percurrant in æquali tempore, nam hoc e&longs;t idem per <lb/>diuer&longs;a explicare. </s> <s id="N10D13">Demon&longs;tratur autem per cau&longs;am, & à <lb/>priori, ex illo principio mathematico, quod quanto magis li­<lb/>neæ à centro di&longs;ce&longs;&longs;erint, magis participant de motu recto <lb/>ac naturali, <expan abbr="minusq.">minusque</expan> retrahuntur in circumuolutione circull, <lb/>at &longs;uo lo eo explicabitur ex Ari&longs;totele qui &longs;anè in hoc <expan abbr="alijsq.">alijsque</expan> <lb/>dogmatibus mechanicis non vtitur demon&longs;trationibus geo­<lb/>metricis ad exemplum, vt in logica vel phy&longs;ica, neque ad <lb/>confirmationem veritatis probatæ; &longs;ed ve ab&longs;olutè probet <lb/>quod a&longs;&longs;ump&longs;erat, <expan abbr="quodq.">quodque</expan> aliter omninò probare nequiret. </s> </p> <p id="N10D32" type="main"> <s id="N10D34">Ex quibus fæcile apparet quid re&longs;paondendum &longs;it ad quar­<lb/>tum & quintum argumentum, nempe principia mathemati­<lb/>ca non modo in mechanica &longs;cientia de&longs;eruire ad maiorem <lb/>claritatem doctrinæ, & vt hæc aptetur ad praxim circa parti­<lb/>cularia, &longs;ed ab&longs;olutè ad demon&longs;trandas &longs;uas conclu&longs;iones in <lb/>vniuer&longs;um, quas quippe aliter non po&longs;&longs;et omninò probare. <lb/></s> <s id="N10D44">Id quod non &longs;olum verificatur in vni vel altera conclu&longs;ione, <lb/>&longs;ed ferè in omnibus, vt in progre&longs;&longs;u con&longs;tabit. </s> </p> <pb pagenum="24" xlink:href="005/01/032.jpg"/> <p id="N10D4D" type="main"> <s id="N10D4F">Quod <expan abbr="tand&etilde;">tandem</expan> afferebatur de ortu Mechanices ex Phy&longs;ica, <lb/>& Mathematica ad probandum e&longs;&longs;e &longs;cientiam ex vtraque <lb/>conflatam, &longs;i rectè con&longs;ideretur, nullius e&longs;t momenti; nam <lb/>vere dicitur ex Phy&longs;ica &longs;ump&longs;i&longs;&longs;e &longs;ubiectum, & ex Geome­<lb/>tria principia quibus in &longs;uis demon&longs;trationibus procederet; <lb/>ex quo tamen non &longs;equitur, ip&longs;am veluti mixtam quandam <lb/>re&longs;ultare &longs;cientiam, partim &longs;cilicet Phy&longs;icam, partim verò <lb/>Mathematicam; tum quia &longs;pecificatio &longs;cientiarum vt diximus <lb/>non attenditur ex &longs;ubiecto materiali, &longs;ed ex obiecto formali; <lb/>tum etiam, quia nequit vna eademque &longs;cientia, pluribus &longs;cien­<lb/>tijs omnino diuer&longs;is &longs;ubalternari, cum vnitas ip&longs;ius attenda­<lb/>tur penes vnitatem eiu&longs;dem obiecti formalis, quod mutuari <lb/>debet vel ex vna, vel ex altera &longs;uperiori &longs;cientia. </s> <s id="N10D6E">Quare cum <lb/>Ari&longs;toteles ait, Mechanica problemata e&longs;&longs;e Mathematicarum <lb/>quæ&longs;tionum, naturaliumque communia, non intellexit e&longs;&longs;e <lb/>veluti aggregata & <expan abbr="cõflata">conflata</expan> ex illis vtri&longs;que. </s> <s id="N10D7B">Non enim <expan abbr="cõmu-nia">commu­<lb/>nia</expan> conflantur ex particularibus, &longs;ed particularia ex commu­<lb/>nibus ac vniuer&longs;alibus. </s> <s id="N10D86">Vnde potius &longs;en&longs;it Philo&longs;ophus, Me­<lb/>chanicam facultatem de his rebus agere, quæ communes &longs;unt <lb/>naturalibus ac Mathematicis quæ&longs;tionibus (quamuis &longs;ub di­<lb/>uer&longs;a ratione formali) cuiu&longs;modi &longs;unt quantitas ponderis, &longs;eu <lb/>ip&longs;a ponderantia, quæ dicuntur grauia & leuia, ac virtus qua <lb/>ip&longs;a mouentur aut detinentur. </s> <s id="N10D93">Siquidem de his omnibus <lb/>multa quæruntur in phy&longs;icis, prout &longs;unt affectiones corporis <lb/>naturalis, vel corpora quædam naturalia; <expan abbr="multaq.">multaque</expan> pa­<lb/>riter in mathematicis, prout dimen&longs;ionem habent <lb/>quantitatiuam, aut virtutis, ab&longs;trahendo <lb/>ab hac vel illa materia, <expan abbr="peculiaresq.">peculiaresque</expan> <lb/>fortiuntur pa&longs;&longs;iones in ordine <lb/>ad motum artifi­<lb/>cio&longs;um. </s> </p> <pb pagenum="25" xlink:href="005/01/033.jpg"/> <p id="N10DB2" type="head"> <s id="N10DB4"><emph type="italics"/>Quæ nam de&longs;criptio quidditatiua huius facul­<lb/>tatis colligatur ex dictis, & quo pacto <lb/>ab alijs &longs;cientijs di&longs;tinguatur.<emph.end type="italics"/></s> </p> <p id="N10DBF" type="head"> <s id="N10DC1">ADDITIO QVINTA.</s> </p> <p id="N10DC4" type="main"> <s id="N10DC6">Qvæ dicta &longs;unt recapitulantes, hanc huius facultatis de­<lb/>&longs;criptionem colligere po&longs;&longs;umus ad explicandam to­<lb/>tam quidditatem ip&longs;ius. </s> <s id="N10DCD">Mechanica facultas, e&longs;t <lb/>practica &longs;cientia, quæ geometricis demon&longs;trationibus nixa <lb/>ver&longs;atur circa quantitatem ponderis grauium & leuium, <expan abbr="vir-tuti&longs;q.">vir­<lb/>tuti&longs;que</expan> qua artificiosè ac mirabiliter moueri debent, aut quie­<lb/>&longs;cere ad finem intentum ab Artifice. <!-- KEEP S--></s> <s id="N10DDD">In qua de&longs;criptione <lb/>ponitur (practica &longs;cientia) loco generis, in quo conuenit cum <lb/>Philo&longs;ophia morali, cum Logica, ac Medicina; per idemque <lb/>di&longs;tinguitur à &longs;cientijs &longs;peculatiuis, quæ &longs;ane non ordinantur <lb/>ad praxim, & à &longs;eruilibus artibus, quæ nullam includunt ratio­<lb/>nem &longs;cientiæ, vt &longs;upra explicuimus. </s> <s id="N10DEA">Per particulam verò <lb/>(geometricis demon&longs;trationibus nixa) explicatur quædam <lb/>differentia, qua talis &longs;cientia conuenit quidem cum &longs;cientijs <lb/>Mathematicis &longs;ubalternatis Geometriæ, vt Per&longs;pectiua, Geo­<lb/>de&longs;ia, & A&longs;tronomia; di&longs;tinguitur autem ab illis quæ vel <lb/>non &longs;ubalternantur Geometriæ, vt Mu&longs;ica & Arithmetica, <lb/>vel nullo modo &longs;unt Mathematicæ, vt Metaphy&longs;ica, Philo&longs;o­<lb/>phia naturalis aut moralis, Medicina ac Logica. <!-- KEEP S--></s> <s id="N10DFC">Denique <lb/>per cæteras particulas explicatur vltima differentia, ex pro­<lb/>prio obiecto ac fine de&longs;umpta, qua certè huiu&longs;modi &longs;cientia <lb/>optimè di&longs;tinguitur ab illis quæ non ver&longs;antur circa quantita­<lb/>tem aliquam; tum ab illa contemplatione Logica, aut Me­<lb/>taphi&longs;ica, quæ tantum ver&longs;atur circa quantitatem prædica­<lb/>mentalem; item à Phy&longs;ica quæ circa quantitatem &longs;olum <lb/>ver&longs;atur in quantum e&longs;t affectio corporis naturalis, & in ordi­<lb/>ne ad principium motus & quietis naturalis. </s> <s id="N10E0F">Rur&longs;us non <lb/>minus di&longs;tinguitur, eadem differentia, à reliquis di&longs;ciplinis <lb/>Mathematicis, nam licet conueniat cum illis in hoc quod e&longs;t <pb pagenum="26" xlink:href="005/01/034.jpg"/>ver&longs;ari circa quantitatem modo quodam ab&longs;tracto à materia, <lb/>illam tamen contrahit ad quantitatem ponderis grauium, & <lb/>leuium, ac virtutis qua debent moueri, &longs;icet non determi­<lb/>net materiam ponderantem, aut virtutis mouentis. </s> <s id="N10E21">Per <lb/>quod &longs;anè primo di&longs;tinguitur ab Arithmetica & Mu&longs;ica, quæ <lb/>ver&longs;atur circa quantitatem di&longs;cretam; non autem continuam <lb/>&longs;icut grauium ac lenium; deinde à Geometria propriè dicta, <lb/>& a Stereometria quæ ver&longs;antur circa quantitatem <expan abbr="cõtinuam">continuam</expan> <lb/>planorum ac &longs;olidorum, ab&longs;trahendo à grauitate aut &longs;euitate, <lb/>& à quocunque motu illorum. </s> <s id="N10E34">Denique di&longs;tinguitur à Per­<lb/>&longs;pectiua quæ &longs;anè quantitatem con&longs;ideran in lineis vi&longs;ualibus, <lb/>& à Geode&longs;ia quæ illam con&longs;iderat in aceruis tanquam co­<lb/>nis, vel in puteis tanquam cylindris; tandem ab Astronomias <lb/>quæ illam con&longs;iderat in corporibus cele&longs;ribus eorumque <lb/>di&longs;tantijs, ac motibus à natura præ&longs;criptis. </s> <s id="N10E41">Cum igitur per <lb/>idem res <expan abbr="cõ&longs;tituatur">con&longs;tituatur</expan> in e&longs;&longs;e &longs;ui, per quod di&longs;tinguitur ab alijs, <lb/>vt recepti&longs;&longs;imum e&longs;t in doctrina Peripatetica, &longs;atis videtur <lb/>explicata con&longs;titutio & e&longs;&longs;entia huius &longs;cientiæ per traditam <lb/>definitionem &longs;eu quidditatiuam de&longs;criptionem, cum per eam <lb/>con&longs;tet &longs;ufficienter ab alijs &longs;cientijs ac facultatibus di&longs;tingui. </s> </p> <p id="N10E52" type="head"> <s id="N10E54"><emph type="italics"/>De vnitate &longs;cientiæ Mechinicæ <lb/>eiu&longs;que partibus.<emph.end type="italics"/></s> </p> <p id="N10E5D" type="head"> <s id="N10E5F">ADDITIO SEXTA,</s> </p> <p id="N10E62" type="main"> <s id="N10E64">Ex peditis ijs quæ ad quæ&longs;tionem, an &longs;it, & quid &longs;it Hæc <lb/>&longs;cientia, pertinere videbantur, &longs;equitur inquirendum, <lb/>quotuplex &longs;it; vtrum &longs;cilicet &longs;it vna vel multiplex, & quas <lb/>habeat partes. </s> <s id="N10E6D">Qua in re &longs;upponimus primo, &longs;ermonem e&longs;&longs;e <lb/>de &longs;cientia totali, prout e&longs;t aggregatum quoddam ex omni­<lb/>bus &longs;cientijs partialibus, &longs;iue actualibus, &longs;iue habitualibus, <lb/>nempe ex omnibus conclu&longs;ionibus demon&longs;tratis de &longs;ubiecto <lb/>adæquato, circa quod huiu&longs;modi facultas ver&longs;atur. </s> <s id="N10E78">Deinde <lb/>&longs;upponimus vnitatem &longs;cientiæ totalis de &longs;umi, tùm ex vnitate <lb/>ordinis quo conclu&longs;iones ac partes illius coaptantur inter &longs;e, <pb pagenum="27" xlink:href="005/01/035.jpg"/>ad componendam integram &longs;cientiam de eodem &longs;ubiecto <lb/>materiali ac pa&longs;&longs;ionibus illius; tum ex vnitate obiecti form­<lb/>lis circa quod omnes &longs;cientiæ partiales conueniunt. </s> </p> <p id="N10E88" type="main"> <s id="N10E8A">Quibus po&longs;itis dicendum e&longs;t, Mechanicam facultatem e&longs;­<lb/>&longs;e vnicam &longs;cientiam totalem vnitate ordinis, ac obiecti for­<lb/>malis, &longs;ub quà &longs;cientia totali tanquam &longs;ub &longs;pecie atoma con­<lb/>tinentur omnes conclu&longs;iones, vel &longs;cientiæ partiales Mecha­<lb/>nicæ. </s> <s id="N10E95">Id quod facile probatur ex eo, quia omnis Mechani­<lb/>ca cognitio ver&longs;atur circa eandem rationem formalem obie­<lb/>cti ad&etail;quati, nempe quantitatem ponderis artificiosè mouen­<lb/>di, aut detinendi, licet non de eodem pondere, vel de ei&longs;dem F<lb/>ponderantibus in qualibet parte huius &longs;cientiæ persè agatur. <lb/>Deinde probatur, quia omnes conclu&longs;iones demon&longs;tratæ in <lb/>hac &longs;cientia, <expan abbr="ordinãtur">ordinantur</expan> ad plenam cognitionem obiecti expli­<lb/>cati, &longs;iue per contemplationem partium illius, agendo de <lb/>hoc, vel illo graui, aut leui quod moueri debet, aut quie&longs;ce­<lb/>re, &longs;iue per contemplationem plurium pa&longs;&longs;ionum quas idem <lb/>&longs;ubiectum patitur, quatenus cadit &longs;ub artificio&longs;am motionem <lb/>aut quietem. </s> <s id="N10EB3">Rur&longs;us plurimæ conclu&longs;iones in ea demon&longs;tra­<lb/>tæ, de&longs;eruiunt tanquam principia in demon&longs;trationibus reli­<lb/>quarum; vnde talis apparet ordo & connexio inter illas ad <lb/>inuicem, vt indubitanter ad eandem omninò &longs;cientiam tota­<lb/>lem in &longs;pecie &longs;umptam pertinere ab omnibus dicantur. </s> </p> <p id="N10EBE" type="main"> <s id="N10EC0">Diuiditur autem hæc &longs;cientia totalis in plures partes ve­<lb/>luti integrantes, ratione &longs;ubiecti. </s> <s id="N10EC5">Porrò cum eius &longs;ubiectum <lb/>non &longs;it vna & eadem indiui&longs;ibilis entitas, &longs;ed multiplex &longs;ub <lb/>ratione illa communi iam explicata corporis artificiosè mo­<lb/>bilis, tot erunt partes huius &longs;cientiæ, quot &longs;unt partes ip&longs;ius <lb/>adæquati &longs;ubiecti de quo demon&longs;trat qua ratione moueri de­<lb/>beat aut quie&longs;cere. </s> <s id="N10ED2">Et licet partes ip&longs;æ adæquati &longs;ubiecti <lb/>comparari po&longs;&longs;ent ad illud tanquam &longs;pecies ad genus, &longs;ub <lb/>quo continentur, vt &longs;ingula elementa, aut mixta re&longs;pectu cor­<lb/>poris in vniuer&longs;um quod artificiosè moueri pote&longs;t, aut quie­<lb/>&longs;cere; nihilominus cum ratio &longs;pecificans &longs;cientiam, in præ&longs;enti <lb/>non attendatur penes propriam differentiam &longs;ubiecti mate­<lb/>rialis, &longs;ed penes rationem formalem &longs;ub qua con&longs;ideratur in <pb pagenum="28" xlink:href="005/01/036.jpg"/>ip&longs;a &longs;cientia; hinc e&longs;t, vt commodius ac magis propriè &longs;pe­<lb/>cies ip&longs;æ corporum grauium; ac leuium comparentur ad gra­<lb/>ue & leue in communi, tanquam partes integrantes ad totum <lb/>quod con&longs;tituunt; præ&longs;ertim cum etiam genus dicat totum <lb/>confusè in compo&longs;itione Metaphy&longs;ica vt e&longs;t communis do­<lb/>ctrina &longs;umpta ex Ari&longs;totele lib. 5 Met. <!-- REMOVE S-->cap. 20. </s> </p> <p id="N10EF2" type="main"> <s id="N10EF4">Iuxtà hæc igitur Mechanica &longs;cientia primò diuiditur in <lb/>Centrobaricam quæ quidem centrum grauitatis in quolibet <lb/>corpore &longs;peculatur, & in Machinariam quæ ver&longs;atur circa <lb/>machinamenta quibus ip&longs;a corpora mouentur, aut detinen­<lb/>tur, &longs;iue grauia &longs;int, &longs;iue leuia. </s> <s id="N10EFF">Rur&longs;us Centrobaricam comi­<lb/>tatur, ab <expan abbr="eaq.">eaque</expan> dependet Sphæropœia, quæ motum circa cen­<lb/>trum &longs;phæricorum corporum contemplatur, <expan abbr="modumq.">modumque</expan> quo <lb/>ip&longs;a conficienda &longs;unt exhibet ad imitationem corporum cœ­<lb/>le&longs;tium, prout Archimedem confeci&longs;&longs;e traditur; quem etiam <lb/><arrow.to.target n="marg12"/> librum de Sph&etail;ropœia edidi&longs;&longs;e refert Carpus Antiochen&longs;is <lb/>apud Pappum Alexandrinum. </s> <s id="N10F19">Machinaria verò diuiditur in <lb/>Manganariam, cuius ope, exigua virtute, ingentia transferun­<lb/>tur pondera, & in Organopeticam, quæ in&longs;trumenta omnia <lb/>ad corporum motionem, aut detentionem accommodata ac <lb/>fabrefacta con&longs;iderat, <expan abbr="modumq.">modumque</expan> quo fieri debent rationabili­<lb/>ter tradit. </s> <s id="N10F2A">Sub Manganaria continetur Mechanopætica, quæ <lb/>aquam ex imis facilè haurire ac in <expan abbr="altũ">altum</expan> tollere docet, & &longs;iqua <lb/>e&longs;t alia &longs;peculatio quæ ad corpus aliquod <expan abbr="leuãdum">leuandum</expan> aut tran&longs;­<lb/>ferendum ordinatur. </s> <s id="N10F3B">Sub Organopetica verò continetur Po­<lb/>liorcetica, quæ ver&longs;atur circa bellicas machinas, vt Arietes ad <lb/>quatiendos muros, vel Catapultas & alias quibus &longs;agittæ, la­<lb/>pides, ac tela, in longi&longs;&longs;ima viæ &longs;patia emittuntur, & videre <lb/>e&longs;t apud Athenæum, Heronem mechanicum, & Apolliodo­<lb/>rum; & in Thaumaturgicam, de qua Hero Alexandrinus, <lb/>quæque tandem diuiditur in tres partes, quarum prima ver­<lb/>&longs;atur circa clep&longs;ydras, fi&longs;tulas, vario&longs;que ductus, quibus ex <lb/>vno va&longs;e in aliud aqua transfunditur, aut foris emittitur ad <lb/>con&longs;tituendas fontes artificiales, alia&longs;que commoditates pr&etail;­<lb/>&longs;tandas. </s> <s id="N10F52">Secunda verò docet quo pacto rotis, neruis, tim­<lb/>panis, <expan abbr="alijsq.">alijsque</expan> in&longs;trumentis motus veluti animatus præ&longs;tetur <pb pagenum="29" xlink:href="005/01/037.jpg"/>in&longs;en&longs;ibilibus, vt fertur de &longs;tatua Dedali ac Vulcani, de Ar­<lb/>chitæ columba, ac &longs;imilibus. </s> <s id="N10F62">Tertia modum tradit, quo ex <lb/>inclu&longs;o aere varij emittantur &longs;onitus ad morum vel percu&longs;&longs;io­<lb/>nem aqu&etail;, vt de &longs;erpentum &longs;ibilis, ac volucrum cantibus, <expan abbr="hu-manisq.">hu­<lb/>manisque</expan> vocibus imitatis, à pluribus enarratur: de que armo­<lb/>nia quam reddebant argentei remi celeberrimi illius nauigij <lb/>Cleopatræ Aegypti Reginæ cum aquam offenderent, ob &longs;pi­<lb/>ritum inter thecas eorum re&longs;eratum, qui agitatione remigum, <lb/><expan abbr="aquarumq.">aquarumque</expan> percu&longs;&longs;ione per varia <expan abbr="artificio&longs;aq.">artificio&longs;aque</expan> foramina exire <lb/>cogebatur. </s> <s id="N10F80">Et hæc de diui&longs;ione &longs;eu partibus Mechanicæ fa­<lb/>cultatis attigi&longs;&longs;e &longs;ufficiat, vt omittamus alias, quæ non tàm <lb/>propriè partes illius, quàm annexæ, aut mixtæ facultates vi­<lb/>dentur, vt Architectonica, quæ licet multum occupetur in <lb/>con&longs;ideratione artificio&longs;æ motionis, aut quietis grauium & <lb/>leuium, vlterius tamen huiu&longs;modi con&longs;iderationem ordinat <lb/>ad opus con&longs;truendum ex illis, tanquam ad proprium finem, <lb/>& obiectum primarium: Vnde Vitruuius potius ip&longs;am Ma­<lb/>chinariam facultatem, partem &longs;eu portionem facit Archite­<lb/>ctonicæ. </s> <s id="N10F95">Item Nautica quæ licet contempletur artificio&longs;am <lb/>motionem, aut quietem nauigij eiu&longs;que membrorum, quæ <lb/>certè grauia aut leuia &longs;unt; quia tamen hæc con&longs;iderat in or­<lb/>dine ad incolumem tran&longs;uectionem, inter Mechanicas ab&longs;o­<lb/>lutè, & communiter non connumeratur. </s> <s id="N10FA0">Verum cum talis <lb/>differentia valde accidentaria &longs;it & ab extrin&longs;eco fine de&longs;um­<lb/>pta, non minus forta&longs;&longs;e inter Mechanicas facultates propriè <lb/>poterit <expan abbr="cõputari">computari</expan>. </s> <s id="N10FAD">Non enim apparet in quo e&longs;&longs;entialiter diffe­<lb/>rat artificio&longs;a tran&longs;uectio quæ per nauim fit, ab ea, <lb/>quæ per plau&longs;trum, aut currum; neque <lb/>intere&longs;t &longs;i per aquas, an per aera <lb/>moles aut pondera tran­<lb/>sferantur. </s> </p> <pb pagenum="30" xlink:href="005/01/038.jpg"/> <p id="N10FBE" type="margin"> <s id="N10FC0"><margin.target id="marg12"/><emph type="italics"/>Lib.<emph.end type="italics"/> 8. <emph type="italics"/>Ma­<lb/>th. <gap/>.<emph.end type="italics"/></s> </p> <p id="N10FD3" type="head"> <s id="N10FD5"><emph type="italics"/>Quem gradum perfectionis, aut dignitatis fa­<lb/>cultas Mechanica obtineat inter &longs;cientias.<emph.end type="italics"/></s> </p> <p id="N10FDE" type="head"> <s id="N10FE0">ADDITIO SEPTIMA.</s> </p> <p id="N10FE3" type="main"> <s id="N10FE5">Svpere&longs;t vt qualis hæc facultas &longs;it, quamque dignitatem <lb/>inter cæteras, artes ac &longs;cientias obtineat, videamus. </s> <s id="N10FEA">Et <lb/>quidem &longs;i recepti&longs;&longs;imam Philo&longs;ophi doctrinam &longs;pectemus, <lb/>triplici ex capite explorandum id e&longs;&longs;e comperiemus. </s> <s id="N10FF1">Nempe <lb/>ex fine ad quem &longs;cientia ex &longs;e ordinatur, & obiecto circa <lb/>quod ver&longs;atur; & ex certitudine aut euidentia qua procedit. <lb/></s> <s id="N10FF9">Nam primo Met. <!-- REMOVE S-->cap. <gap/>. </s> <s id="N11000">Scientiarum, illam, quæ gratia &longs;ui ip­<lb/>&longs;ius e&longs;t, & propter ip&longs;um &longs;cire, vt omnis &longs;cientia &longs;peculatiua, <lb/>præferendam e&longs;&longs;e, ait, illi, quæ aliorum gratia eligitur, vt e&longs;t <lb/>omnis &longs;cientia practica. </s> <s id="N11009">Deinde ibidem & clarius lib. p. </s> <s id="N1100C">de <lb/>anima cap. 1. Notitiarum vel &longs;cientiarum, alteram altera ait, <lb/>e&longs;&longs;e præ&longs;tantiorem, aut &longs;ecundum certitudinem, aut ex eo <lb/>quod meliorum aut mirabiliorum &longs;it, quod etiam docuerat <lb/>lib. 8. Topic. <!-- REMOVE S-->cap. 2. Inquiens, &longs;cientiam &longs;cientia e&longs;&longs;e melio­<lb/>rem, aut eo quod exactior e&longs;t, aut quod meliorum. </s> <s id="N1101B">Per me­<lb/>liora autem intelligit tum per &longs;e nobiliora, tum etiam &longs;upe­<lb/>riora, quæ &longs;unt vniuer&longs;aliora, ac &longs;impliciora. </s> </p> <p id="N11022" type="main"> <s id="N11024">Ex quo triplici capite facile intelligemus, <expan abbr="Mechanicã">Mechanicam</expan> facul<lb/><expan abbr="tat&etilde;">tatem</expan> <expan abbr="inferior&etilde;">inferiorem</expan> <expan abbr="gradũ">gradum</expan> perfectionis obtinere inter Mathematicas <lb/>di&longs;ciplinas, ac &longs;cientias omnes merè &longs;peculatiuas &longs;ecundum <lb/>eam partem, qua merè &longs;peculatiuæ, ac demon&longs;tratiuæ &longs;cien­<lb/>tiæ &longs;unt, vt Phy&longs;ica ac Metaphy&longs;ica: perfectiorem tamen e&longs;&longs;e <lb/>multis &longs;cientijs practicis, vt Agricultura, Architectura, Nau­<lb/>tica, &longs;i modo ab illa di&longs;tinguitur, & alijs huiu&longs;modi. </s> </p> <p id="N11042" type="main"> <s id="N11044">Id quod planum fieri pote&longs;t &longs;igillatim di&longs;currendo per &longs;in­<lb/>gulas &longs;cientias enumeratas. </s> <s id="N11049">Nam quod attinet ad Mathema­<lb/>ticas, Arithmeticam, Geometriam, A&longs;trologiam, Mu&longs;icam, <lb/>ac Per&longs;pectiuam, & &longs;i quæ &longs;unt aliæ huiu&longs;modi; nulli dubium <lb/>e&longs;t, eas omnes præ&longs;tantiores e&longs;&longs;e &longs;cientia Mechanica; tum <lb/>quia &longs;unt gratia &longs;ui, hoc e&longs;t merè &longs;peculatiuæ, ac de nobilio-<pb pagenum="31" xlink:href="005/01/039.jpg"/>ribus, &longs;eu amplioribus, ac &longs;implicioribus &longs;ubiectis pertractant, <lb/>vt per &longs;e patet; tum etiam quia vel parem, vel maiorem cer-<lb/>titudinem, & euidentiam habent, præ&longs;ertim illæ, quibus ip&longs;a <lb/>Mechanica &longs;ubalternatur, & à quibus accipit &longs;ua principia, <lb/>vt Geometria ac Stereometria. </s> <s id="N11061">Quandoquidem immedia­<lb/>tius attingunt primam rationem a&longs;&longs;entiendi, in qua fundatur <lb/>tota euidentia. </s> <s id="N11068">Vnde vniuer&longs;aliter colligit Ari&longs;toteles primo <lb/>Metaphy&longs;ices cap. 2. Omnem &longs;cientiam &longs;ubalternantem, per­<lb/>fectiorem e&longs;&longs;e &longs;cientia &longs;ubalternata. </s> </p> <p id="N1106F" type="main"> <s id="N11071">Quod verò attinet ad Phy&longs;icam, ac Metaphy&longs;icam, idem <lb/>&longs;imiliter con&longs;tat ex longe maiori nobilitate obiecti, <expan abbr="modoq.">modoque</expan> <lb/>indagandi &longs;peculatiuo, quo ip&longs;æ circa illud ver&longs;antur, etiam&longs;i <lb/>non &longs;emper parem <expan abbr="obtineãt">obtineant</expan> certitudinem, & euidentiam. <lb/></s> <s id="N11083">Quod nihil vtique ob&longs;tat, cum in &longs;ententia Ari&longs;totelis lib. 1. <lb/>de par. </s> <s id="N11088">animal. <!-- KEEP S--></s> <s id="N1108C">cap. 5. hoc quod e&longs;t, res illas &longs;uperiores leui­<lb/>ter tantum nos po&longs;&longs;e attingere, non tollat eius cogno&longs;cendi <lb/>generis excellentiam, qua certè amplius oblectamur, quàm <lb/>cum hæc nobis iuncta omnia tenemus. </s> <s id="N11095">Et ratio e&longs;t, quia ex­<lb/>cellentia cognitionis, quæ attenditur ex parte obiecti, &longs;umitur <lb/>ex propria differentia, <expan abbr="proindeq.">proindeque</expan> e&longs;&longs;entialiter <expan abbr="illã">illam</expan> &longs;ibi vendicat <lb/>ip&longs;a <expan abbr="&longs;ci&etilde;tia">&longs;cientia</expan>, vt talis cognitio e&longs;t ex proprio &longs;uo genere. </s> <s id="N110AA">Perfe­<lb/>ctio verò cognitionis, quæ attenditur ex maiori certitudine, <lb/>aut euidentia; licet maxima &longs;it, non e&longs;t tamen e&longs;&longs;entialis, cum <lb/>&longs;upponat &longs;cientiam ip&longs;am <expan abbr="con&longs;titutã">con&longs;titutam</expan> in e&longs;&longs;e talis &longs;cientiæ cum <lb/>&longs;ufficienti certitudine, aut euidentia. </s> </p> <p id="N110B9" type="main"> <s id="N110BB">Quod &longs;i comparemus Mechanicam facultatem cum parti­<lb/>bus quibu&longs;dam, ac &longs;ubalternatis &longs;cientijs Phy&longs;icæ, præ&longs;ertim <lb/>practicis, vt Medicina, & Agricultura, <expan abbr="alijsq.">alijsque</expan> annexis, mixtis, <lb/>vel &longs;ubalternatis etiam Mathematicis, vt Architectura, & <lb/>Nautica; diuer&longs;a omnino ratio e&longs;t. </s> <s id="N110C6">Nam vel &longs;ubiectum illa­<lb/>rum fecundum &longs;uam rationem &longs;pecificam ignobilius e&longs;t gra­<lb/>ui, & leui, virtuteque eorum motrici in vniuer&longs;um, vt multa <lb/>de quibus tanquam de &longs;ubiectis partialibus agitur in Medici­<lb/>na, & Agricultura: Vel tanta e&longs;t incertitudo, & imperfectio <lb/>inferendi conclu&longs;iones in talibus &longs;cientijs, vt ex genere &longs;uo <lb/>vix &longs;cientiæ <expan abbr="nũcupari">nuncupari</expan> po&longs;&longs;int, potiu&longs;que ex probabilibus, <expan abbr="quã">quam</expan> <pb pagenum="32" xlink:href="005/01/040.jpg"/>ex <expan abbr="demõ&longs;tratis">demon&longs;tratis</expan> con&longs;tare <expan abbr="videãtur">videantur</expan> magna <expan abbr="&longs;alt&etilde;">&longs;altem</expan> ex parte. </s> <s id="N110EE">Vnde <lb/>licet de rebus præ&longs;tantioribus agant <expan abbr="&longs;ecundũ">&longs;ecundum</expan> <expan abbr="ration&etilde;">rationem</expan> obiecti <lb/>totalis, vt e&longs;t corpus animale &longs;anabile; aut <expan abbr="vegetatiuũ">vegetatiuum</expan> germina­<lb/>bile; nullatenus tamen <expan abbr="Mechanicã">Mechanicam</expan> <expan abbr="facultat&etilde;">facultatem</expan>, quæ de familia­<lb/>rioribus omnimoda <expan abbr="cũ">cum</expan> <expan abbr="euid&etilde;tia">euidentia</expan> tractat, antecellere <expan abbr="putabũtur">putabuntur</expan>. </s> </p> <p id="N11119" type="main"> <s id="N1111B">Enim uero, vt Ari&longs;toteles adnotauit primo de partibus ani­<lb/>mal. </s> <s id="N11120">cap. 5. etiam nobis propiora, & natura familiariora ali­<lb/>quid cum rerum diuinarum &longs;tudio rependunt, atque compen­<lb/>&longs;ant, modò cau&longs;as per&longs;picere valeamus; cum in omnibus na­<lb/>turæ numen, & hone&longs;tum, <expan abbr="pulchrumq.">pulchrumque</expan> in&longs;it ingenium. </s> </p> <p id="N1112D" type="main"> <s id="N1112F">Accedit, quod &longs;æpe vtilitas refunditur in dignitatem obie­<lb/>cti; vtilitas enim attenditur ex fine, ad quem ordinatur &longs;cien­<lb/>tia; qui profectò in &longs;cientijs practicis coincidit cum obiecto <lb/>formali. </s> <s id="N11138">Eadem namque &longs;anitas animalis, e&longs;t finis medicinæ, <lb/>& ratio, &longs;ub qua Medicina agit de &longs;uis &longs;ubiectis. </s> <s id="N1113D">Eademque <lb/>directio operationum intellectus, e&longs;t finis Logicæ &longs;cientiæ, & <lb/>ratio &longs;ub qua de ip&longs;is operationibus agitur in illa. </s> <s id="N11144">Cum igi­<lb/>tur talis, ac tanta &longs;it vtilitas Mechanicæ &longs;cientiæ ad fines præ­<lb/>&longs;tanti&longs;&longs;imos admirabili cum artificio con&longs;equendos, vt ad le­<lb/>uanda ingentia pondera, parua, & exigua virtute, ad commo­<lb/>ditates tam plurimas, <expan abbr="vrbiumq.">vrbiumque</expan> ornatum tam varium: ad &longs;ub­<lb/>mini&longs;trandas tot machinas, & in&longs;trumenta in bello, vt belli­<lb/>gerare potius Mechanica, quam armis ip&longs;is, homines videan­<lb/>tur: ad aptius mouenda Nauigia; ingentes paruo momento <lb/>excitandas moles, <expan abbr="immaniaq.">immaniaque</expan> euertenda ædificia: ad aquas ar­<lb/>tificio&longs;i&longs;&longs;imè <expan abbr="&longs;ublimãdas">&longs;ublimandas</expan>, <expan abbr="aeremq.">aeremque</expan> perpetuis follibus emitten­<lb/>dum; voces tàm varias effingendas, concentum æquabiliter <lb/>efformandum, motum qua&longs;i animalem in&longs;en&longs;ibilibus imper­<lb/>tiendum, & &longs;imilia; ingenue fatendum e&longs;t nec e&longs;&longs;e artem, <lb/>quæ &longs;e Mechanicæ arti in dignitate valeat comparari, nec <lb/>e&longs;&longs;e &longs;cientiam practicam, quam ip&longs;a ex certitudine, & euiden­<lb/>tia, qua procedit, & ex dignitate, ac præ&longs;tantia finis, non an­<lb/>tecellat; ita vt in quo &longs;uperatur ex parte &longs;ubiecti nobilioris à <lb/>Medicina, vel Logica, compen&longs;etur, aut vincatur ex parte <lb/>digni&longs;&longs;imi finis, & obiecti formalis, dum admirabili artificio <lb/>intendit ip&longs;os naturæ fines Naturam emulando &longs;uperare. </s> </p> <pb pagenum="33" xlink:href="005/01/041.jpg"/> <p id="N11183" type="head"> <s id="N11185"><emph type="italics"/>De Dignitatibus, <expan abbr="admirandisq.">admirandisque</expan> circuli <lb/>proprietatibus.<emph.end type="italics"/></s> </p> <p id="N11192" type="head"> <s id="N11194">Textus Secundus.</s> </p> <p id="N11197" type="main"> <s id="N11199">D<emph type="italics"/>e numero autem eorum quæ hoc in genere du­<lb/>bitantur, illa e&longs;&longs;e dicuntur, quæ circa vectem <lb/>fiunt: Ab&longs;urdum enim e&longs;&longs;e videtur, magnum <lb/>moueri pondus ab exigua virtute <expan abbr="cũ">cum</expan> pluri præ­<lb/>&longs;ertim pondere. </s> <s id="N111AB">Quod enim vna vecte <expan abbr="qui&longs;piã">qui&longs;piam</expan> <lb/>mouere non pote&longs;t, idip&longs;um ponderis citiùs mouet, vectis ad <lb/>illud pondus adiungens. </s> <s id="N111B6">Omnium autem huiu&longs;modi cau&longs;æ <lb/>principium habet circulus. </s> <s id="N111BB">Istud verò ratione contingit. </s> <s id="N111BE">Ex <lb/>admirabili etenim, mirandum accidere quippiam, non est ab­<lb/>&longs;urdum.<emph.end type="italics"/></s> </p> <p id="N111C7" type="head"> <s id="N111C9">COMMENTARIVS.<!-- KEEP S--></s> </p> <p id="N111CD" type="main"> <s id="N111CF">Qvæcunque maxima omnium admiratione præter <lb/>naturam à Mechanicis patrantur, ea quippe non <lb/>ni&longs;i in&longs;trumentorum ac <expan abbr="machinarũ">machinarum</expan> beneficio con­<lb/>&longs;equi, in præ&longs;entibus &longs;upponit Ari&longs;toteles, atque <lb/>inter ip&longs;a in&longs;trumenta præcipue hic vectem commemorat. <lb/></s> <s id="N111DF">Præmittit autem exemplum de magno pondere quod ab exi­<lb/>gua virtute admirandum in modum, ip&longs;ius vectis adminiculo <lb/>con&longs;tat moueri. </s> <s id="N111E6"><expan abbr="Rationemq.">Rationemque</expan> admirationis ac dubitationis <lb/>annectit: Quia &longs;cilicet potius oppo&longs;itum ex eo &longs;equi deberet, <lb/>cum vectis adminiculo, pondus ponderi adiungatur, <expan abbr="inqui&etilde;s">inquiens</expan>. <lb/></s> <s id="N111F5">Quod enim &longs;ine vecte qui&longs;piam mouere non pote&longs;t, idip&longs;um <lb/>citius mouet, vectis ad illud pondus adiungens. </s> <s id="N111FA">Verum enim <lb/>uero huius ac &longs;imilium miraculorum omnium cau&longs;as refert <lb/>ad naturam circuli. </s> <s id="N11201">Nam vt inferius docet, quæ circa libram <lb/>fiunt, ad circulum rediguntur; quæ vero circa vectem, ad ip­<lb/>&longs;am libram; alia autem fere omnia quæ circa Mechanicas <pb pagenum="34" xlink:href="005/01/042.jpg"/>&longs;unt motiones, ad vectem. </s> <s id="N1120D">Interim ex admirabili (inquiens) <lb/>mirandum accidere quippiam non e&longs;&longs;e ab&longs;urdum. </s> <s id="N11212">Subin­<lb/>telligendo, admirabilem profecto e&longs;&longs;e ip&longs;am naturam circuli <lb/>ex qua tot admiranda procedunt, vt &longs;tatim probare aggredi­<lb/>tur in &longs;equentibus. </s> </p> <p id="N1121B" type="head"> <s id="N1121D"><emph type="italics"/>De Prima Circuli admiranda Proprietate.<emph.end type="italics"/><!-- KEEP S--></s> </p> <p id="N11225" type="head"> <s id="N11227">Textus Tertius.</s> </p> <p id="N1122A" type="main"> <s id="N1122C">M<emph type="italics"/>axime autem e&longs;t admirandum &longs;imul <lb/>contraria fieri; Circulus verò ex huiu&longs;mo­<lb/>di e&longs;t con&longs;titutus: &longs;tatim enim ex commoto <lb/>effectus e&longs;t & manente, quorum natura ad <lb/>&longs;e inuicem est contraria. </s> <s id="N1123A">Quamobrem i&longs;thæc <lb/>cernentes minùs admirari conuenit contingentes in illo con­<lb/>trarietates.<emph.end type="italics"/></s> </p> <p id="N11243" type="head"> <s id="N11245">COMMENTARIVS.<!-- KEEP S--></s> </p> <p id="N11249" type="main"> <s id="N1124B">Ex quatuor igitur conditionibus &longs;eu proprietatibus <lb/>colligit, admirabilem e&longs;&longs;e naturam circuli. </s> <s id="N11250">Ac pri­<lb/>mò quòd in fieri ex contrarijs con&longs;tituatur, nempe ex <lb/>commoto & manente. </s> <s id="N11257">Quandoquidem in de&longs;criptione cir­<lb/>culi, alterum &longs;emidiametri extremum mouetur in gyrum, al­<lb/>terum vero quie&longs;cit, quod centrum denominatur. </s> <s id="N1125E">Imò ma­<lb/>nente ip&longs;o altero extremo, quod dicitur centrum, quod reli­<lb/>quum e&longs;t eiu&longs;dem &longs;emidiametri, circumuehitur totum. </s> </p> <p id="N11265" type="main"> <s id="N11267">Nec ob&longs;tat quod nonnulli obijciunt, centrum in rigore lo­<lb/>quendo non e&longs;&longs;e partem &longs;emidiametri, ac proinde nec circuli, <lb/>nam &longs;ufficit e&longs;&longs;e illius terminum intrin&longs;ecum, &longs;iue extremum, <lb/>quo immoto, &longs;i tota longitudo &longs;emidiametri circumducatur, <lb/>circulus con&longs;tituatur. </s> <s id="N11272">Cum igitur admirandum valde &longs;it, &longs;i­<lb/>mul contraria fieri, aut aliquid effici ex contrarijs, & hoc con­<lb/>tingat in ip&longs;a con&longs;titutione circuli; minus admirandum e&longs;&longs;e <pb pagenum="35" xlink:href="005/01/043.jpg"/>relinquitur (concludit Ari&longs;toteles) &longs;i ex ip&longs;o circulo con&longs;ti­<lb/>tuto, aliæ po&longs;tea oriantur contrarietates, vel alia contraria in <lb/>ip&longs;o con&longs;iderentur, vt mox ex dicendis patebit. </s> </p> <p id="N11282" type="head"> <s id="N11284"><emph type="italics"/>De &longs;ecunda circuli proprietate.<emph.end type="italics"/></s> </p> <p id="N1128B" type="head"> <s id="N1128D">Textus Quartus.</s> </p> <p id="N11290" type="main"> <s id="N11292">I<emph type="italics"/>n primis enim lineæ illi, quæ circuli orbem am­<lb/>plectitur, nullam habenti latitudinem contraria <lb/>quodammodo ine&longs;&longs;e apparans, concauum &longs;cilicet, <lb/>& curuum. </s> <s id="N1129E">Hæc autem eo à &longs;e inuicem di&longs;tant <lb/>modo, quo magnum, & paricum, illorum etenim <lb/>medium e&longs;t æquale: horum verò rectum; quapropter cum ad <lb/>&longs;e inuicem commutantur, illa <expan abbr="quid&etilde;">quidem</expan> prius æqualia fieri nece&longs;&longs;e <lb/>est, quam extremorum vtrumlibet: lineam vero rectam, <lb/>quando e&longs;t curua, concaua, aut ex huiu&longs;modi rur&longs;um curua &longs;it, <lb/>& circularis. </s> <s id="N112B1">Vnum quidem igitur i&longs;tuc ab&longs;urdum ine&longs;t circulo.<emph.end type="italics"/></s> </p> <p id="N112B6" type="head"> <s id="N112B8">COMMENTARIVS.<!-- KEEP S--></s> </p> <p id="N112BC" type="main"> <s id="N112BE">Secundò admirabilem &longs;e natura circuli o&longs;tendit, &longs;i &longs;u­<lb/>matur infacto e&longs;&longs;e, quod cum in primis (inquit Ari&longs;to­<lb/>teles) linea, quæ ip&longs;ius circuli orbem complectitur, ac <lb/>peripheria, &longs;eu <expan abbr="circunfer&etilde;tia">circunferentia</expan> nuncupatur, &longs;it per &longs;e quoad la­<lb/>titudinem, & profunditatem indiui&longs;ibilis, &longs;imul tamen tan­<lb/>quam ex duobus contrarijs inter &longs;e coniunctis con&longs;tituatur <lb/>concaua, & curua, &longs;iuè conuexa. </s> <s id="N112D1">Etenim e&longs;t verè terminus <lb/>extimus, & conuexum ip&longs;ius circuli, ac &longs;imul ambiens, & <lb/>complectens in &longs;ua concauitate ip&longs;am &longs;uperficilem circuli: <lb/>Concauum autem, & conuexum &longs;e habent &longs;icut magnum, <lb/>& paruum. </s> <s id="N112DC">Horum enim medium e&longs;t æquale, illorum verò <lb/>rectum. </s> <s id="N112E1">Quarè &longs;icut cum magnum, & paruum inuicem, <lb/>commutantur, prius perueniunt ad æquale, quàm ad hoc vt <lb/>magnum con&longs;tituatur paruum, & paruum con&longs;tituatur ma­<pb pagenum="36" xlink:href="005/01/044.jpg"/>gnum: ita quælibet linea curua, &longs;eu conuexa antequam fiat <lb/>concaua, prius debet fieri recta: ab&longs;urdum igitur apparet, ean­<lb/>dem omnino circuli periferiam, &longs;imul con&longs;titui concauam, <lb/>& conuexam. </s> </p> <p id="N112F3" type="main"> <s id="N112F5">Nec difficultatem euadunt, qui dicunt, concauum, & con­<lb/>uexum realiter non e&longs;&longs;e idem in circulo, &longs;eu curuitatem, & <lb/>concauitatem non reperiri in eadem linea, &longs;ed in diuer&longs;is, ità <lb/>vt in circunferentia &longs;it tantum curuitas, &longs;eù conuexum, con­<lb/>cauitas verò &longs;it potius in corpore extrin&longs;eco ambiente per li­<lb/>neam illi corre&longs;pondentem. </s> <s id="N11302">Etenim cum linea corporis con­<lb/>tinentis ambiens circulum, penetretur in eodem &longs;pacio cum <lb/>circunferentia ip&longs;ius circuli, <expan abbr="con&longs;idereturq.">con&longs;idereturque</expan> &longs;ola quantitas <lb/>ab&longs;tracta, & figura vtriu&longs;que lineæ coincidentis, eadem &longs;em­<lb/>per difficultas ob&longs;tabit; nempè quo pacto fieri po&longs;&longs;it, vt <expan abbr="ead&etilde;">eadem</expan> <lb/>longitudo latitudinis expers, circulum terminans, &longs;eù circu­<lb/>lariter exten&longs;a, &longs;imul &longs;it concaua, & conuexa. </s> <s id="N11319">Sed nihil pro­<lb/>hibet eandem circumferentiam indiuisibilem quoad latitudi­<lb/>nem, & profunditatem, &longs;imul e&longs;&longs;e concauam, & conuexam <lb/>re&longs;pectu diuer&longs;orum, vt in alijs etiam linearum figuris, ac &longs;u­<lb/>perficiebus poterit exemplificari: & vt eadem via dicitur <lb/>acliuis, & decliuis; idemque magnum, & paruum rei pectu di­<lb/>uer&longs;orum, quæ cum illo comparantur. </s> <s id="N11328">Quo fit, vt admiran­<lb/>dam quidem e&longs;&longs;e huiu&longs;modi proprietatem circuli iure dica­<lb/>mus, nullam tamen in &longs;e <expan abbr="repugnantiã">repugnantiam</expan> inuoluere admittamus. </s> </p> <p id="N11333" type="head"> <s id="N11335"><emph type="italics"/>De tertia Circuli proprietate.<emph.end type="italics"/></s> </p> <p id="N1133C" type="head"> <s id="N1133E">Textus Quintus.</s> </p> <p id="N11341" type="main"> <s id="N11343">A<emph type="italics"/>ltervm autem, quod &longs;imul contrarijs <lb/>mouetur motionibus: &longs;imul enim ad anterio­<lb/>rem mouetur locum, & ad po&longs;teriorem. </s> <s id="N1134D">Et <lb/>ea, quæ circulum de&longs;cribit, linea eodem &longs;e <lb/>habet modo: Ex que enim incipit loco, illius <lb/>extremum, ad eundem rur&longs;us redit: Illa <lb/>enim continuò commota, extremum rur&longs;us efficitur primum.<emph.end type="italics"/><pb pagenum="37" xlink:href="005/01/045.jpg"/><emph type="italics"/>Quamobrem manife&longs;tum, quod inde mutatum e&longs;t. </s> <s id="N11361">Quaprop­<lb/>ter (vt dictum e&longs;t prius) non e&longs;t inconueniens, ip&longs;um miraculo­<lb/>rum omnium e&longs;&longs;e principium.<emph.end type="italics"/></s> </p> <p id="N1136A" type="main"> <s id="N1136C"><emph type="italics"/>Ea igitur, quæ circa libram fiunt, ad circulum referuntur: <lb/>“quæ vero circa vectem, ad ip&longs;am libram; alia autem ferè om-<emph.end type="italics"/><arrow.to.target n="marg13"/><lb/><emph type="italics"/>nia, quæ circa Menbanicas &longs;unt motiones, ad vectem. </s> <s id="N1137C">Prae­<lb/>tereà etiam quoniam vnica exi&longs;tente, quæ ex centro e&longs;t linea, <lb/>nullum aliud alij, quæ in illa &longs;unt, punctorum æqua velocitate <lb/>feratur; &longs;ed citius &longs;emper, quod à manente termino e&longs;t remo­<lb/>tius, <expan abbr="pleraq.">pleraque</expan> miraculorum accidunt in circuli motionibus: de <lb/>quibus in ijs, quæ po&longs;thac adducentur, quæ&longs;tionibus erit ma­<lb/>nife&longs;tam.”<emph.end type="italics"/></s> </p> <p id="N11391" type="margin"> <s id="N11393"><margin.target id="marg13"/>Verba re­<lb/>&longs;ecanda.</s> </p> <p id="N1139A" type="main"> <s id="N1139C"><emph type="italics"/>Quoniam autem secundum contrarias &longs;imul motiones mo­<lb/>uetur circulus; & alienum quidem diametri extremum, vbi A, <lb/>in ante mouetur, alterum verò vbi B, ad retro; efficiunt non­<lb/>nulli, vt ab vnica motione multi contrario &longs;imul moueantur <lb/>circuli; quemadmodum &longs;unt illi, quos in locis proponunt &longs;acris, <lb/>æneos, & ferreos fabricantes orbiculos. </s> <s id="N113AB">Si enim AB, circu­<lb/>lum alier contingerit, circulus in quo CD, mota circuli, in quo <lb/>AB, diametro in ante, mouebitur CD, ad retro diametro cir­<lb/>culi, vbi e&longs;t A, circà idem mota, In contrarium igitur moue­<lb/>bitur circulus vbi CD, ad illum, vbi AB, El rur&longs;us ip&longs;e con­<lb/>tiguum vbi EF, in contrarium &longs;ibi ip&longs;i mouebitur propter ean­<lb/>dem cau&longs;am. </s> <s id="N113BA">Eodem etiam modo &longs;i plures fuerint, idem <lb/>facient, vno &longs;olo commoto. </s> <s id="N113BF">Hanc lgitur in circulo exi&longs;tentem <lb/>animaduertens naturam Architecti, in&longs;trumentum fabricant, <lb/>celantes principium, vt machinæ &longs;olum manife&longs;tum &longs;it illud, <lb/>quod admirationem præ&longs;tat, cau&longs;a verò lateat.<emph.end type="italics"/></s> </p> <p id="N113CA" type="head"> <s id="N113CC">COMMENTARIVS.<!-- KEEP S--></s> </p> <p id="N113D0" type="main"> <s id="N113D2">Tertio illud quoque admiratione dignum &longs;e&longs;e offert in <lb/>circulo, quod, inquit Ari&longs;toteles, contrarijs &longs;imul fe­<lb/>ratur motionibus, antror&longs;um videlicet, ac retror&longs;um, <lb/>&longs;ur&longs;um, ac deor&longs;um. </s> <s id="N113DB">Dum enim pars circuli &longs;uperior de&longs;cen­<lb/>dit, ac mouetur antror&longs;um, v. <!-- REMOVE S-->g. <!-- REMOVE S-->ad dexteram, altera pars illi <pb pagenum="38" xlink:href="005/01/046.jpg"/>oppo&longs;ita, quæ e&longs;t inferior, a&longs;cendit, ac mouetur retror&longs;um ad <lb/>leuam. </s> <s id="N113EB">Quod &longs;i huiu&longs;modi po&longs;itiones formaliter non con­<lb/>&longs;tituantur ni&longs;i in quadam relatione, ac re&longs;pectu vnius partis ad <lb/>alteram, hoc parum refert, cum fundamentaliter &longs;emper im­<lb/>portent realem oppo&longs;itionem, ac diuer&longs;itatem loci, in quo <lb/>ip&longs;e partes relatæ con&longs;tituuntur, vel ad quem tendunt <expan abbr="tanquã">tanquam</expan> <lb/>ad terminum &longs;ui motus. </s> <s id="N113FC">Quapropter idem Philo&longs;ophus &longs;u­<lb/><figure id="id.005.01.046.1.jpg" xlink:href="005/01/046/1.jpg"/><lb/>biungit ex hac contra­<lb/>rietate fieri, vt vnius <lb/>circuli motione, alij cir­<lb/>culi in contrarium mo­<lb/>ueantur. </s> <s id="N1140F">Vt &longs;i con&longs;ti­<lb/>tuatur circulus, qui pri­<lb/>mò moueri debeat in­<lb/>ter alios quaruor, <expan abbr="&longs;intq.">&longs;intque</expan> <lb/>omnes denticulati, <lb/>quem admodum videre <lb/>e&longs;t in horologijs, <expan abbr="alijsq.">alijsque</expan> <lb/>&longs;imilibus machinis, vt <lb/>in hac figura: Nam pars <lb/>&longs;uperor medij circuli, <lb/>quæ de&longs;cendit, impellit partem inferiorem &longs;uperioris circuli, <lb/>facitque eam a&longs;cendere. </s> <s id="N11430">Et pars inferior eiu&longs;dem medij cir­<lb/>culi, a&longs;cendendo facit de&longs;cendere partem &longs;uperiorem circuli <lb/>inferioris. </s> <s id="N11437">Deinde &longs;imiliter idem circulus medius dum dex­<lb/>tror&longs;um mouetur, mouet circulum dexterum &longs;ini&longs;tror&longs;um, & <lb/>&longs;ini&longs;trum dextror&longs;um. </s> </p> <p id="N1143E" type="main"> <s id="N11440">Eodem que modo &longs;e habet, &longs;ubiungit Ari&longs;toteles, linea illa <lb/>quæ in vno extremo manens, altero circumlata, circulum <lb/>de&longs;cribit; nempe &longs;emidiameter. </s> <s id="N11447">Quandoquidem contraria <lb/>&longs;imiliter admittit; nimirum primum & extremum &longs;imul; &longs;eu <lb/>principium ac terminum &longs;ui motus in eodem loco. </s> <s id="N1144E">Ex quo <lb/>enim puncto incipit circunduci, ad idem po&longs;tremo reuertitur <lb/>tanquam ad terminum &longs;ui motus. </s> <s id="N11455">Et &longs;ic <expan abbr="extremũ">extremum</expan> rur&longs;us effici­<lb/>tur <expan abbr="primũ">primum</expan>. </s> <s id="N11462">Quapropter concludit: Non e&longs;t inconueniens ex <lb/>ip&longs;a &longs;emidiametro <expan abbr="de&longs;criptũ">de&longs;criptum</expan>, <expan abbr="miraculorũ">miraculorum</expan> <expan abbr="pluriũ">plurium</expan> e&longs;&longs;e <expan abbr="principiũ">principium</expan>. </s> </p> <pb pagenum="39" xlink:href="005/01/047.jpg"/> <p id="N1147B" type="main"> <s id="N1147D">Quæ autem de libra ac vatia punctorum &longs;emidiametri ve­<lb/>locitate hìc docet Ari&longs;toteles, fru&longs;tra interpo&longs;ita &longs;unt ac præ­<lb/>ter Auctoris intentum, cum ad rem de qua agitur non perti­<lb/>neant, ac alibi proprijs in locis repetantur. </s> <s id="N11486">Quare ex hoc <lb/>textu re&longs;ecanda e&longs;&longs;ent, incipiendo à particula (Ea igitur) <lb/>v&longs;que ad (erit manife&longs;tum) inclu&longs;iue, prout lineis consi­<lb/>gnauimus. </s> </p> <p id="N1148F" type="head"> <s id="N11491"><emph type="italics"/>De Quarta Circuli Proprietate.<emph.end type="italics"/><!-- KEEP S--></s> </p> <p id="N11499" type="head"> <s id="N1149B">Textus Sextus.</s> </p> <p id="N1149E" type="main"> <s id="N114A0">I<emph type="italics"/>n primis igitur quæ accidunt circa libram du­<lb/>bitare faciunt, quam nam ob cau&longs;am exactio­<lb/>res minoribus maiores &longs;unt libræ. </s> <s id="N114AA">Huius au­<lb/>tem rei principium est quamobrem in ip&longs;o cir­<lb/>culo, quæ plus à centro di&longs;tat linea eadem vi <lb/>commota, citius fertur, quàm illa quæ minus distat. </s> <s id="N114B3">Citius <lb/>enim bifariam dicitur: &longs;iue enim in minori tempore æqualem <lb/>pertran&longs;it locum, citius feci&longs;&longs;e dicimus: &longs;eu in æquali maio­<lb/>rem. </s> <s id="N114BC">Maior autem in æquali tempore, maiorem de&longs;cribit cir­<lb/>culum: qui enim extra e&longs;t, maior eo qui intus e&longs;t. </s> <s id="N114C1">Horum <lb/>autem cau&longs;a, quoniam duas fertur lationes ea quæ circulum <lb/>de&longs;cribit linea. </s> <s id="N114C8">Quandoquidem igitur in proportione fertur <lb/>aliqua id quod fertur, &longs;uper rectam ferri nece&longs;&longs;e: Et hæc dia­<lb/>meter efficitur figuræ quam faciunt illæ quæ in huiu&longs;modi pro­<lb/>portione coaptantur lineæ. </s> <s id="N114D1">Sit enim proportio &longs;ecundum quam <lb/>latum fertur, quam habet AB ad AC. & A quidem fertur <lb/>ver&longs;us B: A B vero &longs;ubter&longs;eratur ver&longs;us MC: latum au­<lb/>tem &longs;it A quidem ad D. <!-- KEEP S--></s> <s id="N114DB">Vbi autem est A B ver&longs;us E: quo­<lb/>niam igitur lationis erat proportio, quam A B habet ad A C, <lb/>nece&longs;&longs;e e&longs;t & A D ad A E hanc habere proportionem. </s> <s id="N114E2">Simile <lb/>igitur est proportione paruum quadrilaterum maiori: quam­<lb/>obrem & eadem illorum e&longs;t diameter, & A erit ad F. <!-- KEEP S--></s> <s id="N114EA">Eodem <lb/>etiam o&longs;tendetur modo, vbicunque latio deprahendatur; &longs;em-<emph.end type="italics"/><pb pagenum="40" xlink:href="005/01/048.jpg"/><emph type="italics"/>per enim &longs;upra diametrum erit. </s> <s id="N114F8">Manife&longs;tum igitur, quod id <lb/>quod &longs;ecundum diametrum duabus fertur lationibus, nece&longs;&longs;a­<lb/>riò &longs;ecundum laterum proportionem fertur. </s> <s id="N114FF">Si enim &longs;ecun­<lb/>dum aliam quampiam, non fertur &longs;ecundam diametrum. <lb/></s> <s id="N11505">Si autem in nulla fertur proportione &longs;ecundum duas lationes <lb/>nullo in tempore, rectam e&longs;&longs;e lationem, e&longs;t impo&longs;&longs;ibile. </s> <s id="N1150A">Sit enim <lb/>recta. </s> <s id="N1150F">Po&longs;ita igitur hac pro diametro, & circumrepletis late­<lb/>ribus, illud quod fertur, &longs;ecundum laterum proportionem fer­<lb/>ri nece&longs;&longs;e e&longs;t: hoc enim demon&longs;tratum e&longs;t prius. </s> <s id="N11516">Non igitur <lb/>rectam efficiet id quod &longs;ecundum nullam proportionem, in nul­<lb/>lo fertur tempore. </s> <s id="N1151D">Si autem &longs;ecundum quampiam feratur <lb/>proportionem, & in tempore quopiam, hoc nece&longs;&longs;e est tempus <lb/>rectam e<32>e lationem, per ea quæ retro &longs;unt dicta. </s> <s id="N11524">Quamob­<lb/>rem circulare e&longs;t id, quod &longs;ecundum nullam proportionem nul­<lb/>lo in tempore duas fertur lationes.<emph.end type="italics"/></s> </p> <p id="N1152D" type="head"> <s id="N1152F">COMMENTARIVS.<!-- KEEP S--></s> </p> <p id="N11533" type="main"> <s id="N11535">Qvartò denique occa&longs;ione &longs;umpta ex eo, cur maio­<lb/>res libræ exactiores &longs;int minoribus, vt huius rei <lb/>principium vel cau&longs;a innote&longs;cat, aliam circuli pro­<lb/>prietatem non minus ad mitandam Ari&longs;toteles <lb/>proponit, quam in &longs;uperiori etiam textu interpo&longs;itè in&longs;inua­<lb/>uerat: Nempe in vna <expan abbr="eademq.">eademque</expan> linea quæ e&longs;t à centro ad cir­<lb/>cumferentiam, nullum e&longs;&longs;e punctum, quod æquali velocitate <lb/>moueatur re&longs;pectu aliorum, quæ &longs;unt in eadem linea; &longs;ed <lb/>citius &longs;emper feratur punctum quod à manente termino, &longs;ci­<lb/>licet centro, e&longs;t remotius. </s> <s id="N1154E">Quamobrem ait in ip&longs;o circulo <lb/>quæ plus à centro di&longs;tat linea, eadem vi commota, citius fer­<lb/>tur, quàm illa, quæ minus di&longs;tat &c. </s> <s id="N11555">Quod ita &longs;e habere <lb/>o&longs;tendit ex eo, quia dupliciter aliquid intelligimus velocius <lb/>alio moueri; nempe, vel quia in minori tempore, æquale <lb/>&longs;patium pertran&longs;it; vel quia eodem tempore, maius interual­<lb/>lum percurrit. </s> <s id="N11560">Et hoc pacto inquit in de&longs;criptione circuli <lb/>contingere vt puncta quæ magis à centro di&longs;tant, velocius <lb/>moueantur. </s> <s id="N11567">Siquidem eodem tempore maiorem de&longs;cribunt <pb pagenum="41" xlink:href="005/01/049.jpg"/>ambitum. </s> <s id="N1156F">Maior enim e&longs;t circum &longs;erentia circuli continentis, <lb/>quàm contenti. </s> <s id="N11574">Si autem circa idem centrum plures circuli <lb/>ducantur, &longs;emper ille qui coeteros continet, à remotiori pun­<lb/>cto &longs;emidiametri de&longs;cribetur, <expan abbr="proindeq.">proindeque</expan> quò remotiora erunt <lb/>ip&longs;a puncta &longs;emidiametri à centro, eò velocius mouebuntur. </s> </p> <p id="N11581" type="main"> <s id="N11583">Horum autem cau&longs;am e&longs;&longs;e inquit Ari&longs;toteles, quoniam &longs;e­<lb/>midiameter circulum de&longs;cribens mouetur motu quodam <lb/>mixto ex duabus lationibus, nempe naturali, ac præternatu­<lb/>rali, vt infra &longs;equenti textu probabitur; quam duplicem la­<lb/>tionem partes &longs;emidiametri non æquè participant, hoc e&longs;t <lb/>non participant &longs;ecundum eandem proportionem. </s> <s id="N11590">Quando­<lb/>quidem, vt infra pariter ip&longs;e Philo&longs;ophus o&longs;tendit, partes quæ <lb/>remotiores &longs;unt à centro, magis participant de latione natu­<lb/>rali: contra verò quæ centro &longs;unt viciniores, magis partici­<lb/>pant de motione præternaturali. </s> <s id="N1159B">Si enim &longs;ecundum eandem <lb/>aliquam proportionem, duplicem illam lationem omnes ip­<lb/>sæ participarent, non vtique mouerentur motu circulari, &longs;ed <lb/>recto, vt &longs;tatim ip&longs;e demon&longs;trat. </s> <s id="N115A4">Quare &longs;uppo&longs;ito quòd mo­<lb/>bile tanto velocius monetur, quanto magis participat de mo­<lb/>tu naturali, vt ex dicendis etiam tex. <!-- REMOVE S-->8. con&longs;tabit, a primo ad <lb/>vltimum conuincitur, puncta vel partes &longs;emidiametri quò <lb/>plus à centro di&longs;tauerint in de&longs;criptione circuli, eò cœlerius <lb/>moueri, quò vero minus, eo tardius. </s> </p> <p id="N115B3" type="main"> <s id="N115B5">Et confirmari pote&longs;t argumento quod idem Philo&longs;ophus, <lb/>alijs interpo&longs;itis, &longs;equenti textu adiecit; nimirum, quia &longs;i <lb/>duobus (inquit) ab eadem potentia latis, hoc quidem plus <lb/>repellatur vel impediatur ab aliquo, illud verò minus; ratio­<lb/>ni con&longs;entaneum e&longs;t, tardius moueri id quod plus præpedi­<lb/>tur, aut repellitur: Sed lineæ circumductæ in circulo, vel pun­<lb/>cta quæ &longs;unt in eius diametro, quò magis appropinquantur <lb/>centro, eò magis repelluntur in motu circulari ac impediun­<lb/>tur ab ip&longs;o centro; ergo tardius mouentur. </s> <s id="N115C8">Minor propo&longs;itio <lb/>huius argumenti probatur; quia cum centrum &longs;it fixum & <lb/>immotum, <expan abbr="eiq.">eique</expan> colligatæ &longs;int omnes partes diametri per lon­<lb/>gitudinem exten&longs;æ, illæ quæ magis ei appropinquantur, ma­<lb/>gis vinciuntur ac detinentur nè moueantur: quæ verò magis <pb pagenum="42" xlink:href="005/01/050.jpg"/>ab eo di&longs;tant, magis relaxantur, <expan abbr="magisq.">magisque</expan> &longs;oluuntur à princi­<lb/>pio detinente, ac propterea minus impediuntur nè ad im­<lb/>pul&longs;um vel motum alterius moueantur, & &longs;ic velocius fe­<lb/>runtur. </s> </p> <p id="N115E6" type="main"> <s id="N115E8">Verum enim uero, vt primum ac principale Ari&longs;totelis ar­<lb/>gumentum omninò concludat id quod intendit, examinanda <lb/>ac probanda &longs;unt nonnulla quæ in eo a&longs;&longs;umuntur, ac difficul­<lb/>tatem non paruam inuoluunt. </s> <s id="N115F1">Quorum vnum hic, reliqua <lb/>verò in &longs;equentibus ip&longs;e pertractat. </s> <s id="N115F6">Illud igitur hic &longs;tatim <lb/>aggreditur probandum, quod de proportione duarum latio­<lb/>num docuerat, eam &longs;cilicet &longs;olùm dari in eo quod fertur mo­<lb/>tu recto. </s> <s id="N115FF">Quod quippe antequam probetur, &longs;ano modo in­<lb/>telligendum e&longs;t. </s> <s id="N11604">Etenim in partibus etiam circuli, dum vni­<lb/>formiter difformiter, geminata ac mixta quadam latione du­<lb/>cuntur in gyrum, &longs;emper aliqua &longs;eruatur vtriu&longs;que lationis <lb/>proportio; vt &longs;cilicet magis vel minus participent de motu <lb/>naturali, aut præternaturali, iuxta di&longs;tantiam vel propinqui­<lb/>tatem quam partes ip&longs;æ habent cum centro. </s> <s id="N11611">Quare expli­<lb/>candus e&longs;t Ari&longs;toteles, vt loquatur de proportione eadem, <lb/>non vero de quacunque. </s> <s id="N11618">Nam reuera, vt etiam Baldus de <lb/>mon&longs;trat, licet circulus fiat, proportionibus quidem duarum <lb/>lationum &longs;eruatis; nunquam tamen eadem erit proportio <lb/>vni<gap/>s lationis ad alteram re&longs;pectu cuiu&longs;que partis ip&longs;ius cir­<lb/>culi vel &longs;emidiametri, &longs;icut cum quippiam duabus lationibus <lb/>fertur &longs;uper rectam: & hoc &longs;olum probat Ari&longs;toteles, vt &longs;ta­<lb/>tim videbimus; illud vtique intendens, quòd &longs;i eadem &longs;em<lb/>per proportio vtriu&longs;que lationis &longs;eruaretur in de&longs;criptione <lb/>circuli, motus ille e&longs;&longs;et rectus, & non circularis de quo <lb/>agitur. </s> </p> <p id="N1162F" type="main"> <s id="N11631">Rur&longs;us antequam ad exactam eius probationem ex Geo­<lb/>metricis principijs accedamus, idem prælibare licebit exem­<lb/>plo huius figuræ, quod non parum ad dilucidationem textus, <lb/><expan abbr="doctrinæq.">doctrinæque</expan> Ari&longs;totelis conducet. </s> <s id="N1163D">Sit enim corpus &longs;eu pon­<lb/>dus quod moueri debeat con&longs;titutum &longs;uper planum vbi A, <lb/>mouentia verò vbi B, C. <!-- KEEP S--></s> <s id="N11645">Deinde &longs;upponamus æquali virtu­<lb/>te & æquali &longs;imul tempore vtrumque mouens ad &longs;e pondus <pb pagenum="43" xlink:href="005/01/051.jpg"/><figure id="id.005.01.051.1.jpg" xlink:href="005/01/051/1.jpg"/><lb/>ip&longs;um trahere; quod e&longs;t, eandem &longs;emper proportionem ad <lb/>inuicem &longs;eruare, vt beneficio trochlearum vel alterius in&longs;tru­<lb/>menti. </s> <s id="N11659">Tunc enim dicimus primo, corpus ip&longs;um mobile A <lb/>moueri motu quodam mixto ex duabus lationibus, nempe <lb/>qua appropinquatur ad B, & qua appropinquantur ad C. <lb/><!-- KEEP S--></s> <s id="N11662">Quia durante huiu&longs;modi motu, non datur in&longs;tans in quo non <lb/>magis ip&longs;um pondus A appropinquetur ad B, ac &longs;imul ad C. <lb/><!-- KEEP S--></s> <s id="N11669">Præterea dicimus, huiu&longs;modi motum nece&longs;&longs;ariò e&longs;&longs;e rectum, <lb/>non verò circularem, &longs;eu pondus non ni&longs;i &longs;uper rectam tunc <lb/>&longs;emper moueri. </s> <s id="N11670">Etenim &longs;eruata eadem proportione, pon­<lb/>dus ip&longs;um, & quælibet eius pars æqualiter vtrique mouenti in <lb/>æquali tempore deberet appropinquari: quia non e&longs;&longs;et maior <lb/>ratio cur magis aut citius appropinquaretur ad B, quàm ad C. <lb/><!-- KEEP S--></s> <s id="N1167B">At non po&longs;&longs;et æqualiter vtrique appropinquari, ni&longs;i feratur <pb pagenum="44" xlink:href="005/01/052.jpg"/>per diametrem quadranguli A B C D, quæ e&longs;t recta A D; <lb/>&longs;iquidem in nulla alia parte interiecti &longs;patij, di&longs;tantia e&longs;&longs;et <lb/>æqualis, vt &longs;en&longs;u con&longs;tat: Ergo &longs;eruata eadem proportione in <lb/>ip&longs;a duplici latione re&longs;pectu mobilis & cuiu&longs;que partis ip&longs;ius, <lb/>motus nece&longs;&longs;ariò erit rectus, &longs;eu <expan abbr="põdus">pondus</expan> & quælibet eius pars, <lb/>non ni&longs;i per rectam lineam poterit moueri. </s> </p> <p id="N11691" type="main"> <s id="N11693">Deinde quod infert Ari&longs;toteles, circulare e&longs;&longs;e id quod &longs;e­<lb/>cundum nullam proportionem, nullo in tempore duas pati­<lb/>tur lationes, fal&longs;um e&longs;&longs;et etiam iuxta præfatam explicationé <lb/>proportionis; ni&longs;i per circulare intelligeremus lato modo, id <lb/>quod e&longs;t curuum. </s> <s id="N1169E">quia nimirum non &longs;equitur, aliquid e&longs;&longs;e <lb/>circulare, in rigore loquendo, aut moueri per lineam circula­<lb/>rem, eo quòd moueri non po&longs;&longs;it per lineam rectam; cum plu­<lb/>res &longs;int figuræ ac lineæ non rectæ, nec circulares, vt figura el­<lb/>lip&longs;is, &longs;ectiones parabolicæ, ac lineæ &longs;pirales, <expan abbr="aliæq.">aliæque</expan> irregu­<lb/>lares permultæ. </s> <s id="N116AF">Quæ omnia prænota&longs;&longs;e, ip&longs;a verborum am­<lb/>biguitas po&longs;tulabat, vt clarius ad probationem doctrinæ pro­<lb/>cederemus. </s> </p> <p id="N116B6" type="main"> <s id="N116B8">Iam vero vt Geometricis principijs quæ dicta &longs;unt pateát, <lb/>&longs;ic probat Ari&longs;toteles, quidquid fertur duabus lationibus ad <lb/>inuicem proportionatis, &longs;uper rectam nece&longs;&longs;ariò ferri, ac pro­<lb/>inde non circulariter. </s> <s id="N116C1">Sit inquit proportio ip&longs;arum lationum <lb/><figure id="id.005.01.052.1.jpg" xlink:href="005/01/052/1.jpg"/><lb/>quam habent inter <lb/>&longs;e latera A B & AC <lb/>in dato rectangulo <lb/>A B C D. <!-- KEEP S--></s> <s id="N116D3">Et A <lb/><expan abbr="quid&etilde;">quidem</expan> duplici motu <lb/>feratur, vno quo <lb/><expan abbr="t&etilde;dat">tendat</expan> ver&longs;us B, qua­<lb/>&longs;i ex &longs;e incedendo <lb/>&longs;uper lineam A B: <lb/>altero verò, quo &longs;imul cum ip&longs;a linea A B &longs;ubterferatur ver­<lb/>&longs;us C, &longs;eu ver&longs;us lineam C D cum eadem &longs;emper proportio­<lb/>ne. </s> <s id="N116EC">Tunc dicimus punctum A motu ip&longs;o mixto, nece&longs;&longs;ariò <lb/>ferri per rectam A D, quæ e&longs;t diameter eiu&longs;dem quadrilateri <lb/>A B C D. <!-- KEEP S--></s> <s id="N116F4">Etenim &longs;i <expan abbr="cõ&longs;tituatur">con&longs;tituatur</expan> rectangulus minor A E F G <pb pagenum="45" xlink:href="005/01/053.jpg"/>proportionalis maiori A B C D, ac per motum proprium <lb/>ver&longs;us B, ip&longs;um punctum A peragrauerit quantum e&longs;t v&longs;que <lb/>ad E; & per motum totius lineæ A B, ver&longs;us lineam C D, <lb/>peragrauerit quantum e&longs;t ab A, v&longs;que ad F, &longs;eruata eadem <lb/>proportione ip&longs;orum laterum; certe punctum A reperiri non <lb/>po&longs;&longs;et in E, neque in F; &longs;iquidem non fui&longs;&longs;et latum duabus <lb/>lationibus, nec peragra&longs;&longs;et &longs;pacium &longs;ecundum vtramque po­<lb/>&longs;itionem, &longs;imul accedendo quantum fieri pote&longs;t ad B & ad <lb/>C; &longs;ed vna tantùm latione, alterum &longs;olum &longs;pacium percur­<lb/>ri&longs;&longs;et. </s> <s id="N11712">Reperietur ergo ip&longs;um. </s> <s id="N11715">punctum A vbi vtraque pro­<lb/>gre&longs;&longs;io pote&longs;t verificari, vt in puncto G. <!-- KEEP S--></s> <s id="N1171B">Quia nimirum F G <lb/>e&longs;t æqualis ip&longs;i A E, & E G æqualis ip&longs;i A F, cum &longs;int latera <lb/>oppo&longs;ita eiu&longs;dem rectanguli, vt patet per 34. primi Elemen­<lb/>torum Euclidis. <!-- KEEP S--></s> <s id="N11725">Sed punctum G non pote&longs;t e&longs;&longs;e ni&longs;i in recta <lb/>A D, quæ e&longs;t vtriu&longs;que rectanguli diameter, vt patet per 26. <lb/>&longs;exti, & eodem modo quodlibet aliud punctum, in quo vtra­<lb/>que latio ac latera depræhendantur eadem proportione pro­<lb/>portionalia, vt in H, re&longs;pectu I & K: igitur punctum A, dua­<lb/>bus lationibus proportionalibus latum, nece&longs;&longs;ariò mouebi­<lb/>tur &longs;uper rectam A D, quod erat probandum. </s> </p> <p id="N11734" type="main"> <s id="N11736">Quod quidem clarius adhuc probari po&longs;&longs;et exemplo hu­<lb/>ius quadrati A B C D, cuius latera diui&longs;a &longs;int in quatuor par­<lb/>tes æquales, <expan abbr="efficiantq.">efficiantque</expan> ex illis minora quadrata contenta in <lb/>maiori. </s> <s id="N11743">Nam &longs;i &longs;up­<lb/><figure id="id.005.01.053.1.jpg" xlink:href="005/01/053/1.jpg"/><lb/>ponatur punctum A ex <lb/>&longs;e moueri tanquam na­<lb/>turali ac proprio motu <lb/>ver&longs;us B, &longs;uper rectam <lb/>A B, & eodem tempo­<lb/>re &longs;imul cum ip&longs;a A B, <lb/>qua&longs;i motu alieno de­<lb/>&longs;cendere ver&longs;us C D, <lb/>ac &longs;eruata eadem pro­<lb/>portione vtriu&longs;que mo­<lb/>tus, quæ &longs;it æqualita­<lb/>tis: ab&longs;que dubio, eo-<pb pagenum="46" xlink:href="005/01/054.jpg"/>dem tempore quo A, peragrauerit &longs;pacium AE, &longs;imul pera­<lb/>grabit &longs;pacium AF, & reperietur in G, quandoquidem &longs;unt <lb/>latera eiu&longs;dem quadrati AG, ac proinde æqualia. </s> <s id="N1176D">Et &longs;icut to­<lb/>ta linea AB, coincideret cum linea FH, ita punctum E, coin­<lb/>cideret cum puncto G. <!-- KEEP S--></s> <s id="N11775">Similiterque cum A, peruenerit in I, <lb/>&longs;imul reperietur in K, propter eandem rationem, & &longs;ic de <lb/>&longs;ingulis. </s> <s id="N1177C">Ex quibus con&longs;tabit, ip&longs;um A, moueri per rectam <lb/>diagonalem &longs;eu diametrum AD, quod erat o&longs;tendendum. </s> </p> <p id="N11781" type="head"> <s id="N11783"><emph type="italics"/>Quo pacto linea circulum de&longs;cribens, duabus <lb/>feratur lationibus.<emph.end type="italics"/></s> </p> <p id="N1178C" type="head"> <s id="N1178E">Textus Septimus.</s> </p> <p id="N11791" type="main"> <s id="N11793">Q<emph type="italics"/>vod quidem igitur ea quæ circulum de&longs;cri­<lb/>bit, duas &longs;imul feratur lationes, manifestum <lb/>e&longs;t cùm ex istis, tùm quia &longs;ecundum rectum <lb/>lata ad perpendiculum peruenit, vt &longs;it rur&longs;us <lb/>ip&longs;a à centro <expan abbr="perpendiculũ">perpendiculum</expan>. </s> <s id="N117A5">Sit circulus ABCD, <lb/>extremum autem vbi e&longs;t B. feratur ad ip&longs;um <lb/>D, peruenit &longs;ane aliquando ad ip&longs;um C. <!-- KEEP S--></s> <s id="N117AD">Siquidem igitur in <lb/>proportione feratur, quam habet BE, EC, fertur vtique &longs;ecun­<lb/>dum diametrum BC. <!-- KEEP S--></s> <s id="N117B5">Nunc autem, <expan abbr="quoniã">quoniam</expan> in nulla proportione, <lb/>in circunferentia certè fertur vbi BEC. </s> <s id="N117BE">Si autem duobus ab <lb/><expan abbr="ead&etilde;">eadem</expan> potentia latis, hoc <expan abbr="quid&etilde;">quidem</expan> plus repellatur, illud vero minus, <lb/>rationi <expan abbr="con&longs;entaneũ">con&longs;entaneum</expan> e&longs;t, tardius moueri id quod plus repellitur <lb/>eo quod repellitur minus. </s> <s id="N117D2">Quod videtur accidere maiori & mi­<lb/>nori illarum quæ ex centro circulos de&longs;cribunt. </s> <s id="N117D7"><expan abbr="Quoniã">Quoniam</expan> enim <lb/>propius e&longs;t manenti, eius quæ minor e&longs;t, <expan abbr="extremũ">extremum</expan>, quam id quod <lb/>e&longs;t maioris, veluti rectum in contrarium, ad medium, tardius <lb/>fertur minoris extremum. </s> <s id="N117E7">Omne quidem igitur circulum de­<lb/>&longs;cribenti i&longs;tud accidi<gap/>: <expan abbr="ferturq.">ferturque</expan> eam quæ &longs;ecundum naturam <lb/>e&longs;t lationem, &longs;ecundum circumferentiam: illam vero quæ præ­<lb/>ter naturam, in tran&longs;uer&longs;um & &longs;ecundum centrum. </s> <s id="N117F6">Maio-<emph.end type="italics"/><pb pagenum="47" xlink:href="005/01/055.jpg"/><emph type="italics"/>rem autem &longs;emper eam quæ præter naturam e&longs;t ip&longs;a minor <lb/>fertur: quia enim centro e&longs;t vicinior quod trahit, vincitur <lb/>magis.<emph.end type="italics"/></s> </p> <p id="N11808" type="head"> <s id="N1180A">COMMENTARIVS.<!-- KEEP S--></s> </p> <p id="N1180E" type="main"> <s id="N11810">Qvamuis Philo&longs;ophus &longs;uperiori textu &longs;emel atque <lb/>iterum a&longs;&longs;ump&longs;erit, &longs;emidiametrum, &longs;eu lineam <lb/>circulum de&longs;cribentem, duabus ferri lationibus, <lb/>prout explicuimus; huc tamen illud probandum <lb/>reliquit, & ex dictis etiam de motu antror&longs;um & retror&longs;um <lb/>manife&longs;tum e&longs;&longs;e docet. </s> <s id="N1181D">Id igitur hic probat ex eo. </s> <s id="N11820">Nam &longs;i <lb/>in de&longs;criptione circuli, &longs;emidiameter vnam tantum lationem <lb/>pateretur, vt verbi gratia naturalem, qua rectà tenderet ver­<lb/>&longs;us, vnam aliquam differentiam &longs;itus, nunquam ad ip&longs;ius dia­<lb/>metri perpendiculum perueniret. </s> <s id="N1182B">Implicat enim vnica la­<lb/>tione, aliquid &longs;imul rectà tendere, ac in tran&longs;uer&longs;um, quem­<lb/>admodum &longs;e habet perpendiculum ad diametrum à qua pro­<lb/>pendit: At &longs;emidiameter circulum de&longs;cribendo, aliquando <lb/>peruenit ad &longs;uum perpendiculum, ita vt coincidat cum illo: <lb/>Ergo non vnica, &longs;ed duplici latione conuincitur ferri. </s> </p> <figure id="id.005.01.055.1.jpg" xlink:href="005/01/055/1.jpg"/> <p id="N1183D" type="main"> <s id="N1183F">Sit enim circulus de­<lb/>&longs;cribendus ABCD, circa <lb/>centrum E. <!-- KEEP S--></s> <s id="N11847">Sitque dia­<lb/>meter AC, &longs;emidiameter <lb/>vero circulum de&longs;cribens <lb/>AE. <!-- KEEP S--></s> <s id="N11851">Si igitur ip&longs;a recta <lb/>A E, altero eius extremo <lb/>manente in centro E, al­<lb/>tero vero nempè A, cir­<lb/>cumferatur, aliquando <lb/>ab&longs;que dubio erit in ED, <lb/>quæ e&longs;t perpendicularis <lb/>diametro AC. <!-- KEEP S--></s> <s id="N11863">Per <expan abbr="motũ">motum</expan> <lb/>autem naturalem ip&longs;a AE, de&longs;cendi&longs;&longs;et in FD, vel aliò rectè <lb/>tran&longs;lata fui&longs;&longs;et. </s> <s id="N1186E">Non ergo linea circulum de&longs;cribens fertur, <pb pagenum="48" xlink:href="005/01/056.jpg"/>vnico tantum modo motu ver&longs;us vnicam differentiam &longs;itus, <lb/>&longs;ed duplici motu, nempe mixto ex naturali & præternaturali; <lb/>ver&longs;us duplicem differentiam &longs;itus. </s> <s id="N1187A">Naturali quippe, quo in <lb/>propo&longs;ita figura fertur ver&longs;us latus F D, præternaturali verò, <lb/>quo retrahitur in tran&longs;uer&longs;um ver&longs;us latus E D, eo quòd alte­<lb/>rum eius extremum detineatur in centro E, vt clarius infra <lb/>patebit. </s> </p> <p id="N11885" type="main"> <s id="N11887">Quibus ita con&longs;titutis, reuertitur Ari&longs;toteles ad <expan abbr="probandũ">probandum</expan>, <lb/>partes vel puncta &longs;emidiametri, eò velocius moueri, quò plus <lb/>à centro di&longs;tauerint; eò verò tardius, quò magis ad centrum <lb/>acce&longs;&longs;erint. </s> <s id="N11896">Quod cum ad doctrinam in &longs;uperiori textu tra­<lb/>ditam &longs;pectet, <expan abbr="illucq.">illucque</expan> propterea à nobis tran&longs;latum &longs;it, ac &longs;a­<lb/>tis expo&longs;itum, non e&longs;t cur hic rur&longs;us idem repetatur ac denuo <lb/>exponatur. </s> <s id="N118A3">Acceptionem autem & explicationem motus <lb/>naturalis ac præternaturalis, qua v&longs;i &longs;umus, &longs;ump&longs;imus ex co­<lb/>dem Philo&longs;opho textu &longs;equenti, & lib. 1. Metheororum c. <!-- REMOVE S-->5. <lb/>Vbi di&longs;currentium &longs;yderum ac fulminum motum quem in <lb/>&longs;ublimi aere obliquè fieri con&longs;picimus, ex duabus pariter la­<lb/>tionibus docet con&longs;tare. </s> <s id="N118B2">Vna quidem naturali, qua prout <lb/>accen&longs;a ac leuia corpora, &longs;ur&longs;um rectà tendere debent: <lb/>altera verò præternaturali, qua prout à con&longs;tipan­<lb/>te frigore extruduntur ac propelluntur (in­<lb/>&longs;pi&longs;&longs;ata &longs;cilicet ac grauitante magis eo­<lb/>rum exhalationis materia) deor­<lb/>&longs;um inclinant. </s> <s id="N118C1">Ex his enim <lb/>duabus lationibus <lb/>medius qui­<lb/>dam mo­<lb/>tus <lb/>re&longs;ultat, quo vt ip&longs;e inquit, &longs;ydera <lb/>videntur volare, & obliquè <lb/>tanquam proiecta <lb/>per aera <lb/>ferri. </s> </p> <pb pagenum="49" xlink:href="005/01/057.jpg"/> <p id="N118DA" type="head"> <s id="N118DC"><emph type="italics"/>Qua ratione partes diametri a centro remotio­<lb/>res magis participent de motu naturali, <lb/>propinquiores verò magis de præ­<lb/>ternaturali.<emph.end type="italics"/></s> </p> <p id="N118E9" type="head"> <s id="N118EB">Textus Octauus</s> </p> <p id="N118EE" type="main"> <s id="N118F0">Q<emph type="italics"/>vod autem magis quod præter naturam <lb/>e&longs;t mouetur ip&longs;a minor, quam maior illarum, <lb/>quæ ex centro circulos de&longs;cribunt, ex ijs est <lb/>manifestum. </s> <s id="N118FC">Sit circulus vbi B C D E, & <lb/>alter in hoc minor, vbi M N O P, circà <lb/>idem centrum A, & projiciantur diametri <lb/>in magno quidem, in quibus C D, B E, in minori verò ip&longs;æ <lb/>M O, N P: & altera parte longius quadratum &longs;uppleatur <lb/>D K R C: &longs;iquidem A B circulum de&longs;cribens ad id perue­<lb/>niet, vnde e&longs;t egre&longs;&longs;a; manife&longs;tum e&longs;t, quod ad ip&longs;am fertur <lb/>AB. <!-- KEEP S--></s> <s id="N1190E">Similiter etiam A M ad ip&longs;am A M perueniet. </s> <s id="N11911">T ardiùs <lb/>autem fertur A M, quam A B quemadmodum dictum <lb/>e&longs;t: quia maior fit repul&longs;io, & magis retrabitur A M. </s> <s id="N11918">Du­<lb/>catur igitur ip&longs;a A L F, & ab ip&longs;o L perpendiculum ad ip­<lb/>&longs;am AB, ip&longs;a LQ in minore circulo: & rur&longs;um ab L du­<lb/>catur iuxtà A B L S, & S T ad ip&longs;am A B perpendicu­<lb/>lum, & ip&longs;a FX: ip&longs;æ igitur vbi &longs;unt ST, & LQ, æqua­<lb/>les: ip&longs;a ergò B T minor est, quam M <expan abbr="q.">que</expan> Aequales enim <lb/>rectæ lineæ in &etail;qualibus coniecta circulis perpendiculares à <lb/>diametro, minorem diametri re&longs;ecant &longs;ectionem in maioribus <lb/>circulis. </s> <s id="N1192F">Est autem ip&longs;a S T æqualis ip&longs;i L <expan abbr="q.">que</expan> In quan­<lb/>to autem tempore ip&longs;a AL ip&longs;am ML lata e&longs;t, in tanto tem­<lb/>poris &longs;patio in maiori circulo, maiorem, quam &longs;it B S, latum <lb/>erit extremum ip&longs;is AB. <!-- KEEP S--></s> <s id="N1193D">Latio quidem igitur &longs;ecundum na­<lb/>turam æqualis: Ea autem, quæ præter naturam e&longs;t minor, <lb/>videlicet B T, quam M <expan abbr="q.">que</expan> Oportet autem proportiona-<emph.end type="italics"/><pb pagenum="50" xlink:href="005/01/058.jpg"/><emph type="italics"/>biliter e&longs;&longs;e, &longs;icut quod est fecundum naturam, ita quod est <lb/>præter naturam, ad id, quod est præter naturan; maiorem <lb/>igitur circumferentiam pertran&longs;iuit, quam &longs;it ip&longs;a S B. </s> <s id="N11955">Ne­<lb/>ce&longs;&longs;e autem e&longs;t ip&longs;am F B. in hoc tempore pertran&longs;i<32>e: hic <lb/>enim erit, quando proportionabiliter vtrinque accidis, quod e&longs;t <lb/>præter naturam, ad id quod e&longs;t &longs;ecundum naturam. </s> <s id="N1195E">Si igi­<lb/>tur maius e&longs;t, quod &longs;ecundum naturam in maiori, & quod e&longs;t <lb/>præter naturam, magis vtique hic coincidit vno modo: ita <lb/>quod B &longs;it latum per ip&longs;am B F in tanto tempore, in quo <lb/>M punctum per ip&longs;am M L. <!-- KEEP S--></s> <s id="N1196A">Hic enim &longs;eeundum naturam <lb/>quidem &longs;igno B fit X F: e&longs;t enim ab ip&longs;o F perpendiculum: <lb/>præter naturam verò ad ip&longs;am X B. </s> <s id="N11971">E&longs;t autem quem ad­<lb/>modum FX ad X B, &longs;ic L Q ad M <expan abbr="q.">que</expan> Manife&longs;tum <lb/>autem &longs;i coniunguntur ab ip&longs;a B M ad FL. </s> <s id="N1197C">Si autem mi­<lb/>nor, aut maior, quam &longs;it FB erit illa, quam latum e&longs;t B, <lb/>non &longs;imiliter erit, neque proportionale in vtri&longs;que quod e&longs;t &longs;e­<lb/>cundum naturam ad id quod e&longs;t præter naturam. </s> <s id="N11985">Quam igi­<lb/>tur ob cau&longs;am ab eadem potentia celerius fertur id quod plus <lb/>à centro di&longs;tat punctum ex ijs, quæ dicta &longs;unt e&longs;t mani­<lb/>fe&longs;tum.<emph.end type="italics"/></s> </p> <p id="N11990" type="head"> <s id="N11992">COMMENTARIVS.<!-- KEEP S--></s> </p> <p id="N11996" type="main"> <s id="N11998">Ex a&longs;&longs;umptis ab Ari&longs;totele in illo priori argumento <lb/>iam &longs;upra textu 6. à nobis expo&longs;ito ad o&longs;tenden­<lb/>dum in ip&longs;o circulo, quæ plus à centro di&longs;tat linea <lb/>eadem vi commota citius ferri quàm illa, quæ minus di&longs;tat; <lb/>illud dumtaxat ci probandum reman&longs;erat, videlicet partes <lb/>lineæ circulum de&longs;cribentis, quò viciniores centro &longs;unt, eò <lb/>magis detrahi à motu naturali, <expan abbr="magisq.">magisque</expan> participare de motu <lb/>præternaturali; E contrà verò quo remotiores &longs;unt à cen­<lb/>tro, magis participare de motu naturali, vt inde inferatur ve­<lb/>locius moueri. </s> <s id="N119B3">Probat autem hoc modo; &longs;it enim, inquit, <lb/>Circulus B C D E; & alter in hoc minor vbi M N O P <lb/>circà idem centrum A. <expan abbr="Sintq.">Sintque</expan> Diametri maioris quidem C. <lb/>D, & B E; minoris verò M O, & N P. <!-- KEEP S--></s> <s id="N119C1">Deinde complea-<pb pagenum="51" xlink:href="005/01/059.jpg"/><figure id="id.005.01.059.1.jpg" xlink:href="005/01/059/1.jpg"/><lb/>tur quadrangulum rectangulum D K R C nempe ducen­<lb/>do lineam K R. paralellam, & æqualem ip&longs;i D C. per pun­<lb/>ctum B, & claudendo ip&longs;as K R & D C per lineas D K <lb/>& C R. <!-- KEEP S--></s> <s id="N119D6">Cum igitur motus naturalis cuiu&longs;libet lineæ dica­<lb/>tur ille, quo recta fertur ver&longs;us eam partem in quam tendit, <lb/>&longs;i linea A B &longs;tantis circuli de&longs;cripti deor&longs;um tenderet &longs;im­<lb/>plici motu naturali, ab&longs;que dubio rectè, ac perpendiculari­<lb/>ter tota &longs;imul caderet, & coincid<gap/>et cum C R. <!-- KEEP S--></s> <s id="N119E4">Quoniam <lb/>vero non pote&longs;t ita ferri &longs;implici motu naturali, eò quod al­<lb/>terum eius extremum detineatur in centro, illæ partes ip­<lb/>&longs;ius dicentur magis participare de motu naturali, quæ re­<lb/>ctius tendunt in ip&longs;am C R; hoc e&longs;t per lineam magis appro­<lb/>pinquantem ad perpendiculum; &longs;icut è contrà illæ dicentur <lb/>magis detrahi à motu naturali, quæ magis incuruantur ten­<lb/>dendo ver&longs;us lineam C D. <!-- KEEP S--></s> <s id="N119F6">Itaque progre&longs;&longs;as perpendicu­<lb/>laris ver&longs;us C R erit motus naturalis, ver&longs;us autem C D erit <lb/>præternaturalis Quod certè videtur &longs;upponere Ari&longs;toteles. <lb/><!-- KEEP S--></s> <s id="N119FF">Nunc autem &longs;ic procedit ad o&longs;tenden lum propo&longs;itum, <lb/>nempè partem diametri propinquiorem centro, vt A M <pb pagenum="52" xlink:href="005/01/060.jpg"/>magis detrahi à motu naturali, ac tardiùs moueri, quàm <lb/>M B quæ magis di&longs;tat ab illo. </s> <s id="N11A0B">Ducatur inquit à centro li­<lb/>nea A L F; & à puncto L perpendicularis ip&longs;i A B quæ <lb/>&longs;it L Q, & rur&longs;us ab eodem L ducatur L S paralella ei­<lb/>dem A B. </s> <s id="N11A14">Deinde à puncto S excitetur alia perpendicu­<lb/>laris eidem AB. <expan abbr="Sitq.">Sitque</expan> ST; & ab F item eidem perpendicu­<lb/>laris F X. <!-- KEEP S--></s> <s id="N11A20">His po&longs;itis linea QL erit æqualis lineæ T S, vt <lb/>patet ex 34. primi Euclidis, cum &longs;int latera oppo&longs;ita rectan­<lb/>guli T L. <!-- KEEP S--></s> <s id="N11A28">Cumque &longs;pacium, quod naturali motu tran&longs;cur­<lb/>runt puncta M, & B men&longs;uretur ip&longs;is perpendicularibus. <lb/></s> <s id="N11A2E">QL & T S, vt dictum e&longs;t, motus naturalis per lationem ip­<lb/>&longs;ius B v&longs;que ad S æqualis erit motui naturali per lationem <lb/>ip&longs;ius M v&longs;que ad L. <!-- KEEP S--></s> <s id="N11A36">At motus præternaturales eorundem <lb/>punctorum M, & B tunc erunt inæquales. </s> <s id="N11A3B">Nam &longs;pacium <lb/>quod præternaturaliter percurri&longs;&longs;et punctum M e&longs;&longs;et ip&longs;a <lb/>M <expan abbr="q;">que</expan> & &longs;patium, quod præternaturaliter percurri&longs;&longs;et <lb/>punctum B e&longs;&longs;et ip&longs;a B T. <!-- KEEP S--></s> <s id="N11A49">Maior autem e&longs;t M Q, quàm <lb/>&longs;it B T. <!-- KEEP S--></s> <s id="N11A4F">Siquidem ex æqualibus rectis lineis perpendicula­<lb/>riter cadentibus à communi diametro ad circumferentias <lb/>totidem circulorum inæqualium, ea, quæ e&longs;t in minori <lb/>circulo maiorem re&longs;ecat diametri portionem, vt con&longs;tat <lb/>ex doctrina de Sinibus, & patere pote&longs;t in perpendicularibus <lb/>QL T S, & HI; quæ cum &longs;ine æquales inter duas paralel­<lb/>las, inæquales re&longs;ecant portiones diametri E G; nempe tan­<lb/>to maiorem, quanto in minori circulo, vt e&longs;t QM re&longs;pectu <lb/>T B, & ip&longs;a T B re&longs;pectu H G. <!-- KEEP S--></s> <s id="N11A63">Igitur punctum M quod &longs;a­<lb/>nè propinquius e&longs;t centro, magis mouetur motu præterna­<lb/>turali, quàm punctum B, quod remotius e&longs;t ab illo. </s> <s id="N11A6A">Id quod <lb/>primo loco erat probandum. </s> </p> <p id="N11A6F" type="main"> <s id="N11A71">Vlterius verò quod punctum B magis moueatur motu <lb/>&longs;ecundum naturam, quam ip&longs;um punctum M probatur ex <lb/>eo; Nam quo tempore punctum M latum fuerit v&longs;que ad <lb/>L; punctum B eodem tempore perueniet v&longs;que ad F. <!-- KEEP S--></s> <s id="N11A7B">Ete­<lb/>nim cum ita &longs;e habere debeat motus naturalis ip&longs;ius B ad <lb/>motum præter naturam eiu&longs;dem B quemadmodum &longs;e ha­<lb/>bet motus naturalis ip&longs;ius M ad motum præter naturam <pb pagenum="53" xlink:href="005/01/061.jpg"/>eiu&longs;dem M talis proportio &longs;olum verificari pote&longs;t in F, <lb/>nam proportio, quam habet linea F X referens &longs;pacium <lb/>tran&longs;actum &longs;ecundum naturam ad B X, quod ab eodem <lb/>puncto B tran&longs;actum e&longs;t præter naturam in maiori circulo, <lb/>eadem e&longs;t, ac proportio lineæ QL tran&longs;actæ &longs;ecundum <lb/>naturam ad lineam M Q tran&longs;actam præter naturam in mi­<lb/>nori circulo. </s> <s id="N11A95">Quod inde patere pote&longs;t, nam &longs;i ducantur re­<lb/>ctæ B F, & M L efficientur duo triangula æquiangula <lb/>B X F, & M Q L quæ per 4. &longs;exti habebunt latera pro­<lb/>portionalia circà æquales angulos: Vnde &longs;icut &longs;e habet F X <lb/>ad X B circa angulum. </s> <s id="N11AA0">rectum X, ita &longs;e habet L Q ad <lb/>QM circà angulum rectum <expan abbr="q.">que</expan> Et permutando, &longs;icut &longs;e <lb/>habet F X ad L Q, ità X B ad QM per 16. Quinti. </s> <s id="N11AAB">Ita­<lb/>que proportionabiliter punctum B, vel quodlibet aliud, <lb/>quanto magis di&longs;tat à centro, tanto magis mouebitur motu <lb/>naturali; &longs;iquidem F X <gap/> <gap/>, quam L Q, <expan abbr="proindeq.">proindeque</expan> <lb/>velociùs feretur, &longs;eù maius &longs;patium in eodem tempore per­<lb/>curret, quam punctum M, vel aliud, quod propinquius <lb/>&longs;it centro; Et hoc erat probandum, vt omnino con&longs;taret <lb/>quidquid a&longs;&longs;umptum fuerat ex eodem Ari&longs;totele in explica­<lb/>tione quartæ proprietatis circuli, & a&longs;&longs;ignatione cau&longs;æ illius, <lb/>vt ibidem commonuimus. </s> </p> <p id="N11AC8" type="head"> <s id="N11ACA"><emph type="italics"/>De In&longs;trumentis, ac Machinis naturam cir­<lb/>culi in motione participantibus.<emph.end type="italics"/></s> </p> <p id="N11AD3" type="head"> <s id="N11AD5">ADDITIO PRIMA.<!-- KEEP S--></s> </p> <p id="N11AD9" type="main"> <s id="N11ADB">Attenta natura circuli cum &longs;uis proprietatibus modò <lb/>explicatis ad hoc acumen humani ingenij iam pridem <lb/>peruenit, vt machinas qua&longs;dam excogitaret, quæ naturam <lb/>ip&longs;ius circuli participantes, motricem potentiam in motu <lb/>grauium ac leuium iuuarent. </s> <s id="N11AE6">Huiu&longs;modi autem machinas <lb/>in&longs;trumenta mechanica communiter appellamus, vtpotè <lb/>quæ mechanica &longs;peculatione adinuenta &longs;unt, <expan abbr="eademq.">eademque</expan> arte <pb pagenum="54" xlink:href="005/01/062.jpg"/>adhibentur tanquam in&longs;trumenta ad leuanda pondera, vel <lb/>quomodolibet mouenda grauia, quæ re&longs;pectiuè dicuntur <lb/>etiam leuia. </s> <s id="N11AFA">Sunt autem hæc in&longs;trumenta præcipua &longs;ex, ad <lb/>quæ cætera omnia reducuntur: nempè Libra. <!-- KEEP S--></s> <s id="N11B00">Vectis, Tro­<lb/>chlea, Axis in Peritrochio, Cuneus, & Cochlea Et licet Ari­<lb/>&longs;toteles di&longs;tinctam eorum tractationem prætermi&longs;erit, ac <lb/>non ni&longs;i quatuor ex ip&longs;is hic, vel in &longs;equentibus quæ&longs;tionibus <lb/>pro opportunitate meminerit, &longs;upponit nihilominus <expan abbr="tanquã">tanquam</expan> <lb/>certum, illa omnia ac &longs;imilia participare naturam circuli, <lb/>eorumque vim qua motricem augent potentiam in hoc ip­<lb/>&longs;o con&longs;i&longs;tere, vt circuli proprietatem &longs;apiendo, faciliùs & <lb/>mouerentur, & motum præ&longs;tarent oneribus ac ponderibus <lb/>mouendis, cum circularis &longs;ine orbicularis figura &longs;it omnium <lb/>mouenti&longs;&longs;ima. </s> <s id="N11B1B">Ait enim &longs;upra tex. <!-- REMOVE S-->5. Ea igitur quæ circa <lb/>libram fiunt, ad circulum referuntur: quæ verò circa vectem, <lb/>ad ip&longs;am libram: alia autem ferè omnia, quæ circa mecha­<lb/>nicas &longs;unt motiones, ad vectem. </s> <s id="N11B26">Ex quibus infertur &longs;iue im­<lb/>mediate, &longs;iue mediante, alia quadam ab&longs;tracta ratione quam <lb/>ip&longs;a participent, mechanica penè omnia in&longs;trumenta in &longs;uis <lb/>motionibus ad circuli naturam referri. </s> <s id="N11B2F">Quod vt clarius te­<lb/>neatur, pauca &longs;altem de &longs;ingulis ip&longs;is in&longs;trumentis hic adij­<lb/>cere opere pretium putauimus, ea &longs;cilicet tantum mo­<lb/>do, quæ ad in&longs;titutam textus dilucidationem no­<lb/>uerimus pertinere, Cum exacta huiu&longs;modi <lb/>in&longs;trumentum tractatio habeatur apud <lb/>Heronem, Pappum, & alios ve­<lb/>teres, noui&longs;simè verò & <lb/>accurati&longs;simè apud <lb/>Guidum Vbal-<lb/>dum <lb/><gap/> Marchionibus Montis, qui &longs;i­<lb/>gillatim de illis præcla<lb/>rum librum in­<lb/>&longs;tituit. </s> </p> <pb pagenum="55" xlink:href="005/01/063.jpg"/> <p id="N11B53" type="head"> <s id="N11B55">DE LIBRA.</s> </p> <p id="N11B58" type="main"> <s id="N11B5A">Libra, quæ inter mechanica in&longs;trumenta iure <lb/>primum &longs;ibi vendicat locum, eo quod imme­<lb/>diatius, ac magis participet <expan abbr="naturã">naturam</expan> circuli in <lb/>&longs;uis motionibus, e&longs;t <expan abbr="iugũ">iugum</expan> <expan abbr="quoddã">quoddam</expan> ex medio <lb/>liberè &longs;u&longs;pen&longs;um, <expan abbr="axeq.">axeque</expan> <expan abbr="&longs;uffultũ">&longs;uffultum</expan>, ac plano ho­<lb/>rizontis <expan abbr="parallelũ">parallelum</expan>, ex cuius <expan abbr="vtraq;">vtraque</expan> extremitate gemina lanx <lb/>pendet, <expan abbr="cuiusq.">cuiusque</expan> conuer&longs;ione circa ip&longs;um axem, dum altera <lb/>eleuatur, altera deprimitur, póndus vel exce&longs;&longs;us <expan abbr="põderis">ponderis</expan> cu<lb/>iu&longs;libet, deprehenditur, ac men&longs;uratur. </s> <s id="N11B91">Qua in de&longs;criptione <lb/>&longs;upponitur <expan abbr="iugũ">iugum</expan> ex medio, trutina, &longs;eu axe &longs;u&longs;pen&longs;um, con&longs;ti­<lb/>tui, ac manere parallelum plano horizontis propter <expan abbr="æqui-ponderantiã">æqui­<lb/>ponderantiam</expan> vtriu&longs;que medietatis: <expan abbr="motumq.">motumque</expan> circularem, &longs;eu <lb/><expan abbr="conuer&longs;ion&etilde;">conuer&longs;ionem</expan> circa fulcimentum tanquam circa <expan abbr="centrũ">centrum</expan> im­<lb/>motum, non ni&longs;i ratione <expan abbr="inæqualiũ">inæqualium</expan> <expan abbr="ponderũ">ponderum</expan> in gemina lance <lb/>vtrinque pendentium illi competere: vnde &longs;i pondera &longs;int <lb/>æqualia, libra &longs;emper maneat, & in æquilibrio con&longs;tituatur, <lb/>&longs;eu æquidi&longs;tans à plano horizontis. </s> <s id="N11BBF">Deinde ita &longs;upponitur, <lb/>pondera in lancibus impo&longs;ita, ex vtraque iugi extremitate <lb/><expan abbr="p&etilde;dere">pendere</expan>, vt hoc non &longs;it <expan abbr="nece&longs;&longs;ariũ">nece&longs;&longs;arium</expan>, <expan abbr="neq;">neque</expan> e&longs;&longs;entialiter pertineat <lb/>ad <expan abbr="con&longs;titution&etilde;">con&longs;titutionem</expan> libræ, &longs;ed potius ad <expan abbr="commoditat&etilde;">commoditatem</expan> ponde­<lb/>randi, cum &longs;atis intelligatur libra e&longs;&longs;entialiter con&longs;tituta <lb/>etiam ab&longs;que lancibus, ponderibus in ip&longs;is iugi extremita­<lb/>tibus, adiacentibus, vt cernere e&longs;t in &longs;equentibus figuris. </s> </p> <p id="N11BE1" type="main"> <s id="N11BE3">Quo autem pacto libra in &longs;ui motione participet natu­<lb/>ram circuli per &longs;e con&longs;tat con&longs;ideranti, iugum, diametri vi­<lb/>cem gerere, axem verò &longs;eu trutinam, aut <expan abbr="fulcimentũ">fulcimentum</expan> quod­<lb/>libet, centri locum tenere, circa quod immotum, ip&longs;a dia­<lb/>meter vertitur dum circulum de&longs;cribit; &longs;iquidem immoto <lb/>axe, &longs;eu fulcimento ip&longs;ius libræ, iugum, alterius extremita­<lb/>tis depre&longs;sione ob exuperantiam <expan abbr="põderis">ponderis</expan>, alterius verò ele­<lb/>uatione, circumagitur, non &longs;ecus ac diameter circulum <lb/>conficiendo. </s> <s id="N11BFE">Quod &longs;i partes iugi vtrinque à centro produ­<lb/>ctæ, non &longs;int inter &longs;e <expan abbr="lõgitudine">longitudine</expan> æquales, quamuis æquipon­<lb/>derantes; tunc quidem in ip&longs;is iugi conuer&longs;ione, ac circum­<pb pagenum="56" xlink:href="005/01/064.jpg"/>latione duo circuli de&longs;cribentur alter altero maior, <expan abbr="tanquã">tanquam</expan> <lb/>à duplici &longs;emidiametro circumlato, vt hic erit in&longs;picere. </s> </p> <figure id="id.005.01.064.1.jpg" xlink:href="005/01/064/1.jpg"/> <p id="N11C19" type="head"> <s id="N11C1B">DE VECTE.</s> </p> <p id="N11C1E" type="main"> <s id="N11C20">Vectis &longs;implex <expan abbr="quoddã">quoddam</expan> <expan abbr="in&longs;trumentũ">in&longs;trumentum</expan> e&longs;t ligneum, <lb/>vel <expan abbr="ferreũ">ferreum</expan> &longs;atis oblongum veluti palus, aut fu&longs;ti<gap/><lb/>grandior, ad promouenda pondera; cuius vt <expan abbr="plu-rimũ">plu­<lb/>rimum</expan> altera extremitas <expan abbr="põderi">ponderi</expan> eleuando &longs;ubijci­<lb/>tur, altera verò manu, &longs;eu <expan abbr="pot&etilde;tia">potentia</expan> præmitur, &longs;ub­<lb/>&longs;trato inter <expan abbr="vtramq;">vtramque</expan> aliquo fulcimento, cui inni­<lb/>tatur, quòd græcè hypomochilion appellatur, <expan abbr="quodq">quoque</expan> <expan abbr="quãto">quanto</expan> pro­<lb/>pinquius ponderi locatur, tanto facilius ip&longs;o vecte leuatur. </s> <s id="N11C52">Ali­<lb/>quando verò altera extremitas <expan abbr="nõ">non</expan> ponderi, &longs;ed fulcimento &longs;ubij­<lb/>citur, vel ei quoquo modo innititur <expan abbr="tanquã">tanquam</expan> manenti valido, pon-<pb pagenum="57" xlink:href="005/01/065.jpg"/><expan abbr="dusq.">dusque</expan> eleuatur, aut deprimitur per vectis <expan abbr="part&etilde;">partem</expan> mediam, quæ e&longs;t <lb/>inter <expan abbr="vtramq.">vtramque</expan> <expan abbr="extremitat&etilde;">extremitatem</expan> iuxta <expan abbr="eleuation&etilde;">eleuationem</expan>, aut <expan abbr="depre&longs;&longs;ion&etilde;">depre&longs;&longs;ionem</expan> al­<lb/>terius extremitatis vbi applicatur <expan abbr="pot&etilde;tia">potentia</expan>: vel certè <expan abbr="põdus">pondus</expan> ele­<lb/>uatur per <expan abbr="alterã">alteram</expan> extremitatem, &longs;i in illa locetur, <expan abbr="manusq.">manusque</expan> aut po­<lb/>tentia in medio adhibeatur. </s> <s id="N11C95">Vnde tres nonnulli &longs;pecies <expan abbr="vectiũ">vectium</expan> di­<lb/>&longs;tinguunt, quas iuxta prædicta figuris <expan abbr="etiã">etiam</expan> hic &longs;tuduimus expri­<lb/>mere; Illud interim admonendo, eas omnes facilè in &longs;uis motio­<lb/>nibus ad <expan abbr="circulũ">circulum</expan> referri, cum ip&longs;æ non ni&longs;i <expan abbr="diametrũ">diametrum</expan>, vel <expan abbr="&longs;emidia-metrũ">&longs;emidia­<lb/>metrum</expan> <expan abbr="circulũ">circulum</expan> circa <expan abbr="immotũ">immotum</expan> <expan abbr="fulcimentũ">fulcimentum</expan> <expan abbr="de&longs;cribent&etilde;">de&longs;cribentem</expan> referant, vt <lb/>per &longs;e patet, ac prima quæ &longs;anè vtilior & frequentius in v&longs;u e&longs;t, <lb/>ad <expan abbr="librã">libram</expan> à <expan abbr="fulcim&etilde;to">fulcimento</expan> inæquales vtrinque partes <expan abbr="habent&etilde;">habentem</expan> euiden­<lb/>ti&longs;simè reducatur, vt amplius deinceps <expan abbr="cõ&longs;tabit">con&longs;tabit</expan>. </s> <s id="N11CDA"><expan abbr="Nã">Nam</expan> hoc quod e&longs;t <lb/>fulciri per <expan abbr="&longs;u&longs;pen&longs;ion&etilde;">&longs;u&longs;pen&longs;ionem</expan> beneficio trutinæ, vel per <expan abbr="&longs;ubiection&etilde;">&longs;ubiectionem</expan> al­<lb/>terius corporis, quod non minus axis, ac centri <expan abbr="vic&etilde;">vicem</expan> &longs;ubeat, e&longs;t <lb/>differentia valde accidentalis. </s> </p> <figure id="id.005.01.065.1.jpg" xlink:href="005/01/065/1.jpg"/> <pb pagenum="58" xlink:href="005/01/066.jpg"/> <p id="N11CFB" type="head"> <s id="N11CFD">DE TROCHLEA.</s> </p> <p id="N11D00" type="main"> <s id="N11D02">Trochlea e&longs;t in&longs;trumentum veluti conce­<lb/>ptaculum quoddam, aut cap&longs;ula, vnum, vel <lb/>plures &longs;triatos orbiculos, &longs;eu rotulas in &longs;e <lb/>continens, axiculis per rotulas traiectis, circa <lb/>quos illæ vertuntur, quibus admoto fune du­<lb/>ctario eleuantur, aut remittuntur onera. </s> <s id="N11D0F">Con&longs;tare autem <lb/>&longs;olet Trochlea ex vno, vel pluribus orbiculis tanquam inter <lb/>thecas in&longs;ertis, non quidem æqualibus, &longs;ed maioribus &longs;uper <lb/>minores adiectis, ne vnius funis circumductus funem alte­<lb/>rius impediat. </s> <s id="N11D1A">In&longs;uper ip&longs;i orbiculo, modò bini &longs;uper binos <lb/>locari con&longs;ueuerunt, ita vt in trochlea quatuor, vel &longs;ex or­<lb/>biculi, duplici, vel triplici ordine <expan abbr="reperiãtur">reperiantur</expan> di&longs;po&longs;iti; modo <lb/>verò non ni&longs;i &longs;inguli &longs;uper &longs;ingulos, totidem ordinibus con­<lb/>tinentur, vt quo potuimus modò hic figuris expre&longs;simus. </s> </p> <figure id="id.005.01.066.1.jpg" xlink:href="005/01/066/1.jpg"/> <p id="N11D2E" type="main"> <s id="N11D30">Reducitur autem Trochlea ad Vectem, & con&longs;equen­<lb/>ter ad libram, quia vnu&longs;qui&longs;que orbiculus illius per diame­<lb/>trum nititur proprio axiculo tanquam fulcimento, quod in­<lb/>ter onus leuandum, aut &longs;u&longs;tinendum, & potentiam eleuan­<lb/>tem locatur, ita vt ad depre&longs;sionem vnius extremitatis dia-<pb pagenum="59" xlink:href="005/01/067.jpg"/>metri, vbi mouentis potentia applicatur, altera extremitas, <lb/>quæ onus &longs;u&longs;tinet, eleuetur; licet hoc non immediatè fiat; <lb/>&longs;ed mediante fune ductario, vt hic ad oculos &longs;pectandum <lb/>proponetur ac infra fu&longs;iùs explicabitur quæ&longs;t. </s> <s id="N11D46">18. Sit enim <lb/>trochleae orbiculus ABC, dia­<lb/><figure id="id.005.01.067.1.jpg" xlink:href="005/01/067/1.jpg"/><lb/>meter verò orbiculi linea ho­<lb/>rizonti parallela AB, & axicu­<lb/>lus C, tanquam centrum lo­<lb/>catum in medio: Deinde per <lb/>funem ductarium ab extremo <lb/>A propendeat onus D, & ab <lb/>extremo B idem funis demit­<lb/>tatur, cui applicata &longs;it poten­<lb/>tia motiua in E. <!-- KEEP S--></s> <s id="N11D64">Dicimus er­<lb/>go totum orbiculum incum­<lb/>bere, ac niti axiculo C tan­<lb/>quam fulcimento per diame­<lb/>trum eius AB in cuius medio <lb/>axiculus e&longs;t locatus, & in cuius <lb/>extremis AB, vtrinque &longs;it tota <lb/>compre&longs;sio, nempe oneris ac potentiæ; <expan abbr="proindeq.">proindeque</expan> ip&longs;am <lb/>diametrum AB, vectis vicem in motione gerere, qua­<lb/>tenus nixa in præfato fulcimento C, ad depre&longs;­<lb/>&longs;ionem extreminitatis B per vim trahen­<lb/>tem in E, extremitas A nece&longs;&longs;ario <lb/>eleuatur, ac &longs;imul cum illa <lb/>pondus D pendens ex <lb/>ip&longs;a, vt per &longs;e <lb/>patet. </s> </p> <pb pagenum="60" xlink:href="005/01/068.jpg"/> <p id="N11D8D" type="head"> <s id="N11D8F">DE AXE IN PERITROCHIO.</s> </p> <p id="N11D92" type="main"> <s id="N11D94">Axis in Peritrochio e&longs;t oblongus quidam <lb/>cylindrus Peritrochio firmiter infixus, ac pa­<lb/>rallelus horizontis plano locatus, cuius ex­<lb/>trema in rotundis foraminibus immoti peg­<lb/>matis expeditè vertuntur. </s> <s id="N11D9F">Peritrochium ve­<lb/>rò, e&longs;t machina rotunda, ad rotæ &longs;eu tympani &longs;imilitudi­<lb/>nem efformata, in cuius conuexa peripheria &longs;tipites qui & <lb/>Scytalæ vocantur, tanquam radij infinguntur; quibus admo­<lb/>ta manu tota machina &longs;imul cum axe ver&longs;atur, ac funibus <lb/>circa axem conuolutis, trahuntur pondera illis alligata; vt <lb/>hic licebit in&longs;picere. </s> </p> <figure id="id.005.01.068.1.jpg" xlink:href="005/01/068/1.jpg"/> <p id="N11DB3" type="main"> <s id="N11DB5">Reducitur <expan abbr="aut&etilde;">autem</expan> <lb/>tota huiu&longs;modi ma <lb/>china, &longs;eu in&longs;tru­<lb/>mentum ad <expan abbr="vect&etilde;">vectem</expan>; <lb/>Nam &longs;i con&longs;idere­<lb/>mus <expan abbr="con&longs;titutũ">con&longs;titutum</expan> ex <lb/>diametro axis, ac <lb/>&longs;emidiametro Pe­<lb/>ritrochij <expan abbr="coincid&etilde;-te">coinciden­<lb/>te</expan> cum illa non ali­<lb/>ter in circumuolu­<lb/>tione &longs;e habere <expan abbr="cõ-perimus">com­<lb/>perimus</expan>, ac <expan abbr="Vect&etilde;">Vectem</expan>, <lb/>qui circa &longs;uum ful­<lb/>cimentum vertitur, <lb/>tanquam circa pro­<lb/>prium centrum. <lb/></s> <s id="N11DF1">E&longs;to enim Axis &longs;imul, ac Peritrochij immobile centrum <lb/>A, circa quod vtriu&longs;que circumferentia de&longs;cripta &longs;it, nem­<lb/>pe tàm Axis, quàm Tympani ip&longs;ius Peritrochij cum &longs;cyta­<lb/>lis; Diameter verò Axis &longs;it linea BC; ac &longs;emidiameter Pe­<lb/>titrochij AD, con&longs;tituentes integram lineam BD. <!-- KEEP S--></s> <s id="N11DFD">Tum <pb pagenum="61" xlink:href="005/01/069.jpg"/>ex Axe per funem BE propendeat onus F; <expan abbr="virtusq.">virtusque</expan> mo­<lb/>uentis applicetur in &longs;cytala vbi e&longs;t ip&longs;um D. <!-- KEEP S--></s> <s id="N11E0C">Ad motum <lb/>igitur deor&longs;um ip&longs;ius D, linea BD, non aliter &longs;e pote&longs;t <lb/>habere, ac vectis firmiter innixa immobili centro A, tan­<lb/>quam fulcimento, ac dum pars AD deprimitur, altera. <lb/></s> <s id="N11E16">nempe AB, eleuabitur &longs;imulque cum puncto B, pondus <lb/>F, quod ab eodem puncto extremo dependet. </s> </p> <figure id="id.005.01.069.1.jpg" xlink:href="005/01/069/1.jpg"/> <p id="N11E20" type="head"> <s id="N11E22">DE CVNEO.</s> </p> <p id="N11E25" type="main"> <s id="N11E27">Cvnevs e&longs;t &longs;implex quoddam in&longs;trumen­<lb/>tum ad findenda, &longs;eu &longs;cindénda corpora apti&longs;­<lb/>&longs;imum accedente percu&longs;&longs;ione. </s> <s id="N11E2E">E&longs;t enim &longs;oli­<lb/>dum, quod ex quadrangulari ba&longs;e <expan abbr="con&longs;urg&etilde;s">con&longs;urgens</expan>, <lb/>quatuor &longs;uperficiebus in peracutam aciem <lb/>terminantibus, clauditur. </s> <s id="N11E3B">Duabus videlicet &longs;ibi oppo&longs;itis <lb/>quadrangularibus, ac altera parte longioribus; duabus verò <lb/>&longs;imiliter oppo&longs;itis, &longs;ed triangularibus in prædictam acutam, <lb/>& oblongam aciem terminantibus. </s> <s id="N11E44">Quæ &longs;anè acies cum in <lb/>rimulam quamlibet <expan abbr="&longs;cind&etilde;dæ">&longs;cindendæ</expan> molis &longs;e in&longs;inuare præualeat, <pb pagenum="62" xlink:href="005/01/070.jpg"/>adueniente valida percu&longs;&longs;ione, vt quæ per malleúm &longs;uper ba­<lb/>&longs;im adactum fieri con&longs;ueuit, facilè totum cuneum cogit ad­<lb/>mittere, <expan abbr="proindeq.">proindeque</expan> partes molis ab inuicem &longs;ecedere, quod <lb/>e&longs;t molem ip&longs;am &longs;cindi, ac diuidi. </s> <s id="N11E5E">Cunei ergo figura &longs;ic de­<lb/>lineanda cen&longs;uimus ex quadrata ba&longs;i ABCD, excitando <lb/>&longs;uperficiem quadrangularem DBEF, ac aliam triangula­<lb/>rem CDE, quæ &longs;imul cum &longs;uis oppo&longs;itis omnes quatuor <lb/>de&longs;inant, ac terminentur in aciem EF. </s> </p> <figure id="id.005.01.070.1.jpg" xlink:href="005/01/070/1.jpg"/> <p id="N11E6E" type="main"> <s id="N11E70">Refertur auté hoc quoque in&longs;tru­<lb/>mentum ad vecté, eo quod ex duplici <lb/>vecte videatur con&longs;tare, vt infra qu&etail;&longs;t. <lb/></s> <s id="N11E78">17. ex Ari&longs;totele magis ex profe&longs;&longs;o <lb/>probabitur. </s> <s id="N11E7D">Etenim &longs;i con&longs;iderentur <lb/>duo eius latera, quæ ex ba&longs;i in aciem <lb/>terminantur, vt CE, & DE non &longs;e­<lb/>cus ac duo vectes &longs;ibi inuicem obuer­<lb/>&longs;i, & cóntra conantes reperientur, quo­<lb/>rum <expan abbr="vtiq;">vtique</expan> fulcimenta &longs;unt partes &longs;cin­<lb/>dendi corporis vtrinque con&longs;titutæ vt <lb/>GH, quibus intrando cuneus innititur. </s> <s id="N11E92">Onera verò &longs;unt re­<lb/><figure id="id.005.01.070.2.jpg" xlink:href="005/01/070/2.jpg"/><lb/>reliquæ eiu&longs;dem corporis partes <lb/>&longs;ucce&longs;siuè dimouend&etail;, & adinui­<lb/>cem &longs;eparándæ per aciem intran­<lb/>tem vbi E, vt in propo&longs;ita figu<lb/>ra e&longs;t l, & K. <!-- KEEP S--></s> <s id="N11EA6">Nam pars vbi K <lb/>e&longs;t onus re&longs;pectu vectis CE in­<lb/>nixæ in G; & pars vbi I, e&longs;t <lb/>onus re&longs;pectu vectis DE innixæ <lb/>in H. <!-- KEEP S--></s> <s id="N11EB2">Et extrema in quibus ap­<lb/>plicatur potentia &longs;unt initia ip&longs;o­<lb/>rum laterum ex parte ba&longs;is vbi <lb/>fit tota percu&longs;&longs;io, nempe vbi C <lb/>& D, quæ omnia aperti&longs;&longs;imè <lb/>citata quæ&longs;tione amplius con&longs;ta­<lb/>bunt. </s> </p> <pb pagenum="63" xlink:href="005/01/071.jpg"/> <p id="N11EC5" type="head"> <s id="N11EC7">DE COCHLEA.</s> </p> <p id="N11ECA" type="main"> <s id="N11ECC">Cochlea in&longs;trumentum e&longs;t veluti com­<lb/>po&longs;itum ex cuneo, & cylindro, &longs;eu e&longs;t &longs;tria­<lb/>tus quidam cylindrus &longs;trigas habens admo­<lb/>dum helicis &longs;pirulatim circumuolutas, cuius <lb/>vertigine pondera helici <lb/><figure id="id.005.01.071.1.jpg" xlink:href="005/01/071/1.jpg"/><lb/>congruè applicata, facillimè mouentur. <lb/></s> <s id="N11EE0">Exemplum &longs;it erectus cylindrus AB, <lb/>cuius helices, vel &longs;trigæ circumuolutæ, <lb/>&longs;int CD, EF; manubrium verò cylin­<lb/>dri G. <!-- KEEP S--></s> <s id="N11EEA">Etenim &longs;i in principio helicis <lb/>vbi C, onus congruè applicetur, vt <lb/>pila &longs;uper&longs;ignata H; ita tamen vt ex <lb/>aduer&longs;o non po&longs;&longs;it moueri, ni&longs;i &longs;uper <lb/>rectam IK, qua&longs;i intercepta inter cy­<lb/>lindrum & planum quoddam paralle­<lb/>lum cylindro; ab&longs;que dubio, ad cir­<lb/>cumuolutionem manubrij totiu&longs;que <lb/>cylindri, pondus H paulatim a&longs;cendet <lb/>ex C ad D, deinde ad E & F, & &longs;ic <lb/>deinceps. </s> </p> <p id="N11F01" type="main"> <s id="N11F03">Idemque pote&longs;t exemplificari in. <lb/></s> <s id="N11F07">alia ip&longs;ius cochleæ figura æquidi&longs;tantis <lb/>ab horizonte, vt AB, &longs;i apponatur <lb/>illi onus CD, tanquam cylindri con­<lb/>caui ac &longs;triati, qui & Tylum à Pappo, & alijs Mechanicis, <lb/><figure id="id.005.01.071.2.jpg" xlink:href="005/01/071/2.jpg"/><pb pagenum="64" xlink:href="005/01/072.jpg"/>& Cochleæ fœmina vulgò appellatur. </s> <s id="N11F1B">Nam ad conuer&longs;io­<lb/>nem manubrij totiu&longs;que cylindri &longs;uper proprium axem, <lb/>mouebitur etiam ip&longs;um Tylum CD. <!-- KEEP S--></s> <s id="N11F23">Quæ omnia fusè Gui­<lb/>dus Vbaldus demon&longs;trat. </s> <s id="N11F28">Ex cuius doctrina illud tandem <lb/>hic relinquitur adnotandum, ac &longs;imul in propo&longs;ito conclu­<lb/>dendum, Cochleæ helices, aliud non e&longs;&longs;e, quàm latus <lb/>cunei circa idem cylindrum iterum atque iterum circumuo­<lb/>lutum. </s> <s id="N11F33">Vnde apparet quomodo etiam cochlea reducatur <lb/>ad vectem; nimirum eodem pror&longs;us pacto, quo cuneus, vt <lb/>latius ip&longs;e pro&longs;equitur. </s> </p> <p id="N11F3A" type="head"> <s id="N11F3C"><emph type="italics"/>De Centro grauitatis <expan abbr="naturaliq.">naturalique</expan> mobilitate <lb/>grauium, & leuium.<emph.end type="italics"/></s> </p> <p id="N11F49" type="head"> <s id="N11F4B">ADDITIO SECVNDA.<!-- KEEP S--></s> </p> <p id="N11F4F" type="main"> <s id="N11F51">Po&longs;t con&longs;iderationem in&longs;trumentorum, ac machinarum <lb/>circuli naturam participantium, vt aptam ac debitam <lb/>eorum applicationem ad motum <expan abbr="grauiũ">grauium</expan>, & leuium cogno­<lb/>&longs;camus, con&longs;ideranda nobis erit mobilitas ip&longs;a tàm natu­<lb/>ralis, quàm præternaturalis, & artificio&longs;a illorum, cui ada­<lb/>ptari debent in&longs;trumenta, & ad quam ex in&longs;tituto ordinan­<lb/>tur. </s> <s id="N11F64">Cumque naturalis mobilitas grauium &longs;it penes cen­<lb/>trum grauitatis illorum, aliquid primò dicendum occurrit <lb/>de centro grauitatis in communi, vt quàm breui&longs;&longs;imè quæ <lb/>nece&longs;&longs;aria &longs;unt ad intelligentiam præfatæ motionis expe­<lb/>diantur. </s> </p> <p id="N11F6F" type="main"> <s id="N11F71"><arrow.to.target n="marg14"/> Centrum igitur grauitatis vniu&longs;cuiu&longs;que corporis iuxta <lb/>doctrinam Heronis, ac Pappi Alexandrini, e&longs;t punctum il­<lb/>lud intra po&longs;itum, à quo &longs;i ip&longs;um corpus graue &longs;u&longs;pendatur, <lb/>vel etiam &longs;u&longs;pen&longs;um feratur, <expan abbr="eãdem">eandem</expan> &longs;emper &longs;uarum partium <lb/>&longs;eruat po&longs;itionem quippe quæ in ip&longs;a &longs;u&longs;pen&longs;ione, aut latio­<lb/>ne corporis minimè circumuertuntur, cum vndique &longs;int <lb/>æqualium momentorum. </s> <s id="N11F87">Quod præclarè explicat Federi­<lb/>cus Commandinus. </s> <s id="N11F8C">Si enim, inquit, per tale centrum du-<pb pagenum="65" xlink:href="005/01/073.jpg"/>catur planum, figuram ip&longs;ius corporis quomodocunque<arrow.to.target n="marg15"/> &longs;e­<lb/>cans, &longs;emper in partes æqueponderantes ip&longs;am diuidet, <lb/>quamuis aliquando &longs;int inæqualis dimentionis. </s> <s id="N11F9C">Porrò in <lb/>diui&longs;ione corporis per eius centrum grauitatis, partes diui­<lb/>&longs;æ non &longs;emper &longs;unt eiu&longs;dem magnitudinis, &longs;eu dimentionis, <lb/>&longs;unt tamen eiu&longs;dem ponderis, & grauitatis, vt Guidus<arrow.to.target n="marg16"/> Vbal­<lb/>dus &longs;atis demon&longs;trat. </s> <s id="N11FAB">Quod &longs;anè, vt idem animaduertit, in­<lb/>telligendum e&longs;t de partibus mente tantum diui&longs;is, non au­<lb/>tem re, ac &longs;eor&longs;um con&longs;titutis, vt quæ ab inuicem &longs;eiunctæ <lb/>ponderantur in libra: Cum alia tunc &longs;it ratio grauitandi, <lb/>iuxta &longs;cilicet propriam magnitudinem maiorem, aut mino­<lb/>rem, quæ in propo&longs;ito quando partes coniunctæ &longs;unt com­<lb/>pen&longs;atur à po&longs;itione, ac &longs;itu vnius re&longs;pectu alterius iuxta di­<lb/>&longs;tantiam à centro, à quo totum corpus &longs;u&longs;penditur. </s> </p> <p id="N11FBC" type="margin"> <s id="N11FBE"><margin.target id="marg14"/>Lib.8. Me­<lb/>them. <!-- REMOVE S-->col­<lb/>lection.</s> </p> <p id="N11FC9" type="margin"> <s id="N11FCB"><margin.target id="marg15"/>Lib. de <expan abbr="C&etilde;-tro">Cen­<lb/>tro</expan> grauit. <lb/></s> <s id="N11FD7">&longs;olidorum.</s> </p> <p id="N11FDA" type="margin"> <s id="N11FDC"><margin.target id="marg16"/>In primum <lb/>l.b. </s> <s id="N11FE3"><expan abbr="Aequi-põder">Aequi­<lb/>ponder</expan>. <!-- REMOVE S-->Ar­<lb/>chimedis. <lb/></s> <s id="N11FF0">propo&longs;<gap/>lt.</s> </p> <p id="N11FF5" type="main"> <s id="N11FF7">Quapropter &longs;i punctum <lb/>A fuerit centrum grauita­<lb/><figure id="id.005.01.073.1.jpg" xlink:href="005/01/073/1.jpg"/><lb/>tis corporis BCD <expan abbr="quo-modocumq;">quo­<lb/>modocumque</expan> diui&longs;i per <expan abbr="pla-nã">pla­<lb/>nam</expan> EF tran&longs;euntem per ip­<lb/>&longs;ummet centrum, atque <lb/>idem corpus ex eodem <lb/>puncto &longs;u&longs;penderetur, cer­<lb/>tè quo ad po&longs;itionem ac <lb/>di&longs;po&longs;itionem &longs;uarum par­<lb/>tium inuariatum omnino maneret; ita vt nullo pacto ip&longs;um <lb/>B, ac D verterentur circa punctum A tanquam circa cen­<lb/>trum, &longs;ed eadem qua prius po&longs;itione manerent, &longs;iue pars <lb/>BEFC æqualis dimentionis inueniretur parti EDF, &longs;iue <lb/>inæqualis: &longs;emper enim &longs;ic coniunctæ æqueponderaret, e&longs;­<lb/>&longs;entque æqualium momentorum. </s> <s id="N12026">Cumque in his, quæ &longs;u­<lb/>&longs;penduntur ex aliquo puncto, vel etiam &longs;ic &longs;u&longs;pen&longs;æ ferun­<lb/>tur non detur motus circumuolutionis ab&longs;que exuperantia <lb/>alterius partis eorum, nec vna po&longs;&longs;it aliam &longs;uperare ni&longs;i per <lb/>exce&longs;&longs;um ponderis ip&longs;ius; hinc e&longs;t, vt immotæ ambæ ip&longs;æ <lb/>partes per&longs;euerarent tanquam in æquilibrio con&longs;titutæ. <lb/></s> <s id="N12034">Idemque contingeret quocunque alio modo ip&longs;um corpus <pb pagenum="66" xlink:href="005/01/074.jpg"/>&longs;u&longs;pen&longs;um, aut etiam latum à principio con&longs;titueretur. </s> </p> <p id="N1203C" type="main"> <s id="N1203E">Quod &longs;i contra definitionem, &longs;eu de&longs;criptionem tradi­<lb/>tam afferatur, multa dari po&longs;&longs;e corpora talis figuræ, vt cen­<lb/>trum grauitatis illorum non &longs;it intra, &longs;ed extra, quemadmo­<lb/>dum exempli gratia in rota AB cuius quidem centrum <lb/>e&longs;&longs;et in C. <!-- KEEP S--></s> <s id="N1204A">Sicut etiam in corpore irregulari DE cuius <lb/><figure id="id.005.01.074.1.jpg" xlink:href="005/01/074/1.jpg"/><lb/>centrum e&longs;&longs;et in F. <!-- KEEP S--></s> <s id="N12056">Occurrit Guidus Vbaldus dicens, etiam <lb/>prædicta centra intra figuram e&longs;&longs;e quatenus verè continen­<lb/>tur ab ambitu eiu&longs;dem figuræ ip&longs;orum corporum. </s> </p> <p id="N1205D" type="main"> <s id="N1205F">His autem &longs;ic &longs;tabilitis de centro grauitatis, dicendum <lb/>e&longs;t naturalem mobilitatem grauium, & leuium re&longs;pectiuè <lb/>(hoc e&longs;t corporum magis, aut minus grauium, vt explicui­<lb/>mus) e&longs;&longs;e innatam quandam aptitudinem, ac propen&longs;ionem <lb/>ad motum deor&longs;um ex principio intrin&longs;eco tum actiuo, tum <lb/>pa&longs;&longs;iuo per rectam lineam, quæ centrum grauitatis ip&longs;ius <lb/>grauis, <expan abbr="centrumq.">centrumque</expan> mundi connectit. </s> <s id="N12072">Id quod aperti&longs;&longs;imè <lb/>con&longs;tabit con&longs;ideranti graue quodcumque &longs;eclu&longs;o omni <lb/>impedimento, ac detentione, &longs;tatim &longs;uo pondere, & ex &longs;e <lb/>centrum vniuer&longs;i expetere, nec vnquam quie&longs;cere donec <lb/>ad illud &longs;i fieri po&longs;&longs;et, perueniat. </s> </p> <p id="N1207D" type="main"> <s id="N1207F">Diximus autem huiu&longs;cemodi aptitudinem e&longs;&longs;e ex prin­<lb/>cipio intrin&longs;eco tum actiuo tum pa&longs;&longs;iuo; nam id per quod <lb/>grauia formaliter con&longs;tituuntur apta, & in actu primo ad <lb/>motum localem deor&longs;um, non modò e&longs;t potentia pa&longs;&longs;iua <lb/>ip&longs;is innata, &longs;icut cuilibet corpori ad recipiendum talem <lb/>motum, &longs;iue producatur à &longs;e ip&longs;o &longs;iue ab alio: &longs;ed præcipuè <pb pagenum="67" xlink:href="005/01/075.jpg"/>e&longs;t intrin&longs;eca ip&longs;a grauitas, quæ tanquam proprium ope­<lb/>randi principium e&longs;t illis ratio, vt moueantur deor&longs;um, &longs;eu <lb/>forma qua in &longs;e &longs;eclu&longs;is impedimentis, talem motum pro­<lb/>ducunt. </s> <s id="N12097">Quod optimè expre&longs;&longs;it Ari&longs;toteles lib. 8. Phy&longs;ic. <lb/><!-- REMOVE S-->tex. <!-- REMOVE S-->32. & lib. 1. de Cœlo, tex. <!-- REMOVE S-->17. & lib. 4. tex. <!-- REMOVE S-->6. Ratio au­<lb/>tem e&longs;t manife&longs;ta, quia &longs;en&longs;u con&longs;tat, efficaciam, ac celeri­<lb/>tatem in motu deor&longs;um cre&longs;cere cre&longs;cente grauitate cor­<lb/>poris, ac minui ad diminutionem illius (vt idem Philo&longs;o­<lb/>phus ob&longs;eruauit 1. de Cœlo tex. <!-- REMOVE S-->89.) quod non po&longs;&longs;et con­<lb/>tingere &longs;i in ip&longs;o corpore graui grauitas non e&longs;&longs;et propria <lb/>cau&longs;a effectiua ip&longs;ius motus, quæ &longs;imul cum effectu cre&longs;ce­<lb/>ret, ac decre&longs;ceret. </s> <s id="N120B3">Sicut calor, qui dum intenditur, aut re­<lb/>mittitur, efficacius aut remi&longs;&longs;ius operatur, <expan abbr="maioremq.">maioremque</expan> aut <lb/>minorem calefactionis motum producit, eo quod &longs;imiliter <lb/>e&longs;t ratio formalis calefaciendi, &longs;icut grauitas &longs;e deor&longs;um <lb/>mouendi. </s> <s id="N120C2"><expan abbr="Nullumq.">Nullumque</expan> e&longs;t inconueniens, idem corpus e&longs;&longs;e <lb/>po&longs;&longs;e mouens & motum, cum in corpore graui &longs;it potentia <lb/>receptiua motus, & grauitas, quæ e&longs;t <expan abbr="pot&etilde;tia">potentia</expan> effectiua illius. </s> </p> <p id="N120D0" type="main"> <s id="N120D2">Diximus verò grauia moueri deor&longs;um per <expan abbr="rectã">rectam</expan> lineam, <lb/>quæ centrum grauitatis ip&longs;orum, <expan abbr="centrumq.">centrumque</expan> mundi conne­<lb/>ctit: Nam &longs;en&longs;u pariter con&longs;tat, illa non tendere ad ip&longs;um <lb/>mundi centrum per lineam aliquam obliquam, neque per <lb/>lineam rectam, quæ ab extremo quoddam, vel quauis alia <lb/>parte ip&longs;ius ad mundi centrum extendatur, &longs;ed per <expan abbr="eã">eam</expan>, quam <lb/>diximus <expan abbr="lineã">lineam</expan>, quæ ab eius centro grauitatis rectà ad mun­<lb/>di centrum propendet. </s> <s id="N120F3">Omnis enim grauitas cuiu&longs;que <lb/>grauis ita in ip&longs;o grauitatis centro colligitur, & coacerua­<lb/>tur, vt extra ip&longs;um nihil grauitare propemodum in corpori­<lb/>bus videatur: <expan abbr="proindeq.">proindeque</expan> non ni&longs;i ip&longs;omet centro rectà deor­<lb/>&longs;um eadem corpora ferri con&longs;picimus naturali propen&longs;io­<lb/>ne. </s> <s id="N12104">Quo pariter fit, vt &longs;i aliundè quàm ab ip&longs;ius grauitatis <lb/>centro graue aliquod &longs;u&longs;pendatur, &longs;tatim grauitatis centro <lb/>deor&longs;um tendente conuertatur, nec manere vnquam po&longs;&longs;it <lb/>donec ip&longs;um grauitatis centrum &longs;ub puncto &longs;u&longs;pen&longs;ionis per <lb/>lineam horizonti perpendicularem con&longs;tituatur. </s> <s id="N1210F">Quando­<lb/>quidem tunc idem e&longs;t, ac &longs;i corpus per ip&longs;ummet grauita­<pb pagenum="68" xlink:href="005/01/076.jpg"/>tis centrum &longs;u&longs;penderetur, cum per eandem lineam ei li­<lb/>ceat grauitare, vt latius ac rectè pro&longs;equitur Guidus Vbal­<lb/>dus loco citato. </s> </p> <p id="N1211D" type="head"> <s id="N1211F"><emph type="italics"/>De præternaturali, & artificio&longs;a mobilitate <lb/>grauium, & leuium.<emph.end type="italics"/></s> </p> <p id="N12128" type="head"> <s id="N1212A">ADDITIO TERTIA.<!-- KEEP S--></s> </p> <p id="N1212E" type="main"> <s id="N12130">Iam verò præternaturalis mobilitas grauium, & leuium <lb/>in eo relinquitur con&longs;i&longs;tere, quod e&longs;t, ip&longs;a grauia, & le­<lb/>uia &longs;ecundum quamcumque po&longs;itionem, etiam repugnanti­<lb/>bus naturæ legibus, moueri po&longs;&longs;e arte ac violentia, à princi­<lb/>pio extrin&longs;eco: ita tamen vt <expan abbr="quandoq.">quandoque</expan> eadem grauitas in­<lb/>trin&longs;eca, quæ &longs;uperatur à violentia, non parum ad &longs;e ip&longs;am <lb/>euincendam, & ad &longs;ui motionem præternaturalem, & artifi­<lb/>cio&longs;am augendam concurrat. </s> </p> <p id="N12145" type="main"> <s id="N12147">Con&longs;tat enim hoc cum aperta deductione ex dictis de <lb/>mobilitate naturali, tùm clara ac patenti experientia; <lb/>ita vt nulla ferè indigeat probatione, aut explicatione, præ­<lb/>&longs;ertim in doctrina Ari&longs;totelis, qui quantum attinet ad prin­<lb/>cipium extrin&longs;ecum, à quo prouenire diximus præternatu­<lb/>ralem motionem, cum 8 Phy&longs;icor. <!-- REMOVE S-->tex. <!-- REMOVE S-->33. dixi&longs;&longs;et: Omnia, <lb/>quæ mouentur, aut natura moueri, aut præter naturam, ac <lb/>violentia; mox addit: Et quæ vi & præter naturam, omnia <lb/>à quodam, & ab alio. </s> <s id="N1215E">Iuxta commune illud pronuntiatum <lb/>à &longs;e prius traditum, & ab omnibus receptum nimirum, om­<lb/>ne quod mouetur, ab alio moueri. </s> <s id="N12165">Quod quippè loquendo <lb/>&longs;altem de motu præternaturali in rebus inanimatis, e&longs;t ir­<lb/>refragabile. </s> </p> <p id="N1216C" type="main"> <s id="N1216E">Illud tamen apud nonnullos adhuc non e&longs;t omnino ex­<lb/>ploratum, ac non paruam habet difficultatem, quo videli­<lb/>cet pacto violentia ip&longs;a corporibus ab extrin&longs;eco inferatur; <lb/>quauè ratione, eadem corpora po&longs;tquam ab impul&longs;ore, vel <lb/>proijciente rece&longs;&longs;erint, ex &longs;e præternaturaliter moueantur. <pb pagenum="69" xlink:href="005/01/077.jpg"/>Quod cum partim ad merè phy&longs;icam &longs;peculationem perti­<lb/>neat in 7. & 8. de phy&longs;ico auditu; partim verò infra cum <lb/>Ari&longs;totele quæ&longs;t. </s> <s id="N12182">32. & 33. explicandum &longs;it, hìc non erit <lb/>di&longs;cutiendum, &longs;ed tantum ex dicendis, ac probandis &longs;uppo­<lb/>nere oportet, nullam vnquam inferri po&longs;&longs;e violentiam per <lb/>motum localem ab&longs;que productione, ac impre&longs;&longs;ione quali­<lb/>tatis cuiu&longs;dam in ip&longs;o mobili, quæ communiter appellari &longs;o­<lb/>let impetus &longs;iue impul&longs;us, ac de qua &longs;æpe nobis redibit &longs;er­<lb/>mo in ijs quæ&longs;tionibus. </s> </p> <p id="N12191" type="main"> <s id="N12193">Diximus autem grauitatem <expan abbr="quandoq.">quandoque</expan> ad &longs;ui motionem <lb/>violentam concurrere, quia cum deor&longs;um magna vi ponde­<lb/>ra extruduntur, vis illata, & impetus incu&longs;&longs;us, grauitate mo­<lb/>bilis intenditur, & augetur, vt quæ&longs;t. </s> <s id="N121A0">32. probabitur. </s> <s id="N121A3">Vnde <lb/>licet quoad velocitatem, & modum tunc motus ip&longs;e deor­<lb/>&longs;um <expan abbr="cõ&longs;tituatur">con&longs;tituatur</expan> præternaturalis, ad eum tamen grauitas ip­<lb/>&longs;a non minus, ac impetus concurrit. </s> <s id="N121B0">Quod contra &longs;e habet <lb/>cum &longs;ur&longs;um, vel ad latera graue transfertur; quia grauitas <lb/>&longs;icut &longs;emper tendit deor&longs;um, ita <expan abbr="cuicumq;">cuicumque</expan> alio motui &longs;em­<lb/>per ob&longs;i&longs;tit, quamuis propriè non contrarietur virtuti, à qua <lb/>talis motus procedit, nec &longs;it incompo&longs;&longs;ibilis cum illa in eo­<lb/>dem &longs;ubiecto, vt ibidem explicabitur. </s> </p> <p id="N121C1" type="main"> <s id="N121C3">Deinde moueri po&longs;&longs;e diximus ip&longs;a grauia <expan abbr="&longs;ecundũ">&longs;ecundum</expan> quam­<lb/>cumque po&longs;itionem atte, ac violentia; quia nec violentiæ <lb/>præ&longs;cripta e&longs;t po&longs;itio &longs;ecundum quam duntaxat mouere <lb/>valeat, non verò &longs;ecundum aliam, nec arti deficiunt præce­<lb/>pta, & in&longs;trumenta, quibus ita vis eis applicetur; vt quoquò <lb/>ver&longs;um, etiam contra naturæ leges grauia transferantur. </s> <s id="N121D4">Vn­<lb/>de pluribus, ac innumeris penè modis arte comparatis vio­<lb/>lentia pote&longs;t inferri. </s> <s id="N121DB">Quos tamen Ari&longs;toteles 7. Phy&longs;ic. <!-- REMOVE S-->tex. <lb/><!-- REMOVE S-->10. ad quatuor tantum reducit, iuxta quos to idem &longs;pecies <lb/>motus violenti con&longs;tituit: Quadrifariam, inquiens, moueri <lb/>quidquid ab alio per violentiam &longs;ecundum locum mouetur. <lb/></s> <s id="N121E8">Nimirum vel per Pul&longs;ionem, vel per Tractionem, vel per <lb/>Vectionem, vel per Vertiginem. </s> <s id="N121ED">Pul&longs;ionem autem di&longs;tin­<lb/>guit in Impul&longs;ionem, & Expul&longs;ionem. </s> <s id="N121F2">Impul&longs;ionem ait e&longs;&longs;e <lb/>cum pellens ita pellit, vt pul&longs;um non de&longs;erat, &longs;ed comite­<pb pagenum="70" xlink:href="005/01/078.jpg"/>tur: Expul&longs;ionem verò, tum vbi pepulit, pul&longs;um ip&longs;um re­<lb/>linquit, de quo genere e&longs;t proiectio. </s> <s id="N121FE">Tractionem deinde ait <lb/>e&longs;&longs;e motum trahentis non &longs;eparatum à motu eius, quod <lb/>trahitur: <expan abbr="ideoq.">ideoque</expan> e&longs;&longs;e motum ad &longs;e ip&longs;um, & ad alterum. </s> <s id="N12209">Ve­<lb/>ctionem verò e&longs;&longs;e motum per accidens; nam id quod vehi­<lb/>tur ex co mouetur, quia e&longs;t in eo, quod mouetur. </s> <s id="N12210">Quoniam <lb/>verò id quod vehit mouetur aut pul&longs;um, aut tractum, aut <lb/>vertigine actum, ex hoc infert, vt & Vectio tripliciter fieri <lb/>po&longs;sit, iuxta triplicem motum prædictum. </s> <s id="N12219">Denique Verti­<lb/>ginem ait e&longs;&longs;e motum compo&longs;itum ex tractione, & pul&longs;io­<lb/>ne. </s> <s id="N12220">Ad quas quippe quatuor &longs;pecies reuocari po&longs;&longs;unt aliæ <lb/>quam plures motiones præternaturales, ac violentæ, quibus <lb/>accommodata &longs;unt in&longs;trumenta, ac machinamenta, de qui­<lb/>bus Additione prima egimus, cunctaquè alia, quæ ex illis <lb/>con&longs;tantur, vel ad ea reducuntur. </s> </p> <p id="N1222B" type="main"> <s id="N1222D">Quamobrem præternaturalis mobilitas grauium, ac le­<lb/>nium pluries vocatur etiam artificio&longs;a. </s> <s id="N12232">Nam licet interdum <lb/>à cau&longs;is naturalibus, nulla interueniente hominum indu&longs;tria <lb/>aut violentia, vis aliqua corporibus inferatur, qua præterna­<lb/>turaliter ip&longs;a compelluntur moueri, vt cum ignitos lapides <lb/>è montibus quibu&longs;dam videmus erumpere, & in altum &longs;u­<lb/>&longs;tolli; vel ferrea corpora à magnete &longs;ur&longs;um attrahi, ac pen­<lb/>dentia &longs;u&longs;tineri. </s> <s id="N12241">Sæpius tamen corpora non ni&longs;i artificio&longs;a <lb/>violentia ex indu&longs;tria ip&longs;is illata præternaturaliter, vt dice­<lb/>bamus con&longs;tat moueri. </s> <s id="N12248">Ita vt etiam motus eorum præter­<lb/>naturales, qui ab aliqua cau&longs;a naturali oriuntur, <expan abbr="aliosq.">aliosque</expan> &longs;imi­<lb/>les, ad imitationem naturæ, ars ip&longs;a violentiam applicando, <lb/>augendo, minuendo, ac di&longs;tinguendo producat. </s> <s id="N12255">Vt per&longs;pi­<lb/>cuè ob&longs;eruare e&longs;t in motibus violentis &longs;ulfurei pulueris <lb/>virtute, ac artis magi&longs;terio productis ad euerrendas moles, <lb/>explodendas ingentes pilas, ac diruendas portas vrbium, <lb/>ac munitionum: nec non in motibus, qui aéris, vel aquæ <lb/>beneficio multimoda cum arte di&longs;po&longs;ito fiunt, ad nauium <lb/>admirabilem lationem, <expan abbr="earumq.">earumque</expan> cur&longs;us moderationem; & <lb/>ad tam varios machinarum &longs;e mouentium, &longs;eu &longs;piritalium <lb/>v&longs;us, de quibus &longs;crip&longs;it Hero, cum in iis omnibus ars natu-<pb pagenum="71" xlink:href="005/01/079.jpg"/>ram æmulando, vel eam comitando magnopere elucear, <lb/>nec minus ad ip&longs;am vim præternaturaliter inferendam con­<lb/>ducat. </s> </p> <p id="N12275" type="main"> <s id="N12277">Ad hanc igitur motionem artificio&longs;am, ac præternatura­<lb/>lem vniuer&longs;a facultas Mechaniça ordinatur, vt &longs;upra expli­<lb/>cuimus: quatenus mirabili &longs;uo magisterio rationabiliter per <lb/>cau&longs;as procedendo, docet quo pacto grauia cuncta, aut le­<lb/>uia po&longs;&longs;int &longs;ecundum omnem po&longs;itionem moueri, & cuius <lb/>virtute, quauè proportione illius ad pondus; in qua di&longs;tan­<lb/>tia, <expan abbr="quibusq.">quibusque</expan> adminiculis, machinis, & in&longs;trumentis, & id ge­<lb/>nus alia; quæ non parua ex parte con&longs;tabunt ex is, quæ <lb/>Ari&longs;toteles vltra &longs;uperius allata, & à nobis expo&longs;ita, in &longs;e­<lb/>quentibus quæ&longs;tionibus tradit. </s> <s id="N12290">Cum alias exacta, & pe­<lb/>culiaris vniu&longs;cuiu&longs;que grauis, aut leuis prout artificiosè mo­<lb/>ueri debeat con&longs;ideratio, ad di&longs;tinctas Mechanicæ facul­<lb/>tatis partes iam enumeratas, quas ip&longs;e Philo&longs;ophus non e&longs;t <lb/>aggre&longs;&longs;us; quippe qui vniuer&longs;alia duntaxat principia huius <lb/>admirabilis di&longs;ciplin&etail; in hac prima parte afferre &longs;tatuerit, <lb/>cau&longs;as po&longs;tea in &longs;ecunda parte allaturus eorum, quæ in &longs;e­<lb/>quentibus quæ&longs;tionibus proponuntur ad maiorem explica­<lb/>tionem, & applicationem eorundem principiorum, ex qui­<lb/>bus aliæ infinitæ penè conclu&longs;iones po&longs;&longs;unt deduci. </s> </p> <p id="N122A5" type="main"> <s id="N122A7">Sed illud hic &longs;ummopere animaduertendum putauimus <lb/><expan abbr="Archimed&etilde;">Archimedem</expan>, quem iure inter huius di&longs;ciplinæ parentes opti­<lb/>mos literæ omnes maxima cum laude commemorant, non <lb/>diuer&longs;a ab ijs, qu&etail; Ari&longs;toteles tradidit principia a&longs;&longs;ump&longs;i&longs;&longs;e, <lb/>ac in &longs;uis de æqueponderantibus libris protuli&longs;&longs;e, vt falsò <lb/>nonnulli commini&longs;cuntur; quin imò tradita ab ip&longs;o Philo&longs;o­<lb/>pho &longs;uppo&longs;ui&longs;&longs;e, & amplius, ad particularia de&longs;cendendo, <lb/>extendi&longs;&longs;e, ac planiora reddidi&longs;&longs;e, vt ingenuè fatetur Guidus <lb/>Vbaldus in Præfatione primi de æqueponderantibus libri <lb/><expan abbr="eiu&longs;d&etilde;">eiu&longs;dem</expan> Archimedis. <!-- KEEP S--></s> <s id="N122C3">Ari&longs;toteles enim (vt vel vno vtar exem­<lb/>plo) loquendo de motione circulati, ad quam reducuntur <lb/>penè omnes motiones, quæ mechanicis in&longs;trumentis, atque <lb/>artibus fiunt, præ&longs;tanti&longs;simum illud con&longs;tituit principium, <lb/>quæ &longs;unt in maiori à centro di&longs;tantia, maiorem quoque ha­<pb pagenum="72" xlink:href="005/01/080.jpg"/>bere virtutem ad motum, <expan abbr="velociusq.">velociusque</expan> moueri, vt &longs;upra vidi­<lb/>mus tex. <!-- REMOVE S-->6. Quod &longs;anè principium non &longs;olum admittit Ar­<lb/>chimedes, at que &longs;upponit, &longs;ed con&longs;equenter ad illud vlte­<lb/>rius inquirit, <expan abbr="tradiditq.">tradiditque</expan> quanto maior &longs;it virtus, quæ habe­<lb/>tur in maiori illa di&longs;tantia, <expan abbr="eamq">eamque</expan> ab ip&longs;ius di&longs;tantiæ pro­<lb/>portione indagando, recepti&longs;simum aliud fundamentum <lb/><arrow.to.target n="marg17"/> mechanicum &longs;tatuit, nimirum, it a &longs;e habere pondus ad pon­<lb/>dus, vt di&longs;tantia ad di&longs;tantiam à puncto vnde pondera &longs;u­<lb/>&longs;penduntur, permutata videlicet ratione, vt infra quæ&longs;t. </s> <s id="N122F0">3. <lb/>explicabitur. </s> <s id="N122F5">Cui fundamento tota Archimedis doctrina, <lb/><expan abbr="veraq.">veraque</expan> mechanica innititur contemplatio. </s> <s id="N122FD">Illud tamen an­<lb/>tea patefecerat Ari&longs;toteles in &longs;uis mechanicis, quæ&longs;t. </s> <s id="N12302">3. illis <lb/>verbis, quod igitur motum pondus ad mouens, longitudo <lb/>patitur ad longitudinem. </s> <s id="N12309">Quem locum miror non animad­<lb/>uerti&longs;&longs;e Guidum Vbaldum in confirmationem &longs;uæ <expan abbr="veræq.">veræque</expan> <lb/>&longs;ententiæ; cum planè animaduerti&longs;&longs;et Archimedem in con­<lb/>&longs;tituendis &longs;uis mechanicis po&longs;tulatis &longs;uppo&longs;ui&longs;&longs;e ea, quæ de <lb/>mechanicis principijs Philo&longs;ophus tradiderat. </s> <s id="N12318">Sed iam ad <lb/>exponendas ip&longs;ius Philo&longs;ophi quæ&longs;tiones accedamus. </s> </p> <p id="N1231D" type="margin"> <s id="N1231F"><margin.target id="marg17"/>Lib. 1. <lb/>Acqui<gap/> <expan abbr="õd">ond</expan>. <lb/></s> <s id="N1232D">p<gap/>opo&longs;it.6.</s> </p> <figure id="id.005.01.080.1.jpg" xlink:href="005/01/080/1.jpg"/> <pb pagenum="73" xlink:href="005/01/081.jpg"/> <p id="N1233B" type="head"> <s id="N1233D">SECVNDA PARS <lb/>MECHANICES <lb/>ARISTOTELIS STAGIRITAE <lb/>IN QVA PLVRES QVAESTIONES <lb/>continentur, ac &longs;oluuntur iuxta principia in <lb/>priori parte tradita.</s> </p> <p id="N1234A" type="main"> <s id="N1234C"><emph type="italics"/>Explicata vniuer&longs;ali doctrina principiorum, <lb/>ex quibus tanquam ex iactis fundamen­<lb/>tis inconficiendis demon&longs;trationibus omnis <lb/>mechanica &longs;tructura con&longs;urgit, particulares <lb/>quæ&longs;tiones Philo&longs;ophus proponit, in qua­<lb/>rum &longs;olutionibus ip&longs;a vniuer&longs;alis doctrina, <lb/>vt præmonuimus, applicatur.<emph.end type="italics"/></s> </p> <p id="N1235F" type="head"> <s id="N12361">Quæ&longs;tio Prima.</s> </p> <p id="N12364" type="main"> <s id="N12366">C<emph type="italics"/>vr autem maiores libræ exactio­<lb/>res &longs;unt minoribus, palam e&longs;t ex ijs. <lb/></s> <s id="N1236F">Spartum enim fit centrum, id <expan abbr="namq.">namque</expan> <lb/>manet. </s> <s id="N12374">Quod autem libræ vtrinque <lb/>e&longs;t, exeuntes à centro.<emph.end type="italics"/></s> </p> <p id="N1237B" type="main"> <s id="N1237D"><emph type="italics"/>Ab eodem igitur pondere citius mo­<lb/>ueri nece<32>e e&longs;t extremum libræ, quo <lb/>plus à &longs;parto di&longs;ce&longs;&longs;erit. </s> <s id="N12386">Et nonnulla <lb/>quidem in paruis libris impo&longs;ita non manife&longs;ta &longs;en&longs;ui &longs;unt <lb/>pondera: in magnis autem manife&longs;ta. </s> <s id="N1238D">Nihil enim prohibet <lb/>minorem moueri magnitudinem, quàm vt vi&longs;ioni &longs;it mani­<lb/>fe&longs;ta. </s> <s id="N12394">In magna autem libra idem pondus vi&longs;ibile efficit ma-<emph.end type="italics"/><pb pagenum="74" xlink:href="005/01/082.jpg"/><emph type="italics"/>gnitudo. </s> <s id="N123A0">Quædam verò manifesta quidem &longs;unt in vtri&longs;que, <lb/>&longs;ed multò magis in maioribus, quoniam multò maior inclina­<lb/>tionis fit magnitudo ab eodem pondere in maioribus. </s> <s id="N123A7">Quam­<lb/>obrem machinantur ÿ, qui purpuram vendunt. </s> <s id="N123AC">vt pendendo <lb/>defraudent, tum ad medium &longs;partum non ponentes, tum plum­<lb/>bum in alterutram libræ partem infundentes, aut ligni, quod <lb/>ad radicem vergebat, in eam, quam deferri volunt partem <lb/>con&longs;tituentes: aut &longs;i nodum habuerit. </s> <s id="N123B7">Ligni enim grauior il­<lb/>la est pars, in qua est radix. </s> <s id="N123BC">Nodus verò radix quædam e&longs;t.<emph.end type="italics"/></s> </p> <p id="N123C1" type="head"> <s id="N123C3">COMMENTARIVS.<!-- KEEP S--></s> </p> <p id="N123C7" type="main"> <s id="N123C9">Tanquam explorati&longs;&longs;imum &longs;upponitur hic ab Ari&longs;to. <lb/><!-- REMOVE S-->tele experimentum, maiores libras, exactiores e&longs;&longs;e <lb/>minoribus: hoc e&longs;t exactè magis o&longs;tendere pondus <lb/>grauium, quæ ponderantur, <expan abbr="eiu&longs;q.">eiu&longs;que</expan> differentias per motum <lb/>&longs;ur&longs;um, ac deor&longs;um, aut &longs;tatum &longs;uarum lancium. </s> <s id="N123D9"><expan abbr="Cau&longs;amq.">Cau&longs;amque</expan> <lb/>ip&longs;e &longs;tatim afferens, docet &longs;partum, quo &longs;u&longs;penditur libra, <lb/>&longs;eu trutinam quamlibet, &longs;ecundum eam partem, &longs;cilicet <lb/>quæ intra foramen bilancis exi&longs;tens in medio iugi, axis vi­<lb/>cem gerit, &longs;e habere tanquam centrum in circulo, quod per <lb/>motum circularem eiu&longs;dem circuli non mouetur: partes <lb/>autem ip&longs;ius iugi vtrinque productas, quæ & brachia nun­<lb/>cupantur, è quorum extremis lances propendunt, con&longs;titui <lb/>tanquam lineas à centro in peripheriam deductas, quæ cir­<lb/>ca idem centrum conuertantur, & aliquantulum per eleua­<lb/>tionem vnius, ac depre&longs;&longs;ionem alterius circumferantur, vt <lb/>videre e&longs;t in &longs;equenti figura. </s> <s id="N123F5">At, inquit, quò plus lineæ à <lb/>centro circuli di&longs;ce&longs;&longs;erint, eo magis, quamuis ab eadem vel <lb/>æquali virtute, valent moueri, maius nempe &longs;pacium eo­<lb/>dem tempore percurrendo, vt idemmet Ari&longs;toteles proba­<lb/>uerat. </s> <s id="N12400">Ergo idem pondus ab extremo libræ propendens <lb/>eò magis illam conuertere, aut mouere valebit, quò maior <lb/>fuerit ip&longs;a libra, &longs;eu quò longioribus brachijs con&longs;tabit. </s> <s id="N12407">Si­<lb/>quidem extremum vbi appenditur pondus, magis di&longs;tabit <lb/>à centro, <expan abbr="maioremq.">maioremque</expan> proinde portionem circuli eodem <pb pagenum="75" xlink:href="005/01/083.jpg"/>tempore, <expan abbr="eademq.">eademque</expan> vi peraget, vt per&longs;picuum e&longs;t in hac fi­<lb/>gura &longs;i brachia libræ AB protrahantur v&longs;que ad CD. <!-- KEEP S--></s> <s id="N1241E">Quia <lb/>nimirum, &longs;icut maio­<lb/><figure id="id.005.01.083.1.jpg" xlink:href="005/01/083/1.jpg"/><lb/>rem efficerent circu­<lb/>lum, videlicet conti­<lb/>nentem, maioremque <lb/>diametrum; ita maio­<lb/>rem arcum eorum ex­<lb/>trema percurrerent. <lb/></s> <s id="N12436">Nam quo tempore <lb/>ac vi A moueretur v&longs; <lb/>que ad F, ip&longs;um C <lb/>moueretur <expan abbr="v&longs;q;">v&longs;que</expan> ad E <lb/>Maior autem e&longs;t CE <lb/>quàm AF, eo quod <lb/>&longs;icut diameter ad dia­<lb/>metrum, ita portio ad <lb/>portionem circuli &longs;e <lb/>habeat. </s> <s id="N1244F">Cum igitur <lb/>facilius &longs;it cernere ac <lb/>di&longs;cernere, quod maius e&longs;t, quàm quod minus; &longs;equitur, eò <lb/>euidentius apparere motum libræ, quò maior fuerit ip&longs;a li­<lb/>bra: ac propterea per motum ip&longs;um maioris libræ exactius­<lb/>præponderantiam grauium, &longs;eu differentiam ponderis in­<lb/>dicati. </s> </p> <p id="N1245E" type="main"> <s id="N12460"><expan abbr="Atq;">Atque</expan> hinc euenire, ait Ari&longs;toteles, vt in paruis libris non­<lb/>nulla pondera &longs;en&longs;um omnino ferè lateant, quæ in magnis, <lb/>illi aperti&longs;&longs;imè innote&longs;cunt. </s> <s id="N1246A">Non quidem ex eo, quod ip&longs;a <lb/>pondera moueant magnas libras, non autem paruas; &longs;ed <lb/>quia motus ab ip&longs;is productus, cum maior &longs;it in maioribus, <lb/>facilius, ac euidentius à &longs;en&longs;u percipitur. </s> <s id="N12473">Vnde quæ mani­<lb/>fe&longs;ta &longs;unt in vtriu&longs;que libris, multo magis (vt idem inquit) <lb/>manife&longs;ta &longs;e præbent in meioribus, quoniam in illis multo <lb/>maior inclinatio cau&longs;atur ab eodem pondere. </s> <s id="N1247C">Id quod in <lb/>omnibus in&longs;trumentis verificatur, quæ ad men&longs;urandum de-<pb pagenum="76" xlink:href="005/01/084.jpg"/>&longs;eruiunt: Nam quo ampliora eò minus obtutum fallunt, & <lb/>euidentius men&longs;uratorum differentias manife&longs;tant. </s> </p> <p id="N12488" type="main"> <s id="N1248A">Denique ex ijs animaduertit Ati&longs;toteles modum, quo <lb/>nonnulli vendentes purpuram, vel crocum, aut aliud huiu&longs;­<lb/>modi, emptores defraudant. </s> <s id="N12491">Ita namque (vt ip&longs;e ait) con­<lb/>&longs;truunt libram, vt &longs;partum quo illa &longs;u&longs;penditur, &longs;eu axis cir­<lb/>ca quem illa conuertitur, non &longs;it pror&longs;us in medio iugi, ac <lb/>proinde vnum brachium illius, &longs;it longius altero, æquè ta­<lb/>men grauitet, vt tegatur deceptio. </s> <s id="N1249C">Infundunt enim plum­<lb/>bum in brachium, quod minorem habet longitudinem, vel <lb/>illud ex grauiori ligno conficiunt, vt puta nodo&longs;o, aut ad ra­<lb/>dicem vergente: & &longs;ic minorem habens longitudinem <lb/>æqueponderat habenti maiorem, <expan abbr="libraq.">libraque</expan> ip&longs;a haud quaquam <lb/>apparet vitio&longs;a &longs;iue iniu&longs;ta. </s> <s id="N124AD">Deinde verò mercem in eam <lb/>lancem imponunt, quæ ex longiori brachio pendet; vbi cer­<lb/>tè quodlibet pondus magis grauitare nece&longs;&longs;e e&longs;t, quàm in <lb/>oppo&longs;ita lance. </s> <s id="N124B6">Siquidem brachij extremum ex quo pen­<lb/>det, magis di&longs;tat a centro; <expan abbr="ideoq.">ideoque</expan> quamuis adulterinæ non <lb/>&longs;int <expan abbr="ponderũ">ponderum</expan> notæ, merces maioris ponderis putatur, quàm <lb/>reuera &longs;it, ac tanti ex fraude venditur. </s> <s id="N124C9">Vnde etiam &longs;i libra <lb/>lancibus vacuis æquilibrium demon&longs;tret, & æqualibus in <lb/>pondere, æqualia addantur, æquè illa ponderare non &longs;equi­<lb/>tur, dum æquè à centro libræ non di&longs;tant. </s> <s id="N124D2">Nàm ratione &longs;i­<lb/>tus quælibet additio ponderis po&longs;tea in ip&longs;is lancibus facta, <lb/>&longs;emper eandem &longs;eruare debet proportionem, vt magis gra­<lb/>uitet in loco di&longs;tantiori, quàm in propinquiori; vt exactius <lb/>adhuc con&longs;tare pote&longs;t ex Archimede in primo lib. <!-- REMOVE S-->Aeque­<lb/>ponderan. <!-- REMOVE S-->po&longs;tulat. </s> <s id="N124E3">2. & explicatione Guidi Vbaldi è Mar­<lb/>chionibus Montis ibidem ac tract. <!-- REMOVE S-->de libra prop. 6. <!-- KEEP S--></s> </p> <p id="N124EB" type="main"> <s id="N124ED">Illud tamen hic minimè prætereundum e&longs;t, non rectè <lb/>Blancanum, hunc Ari&longs;totelis locum expo&longs;ui&longs;&longs;e, <expan abbr="cũ">cum</expan> ex men­<lb/>te illius ait, purpurarios fraudulentos, plumbum in lancem <lb/>illam infundere in quam merces imponitur. </s> <s id="N124FA"><expan abbr="Quãdoquidem">Quandoquidem</expan> <lb/>&longs;i ita e&longs;&longs;et, lanx illa maiorem longitudinem brachij non re­<lb/>quireret ad magis grauitandum. </s> <s id="N12504">Quod &longs;i vtroque ex capi-<pb pagenum="77" xlink:href="005/01/085.jpg"/>te magis grauitaret, nempe ex plumbo adiuncto, & ex ma­<lb/>iori longitudine brachij, nunquam libra ponderibus, ac mer­<lb/>cibus vacua, in æquilibrio po&longs;&longs;et con&longs;titui, fed &longs;atis apertè <lb/>huiu&longs;modi lanx &longs;emper deor&longs;um tenderet, altera verò &longs;ur­<lb/>&longs;um; <expan abbr="ideoq.">ideoque</expan> nulla ex hoc oriretur deceptio, <expan abbr="nullaq.">nullaque</expan> fraus, <lb/>quæ ex deceptione con&longs;equitur. </s> <s id="N1251E">Quando igitur Ari&longs;tote­<lb/>les ait, purpurarios plumbum, vel quid &longs;imile in eam, quam <lb/>deferri volunt partem con&longs;tituere, intelligendus e&longs;t de par­<lb/>te, &longs;eu de brachio libræ minori, quod certè &longs;ur&longs;um a&longs;cende­<lb/>ret ad de&longs;cen&longs;um maioris, ac deferri non po&longs;&longs;et ad con&longs;ti­<lb/>tuendum Aequilibrium, ni&longs;i &longs;imilibus adiumentis quantum <lb/>opus e&longs;t deprimeretur; vt rectè etiam notat Cardanus lib. <lb/><!-- REMOVE S-->1. de principijs prope finem. </s> </p> <p id="N12530" type="head"> <s id="N12532">Quæ&longs;tio Secunda.</s> </p> <p id="N12535" type="main"> <s id="N12537">C<emph type="italics"/>vr &longs;iquidem cur&longs;um &longs;uerit &longs;partum, quan­<lb/>do deor&longs;um lato pondere qui&longs;piam id amouet, <lb/>rur&longs;um a&longs;cendit libra: &longs;i autem deor&longs;um con­<lb/>&longs;titutum fuerit, non a&longs;cendit, &longs;ed manet? </s> <s id="N12543">An <lb/>quia &longs;ur&longs;um quidem &longs;parto existente plus li­<lb/>bræ extra perpendiculum fit: quare nece&longs;&longs;e <lb/>e&longs;t deor&longs;um ferri id quod plus e&longs;t, donec a&longs;cendat, quæ bifa­<lb/>riam libram diuidit, ad ip&longs;um perpendiculum, cùm onus in­<lb/>cumbat ad libræ partem &longs;ur&longs;um raptum.<emph.end type="italics"/></s> </p> <p id="N12554" type="main"> <s id="N12556"><emph type="italics"/>Sit libra recta, vbi BC, &longs;partum autem AD. <!-- KEEP S--></s> <s id="N1255C">Hoc igi­<lb/>tur deor&longs;um proiecto perpendiculum erit, vbi ADM. <!-- KEEP S--></s> <s id="N12562">Si igi­<lb/>tur in ip&longs;o B ponatur onus, B quidem erit, vbi E, C autem <lb/>vbi H s quamobrem ea, quæ bifariam libram &longs;ecat, primò <lb/>quidem erit DM ip&longs;ius perpendiculi: incumbente autem <lb/>onere DG, quare libræ ip&longs;ius vbi EH, quòd extra perpen­<lb/>diculum e&longs;t AM, vbi e&longs;t PQ, maius e&longs;i dimidio. </s> <s id="N12571">Si igitur <lb/>amoueatur onus ab ip&longs;o E, nece&longs;&longs;e e&longs;t deor&longs;um ferri H mi­<lb/>nus enim e&longs;t E. <!-- KEEP S--></s> <s id="N12579">Siquidem igitur &longs;ur&longs;um habuerit &longs;partum,<emph.end type="italics"/><pb pagenum="78" xlink:href="005/01/086.jpg"/><emph type="italics"/>rur&longs;um propter hoc a&longs;cendit libra. </s> <s id="N12585">Si autem deor&longs;um fuerit <lb/>in quod &longs;ub&longs;tat, contrarium facit. </s> <s id="N1258A">Plus enim dimidio fit li­<lb/>bræ, quæ deor&longs;um e&longs;t pars, quàm quod per pendiculum &longs;ecet: <lb/>quapropter non a&longs;cendit. </s> <s id="N12591">Eleuata enim pars leuior e&longs;t.<emph.end type="italics"/></s> </p> <p id="N12596" type="main"> <s id="N12598"><emph type="italics"/>Sit libra recta vbi NG: perpendiculum autem KLM. <lb/><!-- KEEP S--></s> <s id="N1259F">Bifariam igitur &longs;ecatur KG. </s> <s id="N125A2">Impo&longs;ito autem onere in ip&longs;o <lb/>N, erit quidem N vbi O, ip&longs;um autem G, vbi R, KL <lb/>autem vbi LP. </s> <s id="N125A9">Quare maius e&longs;t KO, quam LR, ip&longs;o <lb/>PKL. </s> <s id="N125AE">Et ablato igitur onere, nete<32>e e&longs;t manere; incumbit <lb/>enim ceu onus exce&longs;&longs;us medietatis eius vbi e&longs;t F.<emph.end type="italics"/><!-- KEEP S--></s> </p> <p id="N125B6" type="head"> <s id="N125B8">COMMENTARIVS.<!-- KEEP S--></s> </p> <p id="N125BC" type="main"> <s id="N125BE">Cvm axis vel &longs;partum, quod gerit vicem axis, & quo <lb/>&longs;u&longs;penditur libra, locari po&longs;&longs;it tum &longs;upra, tum infra <lb/>iugum ip&longs;ius libræ, quærit modo Ari&longs;toteles quid <lb/>cau&longs;æ &longs;it, vt &longs;i locetur &longs;upra, appo&longs;ito in alteram lancem <lb/>pondere, de&longs;cendat quippe illa, &longs;ed eo amoto ex &longs;e iterum <lb/>in pri&longs;tinum locum a&longs;cendat: &longs;i verò axis locetur infra, lanx <lb/>illa maneat, & non reuertatur. </s> </p> <p id="N125CD" type="main"> <s id="N125CF">Porrò prima huius quæ&longs;tionis pars &longs;i phy&longs;icè con&longs;idere­<lb/>tur, non paruam videtur inuoluere difficultatem. </s> <s id="N125D4">Etenim <lb/>nullum apparet agens, à quo talis a&longs;cen&longs;us depre&longs;&longs;æ lancis <lb/>procedat. </s> <s id="N125DB">Cum enim quodlibet graue tendat deor&longs;um, cau­<lb/>&longs;a huiu&longs;modi eleuationis, & a&longs;cen&longs;ionis non pote&longs;t e&longs;&longs;e for­<lb/>ma aliqua intrin&longs;eca; nec pro extrin&longs;eca a&longs;&longs;ignari pote&longs;t <lb/>alia, ni&longs;i grauitas alterius lancis, qua &longs;cilicet illa de&longs;cen­<lb/>dendo, hanc faciat a&longs;cendere. </s> <s id="N125E6">Verum cum vtraque lanx <lb/>æqualis molis, & grauitatis con&longs;tituatur, nequit altera alteri <lb/>præponderare, <expan abbr="de&longs;cen&longs;uq.">de&longs;cen&longs;uque</expan> proprio eam eleuare. </s> <s id="N125F1">Simile <lb/><expan abbr="namq.">namque</expan> in inten&longs;ione per eandem qualitatem agere non po­<lb/>te&longs;t in &longs;imile; cum omnis actio procedere debeat ab inæ­<lb/>quali proportione, vt cum Ari&longs;totele &longs;entiunt omnes Phi­<lb/>lo&longs;ophi 1. de generat. </s> <s id="N125FF">tex. <!-- REMOVE S-->48. </s> </p> <pb pagenum="79" xlink:href="005/01/087.jpg"/> <p id="N12608" type="main"> <s id="N1260A">Nihilominus etiam phy&longs;icis principijs inhærendo ex ijs, <lb/>quæ Ari&longs;toteles in præ&longs;entibus docet, optimè huic difficul­<lb/>tati pote&longs;t occurri, <expan abbr="primaq.">primaque</expan> pars quæ&longs;tionis re&longs;olui. </s> <s id="N12615">Nam <lb/>&longs;uppo&longs;ito, quod pars iugi, qu&etail; eleuatur di&longs;tinguatur à parte, <lb/>quæ deprimitur per lineam perpendicularem cadentem à <lb/>centro circa quod conuertitur libra, &longs;eu ab axe, vel &longs;parto <lb/>ad centrum terræ, vt sen&longs;u con&longs;tabit in &longs;equenti figura: &longs;i­<lb/>quidem quidquid libræ e&longs;t ad leuam, v.g. <!-- REMOVE S-->talis lineæ, rapi­<lb/>tur deor&longs;um; quidquid verò e&longs;t ad dexteram attollitur &longs;ur­<lb/>&longs;um: hoc inquam &longs;uppo&longs;ito, ait Ari&longs;toteles, quod &longs;i libra <lb/>axem, &longs;eu centrum habeat &longs;upra iugum, ac per depre&longs;&longs;io­<lb/>nem alterius partis illius, altera eleuetur, plus quippe libræ <lb/>e&longs;&longs;et ex parte eleuata, quàm ex parte depre&longs;&longs;a: <expan abbr="proindeq.">proindeque</expan> <lb/>pars eleuata nece&longs;&longs;eriò de&longs;cendet, & ad de&longs;cen&longs;um illius, <lb/>&longs;equitur depre&longs;&longs;am a&longs;cendere, quou&longs;que vtraque con&longs;titua­<lb/>tur æqualis, ac reuertatur ad æquilibrium. </s> <s id="N12634">Id quod ita &longs;e <lb/>habere &longs;ic probat. </s> <s id="N12639">Nam &longs;i iugum libræ &longs;it BC in æquilibrio <lb/><figure id="id.005.01.087.1.jpg" xlink:href="005/01/087/1.jpg"/><lb/>con&longs;titutum: &longs;partum <lb/>autem quo <expan abbr="&longs;u&longs;p&etilde;ditur">&longs;u&longs;penditur</expan>, <lb/>AD, ita videlicet, vt <lb/>axis &longs;it ip&longs;um D, quod <lb/>e&longs;t punctum &longs;upra lati­<lb/>tudinem iugi. </s> <s id="N12652">Dein­<lb/>de &longs;partum proijciatur <lb/>deor&longs;um, <expan abbr="efficiatq.">efficiatque</expan> per­<lb/>pendicularem ADM. <lb/><!-- KEEP S--></s> <s id="N12661">Tunc &longs;i in ip&longs;o B ponatur onus, B quidem de&longs;cendet in <lb/>E, C autem a&longs;cendet vbi H. <!-- KEEP S--></s> <s id="N12667">Quamobrem linea, quæ in <lb/>priori &longs;itu libram diuidebat bifariam, e&longs;t ip&longs;a perpendicu­<lb/>laris DM. <!-- KEEP S--></s> <s id="N1266F">Illa verò quæ po&longs;tea eodem pacto diuidit in, <lb/>po&longs;teriori &longs;itu propter onus, quod incumbit in E, erit <lb/>DG. <!-- KEEP S--></s> <s id="N12677">Quare ea pars libræ, &longs;eu iugi. </s> <s id="N1267A">EH, quæ e&longs;t extra <lb/>perpendiculum AM ver&longs;us H maior erit dimidio nem­<lb/>pe quantum importat triangulus DGM, quod &longs;patium <lb/>Ari&longs;toteles &longs;ignauit <expan abbr="Pq.">PQ</expan> Si igitur amoueatur onus, quod <pb pagenum="80" xlink:href="005/01/088.jpg"/>deprimit in E, nece&longs;&longs;e e&longs;t deor&longs;um ferri partem vbi H. <lb/><figure id="id.005.01.088.1.jpg" xlink:href="005/01/088/1.jpg"/><lb/><expan abbr="Siquid&etilde;">Siquidem</expan> pars illa ma­<lb/>ior e&longs;t quàm hæc vbi <lb/>E, quæ per <expan abbr="con&longs;equ&etilde;s">con&longs;equens</expan> <lb/>&longs;ur&longs;um a&longs;cendet, & &longs;ic <lb/>rur&longs;us libra con&longs;titue­<lb/>tur in æquilibrio quod <lb/>erat probandum. </s> <s id="N126A7">Se­<lb/>cunda verò pars huius <lb/>quæ&longs;tionis facilius ab <lb/>eodem Ari&longs;totele probatur. </s> <s id="N126B0">Quoniam &longs;i &longs;partum, &longs;eu axis <lb/>infra iugum locetur, maior pars libr&etail; e&longs;&longs;et illa, qu&etail; deor­<lb/>&longs;um ex impo&longs;ito pondere reperiretur depre&longs;&longs;a, quàm qu&etail; <lb/>&longs;ur&longs;um e&longs;&longs;et elata. </s> <s id="N126B9">Porrò plus dimidio contineret, <expan abbr="proin-deq.">proin­<lb/>deque</expan> etiam ablato pondere adhuc magis grauitaret, ac pro­<lb/>pterea ad equilibrium redire minimè po&longs;&longs;et. </s> <s id="N126C4">Id quod &longs;ic <lb/>o&longs;tendit Ari&longs;toteles &longs;it libra in &etail;quilibrio con&longs;tituta NG <lb/><figure id="id.005.01.088.2.jpg" xlink:href="005/01/088/2.jpg"/><lb/><expan abbr="perpendiculũ">perpendiculum</expan> verò bi­<lb/>fariam libram ip&longs;am <lb/>&longs;ecans, ac tendens ad <lb/>centrum mundi, &longs;it ca­<lb/>dens KLM. <!-- KEEP S--></s> <s id="N126DD">Axis verò <lb/>infra <expan abbr="iugũ">iugum</expan> locatus vbi <lb/>L. <!-- KEEP S--></s> <s id="N126E9">Impo&longs;ito po&longs;t h&etail;c <lb/>onere in ip&longs;o N, de­<lb/>&longs;cendet plane ip&longs;um <lb/>N, <expan abbr="eritq.">eritque</expan> exempli gratia, vbi O. </s> <s id="N126F6">Et per con&longs;equens ip&longs;um <lb/>G a&longs;cendet ad R. <!-- KEEP S--></s> <s id="N126FC">Linea verò KL, qu&etail; bifariam diuide­<lb/>bat libram in &longs;itu NG declinabit in PL. <expan abbr="Cumq.">Cumque</expan> maius &longs;it <lb/>KO, quàm KR eo quod vltra dimidium contineat etiam <lb/>triangulum PKL; &longs;equitur vt ablato onere, adhuc nequeat <lb/>pars i&longs;ta libr&etail; &longs;ur&longs;um attolli. </s> <s id="N1270B">Quandoquidem exce&longs;&longs;us il­<lb/>le &longs;upra medietatem, tanquam onus quoddam ei &longs;emper in­<lb/>cumbit. </s> </p> <p id="N12712" type="main"> <s id="N12714">Huic autem Ari&longs;totelis demon&longs;trationi addi etiam po-<pb pagenum="81" xlink:href="005/01/089.jpg"/>te&longs;t alia &longs;umpta ex centro grauitatis, vt proprium e&longs;t me­<lb/>chanicarum &longs;peculationum. </s> <s id="N1271E">Porrò libræ iam explicatæ cen­<lb/>trum grauitatis e&longs;t punctum in medio iugi intrapo&longs;itum, vt <lb/>patet ex definitione. </s> <s id="N12725">Nam circa illud <expan abbr="vndiq.">vndique</expan> partes æqua­<lb/>lium &longs;unt momentorum. </s> <s id="N1272E">Quando autem libra e&longs;t in Aequi­<lb/>librio con&longs;tituta, huiu&longs;modi centrum coincidit in eandem <lb/>lineam perpendiculatem, in qua e&longs;t centrum circumuolu­<lb/>tionis, &longs;eu axis ip&longs;ius libræ, ac centrum mundi; &longs;iue axis po­<lb/>natur &longs;upra, &longs;iue infra <expan abbr="iugũ">iugum</expan>, vt videre e&longs;t in de&longs;criptis figuris. <lb/></s> <s id="N1273E">Quo fit, vt libra in tali po&longs;itione quie&longs;cat; nam centrum <lb/>grauitatis per breuiorem lineam, qua fieri pote&longs;t tendit ad <lb/>centrum mundi; nulla autem breuior e&longs;t recta in ip&longs;um ca­<lb/>dente. </s> <s id="N12747">Quando verò libra per depre&longs;&longs;ionem vnius, & ele­<lb/>uationem alterius partis ip&longs;ius, <expan abbr="nõ">non</expan> manet in æquilibrio, tunc <lb/>centrum grauitatis con&longs;tituitur extra perpendiculum, &longs;eu li­<lb/>neam prædictam cadentem ad centrum mundi per <expan abbr="c&etilde;trum">centrum</expan> <lb/>circumuolutionis ip&longs;ius libræ; ac propterea nece&longs;&longs;ario ip&longs;um <lb/>centrum grauitatis &longs;i &longs;upra e&longs;t in parte eleuata, ablato pon­<lb/>dere partis oppo&longs;itæ de&longs;cendet, ac reuertetur in locum pri­<lb/>&longs;tinum, vt magis centro mundi appropinquetur per viam <lb/>qua pote&longs;t. </s> <s id="N12762">Si verò infra e&longs;t in parte depre&longs;&longs;a, etiam &longs;i pon­<lb/>dus ab illa auferatur, manebit; quia in illo &longs;itu &longs;imiliter & <lb/>adhuc magis appropinquatur centro mundi quo tendit. </s> <s id="N12769">Qu&etail; <lb/>omnia ab&longs;que alia figura per&longs;picua e&longs;&longs;e po&longs;&longs;unt ex de&longs;cri­<lb/>ptis, ac fu&longs;iùs, & exactiùs traduntur, cum à Guidone Vbaldo <lb/>tractatu de libra, tum à Bernardino Baldo in hac quæ&longs;tione, <lb/>qui tantam in centro grauitatis vim e&longs;&longs;e animaduertit ad <lb/>præponderandum, vt hinc colligat, libras quæ axem habent <lb/>&longs;upra iugum, non à quouis paruo pondere moueri, vel peni­<lb/>tus declinare, &longs;ed ab eo <expan abbr="tantũ">tantum</expan>, quod &longs;uperet <expan abbr="re&longs;i&longs;tentiã">re&longs;i&longs;tentiam</expan> cen­<lb/>tri grauitatis, qu&etail; re&longs;i&longs;tentia proportionaliter eo maior ex­<lb/>peritur, quo minus grauitatis <expan abbr="c&etilde;trũ">centrum</expan> di&longs;tat ab axe, &longs;eu centro <lb/>circa quod ip&longs;a libra conuertitur, vt <expan abbr="ibid&etilde;">ibidem</expan> ip&longs;e demon&longs;trat. </s> </p> <p id="N12790" type="main"> <s id="N12792">Verum quamuis prædicta omnia vera &longs;int, adhuc tamen <lb/>aliquod de&longs;ideratur ad adæquatam omnino rationem tra­<lb/>dendam, cur axe exi&longs;tente &longs;upra iugum, &longs;i eleuetur vna pars <pb pagenum="82" xlink:href="005/01/090.jpg"/>illius ad depre&longs;&longs;ionem alterius, <expan abbr="cau&longs;aq.">cau&longs;aque</expan> depre&longs;&longs;ionis remo­<lb/>ueatur, &longs;tatim pars illa eleuata præcipiti cur&longs;u de&longs;cendat, <lb/><expan abbr="redeatq.">redeatque</expan> in pri&longs;tinum locum. </s> <s id="N127A9">Siquidem exce&longs;&longs;us ille partis <lb/>eleuatæ, quem ex Ari&longs;totele explicuimus, <expan abbr="rur&longs;umq.">rur&longs;umque</expan> ratio <lb/>centri grauitatis prædicta non videntur &longs;ufficere, nec tanti <lb/>e&longs;&longs;e momenti, vt <expan abbr="tantã">tantam</expan> motionem <expan abbr="tamquã">tamquam</expan> præcipitem de­<lb/>&longs;cen&longs;um cau&longs;are præualeant. </s> <s id="N127C0">Cum & centrum grauitatis <lb/>parum, aut imperceptibiliter remoueatur à linea illa ca­<lb/>dente ab axe ad centrum mundi; & exce&longs;&longs;us partis eleuatæ <lb/>non modo paruus &longs;it, &longs;ed paruum etiam ab eadem linea di­<lb/>&longs;tet vbi minus præponderantia experitur. </s> <s id="N127CB">Etenim &longs;i huiu&longs;­<lb/>modi exce&longs;&longs;us appenderetur tanquam onus in libra, quæ in <lb/>æquilibrio &longs;it con&longs;tituta, ac prope axem in &longs;imili &longs;itu, ac e&longs;t <lb/>ille, quem in ca&longs;u no&longs;tro retinet, ab&longs;que dubio parum, aut <lb/>nihil præponderaret brachium in quo appenderetur. </s> </p> <p id="N127D6" type="main"> <s id="N127D8">Dicendum ergo e&longs;t vltra cau&longs;as prædictas præcipuè de­<lb/>&longs;cen&longs;ionem illam cau&longs;ari à maiori grauitate, quam eleuatæ, <lb/>ac pondus lancis ab illo pendentis obtinere videtur in eo <lb/>loco. </s> <s id="N127E1">Nam licet in æquilibrio lances con&longs;titutæ, &longs;upponan­<lb/>tur in grauitate æquales: non tamen in quocumque &longs;itu, & <lb/>po&longs;itione, æque po&longs;&longs;unt grauitare. </s> <s id="N127E8">Quodlibet enim libran­<lb/>dum pondus alias inuariatum, quantò magis elongatur à li­<lb/>nea perpendiculari, quæ per punctum axis in&longs;trumenti ca­<lb/>dit ad centrum terræ (quam lineam Geometrici vocant ca­<lb/>thectum) tanto magis grauitat, vt cernere e&longs;t in &longs;tatera, <lb/>vel in alio &longs;imili ad ponderandum apto in&longs;trumento. </s> <s id="N127F5">Non <lb/>quia ratione &longs;itus re vera maiorem, aut minorem grauita­<lb/>tem acquirat, &longs;ed quia magis, vel minus &longs;u&longs;tinetur ab in­<lb/>&longs;trumento in illo &longs;itu iuxta maiorem, aut minorem propin­<lb/>quitatem, quam &longs;itus habet cum linea explicata, vt Guido <lb/>Vbaldus animaduertit, tractatu de Libra, prop. 4. ante med. <lb/></s> <s id="N12803">Cum igitur pondus &longs;uperioris lancis in eo loco magis di&longs;tet <lb/>aliena perpendiculari prædicta, quàm pondus inferioris, &longs;e­<lb/>quitur magis grauitare &longs;uperiorem lancem, quàm grauitet <lb/>inferior, atque adeo hæc ab illa tanquam ab inæquali pro­<lb/>portione virtutis moueri, & &longs;ur&longs;um ferri v&longs;quequo ad æqua-<pb pagenum="83" xlink:href="005/01/091.jpg"/>lem cum illa à cathectu di&longs;tantiam, ac proinde grauitatem <lb/>perueniat, vt in æquilibrio contingit­</s> </p> <p id="N12815" type="main"> <s id="N12817">Superiorem autem lancem modo prædicto à linea ca­<lb/>thectus magis remoueri, &longs;ic pote&longs;t <expan abbr="demõ&longs;trari">demon&longs;trari</expan> exemplo hu­<lb/>ius figuræ. </s> <s id="N12822">Sit cathectus cadens linea AB, quæ tran&longs;eat <lb/>per punctum axis propo&longs;itæ libræ vbi C. <!-- KEEP S--></s> <s id="N12828">Deinde ducatur <lb/>recta DE per longum diuidens iugum libræ, <expan abbr="ip&longs;aq.">ip&longs;aque</expan> DE bi­<lb/>fariam diuidatur in F, & punctum in quo &longs;ecat lineam AB, <lb/>&longs;ignetur G. <!-- KEEP S--></s> <s id="N12836">Po&longs;tea excitentur à puncto D, & à puncto E <lb/>duæ paralellæ perpendiculariter tendentes ad lineam AB, <lb/>ita vt efficiantur duo triangula AEG, & DGB. </s> <s id="N1283D">In his au­<lb/><figure id="id.005.01.091.1.jpg" xlink:href="005/01/091/1.jpg"/><lb/>tem triangulis, an­<lb/>gulus DGB &etail;qua­<lb/>lis e&longs;t angulo EGA <lb/>cum &longs;int ad verti­<lb/>cem per 15. primi <lb/>Eucl. <!-- KEEP S--></s> <s id="N12853">Angulus <expan abbr="etiã">etiam</expan> <lb/>D. &etail;qualis e&longs;t an­<lb/>gulo E cum &longs;int al­<lb/>terni intra ea&longs;dem <lb/>paralellas, vt patet <lb/>per 29. primi eiu&longs;­<lb/>dem Euclidis. <!-- KEEP S--></s> <s id="N12867">Si­<lb/>militer etiam angu­<lb/>lus B æqualis e&longs;t <lb/>angulo A, quia <lb/>vterque ponitur re­<lb/>ctus. </s> <s id="N12874">Cum igitur <lb/>tres anguli vnius <lb/>trianguli æquales <lb/>&longs;int tribus angulis alterius trianguli &longs;equitur per 4. prop. &longs;ex­<lb/>ti, latera eorundem triangulorum, qu&etail; circum &etail;quales an­<lb/>gulos &longs;unt, e&longs;&longs;e inter &longs;e proportionalia. </s> <s id="N12881">Vnde fit vt cum <lb/>vnum latus ex duobus, quibus angulus E continetur, vide­<lb/>licet GE &longs;it maius <expan abbr="quã">quam</expan> latus GD &etail;qualis anguli D. <!-- KEEP S--></s> <s id="N1288D">Siqui­<lb/>dem GE e&longs;t plu&longs;quam dimidium line&etail; DE continet enim <pb pagenum="84" xlink:href="005/01/092.jpg"/>amplius <expan abbr="di&longs;tantiã">di&longs;tantiam</expan> GF, eo quod in F ip&longs;a linea DE bifariam <lb/>diui&longs;a &longs;it, <expan abbr="proindeq.">proindeque</expan> latus GD &longs;it minus dimidio, ad quod <lb/>dee&longs;t &longs;patium GF. Ex. <!-- REMOVE S-->hoc inquam fit, vt alterum latus <lb/>eiu&longs;dem anguli E &longs;it etiam maius altero latere &etail;qualis an­<lb/>guli D, nempe vt AE, maius &longs;it quàm BD. <!-- KEEP S--></s> <s id="N128AA">Iam ergo <lb/>per longiorem perpendicularem &longs;uperior lanx, quàm infe­<lb/>rior à cathectu di&longs;tabit, quod erat demon&longs;trandum, vt hanc <lb/>magis quam illam in eo &longs;itu grauitare a&longs;&longs;eramus. </s> </p> <p id="N128B3" type="main"> <s id="N128B5">Vnum tandem hic &longs;upere&longs;t explicandum, de quo non <lb/>meminit Ari&longs;toteles; Cur nimirum &longs;i axis non con&longs;tituatur <lb/>&longs;upra, nec infra, &longs;ed pror&longs;us in puncto medio longitudinis, <lb/>ac magnitudinis iugi, vt in puncto A propo&longs;it&etail; libr&etail; BC <lb/>in æquilibrio con&longs;titut&etail;; & alterum extremum illius manu, <lb/>vel pondere deor&longs;um trahatur, ablato pondere, vel ce&longs;&longs;ante <lb/>detentione, rur&longs;us ad &etail;quilibrium ip&longs;a libra non reuertatur, <lb/>&longs;ed maneat quomodocumque relinquatur. </s> </p> <p id="N128C6" type="main"> <s id="N128C8">Id quod ex eo prouenire comperiemus, quoniam in hu­<lb/>iu&longs;modi con&longs;titutione libr&etail;, centrum grauitatis coincidit <lb/>cum centro circumuolutionis, &longs;eu axis ip&longs;ius libr&etail;, <expan abbr="proin-deq.">proin­<lb/>deque</expan> habere non pote&longs;t, quo declinet, aut vergat etiam &longs;i <lb/>libra quomodolibet &longs;ituetur, aut moueatur, &longs;ed manebit <lb/><figure id="id.005.01.092.1.jpg" xlink:href="005/01/092/1.jpg"/><lb/>&longs;emper in illo <lb/>tanquam in &longs;uo <lb/>fulcimento, à <lb/>quo &longs;u&longs;tentatur. <lb/></s> <s id="N128E6">Idem enim <expan abbr="pũ-ctum">pun­<lb/>ctum</expan> A e&longs;t cen­<lb/>trum grauitatis <lb/>cum &longs;it in me­<lb/>dio iugi BC, & <lb/>e&longs;t <expan abbr="c&etilde;trum">centrum</expan> axis <lb/>ex con&longs;tructio­<lb/>nis &longs;uppo&longs;itio­<lb/>ne. </s> <s id="N12901">Quare &longs;i in <lb/>illo iugum diui­<lb/>datur per lineam perpendicularem DE, in quo cumque &longs;i-<pb pagenum="85" xlink:href="005/01/093.jpg"/>tu ponatur, &longs;iue in &etail;quilibrio, vt vbi BC, &longs;iue alibi vt in F G <lb/>&longs;emper diuidetur bifariam, atque adeo in duas partes &etail;qui­<lb/>ponderantes, quarum altera, alteram mouere non pote&longs;t, <lb/>cum propter &etail;quiponderantiam, tum propter <expan abbr="æquidi&longs;tãtiam">æquidi&longs;tantiam</expan> <lb/>quam &longs;emper <expan abbr="retiner&etilde;t">retinerent</expan> à perpendiculo, &longs;eu linea cathectus. </s> </p> <p id="N1291D" type="head"> <s id="N1291F">Quæ&longs;tio Tertia.<!-- KEEP S--></s> </p> <p id="N12923" type="main"> <s id="N12925">C<emph type="italics"/>vr exiguæ vires (quemadmodum à principio<lb/>dictum e&longs;t) vecte, magna mouent pondera, <lb/>vectis in&longs;uper onus accipientes? </s> <s id="N12930">cum faci­<lb/>lius &longs;it minorem mouere grauitatem: minor <lb/>autem e&longs;t &longs;ine vecte. </s> <s id="N12937">An quoniam ip&longs;e ve­<lb/>ctis e&longs;t in cau&longs;a libra exi&longs;tens, &longs;partum infer­<lb/>nè habens, in inæqualia diui&longs;a. </s> <s id="N1293E">Hypomochlion enim est &longs;par­<lb/>tum: ambo namque stant vt centrum. </s> <s id="N12943">Quoniam autem ab <lb/>æquali pondere celeriùs mouetur maior earum, quæ à centro <lb/>&longs;unt: duo verò pondera, quod mouet, & quod mouetur: quod <lb/>igitur motum pondus ad mouens, longitudo patitur ad longi­<lb/>tudinem. </s> <s id="N1294E">Semper autem quanto ab hypomochlio di&longs;tabit ma­<lb/>gis, tantò faciliùs mouebit. </s> <s id="N12953">Cau&longs;a autem e&longs;t, quæ retrò com­<lb/>memorata est: quoniam quæ plus à centro distat, maiorem <lb/>de&longs;cribit circulum: quare ab eadem potentia plus &longs;eparabitur <lb/>mouens illud, quod plus ab hypomochlio di&longs;tabit. </s> <s id="N1295C">Sit vectis <lb/>vbi AB, pondus vbi C, quod mouet autem, vbi D, hypo­<lb/>mochlion vbi E, quod autem vbi e&longs;t D, mouens vbi F. mo­<lb/>tum autem vbi C. pondus vbi G.<emph.end type="italics"/><!-- KEEP S--></s> </p> <p id="N12968" type="head"> <s id="N1296A">COMMENTARIVS.<!-- KEEP S--></s> </p> <p id="N1296E" type="main"> <s id="N12970">Qvod Ari&longs;toteles tanquam admirandum, ac vnum <lb/>de numero eorum, qu&etail; pr&etail;ter naturam accidunt in <lb/>principio huius libri textu 2. propo&longs;uerat, hic mo­<lb/>do ad inue&longs;tigandam eius cau&longs;am, iterum proponit, qu&etail;rens <pb pagenum="86" xlink:href="005/01/094.jpg"/>cur exigu&etail; vires adhibito vecte, magna moueant pondera, <lb/>qu&etail; ab&longs;que vecte mouere minimè po&longs;&longs;ent, cum tamen ip­<lb/>&longs;um quoque onus vectis. </s> <s id="N12982">dimouendum &longs;u&longs;cipiant? </s> <s id="N12985">Facilius <lb/>enim e&longs;t, minorem quàm maiorem &longs;uperare grauitatem <lb/>ponderis: minor autem e&longs;t grauitas ponderis ab&longs;que vecte, <lb/>quàm cum vecte. </s> <s id="N1298E">Vnde contrarium forta&longs;&longs;e videtur debe­<lb/>re contingere ab eo, quod de facto contingit. </s> </p> <p id="N12993" type="main"> <s id="N12995">At &longs;tatim Ari&longs;toteles quæ&longs;tioni re&longs;pondet dicens, ve­<lb/>ctem quippe habere rationem libræ, cuius axis, &longs;eu truti­<lb/>na &longs;it infra iugum, vt explicuimus, brachia verò &longs;int inæ­<lb/>qualia. </s> <s id="N1299E">Hypomochlion enim, &longs;eu fulcimentum vectis, axis <lb/>vicem gerit. </s> <s id="N129A3">Similiter namque circa ip&longs;um conuertitur ve­<lb/>ctis, &longs;imiliterque &longs;emper manet immotum. </s> <s id="N129A8">Longitudo au­<lb/>tem vectis vtrinque ex fulcimento proten&longs;a, iugum refert <lb/>libræ, in brachia, &longs;eu partes inæquales diui&longs;um; quarum <lb/>illa, quæ ad pondus leuandum applicatur, &longs;it breuior, illa <lb/>verò in cuius, extremitate virtus adhibetur potentiæ mo­<lb/>tricis &longs;it longior, vt cernere e&longs;t in hac figura, quam tamen <lb/>Ari&longs;toteles exibuit in fine. </s> <s id="N129B7">Sit enim vectis. </s> <s id="N129BA">AB, pondus <lb/>verò vbi C, & potentia mouens vbi D; inter quæ me­<lb/>diet fulcimentum in E. <!-- KEEP S--></s> <s id="N129C2">Tunc &longs;i con&longs;ideretur, eadem erit <lb/><figure id="id.005.01.094.1.jpg" xlink:href="005/01/094/1.jpg"/><pb pagenum="87" xlink:href="005/01/095.jpg"/><figure id="id.005.01.095.1.jpg" xlink:href="005/01/095/1.jpg"/><lb/>ratio ac de libra, cuius iugum &longs;it AB, lances verò C, D, <lb/>& axis, &longs;eu fulcimentum E. <!-- KEEP S--></s> <s id="N129D9">Siquidem ip&longs;um D pendens <lb/>ex longiori brachio libræ, præponderat ip&longs;i C. <!-- KEEP S--></s> <s id="N129DF">Quemad­<lb/>modum potentia applicata in vecte vbi D, &longs;uperat graui­<lb/>tatem ponderis C. <!-- KEEP S--></s> <s id="N129E7">Axis verò <expan abbr="cũ">cum</expan> ponatur infra iugum, &longs;iue <lb/>ip&longs;um iugum &longs;it &longs;u&longs;pen&longs;um per trutinam, aut &longs;partum, &longs;iue <lb/>innixum &longs;it alteri corpori immobili, idem &longs;emper præ&longs;tat, <lb/>ac fulcimentum vectis vbi E. <!-- KEEP S--></s> </p> <p id="N129F5" type="main"> <s id="N129F7">Quoniam autem (pro&longs;equitur Ari&longs;toteles) ab æquali <lb/>pondere celerius, &longs;iue facilius mouetur brachium libræ, <lb/>quod magis à centro di&longs;ce&longs;&longs;erit, vt explicatum e&longs;t de libra, <lb/>quæ alterum brachium longius obtinet, eam ad circulum <lb/>reducendo: hinc fit, vt cum duo &longs;int, quæ in ambis extre­<lb/>mitatibus vectis præsunt, vel ponderant, nempe mouens <lb/>in vna, & motum in alia; illud magis præponderet, quod <lb/>longiorem vectis extremitatem præ&longs;&longs;erit; &longs;eu quanto magis <lb/>à fulcimento di&longs;ce&longs;&longs;erit, quamuis aliàs ip&longs;a ponderantia in <lb/>&longs;e &longs;int æqualia, hoc e&longs;t virtus mouentis æqualis &longs;it moto <lb/>ponderi, & longior pars vectis æquè grauitet, ac breuior. <lb/></s> <s id="N12A0F">Quod totum, vt ip&longs;emet Ari&longs;toteles inquit, de&longs;umitur ab <pb pagenum="88" xlink:href="005/01/096.jpg"/>explicato illo principio; quoniam &longs;cilicet, quæ plus à cen­<lb/>tro di&longs;tat linea, &longs;eu extremitas &longs;emidiametri, maiorem de­<lb/>&longs;cribit circumferentiam, quæ &longs;anè cum magis ad rectam li­<lb/>neam accedat, facilius, ac velocius per ip&longs;am fertur &longs;emidia­<lb/>meter, tanquam per viam magis connaturalem, vt ibidem <lb/>explicuimus. </s> </p> <p id="N12A21" type="main"> <s id="N12A23">Illud autem, quod Ari&longs;toteles interpo&longs;uit, nempe: Quod <lb/>igitur motum pondus admouens, longitudo patitur ad lon­<lb/>gitudinem: idem e&longs;t, ac dicere, eandem proportionem ha­<lb/>bere motricem potentiam ad pondus leuandum, quam ha­<lb/>bet eius longitudo, &longs;eu di&longs;tantia à centro vectis ad longitu­<lb/>dinem, &longs;eu di&longs;tantiam ponderis ab eodem centro vbi e&longs;t <lb/>fulcimentum. </s> <s id="N12A32">Quare &longs;ubiungit: Semper autem quanto ab <lb/>hypomochlio, id e&longs;t fulcimento, di&longs;tabit magis, tanto facilius <lb/>mouebit. </s> <s id="N12A39">Hæc ille, quæ po&longs;tea exactius tradita &longs;unt ab <lb/>Archimede in &longs;uo primo libro æqueponderantium propo­<lb/>&longs;itione &longs;exta; & acuti&longs;&longs;imè probantur à Guido Vbaldo è <lb/>Marchionibus Montis in &longs;uis Mechanicis tractatu de libra <lb/>propo&longs;itione &longs;exta; ac de vecte propo&longs;itione quarta. </s> <s id="N12A44">De­<lb/>mon&longs;trant enim in æquilibrijs, tàm vectis, quàm libræ, ita &longs;e <lb/>habere pondus ad pondus, vt brachium ad brachium ex <lb/>commutata proportione. </s> <s id="N12A4D">Sit enim vectis, aut libra AB &longs;uf­<lb/>fulta, aut &longs;u&longs;pen&longs;a in C. <!-- KEEP S--></s> <s id="N12A53">Brachium autem CA &longs;it verbi <lb/><figure id="id.005.01.096.1.jpg" xlink:href="005/01/096/1.jpg"/><lb/>gratia vnius <lb/>palmi. </s> <s id="N12A60">Bra­<lb/>chium verò <lb/>CB &longs;it qua­<lb/>tuor palmo­<lb/>rum. </s> <s id="N12A6B">Dein­<lb/>de <expan abbr="app&etilde;da-tur">appenda­<lb/>tur</expan> in <expan abbr="Apõ-dus">A pon­<lb/>dus</expan> D, quod <lb/><expan abbr="põderet">ponderet</expan>, vt <lb/>quatuor; & <lb/>in B appen­<lb/>datur pondus E, ponderans vt vnum; ita vt ip&longs;um pondus <pb pagenum="89" xlink:href="005/01/097.jpg"/>E &longs;e habeat ad pondus D eadem proportione, qua bra­<lb/>chium CA &longs;e habet ad brachium CB. <!-- KEEP S--></s> <s id="N12A8F">Tunc quippe dici­<lb/>mus vectem, aut libram man&longs;uram in æquilibrio propter <lb/><expan abbr="cõmutatam">commutatam</expan> proportionem. </s> <s id="N12A99">Etenim quadruplum ponderis <lb/>D commutatur cum quadruplo longitudinis CB. <!-- KEEP S--></s> <s id="N12A9F">Et pon­<lb/>dus E compen&longs;atur à longitudine CA, quæ e&longs;t quarta. <lb/></s> <s id="N12AA5">pars longitudinis CB: &longs;icut pondus E e&longs;t quarta pars pon­<lb/>deris D. <!-- KEEP S--></s> <s id="N12AAB">Quare promi&longs;cue &longs;umendo partes ip&longs;as ponde­<lb/>rantes &longs;iue ratione propriæ grauitatis, &longs;iue ratione di&longs;tan­<lb/>tiæ quam habent à fulcimento, quinque erunt partes ad le­<lb/>uam, & quinque ad dexteram, <expan abbr="vtræq.">vtræque</expan> vtri&longs;que in pondere <lb/>æquales, vel æquè &longs;imul grauitantes. </s> <s id="N12ABA">Siquidem nec pondus <lb/>D, quod e&longs;t vt quatuor: nec pondus E, quod e&longs;t vt vnum, <lb/>&longs;uperare pote&longs;t longitudinem CA, quæ pariter e&longs;t vt vnum. <lb/></s> <s id="N12AC2">Et &longs;ic vnum &longs;upra quatuor ex vtraque parte con&longs;tituunt <lb/>quinquenarium æquale ex commutata proportione longi­<lb/>tudinis, & grauitatis. </s> </p> <p id="N12AC9" type="main"> <s id="N12ACB">Cæterum cum Ari&longs;toteles totam vin &longs;ui argumenti &longs;um­<lb/>p&longs;erit ex eo, quod ab æquali pondere celerius mouetur bra­<lb/>chium, &longs;eu partem libræ, quæ magis à centro di&longs;tenditur; <lb/>cau&longs;am ip&longs;am cur exiguæ vires adhibito vecte magna mo­<lb/>ueant pondera con&longs;tituere videtur in velocitate, quæ bra­<lb/>chij longitudinem con&longs;equitur, vt ait Baldus. <!-- KEEP S--></s> <s id="N12AD9">Quod qui­<lb/>dem ip&longs;e minime approbat. </s> <s id="N12ADE">Quæ enim, ait, velocitas in re <lb/>&longs;tante? </s> <s id="N12AE3">Stant autem vectis, & libra dum manent in æquili­<lb/>brio, & nihilominus parua potentia ingens &longs;u&longs;tinet pondus. </s> </p> <p id="N12AE8" type="main"> <s id="N12AEA">Veruntamen &longs;i verba Ari&longs;totelis exactius pen&longs;entur non <lb/>id &longs;ignificant, nec ille talem cau&longs;am formaliter in maiori <lb/>velocitate, &longs;ed in maiori grauitate, aut virtute con&longs;tituit, <lb/>quæ brachij maiorem longitudinem con&longs;equitur. </s> <s id="N12AF3">Etenim <lb/>cum dixit: <emph type="italics"/>Quoniam autem ab æquali pondere celerius mo­<lb/>uetur maior earum, quæ à centro &longs;unt.<emph.end type="italics"/></s> <s id="N12AFF"> Idem per <emph type="italics"/>celerius<emph.end type="italics"/> ac <lb/>per <emph type="italics"/>facilius<emph.end type="italics"/> intellexit. </s> <s id="N12B10">Quandoquidem paulo po&longs;t id ip&longs;um <lb/>repetens, ait. <emph type="italics"/>Semper autem quanto ab hypomochlio dicta­<lb/>bit magis, tanto facilius mouebit.<emph.end type="italics"/></s> <s id="N12B20"> Et quidem in motu locali <lb/>velocitas &longs;emper facilitatem inuoluit, aut &longs;upponit, <expan abbr="ip&longs;aq.">ip&longs;aque</expan> <pb pagenum="90" xlink:href="005/01/098.jpg"/>maior velocitas, ac facilitas motus, maiorem grauitatem, aut <lb/>maiorem virtutem motiuam nece&longs;&longs;ario indicat, vt palam e&longs;t <lb/>in motibus tàm naturalibus, quàm violentis. </s> <s id="N12B32">Nam corpus <lb/>quò grauius, eò velocius de&longs;cendit, &longs;i non detineatur; & <lb/>proiecta, eò velocius inter medium percurrunt, quo maio­<lb/>rem impul&longs;um à proijciente recipiunt. </s> <s id="N12B3B"><expan abbr="Ip&longs;aq.">Ip&longs;aque</expan> animalia tan­<lb/>to progrediuntur velocius, <expan abbr="citiusq.">citiusque</expan> per incu&longs;&longs;ionem impul­<lb/>&longs;us grauia mouent, quanto maiorem virtutem motiuam <lb/>adepta fuerit cum pari di&longs;po&longs;itione in&longs;trumentorum. </s> <s id="N12B4B">Itaque <lb/>in propo&longs;ito, hoc ip&longs;o quod extremum longiori brachij ve­<lb/>locius mouetur, magis grauitat in illo &longs;itu, &longs;eu maiore in in­<lb/>dicat &longs;e ibi adipi&longs;ci virtutem motiuam, maiu&longs;que pondus <lb/>præualet &longs;u&longs;tinere etiam &longs;i non moueatur. </s> </p> <p id="N12B56" type="head"> <s id="N12B58">Quæ&longs;tio Quarta.</s> </p> <p id="N12B5B" type="main"> <s id="N12B5D">C<emph type="italics"/>vr ij, qui in nauis medio &longs;unt remiges, ma­<lb/>ximè nauem mouent? </s> <s id="N12B65">an quia remus vectis <lb/>est, hypomochlion autem fit &longs;calmus? </s> <s id="N12B6A">&longs;tat <lb/>enim ille: pondus verò mare est, quod propel­<lb/>lit remus: vectem autem mouens est ip&longs;e re­<lb/>mex. </s> <s id="N12B73">Semper autem plus mouet ponderis, <lb/>quantò magis ab hypomochlio distabit quicumque id mouet. <lb/></s> <s id="N12B79">Maior enim ita fit, quæ ex centro. </s> <s id="N12B7C">Scalmus autem hypomo­<lb/>chlion exi&longs;tens, centrum e&longs;t. </s> <s id="N12B81">In medio autem nauis plurimum <lb/>remi intus e&longs;t: illa enim parte lati&longs;&longs;ima e&longs;i nauis: quare ma­<lb/>ior vtrinque remi pars vtrorumque nauis parietum intrin&longs;e­<lb/>cus e&longs;i. </s> <s id="N12B8A">Mouetur autem nauis, quoniam appellente ad ma­<lb/>re remo, extremum illius, quod intus e&longs;t, in ante promouetur: <lb/>nauem verò &longs;calmo alligatam &longs;imul promoueri contingit, <lb/>quo remi extremum. </s> <s id="N12B93">Vbi enim plurimum maris diuidit re­<lb/>mus, eò maximè propelli nece&longs;&longs;e e&longs;i. </s> <s id="N12B98">Plurimùm autem diuidit, <lb/>vbi pars plurima remi à &longs;calmo e&longs;t. </s> <s id="N12B9D">Et eam ob cau&longs;am remi­<lb/>ges, qui in media &longs;unt naui, mouent illam maximè. </s> <s id="N12BA2">Maxima <lb/>enim remi pars à &longs;calmo in nauis medio intus e&longs;t.<emph.end type="italics"/></s> </p> <pb pagenum="91" xlink:href="005/01/099.jpg"/> <p id="N12BAD" type="head"> <s id="N12BAF">COMMENTARIVS.<!-- KEEP S--></s> </p> <p id="N12BB3" type="main"> <s id="N12BB5">Svpponit hic Ari&longs;toteles ab experientia, quod nos in­<lb/>fra ratione probabimus, remiges in nauis medio remi­<lb/>gantes, magis nauem mouere, quàm &longs;i in prora, vel <lb/>puppi remigarent, &longs;iue quàm alij, qui æquali conatu, ac vir­<lb/>tute &longs;imul remigant in alio &longs;itu. </s> <s id="N12BC0"><expan abbr="Cau&longs;amq.">Cau&longs;amque</expan> problematicè <lb/>&longs;ci&longs;citando, vt &longs;olet præmittit, Remum vectem e<gap/>, &longs;cal­<lb/>mum verò fulcimentum, & mare con&longs;titui pondus, quod per <lb/>remum propellitur à remige tanquam à vectem mouente. <lb/></s> <s id="N12BCF">Deinde &longs;ic argumentatur: Tanto magis mouens adhibito <lb/>vecte pondus mouet, quanto magis extremum vectis vbi <lb/>virtutem applicat di&longs;tat a centro, &longs;eu fulcimento: At in <lb/>medio nauis, remi manubrium &longs;iue extremum, in quo vir­<lb/>tus remigis applicatur, magis di&longs;tat à &longs;calmo, qui con&longs;titui­<lb/>tur fulcimentum: Ergo magis pariter nauem mouebit re­<lb/>miger in illo &longs;itu, quàm in alio, vt in prora, vel puppi. </s> <s id="N12BDE">Quod <lb/>autem manubrium remi exi&longs;tentis in medio nauis, magis <lb/>di&longs;tet à &longs;calmo, probat ex eo, quòd nauis in medio, latior <lb/>e&longs;t, quàm ver&longs;us proram, vel puppim; <expan abbr="proindeq.">proindeque</expan> pars remi, <lb/>quæ intus e&longs;t, &longs;iue vbi manubrium, longior pariter e&longs;t iuxta <lb/>proportionem, quam habere debet cum &longs;itu. </s> </p> <p id="N12BEF" type="main"> <s id="N12BF1">Ex quo Ari&longs;toteles aliam quoque rationem de&longs;umit, <lb/>quam cum priori (perob&longs;curè tamen) connectit: Quia ni­<lb/>mirum adhuc foris pars remi in medio nauis con&longs;tituti, lon­<lb/>gior e&longs;t iuxta proportionem prædictam, quæ ad commodi­<lb/>tatem remigationis &longs;emper &longs;eruatur in v&longs;u. </s> <s id="N12BFC">Longior autem <lb/>remi pars externa, &longs;eu palmula, maiorem aquæ portionem <lb/>diuidit, ac propellit, magi&longs;que propterea nauem promouet, <lb/>quàm quæ breuior e&longs;t ratione proportionis, ac &longs;itus. </s> <s id="N12C05">Quare <lb/>ob&longs;eruandum e&longs;t, eam e&longs;&longs;e debitam remorum proportio­<lb/>nem inter &longs;e, quæ e&longs;t inter &longs;itum, & &longs;itum nauis vbi con&longs;ti­<lb/>tuuntur, ita vt vbi latior fuerit nauis, ibi productiores remi <lb/>con&longs;tituantur ex vtraque parte ip&longs;orum, quæ e&longs;t vtrinque à <lb/>scalmo. </s> <s id="N12C12">Hoc e&longs;t tam intus ex parte manubrij, quàm foris <pb pagenum="92" xlink:href="005/01/100.jpg"/>ex parte palmulæ. </s> <s id="N12C1A">Et &longs;ic qui in medio &longs;unt remi, eo quod ibi <lb/>lati&longs;sima &longs;it nauis, longi&longs;&longs;imi &longs;unt, <expan abbr="maximèq.">maximèque</expan> proinde nauim <lb/>promouent; qui verò puppim ver&longs;us, aliquantulum breuio­<lb/>res; ac breui&longs;&longs;imi, qui con&longs;tituuntur ad proram, propter ean­<lb/>dem rationem; <expan abbr="ideoq.">ideoque</expan> minus, ac minus proportionaliter na­<lb/>uem ip&longs;am valent mouere, &longs;eu vniformiter difformiter. </s> </p> <p id="N12C2F" type="main"> <s id="N12C31">Explorati&longs;&longs;imum e&longs;t hoc experimentum, <expan abbr="ratioq.">ratioque</expan> vt vidi­<lb/>mus manife&longs;ta. </s> <s id="N12C3A">Sed contra Ari&longs;totelem obijciunt Blanca­<lb/>nus, & Baldus, quòd mare potius, quàm &longs;calmus rationem <lb/>habere videatur fulcimenti. </s> <s id="N12C43">Siquidem &longs;calmus eo quod af­<lb/>fixus &longs;it naui, non manet, vt <expan abbr="propriũ">proprium</expan> e&longs;t fulcimenti, &longs;ed fer­<lb/>tur cum illa. </s> <s id="N12C4E">Quare in ip&longs;orum &longs;ententia, ita remus con&longs;ti­<lb/>tuitur vectis, vt <expan abbr="centrũ">centrum</expan> habeat in extremitate palmulæ, qua <lb/>mari adhæret, atque innititur tanquam fulcimento; pondus <lb/><expan abbr="aut&etilde;">autem</expan> &longs;it nauis, & <expan abbr="pot&etilde;tia">potentia</expan> mouentis applicetur in manubrio. </s> </p> <p id="N12C62" type="main"> <s id="N12C64">Veruntamen non video cur mobilitas ac latio nauis cum <lb/>&longs;calmo, ob&longs;tet quominus ip&longs;e &longs;calmus habeat rationem ful­<lb/>cimenti, <expan abbr="eaq.">eaque</expan> concedatur mari, quod non minus mouetur <lb/>per impul&longs;um acceptum à palmula. </s> <s id="N12C71">Quapropter vel neu­<lb/>trum horum <expan abbr="dicendũ">dicendum</expan> e&longs;t, habere po&longs;&longs;e rationem fulcimen­<lb/>ti, hoc e&longs;t nec mare, nec &longs;calmum; vel dicendum e&longs;t vtrum­<lb/>que illorum participare huiu&longs;modi rationem, vt exempli <lb/>gratia, &longs;i ponamus vectem AB interpo&longs;itam e&longs;&longs;e inter <lb/><figure id="id.005.01.100.1.jpg" xlink:href="005/01/100/1.jpg"/><lb/>duos lapides CD, quorum C &longs;it ver&longs;us extremitatem B <lb/>retror&longs;um, D verò circa medium ip&longs;ius vectis antror&longs;um; <lb/>& potentia applicetur in extremitate A. <!-- KEEP S--></s> <s id="N12C8D">Etenim &longs;i extre­<lb/>mum A impellatur antror&longs;um ver&longs;us E, D quidem <lb/>&longs;imul feretur in F & C retrocedet in G, vt cuilibet expe­<lb/>riri fas e&longs;t. </s> <s id="N12C96">Quapropter nulla e&longs;&longs;et maior ratio cur potius <pb pagenum="93" xlink:href="005/01/101.jpg"/>lapis C. quàm lapis D con&longs;titueretur fulcimentum in hac <lb/>latione vectis. </s> <s id="N12CA0">Ideoque vtrumque aliquo modo, illam par­<lb/>ticipare dicendum erit. </s> <s id="N12CA5">Cum igitur obijcit Baldus, quod <lb/>tunc Philo&longs;ophi ratio procederet &longs;i &longs;tante naui immobili, re­<lb/>miges in ip&longs;o remigandi actu, mare pul&longs;arent, quia tunc verè <lb/>&longs;calmus fieret fulcimentum mare autem pondus. </s> <s id="N12CAE">Re&longs;pon­<lb/>detur retorquendo illi argumentum: quod tunc procederet <lb/>ratio ab ip&longs;o adducta, &longs;i &longs;tante mare immobili &longs;icut terra, <lb/>remiges appul&longs;a palmula, nauem &longs;calmo alligatam, antror­<lb/>&longs;um impellerent, vt cum Romani <expan abbr="cõtræ">contræ</expan> Carthaginen&longs;es na­<lb/>uales copias primo e&longs;&longs;ent traducturi, ad remigium in arena <lb/>exercebantur; quia tunc verè mare fieret fulcimentum, &longs;cal­<lb/>mus verò cum naui, pondus. </s> </p> <p id="N12CC3" type="main"> <s id="N12CC5">Quoniam verò tàm mare, quàm &longs;calmum diximus<arrow.to.target n="marg18"/> habe­<lb/>re rationem fulcimenti aliquo modo, non autem &longs;impliciter <lb/>propter mobilitatem vtriu&longs;que; examinan dum e&longs;&longs;et, quod­<lb/>nam ex his, minus moueatur, vt hoc potius quàm alterum <lb/>dicatur magis participare rationem fulcimenti. </s> <s id="N12CD4">Sed forta&longs;­<lb/>&longs;e difficile poterit hoc penitus determinari. </s> <s id="N12CD9">Pendet enim <lb/>non modo à proportione partium remi, nempe quomodo <lb/>&longs;e habeat pars, quæ e&longs;t à &longs;calmo ad extremum manubrij ad <lb/>eam, quæ e&longs;t à &longs;calmo ad extremum palmulæ; verùm etiam <lb/>ab applicatione palmulæ in mare, vt &longs;i plus vel minus intro­<lb/>mittatur, <expan abbr="maioremq.">maioremque</expan> portionem aquæ depellat. </s> <s id="N12CEA">Quando­<lb/>quidem &longs;i profundè palmula immergatur, <expan abbr="magnamq.">magnamque</expan> por­<lb/>tionem aquæ per illam remiger conetur depellere, tunc pro­<lb/>cul dubio, minus mouebitur aqua retror&longs;um, quàm nauis an­<lb/>tror&longs;um. </s> <s id="N12CF9">Quod ex eo &longs;it palam, nam &longs;i nauis in mare me­<lb/>diet inter duos &longs;copulos, ad quos palmulæ po&longs;&longs;int pertinge­<lb/>re, &longs;imili conatu remiges &longs;copulos pul&longs;ando ac aquam pul­<lb/>&longs;are con&longs;ueuerunt, magis profecto nauem ip&longs;am mouebunt. <lb/></s> <s id="N12D07">Quod &longs;i alioquin palmulæ minimè immergantur, &longs;ed veluti <lb/>&longs;olam &longs;uperficiem aquæ depellant, certum etiam e&longs;t, magis <lb/>aquam illam depul&longs;am <expan abbr="totamq.">totamque</expan> ferè in &longs;pumam redactam <lb/>abire, quam nauem vlterius progredi, aut moueri </s> </p> <p id="N12D14" type="margin"> <s id="N12D16"><margin.target id="marg18"/>Polyb. <!-- REMOVE S-->lib. <lb/><!-- REMOVE S-->1.longe an­<lb/>te med.</s> </p> <p id="N12D22" type="main"> <s id="N12D24">Tandem addit Baldus, fal&longs;um videri, quod a&longs;&longs;erit Ari&longs;to-<pb pagenum="94" xlink:href="005/01/102.jpg"/>teles, eos qui in media naui &longs;unt remiges, maximè nauim <lb/>mouere, &longs;i per maximè denotet maximo &longs;pacio, aut velo. <lb/></s> <s id="N12D2F">cius. </s> <s id="N12D32">Etenim (inquit) tardius mouent, & minori &longs;patio, <lb/>quod ita probat. </s> <s id="N12D37">E&longs;to enim Remus AB, qui mari fulcitur <lb/><figure id="id.005.01.102.1.jpg" xlink:href="005/01/102/1.jpg"/><lb/>in B Scalmus remi, <lb/>qui ad proram, pup­<lb/>pimve C, qui in <lb/>media naui D. <!-- KEEP S--></s> <s id="N12D49">Ma­<lb/>ior autem remi pars <lb/>e&longs;t à &longs;calmo D ad <lb/>A, quàm ip&longs;ius C <lb/>ad A. <!-- KEEP S--></s> <s id="N12D55">Pellantur re­<lb/>mi, & &longs;tante ceu centro B; feratur ip&longs;um A in E. <!-- KEEP S--></s> <s id="N12D5B">Eodem <lb/>igitur tempore C erit in F, & D in G; &longs;ed maius e&longs;t &longs;pa­<lb/>tium CF &longs;patio DG: ergo vnica impul&longs;ione plus mouit <lb/>&longs;calmum, hoc e&longs;t nauim, potentia ad puppim proramve re­<lb/>migans, quam ea, quæ operatur in media naui. </s> <s id="N12D66">Hæc ille. </s> </p> <p id="N12D69" type="main"> <s id="N12D6B">Sed hoc &longs;chemate nihil demon&longs;tratur contra <expan abbr="Ari&longs;totel&etilde;">Ari&longs;totelem</expan>. <lb/><!-- KEEP S--></s> <s id="N12D74">Nam &longs;i quid ex eo concluderetur, e&longs;&longs;et de motu circulari, <lb/>quo nauis duceretur circa punctum B per arcus CF & DG. <lb/><!-- KEEP S--></s> <s id="N12D7B">Ari&longs;toteles autem loquitur de motu recto. </s> <s id="N12D7E">Deinde non ex <lb/>eo, quod punctum C eodem tempore maius &longs;patium per­<lb/>currat, quàm punctum D vtpotè magis di&longs;tans à centro B, <lb/>iccirco &longs;equitur, magis mouere nauim remiges, qui ibi &longs;cal­<lb/>mum habent affixum. </s> <s id="N12D89">Etenim alia, per quam plura &longs;unt pun­<lb/>cta in ip&longs;a naui, quæ maius adhuc &longs;patium percurrunt, quam <lb/>C, tanquam à centro remotiora; in quibus tamen &longs;i con&longs;ti­<lb/>tueretur &longs;calmus, minus nauem remiges valerent mouere, <lb/>vt in cu&longs;pide puppis, vel proræ. </s> <s id="N12D94">Quare motus ip&longs;ius C, & <lb/>cuiu&longs;libet alterius puncti remotionis à centro, quamuis ve­<lb/>locior &longs;it, quàm m<gap/>us ip&longs;ius D, procedere pote&longs;t magis <lb/>ab impul&longs;u impre&longs;&longs;o in ip&longs;o D, quàm ab impul&longs;u impre&longs;&longs;o <lb/>in eodem C, & &longs;ic magis mouere nauim eos, qui in nauis <lb/>medio &longs;unt remiges, etiam loquendo de motu circulari. </s> </p> <p id="N12DA3" type="main"> <s id="N12DA5">Rur&longs;us ex ip&longs;a Baldi probatione, atque conclu&longs;ione &longs;e­<lb/>queretur, &longs;calmum vnius remi, magis di&longs;tare à &longs;calmo alte-<pb pagenum="95" xlink:href="005/01/103.jpg"/>rius po&longs;t lationem nauis, quàm antea. </s> <s id="N12DB1">Quod &longs;ic pote&longs;t ex <lb/>proprijs di&longs;tinctius expo&longs;itis o&longs;tendi. </s> <s id="N12DB6">Sint duo remi ante <lb/>motionem duæ <lb/><figure id="id.005.01.103.1.jpg" xlink:href="005/01/103/1.jpg"/><lb/>æquales para­<lb/>lellæ, nempe <lb/>ADB in medio <lb/>nauis; & ACB <lb/>ver&longs;us proram. <lb/></s> <s id="N12DCC"><expan abbr="Quorũ">Quorum</expan> <expan abbr="manu-briũ">manu­<lb/>brium</expan> &longs;it A, pal­<lb/>mula verò B <lb/>Sitque scalmus <lb/>vnius in D, al­<lb/>terius verò in <lb/>C, magis <expan abbr="di-&longs;tãs">di­<lb/>&longs;tans</expan> à B. </s> <s id="N12DE8">Dein­<lb/>de po&longs;t latio­<lb/>nem <expan abbr="cõ&longs;tituan-tur">con&longs;tituan­<lb/>tur</expan> ijdem remi <lb/>ADB in EGB, & ACB in EFB, vtrorumque extremis, <lb/>&longs;iue palmulis manentibus in eodem puncto B, & vtrorum­<lb/>que manubrijs æqualiter à priori loco <expan abbr="di&longs;tãtibus">di&longs;tantibus</expan> per æqua­<lb/>les arcus AE vtriu&longs;que remi. </s> <s id="N12E01">Scalmus verò D con&longs;titua­<lb/>tur in G, & &longs;calmus C in F; &longs;itque maius &longs;patium CF, <lb/>quam DG, vt rectè Baldus a&longs;&longs;umebat. </s> </p> <p id="N12E08" type="main"> <s id="N12E0A">Dico igitur punctum G magis di&longs;tare à puncto F (quæ <lb/>e&longs;t di&longs;tantia vnius scalmi ab altero po&longs;t lationem) quàm <lb/>punctum D di&longs;tet à puncto C, quæ erat di&longs;tantia eorun­<lb/>dem ante motionem. </s> <s id="N12E13">Ducantur enim rectæ CD & FG <lb/>&longs;ignantes vtramque di&longs;tantiam. </s> <s id="N12E18">Et à puncto D, vbi prius <lb/>erat &longs;calmus remi exi&longs;tentis in medio nauis, excitetur alia <lb/>recta linea v&longs;que ad G, vbi idem &longs;calmus con&longs;tituitur po&longs;t­<lb/>modum, atque &longs;uper ip&longs;a latera CD, & DG fiat paralel­<lb/>logrammum CDGH. </s> <s id="N12E23">Tunc quippe latus GH erit æquale <lb/>lateri CD & latus GD æquale erit lateri HC, eo quod <lb/>&longs;int oppo&longs;ita, vt patet per 34 primi Euclidis. <!-- KEEP S--></s> <s id="N12E2B">Quoniam <pb pagenum="96" xlink:href="005/01/104.jpg"/>verò &longs;patium DG po&longs;itum e&longs;t minus, quam &longs;patium CF, <lb/>&longs;equitur lineam CH pertingere non po&longs;&longs;e v&longs;que ad pun­<lb/>ctum F, cum ip&longs;a &longs;it æqualis ad DG. <!-- KEEP S--></s> <s id="N12E38">Cumque ip­<lb/><figure id="id.005.01.104.1.jpg" xlink:href="005/01/104/1.jpg"/><lb/>&longs;ius extremum <lb/>vbi H, &longs;it pari­<lb/>ter terminus li­<lb/>ne&etail;, &longs;eu lateris <lb/>GH, &longs;equitur <lb/>vlterius, vt ne­<lb/>que linea GH <lb/>pertingere po&longs;­<lb/>&longs;it <expan abbr="v&longs;q;">v&longs;que</expan> ad pun­<lb/>ctum P. <!-- KEEP S--></s> <s id="N12E5A">Erit <lb/>igitur maior li­<lb/>nea GF quàm <lb/>&longs;it linea GH, & <lb/>linea CD, quæ <lb/>e&longs;t illi æqualis, <lb/>quod erat pro<lb/></s> <s id="N12E6A">bandum. </s> </p> <p id="N12E6D" type="main"> <s id="N12E6F"><expan abbr="It&etilde;">Item</expan> hinc manife&longs;tè apparet fal&longs;um <expan abbr="quoq;">quoque</expan> e&longs;&longs;e, manubrium <lb/>remi ad proram, vel puppim exi&longs;tentis, æquale &longs;patium per­<lb/>tran&longs;ire, ac manubrium alterius remi in nauis medio con&longs;ti­<lb/>tuti, palmulis vtriu&longs;que remi in eodem &longs;itu, &longs;eu puncto ma­<lb/>nentibus, vt à Baldo a&longs;&longs;umebatur ad probandam &longs;uam con­<lb/>clu&longs;ionem. </s> <s id="N12E83">Quod ita facilè o&longs;tenditur ex huiu&longs;que demon­<lb/>&longs;tratis. </s> <s id="N12E88">Nam &longs;i eo tempore quo &longs;calmus D fertur in G, <lb/>&longs;calmus C fertur in H ad æqualem di&longs;tantiam, vt proba­<lb/>tum e&longs;t; vtique manubrium ip&longs;ius remi ad proram con&longs;ti­<lb/>tuti, non erit in E, &longs;ed in I, vbi de&longs;init recta ducta à <lb/>centro B, per punctum H ad arcum AE. <!-- KEEP S--></s> <s id="N12E94">Cumque AI <lb/>differat ab AE tanquam pars à toto, & vterque arcus AE <lb/>&longs;it alter alteri æqualis ex con&longs;tructione, palam fit, maius <lb/>&longs;patium percurrere manubrium A remi ADB in medio <lb/>nauis con&longs;tituti, dum fertur v&longs;que ad E, quàm manubrium <lb/>alterius remi, quo d fertur v&longs;que ad I. <!-- KEEP S--></s> </p> <pb pagenum="97" xlink:href="005/01/105.jpg"/> <p id="N12EA6" type="main"> <s id="N12EA8">Præterea contra experientiam &longs;upponitur à Baldo, remi <lb/>palmulam ceu centrum manere immotam in ip&longs;a remiga­<lb/>tione, qua nauis fertur antror&longs;um. </s> <s id="N12EAF">Nam licet in vno ca&longs;u, vt <lb/>quando remi manubrium motu proprio circa &longs;calmum na­<lb/>uigium per impul&longs;um acceptum in anteriora progrediens <lb/>æqualia &longs;patia pertran&longs;ierint, id verè po&longs;&longs;it contingere, vt <lb/>optimè demon&longs;trat Petrus Nonius propo&longs;it. </s> <s id="N12EBA">2. in &longs;equen. <lb/></s> <s id="N12EBE">problem. </s> <s id="N12EC1">Ari&longs;totelis; nullo tamen modo pote&longs;t veri&longs;icari <lb/>virtute eiu&longs;dem tantum remigationis, de qua e&longs;t nobis &longs;er­<lb/>mo; &longs;ed virtute alterius etiam commotionis, aut impul&longs;us, <lb/>vt &longs;equenti quæ&longs;tione patebit. </s> <s id="N12ECA">Quare nihil ex eo colligi po­<lb/>te&longs;t in propo&longs;ito contra Ari&longs;totelem. <!-- KEEP S--></s> </p> <p id="N12ED0" type="main"> <s id="N12ED2">Demum nec minus contra experientiam e&longs;t, per appul­<lb/>&longs;um palmulæ in B ad dexteram &longs;cilicet nauigij, &longs;calmum <lb/>D ferri in G, & &longs;calmum C in F declinando totum <lb/>ip&longs;um nauigium dextror&longs;um per ip&longs;os arcus DG, & CF. <lb/></s> <s id="N12EDC">Siquidem oppo&longs;itum de facto contingit, etiam &longs;i palmula <lb/>vbi B in &longs;copulum appellat, vel immoto alteri corpori ad­<lb/>hæreat. </s> <s id="N12EE3">Videmus enim per impul&longs;um remigum incu&longs;&longs;um <lb/>in parte dextera &longs;calmum, ac nauigium moueri ad &longs;ini&longs;tram. <lb/></s> <s id="N12EE9">Et ratio ip&longs;a &longs;uadet, quia cum nauis ita &longs;upernatet in aqua, <lb/>vt quoquo uer&longs;um dimoueri valeat, quando nouam po&longs;itio­<lb/>nem acquirit, per impul&longs;um in vno tantum latere acceptum <lb/>nece&longs;&longs;ariò intelligitur conuerti circa centrum &longs;uæ grauita­<lb/>tis. </s> <s id="N12EF4">Illi&longs;a igitur palmula in aquam in parte dextera, ab <expan abbr="eaq.">eaque</expan> <lb/>ob re&longs;i&longs;tentiam repul&longs;a, non &longs;ecus ac &longs;emidiametri extre­<lb/>mum, nauim tanquam circulum ad &longs;ini&longs;tram mouebit. <lb/></s> <s id="N12F00">Idem enim efficit aqua remigationi ob&longs;i&longs;tens, ac &longs;i quis pal­<lb/>mulam repelleret in contrariam partem. </s> <s id="N12F05">Cumque talis <lb/>remigatio fiat per modum circuli circa &longs;calmum proceden­<lb/>do dextror&longs;um, &longs;equitur repul&longs;um accipi, ac fieri per op­<lb/>po&longs;itum procedendo &longs;ini&longs;tror&longs;um. </s> <s id="N12F0E">Quamobrem ad hoc, <lb/>vt nauigium rectà antror&longs;um procedat, ex vtraque parte <lb/>&longs;imul remiges conantur impellere, vt ex vtroque motu cir­<lb/>culari, & contrario, re&longs;ultet vnus rectus, ac mixtus. </s> <s id="N12F17">Vt cer­<lb/>nere e&longs;t in hac figura, in qua &longs;it remus AB, cuius manu­<pb pagenum="98" xlink:href="005/01/106.jpg"/>brium A; palmula B, &longs;calmus verò C; ac &longs;patium, <lb/>quod percurrit pal­<lb/><figure id="id.005.01.106.1.jpg" xlink:href="005/01/106/1.jpg"/><lb/>mula per motum <lb/>proprium ip&longs;ius re­<lb/>mi circa &longs;calmum <lb/><expan abbr="tanquã">tanquam</expan> circa cen­<lb/>trum &longs;it arcus BD. <lb/><!-- KEEP S--></s> <s id="N12F38">Dico igitur per im­<lb/>pul&longs;um incu&longs;&longs;um in <lb/>arcu BD palmu­<lb/>lam nece&longs;&longs;ariò re­<lb/>pelli in oppo&longs;itum per arcum BE, ac per con&longs;equens vir­<lb/>tute huiu&longs;modi remigationis, &longs;calmum C, non ferri in <lb/>F, &longs;ed in G; ita vt arcus. </s> <s id="N12F47">CG re&longs;pondeat ip&longs;i BE: Alio­<lb/>quin repul&longs;us non opponeretur impul&longs;ui. </s> <s id="N12F4C">Iam ergo per im­<lb/>pul&longs;um incu&longs;&longs;um ex parte dextera, &longs;calmus C, & vnà cum <lb/>illo nauigium mouebitur ad &longs;ini&longs;tram. </s> <s id="N12F53">Quod cum &longs;imiliter <lb/>verificetur è contra, vt per impetum incu&longs;&longs;um ex parte &longs;i­<lb/>ni&longs;tra, nauigium moueatur ad dexteram: hinc &longs;it, vt ex <lb/>contrarijs motionibus vtrinque procedentibus. </s> <s id="N12F5C">compona­<lb/>tur vnus motus rectus, quo nauigium fertur antror&longs;um, vt <lb/>per lineam mediam, ac rectam CH. </s> <s id="N12F63">Quod valde diuer­<lb/>&longs;um e&longs;t ab eo, quod a&longs;&longs;umebatur à Baldo. </s> </p> <p id="N12F68" type="head"> <s id="N12F6A">Quæ&longs;tio Quinta.</s> </p> <p id="N12F6D" type="main"> <s id="N12F6F">C<emph type="italics"/>vr paruum exi&longs;tens gubernaculum, & in <lb/>extremo nauigio tantas habet vires, vt ab <lb/>exiguo temone: & ab hominis vnius viri­<lb/>bus alioqui modicè vtentis, magnæ nauigio­<lb/>rum moueantur moles? </s> <s id="N12F7D">An quoniam guber­<lb/>naculum vectis e&longs;t, onus autem mare, guber­<lb/>nator verò mouens e&longs;t? </s> <s id="N12F84">Non autem &longs;ecundum latitudinem, <lb/>veluti remus, mare accipit gubernaculum: non enim in ante <lb/>nauigium mouet, &longs;ed ip&longs;um commotum mare accipiens incli-<emph.end type="italics"/><pb pagenum="99" xlink:href="005/01/107.jpg"/><emph type="italics"/>nat obliquè. </s> <s id="N12F94">Quoniam enim pondus e&longs;t mare, contrario inni­<lb/>xum modo nauem inclinat. </s> <s id="N12F99">Hypomochlion enim in contra­<lb/>rium ver&longs;atur: mare verò anteriùs, & illud exteriùs: illud <lb/>autem &longs;equitur nauis, quoniam illi e&longs;t alligata. </s> <s id="N12FA0">Et remus <lb/>quidem &longs;ecundum latitudinem onus propellens, & ab eodem <lb/>repul&longs;us, in rectum propellit: gubernaculum autem vt obli­<lb/>quum iacet, hinc inde in obliquum motionem facit. </s> <s id="N12FA9">In ex­<lb/>tremo autem, & non in medio iacet, quoniam mouenti facilli­<lb/>mum e&longs;t ab extremo motum mouere. </s> <s id="N12FB0">Prima enim pars celer­<lb/>rimè fertur, & quoniam quemadmodum in ijs, quæ ferun­<lb/>tur, in fine deficit latio, &longs;ic ip&longs;ius continui, in fine imbecilli&longs;­<lb/>&longs;ima e&longs;t latio. </s> <s id="N12FB9">Imbecilli&longs;sima autem ad expellendum e&longs;t fa­<lb/>cilis. </s> <s id="N12FBE">Propter hæc igitur in puppi gubernaculum ponitur: <lb/>nec minus, quoniam parua ibi motione facta, multò maius <lb/>interuallum fit in vltimo. </s> <s id="N12FC5">Quia æqualis angulus &longs;emper <lb/>maiorem &longs;pectat, <expan abbr="tantòq.">tantòque</expan> magis, quantò maiores fuerint il­<lb/>læ, quæ continent. </s> <s id="N12FD0">Ex ijs etiam manife&longs;tum e&longs;t, quam ob <lb/>cau&longs;am magis in contrarium procedit nauigium, quàm re­<lb/>mi ip&longs;ius palmula: eadem magnitudo ij&longs;dem mota viribus, <lb/>in aere plus, quàm in aqua progreditur. </s> <s id="N12FD9">Sit enim AB remus, <lb/>C verò &longs;calmus. </s> <s id="N12FDE">A autem in nauigio &longs;it remi principium, B <lb/>verò in mari palmula. </s> <s id="N12FE3">Si igitur A vbi D <expan abbr="tran&longs;tatũ">tran&longs;tatum</expan> e&longs;t, <expan abbr="nõ">non</expan> erit <lb/>B vbi E; æqualis enim BE ip&longs;i AD; æquale igitur tran&longs;tatum <lb/>erit, &longs;ed erat minus. </s> <s id="N12FF2">Erit igitur vbi e&longs;t F, minor enim BF <lb/>ip&longs;a AD, quare ip&longs;a GF, ip&longs;a DG. <!-- KEEP S--></s> <s id="N12FF8">Similes enim &longs;unt trian­<lb/>guli. </s> <s id="N12FFD">Stans autem erit medium, vbi e&longs;t C. <!-- KEEP S--></s> <s id="N13001">In contrarium <lb/>enim ip&longs;i quod in mari e&longs;t, extremo videlicet B procedit, vbi <lb/>extremum in nauigio e&longs;t A. <!-- KEEP S--></s> <s id="N13009">Non procederet autem vbi e&longs;t <lb/>D, ni&longs;i commoueretur nauigium, & ab eo transferretur, vbi <lb/>remi e&longs;t principium. </s> <s id="N13010">Id ip&longs;um etiam facit gubernaculum, ni­<lb/>&longs;i quod (vt dictum e&longs;t retrò) nihil nauigio ad id, quod in ante <lb/>e&longs;t, confert, &longs;ed &longs;olùm puppim in obliquum pellit, vbicumque <lb/>fuerit: in contrarium enim & modo vergit prora. </s> <s id="N13019">Vbi igitur <lb/>applicatum e&longs;t gubernaculum, id oportet rei motæ ceu quoddam <lb/>intelligere medium, & quemadmodum &longs;calmus remo. </s> <s id="N13020">Me­<lb/>dium autem procedit &longs;ecundum quod gubernaculum tran&longs;-<emph.end type="italics"/><pb pagenum="100" xlink:href="005/01/108.jpg"/><emph type="italics"/>fertur. </s> <s id="N1302E">Siquidem intror&longs;us agit, & puppis eò transfertur, <lb/>prora verò ad contrarium vergit. </s> <s id="N13033">In eodem enim exi&longs;tente <lb/>prora, totum transfertur nauigium.<emph.end type="italics"/></s> </p> <p id="N1303A" type="head"> <s id="N1303C">COMMENTARIVS.<!-- KEEP S--></s> </p> <p id="N13040" type="main"> <s id="N13042">Celebris e&longs;t hæc quæ&longs;tio tum propter communem <lb/>admirationem ortam ex paruitate gubernaculi, ac <lb/>temonis re&longs;pectu magnæ molis nauigij, quæ illius <lb/>beneficio circumfertur: tum propter difficultatem, quæ <lb/>circa &longs;olutionem eiu&longs;dem quæ&longs;tionis, ac doctrinam Philo­<lb/>&longs;ophi hic &longs;e&longs;e offert. </s> <s id="N1304F">Quare vt luculentius in expo&longs;itione <lb/>procedamus, di&longs;tinguendum prius nobis erit inter ip&longs;um <lb/>remonem, &longs;eu clauum, & gubernaculum, quamuis ambo ad <lb/>vnicum pertineant in&longs;trumentum, ac &longs;æpe vnum pro alio <lb/>v&longs;urpetur. </s> <s id="N1305A">Temonem itaque in præ&longs;enti vocamus cum <lb/>Ari&longs;totele alam illam ligneam, &longs;eu tabulam ad alæ veluti <lb/>similitudinem efformatam, quæ duplici cardine liberè in <lb/>dor&longs;o puppis affigitur, <expan abbr="mariq.">marique</expan> ex parte immergitur, & pro <lb/>opportunitate huc atque illuc ad directionem nauis con­<lb/>uertitur. </s> <s id="N1306B">Gubernaculum verò appellamus an&longs;am, qua te­<lb/>mo ip&longs;e manu cietur; cuius videlicet alterum extremum <lb/>lato foramine excipit caput temonis; alterum intra nauim <lb/>&longs;e extendit tanquam manubrium ad v&longs;um Gubernatoris. </s> </p> <p id="N13074" type="main"> <s id="N13076">Deinde duplex con&longs;ideranda erit motio nauis mediante <lb/>huiu&longs;cemodi in&longs;trumento, quod ex gubernaculo, ac temo­<lb/>ne con&longs;truitur. </s> <s id="N1307D">Vna e&longs;t, quæ à gubernatore procedit per <lb/>motum ip&longs;ius gubernaculi, ac temonis, &longs;iue nauis aliunde <lb/>etiam moueatur &longs;iue quie&longs;cat. </s> <s id="N13084">Quandoquidem dum temo, <lb/>qui rectà manebat mouetur in tran&longs;uer&longs;um pura ad dexte­<lb/>ram, vel &longs;ini&longs;tram, nece&longs;&longs;ariò, maris <expan abbr="portion&etilde;">portionem</expan> propellit ver­<lb/>&longs;us eam partem, in quam inclinatur, <expan abbr="nece&longs;&longs;arioq:">nece&longs;&longs;arioque</expan> ab ea pro­<lb/>pter re&longs;i&longs;tentiam repellitur in contrarium: & &longs;ic temo cum <lb/>puppi, cui e&longs;t affixus, repul&longs;o accepto in dextera, mouebi­<lb/>tur ad &longs;ini&longs;tram, vel è conuer&longs;o. </s> <s id="N13097">Non enim aliter &longs;e habet <lb/>gubernaculum &longs;imul cum temone in hac motione, quàm <lb/>remus con&longs;titutus in cu&longs;pide puppis per longum iuxta re-<pb pagenum="101" xlink:href="005/01/109.jpg"/>ctitudinem carinæ, ita vt &longs;calmus &longs;it in ip&longs;a cu&longs;pide, manu­<lb/>brium intra puppim, & palmula foris mari immer&longs;a. </s> <s id="N130A5">Quia <lb/>nimirum eodem pacto &longs;i remi palmula mare propellerer ad <lb/>dexteram, ab eo vtique per re&longs;i&longs;tentiam repul&longs;a, &longs;imul cum <lb/>toto remo, &longs;calmo, ac puppi pergeret ad &longs;ini&longs;tram prora <lb/>manente immota, vel qua&longs;i immota. </s> <s id="N130B0">Et hoc pacto magna <lb/>nauigia ab&longs;que remis &longs;olo temone conuerti &longs;olent in <lb/>portu. </s> </p> <p id="N130B7" type="main"> <s id="N130B9">Altera verò motio nauis, quæ &longs;it mediante gubernaculo, <lb/>ac temone, e&longs;t illa, quæ non procedit ab ip&longs;o gubernatore <lb/>tanquam à mouente, &longs;ed tanquam à &longs;u&longs;tinente temonem <lb/>in obliqua po&longs;itione ad excipiendum impetum maris oc­<lb/>currentis, quo nauis ip&longs;a aliquantulum inclinatur. </s> <s id="N130C4">Obliquè <lb/>namque con&longs;tituto temone, <expan abbr="nauigioq.">nauigioque</expan> ad anteriora progre­<lb/>diente, nece&longs;&longs;ariò mare obuians temonem in ea parte, qua <lb/>tran&longs;uer&longs;um e&longs;t, offendit, <expan abbr="ip&longs;umq.">ip&longs;umque</expan> repellit. </s> <s id="N130D5">Per quem repul­<lb/>&longs;um temo ip&longs;e cum recta in contrarium ferri non po&longs;&longs;it, vi­<lb/>delicet retror&longs;um, eo quod puppi &longs;it affixus procedenti an­<lb/>tror&longs;um, obliquè &longs;altem ab itinere dimouetur, & cum eo <lb/>tota nauis à latere aliquantulum circumuertitur, vt mox in­<lb/>fra latius explicabitur. </s> <s id="N130E2">Illud interim adnotando, eandem <lb/>e&longs;&longs;e rationem de aqua in contrarium fluente, temonemque <lb/>cum naui &longs;tantem feriente, ac de aqua &longs;tante, inquam temo <lb/>obliquè con&longs;titutus dum fertur cum naui offendat. </s> <s id="N130EB">Non <lb/>minus enim vim patitur &longs;olidum manens à fluido currente, <lb/>quod excipit, vt velum à vento, quàm &longs;olidum currens à <lb/>fluido manente; vt verticilla ex papiro, quæ dum ge&longs;tantur <lb/>à pueris currentibus, circumaguntur ab aere quie&longs;cente, vel <lb/>tenuiter obuiante. </s> </p> <p id="N130F8" type="main"> <s id="N130FA">His ergo prænotatis facilè vim &longs;olutionis Ari&longs;totelis in <lb/>hac quæ&longs;tione percipiemus. </s> <s id="N130FF">Ait enim ex eo gubernaculum, <lb/>ac temonem tantas vires habere in motione nauis, quod <lb/>vtrunque &longs;e habeat tanquam vectis, mare autem tanquam <lb/>onus, & gubernator, tanquam potentia. </s> <s id="N13108">Et enim &longs;i loqua­<lb/>mur de prima motione &longs;upra explicata, non minus in illa <lb/>habet rationem vectis gubernaculum cum temone, quàm <pb pagenum="102" xlink:href="005/01/110.jpg"/>remus; Nec minus con&longs;tituitur mouens gubernator, quàm <lb/>remiger, vt per &longs;e patet. </s> <s id="N13116">Si verò loquamur de &longs;ecunda mo­<lb/>tione, adhuc idem in&longs;trumentum in illa con&longs;tituitur vectis <lb/>ad &longs;u&longs;tinendum impetum maris; innixum &longs;cilicet fulcimen­<lb/>to, &longs;eu cardini, quo puppi coniungitur: Non &longs;ecus, ac quod­<lb/>libet lignum alteri quomodolibet innixum ad &longs;u&longs;tinendum <lb/>onus impo&longs;itum. </s> <s id="N13123">Gubernator autem con&longs;tituitur potentia, <lb/>nam adhibendo gubernaculum, temonem ip&longs;um &longs;u&longs;tentat <lb/>obliquum contra fluctus maris, veluti qui vecte pondus <lb/>quod cumque &longs;u&longs;tinet, etiam &longs;i non moueatur. </s> <s id="N1312C">Mare deni­<lb/>que in vtraque motione con&longs;tituitur onus; quoniam vel e&longs;t <lb/>id quod propellitur, vel id quod &longs;u&longs;tinetur per temonem <lb/>tran&longs;uer&longs;um ne directè in oppo&longs;itum fluat. </s> </p> <p id="N13135" type="main"> <s id="N13137">Quamobrem immeritò nonnulli Ari&longs;totelem <expan abbr="redarguũt">redarguunt</expan>, <lb/>dicentes, mare habere potius rationem potentiæ mouentis <lb/>totam puppim cum temone; Nam &longs;icut &longs;axum, vectem cui <lb/>imponitur &longs;emper premit appetendo de&longs;cen&longs;um ad ima, <lb/>& tamen e&longs;t onus re&longs;pectu potentiæ, quæ vectem &longs;u&longs;tinet in <lb/>illo &longs;itu, ita mare, licet &longs;ucce&longs;&longs;iuè temonem impellat, ratio­<lb/>nem habet oneris re&longs;pectu potentiæ manu tenentis temo­<lb/>nem in illo &longs;itu contra ictus eiu&longs;dem maris. </s> <s id="N1314C">Quod &longs;i ip&longs;e <lb/>temo cum puppi, cui adhæret verè &longs;imul moueatur à mare, <lb/>per accidens e&longs;t, <expan abbr="proceditq.">proceditque</expan> à fluxibilitate aquæ, in qua diu <lb/>permanere non pote&longs;t puppis omnino immota ad &longs;u&longs;tinen­<lb/>dum in &longs;uo cardine ip&longs;um temonem. </s> <s id="N1315B">Motus enim fulcimen­<lb/>ti per accidens &longs;e habet ad motum, vel operationem pro­<lb/>priam vectis; vt motus &longs;calmi cum naui, cui e&longs;t affixus ad <lb/>motionem remi, qui tanquam vectis fulcitur in illo; vel mo­<lb/>tus cuiuslibet fulcimenti, quod a&longs;portatur cum curru, ad <lb/>motionem vectis eidem innixi. </s> <s id="N13168">Vnde potentia re&longs;pectu ve­<lb/>ctis dicitur illa, quæ vectem adhibet, onus mouendo, vel &longs;u­<lb/>&longs;tentando, non autem illa, quæ mouet fulcimentum. </s> <s id="N1316F">Quare <lb/>tunc rectè mare diceretur potentia, cum mediante impetu <lb/>incu&longs;&longs;o in temonem, ip&longs;o tanquam vecte adhibito, moueret <lb/><expan abbr="manũ">manum</expan> gubernatoris. </s> <s id="N1317B"><expan abbr="Cũ">Cum</expan> igitur contra accidat, nempe, vt po­<lb/>tius gubernator adhibito temone mare ad latus depellat, <pb pagenum="103" xlink:href="005/01/111.jpg"/>vel <expan abbr="&longs;alt&etilde;">&longs;altem</expan> excipiat re&longs;i&longs;tendo, iure & <expan abbr="quid&etilde;">quidem</expan> optimo guberna­<lb/>tor ab Ari&longs;totele con&longs;tituitur potentia, mare autem onus. </s> </p> <p id="N13192" type="main"> <s id="N13194">Sic autem explicato principio, ac in&longs;trumento vtriu&longs;que <lb/>motionis, explicat Ari&longs;toteles modum, quo procedit &longs;ecun­<lb/>da motio à nobis propo&longs;ita, quæ poti&longs;&longs;ima e&longs;t, & maioris <lb/>longè momenti quam prima: <expan abbr="aitq.">aitque</expan> temonem (quem cum <lb/>gubernaculo &longs;æpè confundit) non accipere mare &longs;ecundum <lb/>latitudinem nauis, &longs;eu quod ad latera nauis e&longs;t, eo modo <lb/>quo accipit remus, depellendo illud retror&longs;um, vt per repul­<lb/>&longs;um inde acceptum, nauigium feratur antror&longs;um, quia nihil <lb/>temo nauigio confert, quo ad motum antror&longs;um, vt in fine <lb/>etiam quæ&longs;tionis idem Philo&longs;ophus animaduertit: Sed ac­<lb/>cipere mare commotum, quod illi obuiat &longs;ecundum longi­<lb/>tudinem nauis à prora in puppim. </s> <s id="N131B1">Nam qua parte temo <lb/>vergit foris, <expan abbr="matiq.">matique</expan> eius ala obuertitur ad alterum latus na­<lb/>uigij, mare &longs;ecundum longitudinem nauis ei obuians exci­<lb/>pit intra <expan abbr="angulũ">angulum</expan>, quem cum naui con&longs;tituit. </s> <s id="N131C2">Excipiendo au­<lb/>tem illud vim patitur in <expan abbr="contrariũ">contrarium</expan>, <expan abbr="tollereturq">tollereturque</expan> ni&longs;i fulciretur <lb/>in cardine. </s> <s id="N131CD">Cum igitur nec auferri po&longs;&longs;it à puppi, nec retro­<lb/>cedere in <expan abbr="directũ">directum</expan> <expan abbr="cõtra">contra</expan> cur&longs;um nauigij, hinc fit, vt cedendo <lb/><expan abbr="&longs;alt&etilde;">&longs;altem</expan> in parte quoad po&longs;itionem, <expan abbr="quã">quam</expan> prius habebat, nauem <lb/><expan abbr="ipsã">ipsam</expan> inclinet obliquè; &longs;iqui­<lb/><figure id="id.005.01.111.1.jpg" xlink:href="005/01/111/1.jpg"/><lb/>dem dimoto vno latere an­<lb/>guli à &longs;ua po&longs;itione, <expan abbr="alterũ">alterum</expan> <lb/>dimoueri nece&longs;&longs;e e&longs;t, cu&longs;pi­<lb/>de manente in eodem &longs;itu. <lb/></s> <s id="N131FB">Quod &longs;ic pote&longs;t amplius <lb/>explicari. </s> <s id="N13200">E&longs;to nauis AB; <lb/>cuius puppis A, prora B, te­<lb/>mo verò AC obliquè con­<lb/>&longs;titutus ad &longs;ini&longs;tram, ac &longs;uf­<lb/>fultus in A, vbi eius cardo <lb/>ad puppim po&longs;itus e&longs;t, & <lb/>vbi <expan abbr="angulũ">angulum</expan> efficiat <expan abbr="cũ">cum</expan> <expan abbr="lõgi-tudine">longi­<lb/>tudine</expan> nauis, qui &longs;it BAC. <lb/></s> <s id="N1321E">Deinde mare obuians incidat in ip&longs;am AC. <!-- KEEP S--></s> <s id="N13222">Tunc dicimus <pb pagenum="104" xlink:href="005/01/112.jpg"/>punctum C fore, vt transferatur ver&longs;us D; punctum verò <lb/>B, quod proram de&longs;ignat, ver&longs;us E, cardine manente <lb/>immoto vbi A. <!-- KEEP S--></s> <s id="N1322F">Etenim cum mare &longs;olum impellat temo­<lb/>nem inquantum obliquè con&longs;tituitur, & à nauis rectitudine <lb/>deuiat, efficacius impellit extremum vbi C, quod magis <lb/>elongatur ab ea, quàm reliquas partes, quæ minus, ac mi­<lb/>nus di&longs;tant. </s> <s id="N1323A"><expan abbr="Proindeq">Proindeque</expan> remi&longs;&longs;ius, ac remi&longs;&longs;ius agit in illas <lb/>vniformiter difformiter v&longs;que ad punctum A, vbi &longs;icut ter­<lb/>minatur di&longs;tantia, ac diuitatio, ita etiam deficit impul&longs;us. </s> <s id="N13241">Ex <lb/>quo &longs;equitur punctum A, per&longs;e non moueri ad talem im­<lb/>pul&longs;um, &longs;ed tantum lineam AC circa illud tanquam &longs;emi­<lb/>diametrum circa centrum conuerti, ac declinare ver&longs;us D. <lb/><!-- KEEP S--></s> <s id="N1324C">Cumque longitudo nauis angulum cum ip&longs;a latitudine te­<lb/>monis efficiat, &longs;equitur vlterius, vt tran&longs;lato ip&longs;o latere <lb/>AC, in AD, &longs;imul transferatur AB in AE, quod e&longs;t na­<lb/>uem declinare à &longs;ua rectitudine, ad obliquam po&longs;itionem <lb/>temonis mare intra angulum excipientis. </s> <s id="N13257">Diximus punctum <lb/>A per &longs;e non moueri ob talem impul&longs;um, nam per acci­<lb/>dens, nempe propter maris incon&longs;tantiam, ac fluxibilitatem <lb/>etiam ip&longs;um puppis extremum aliquantulum dimouetur <lb/>cum cardine, quo temo fulcitur, &longs;icut quodlibet fulcimen­<lb/>tum ad motum vectis ob incon&longs;tantiam &longs;oli. </s> </p> <p id="N13264" type="main"> <s id="N13266">Contrario autem modo temonem innixum, ait Ari&longs;tote­<lb/>les nauem inclinare, quoniam temo rationem habet vectis, <lb/>vt dictum e&longs;t cardini innixi tanquam fulcimento, mare au­<lb/>tem &longs;e habet, vt onus: At omnis vectis mediat inter fulci­<lb/>mentum, & onus, nec aliter quam fulcimento tanquam cen­<lb/>tro inhærendo, onus per modum circuli in contrarium mo­<lb/>uet, aut certè &longs;u&longs;tinet in tali po&longs;itione; Ergo dum temo &longs;u­<lb/>&longs;tinet mare cardini innixus tamquam fulcimento, & angu­<lb/>lum cum naui efficit ad excipiendum mare interius, cardo <lb/>manebit exterius tanquam ex alia parte ip&longs;ius vectis illi <lb/>contraria, ad quam facit nauem inclinari. </s> </p> <p id="N1327D" type="main"> <s id="N1327F">Ad hæc Ari&longs;toteles rationem quandam affert cur in ex­<lb/>tremo nauigij, & non in medio temo, &longs;eu clauus locetur, <lb/><expan abbr="aitq.">aitque</expan> eam e&longs;&longs;e, quoniam id quod fertur, facilius ab incepto <pb pagenum="105" xlink:href="005/01/113.jpg"/>itinere, &longs;eu à rectitudine &longs;ui motus declinat, cum in po&longs;tre­<lb/>ma eius parte ex latere diuer&longs;um aliquem impul&longs;um acce­<lb/>pit, quàm &longs;i accipiat in alia parte anteriori. </s> <s id="N13292">Prima enim. <lb/></s> <s id="N13296">&longs;eu anterior pars lati <expan abbr="cõtinui">continui</expan>, inten&longs;iori impetu fertur, quàm <lb/>partes &longs;ub&longs;equentes, <expan abbr="validiu&longs;q.">validiu&longs;que</expan> propterea in &longs;uo motu per&longs;i­<lb/>&longs;tit, <expan abbr="contrarijsq.">contrarijsque</expan> omnibus ob&longs;i&longs;tit. </s> <s id="N132A9">E contra verò vltima. <lb/></s> <s id="N132AD">pars, tanquam remi&longs;&longs;iorem vim con&longs;ecuta, imbecillius mo­<lb/>uetur, ac facilius cædit. </s> <s id="N132B2">Id quod maximè in proiectis ob­<lb/>&longs;eruare licebit. </s> <s id="N132B7">Impetus namque in ea à proijciente im­<lb/>pre&longs;&longs;us, &longs;emper maior e&longs;t in eorum parte anteriori, quàm in <lb/>&longs;equentibus: &longs;eu illa pars eorum con&longs;tituitur anterior, cæ­<lb/><expan abbr="terasq">terasque</expan> in latione præcedit, in qua maior impetus fuerit <lb/>impre&longs;&longs;us. </s> <s id="N132C2">Vnde cum den&longs;itas materiæ, aut grauitas &longs;ubie­<lb/>cti, inten&longs;ioris impetus capax redat ip&longs;um proiectum, hinc <lb/>fit, vt etiam &longs;i in principio motus pars grauior, vel den&longs;ior <lb/>fuerit po&longs;terior in progre&longs;&longs;u euadat anterior. </s> <s id="N132CB">Quod apertè <lb/>in proiectione baculi experimur quando anteponitur extre­<lb/>mum leuius, & po&longs;ponitur grauius; nam ex &longs;e ip&longs;a extrema <lb/>permutantur in aere, <expan abbr="priusq.">priusque</expan> grauius quàm leuius quo ten­<lb/>debant pertingit. </s> <s id="N132DA">Certum ergo relinquitur, vt quo ante­<lb/>riores fuerint partes ip&longs;is lati continui, eo validius ferantur <lb/>tanquam maiorem adeptæ, aut &longs;ortitæ impetum, quo verò <lb/>po&longs;teriores, eo imbecillius, vnde etiam facilius vincantur. <lb/></s> <s id="N132E6">Hoc ip&longs;um itaque applicando in latione nauis, ait Ari&longs;tote­<lb/>les, quod cum nauis rectà fertur antror&longs;um, facilius e&longs;t illam <lb/>à cur&longs;u deflectere puppim à latere impellendo, quàm aliam <lb/>eiu&longs;dem nauis partem mediam, aut proram. </s> <s id="N132EF">Siquidem in <lb/>puppi tanquam in po&longs;trema lati corporis parte imbecilli&longs;&longs;i­<lb/>ma virtus e&longs;t impetus impre&longs;&longs;i, in <expan abbr="eaq.">eaque</expan> terminatur, ac deficit <lb/>latio. </s> <s id="N132FC">Quare appo&longs;itè clauus in puppi locatur ad excipien­<lb/>dos ibi maris impul&longs;us, vt facilius à rectitudine itineris na­<lb/>uis ip&longs;a deflectat. </s> </p> <p id="N13303" type="main"> <s id="N13305">Quæ profectò Ari&longs;totelis doctrina, <expan abbr="eiusq">eiusque</expan> applicatio, &longs;a­<lb/>no modo intelligenda e&longs;t. </s> <s id="N1330A">Nam licet quando nauigia vni­<lb/>co velo in prora locato feruntur, præcipuus impetus per <lb/>malum circa ip&longs;am proram incutiatur; nihilominus quando <pb pagenum="106" xlink:href="005/01/114.jpg"/>remis, vel pluribus velis nauigare contingit, <expan abbr="puppisq.">puppisque</expan> pari­<lb/>ter obtinet &longs;uum; res aliter &longs;e habet, cum pari, aut maiori <lb/>impetu, tunc puppis quàm prora feratur, quippe quæ illum <lb/>refundere etiam valeat vlterius in ip&longs;am proram. </s> <s id="N13320">Id quod <lb/>patet cum ex maiori velocitate, qua mouetur nauigium, ac <lb/>ip&longs;a prora adhibitis etiam velis, aut remis in puppi, &longs;eu pro­<lb/>pe illam; tum ex maiori conatu, quem adhibent remiges, <lb/>quò magis prope puppim remigauerint; vt hinc in triremi­<lb/>bus ad priores &longs;ingulos remos promouendos con&longs;tituantur <lb/>remiges quini, aut &longs;eni, ad reliquos verò, proram ver&longs;us pro­<lb/>cedendo, quaterni, ac tandem terni. </s> <s id="N13331">Vbi autem maior co­<lb/>natus adhibetur, ibi maior imprimitur impetus. </s> <s id="N13336">Rur&longs;umque <lb/>ob&longs;eruandum e&longs;t impetum, quo per velificationem feruntur <lb/>nauigia, non imprimi in &longs;ola parte, quam antror&longs;um promo­<lb/>uet malus, &longs;ed in ijs quoque partibus vbi funes quibus vela <lb/>retrouer&longs;um tenduntur alligari &longs;olent. </s> <s id="N13341">Etenim magna e&longs;t <lb/>vis, qua per funes, qui dicuntur opiferi, partes nauis vbi pro­<lb/>pe puppim illi colligantur ab antennæ cornibus trahuntur. <lb/></s> <s id="N13349">Vrgent enim antror&longs;um ip&longs;a cornua non minus, ac &longs;æpè ma­<lb/>gis quàm malus; nec alibi eorum impetus recipi pote&longs;t, <lb/>quàm vbi ip&longs;i funes opiferi alligantur. </s> <s id="N13350"><expan abbr="Similiaq.">Similiaque</expan> dici po&longs;­<lb/>&longs;unt de funibus, qui dicuntur propedes, quique veli inferio­<lb/>ra retrouer&longs;um pariter tendentes in po&longs;teriori parte nauis <lb/>ita colligantur, vt repentino <expan abbr="&longs;uperueni&etilde;te">&longs;uperueniente</expan> turbine, vel quan­<lb/>do opus fuerit relaxari protinus po&longs;&longs;int: Nam per hos quo­<lb/>que funes maximè partes ip&longs;æ po&longs;teriores nauis trahuntur. <lb/></s> <s id="N13365">Ex quibus apparet non minus in puppi, quàm in prora im­<lb/>petum iugiter imprimi ad procedendum antror&longs;um. </s> <s id="N1336A">Quare <lb/>Ari&longs;totelis doctrina de ijs, quæ feruntur, & in fine imbecil­<lb/>lam obtinent lationem, non &longs;emper applicari pote&longs;t in la­<lb/>tione nauis, vt ex ip&longs;o retulimus. </s> </p> <p id="N13373" type="main"> <s id="N13375">Aliam deinde, ac &longs;olidiorem rationem eiu&longs;dem &longs;ituatio­<lb/>nis temonis Ari&longs;toteles &longs;ubnectit. </s> <s id="N1337A">Quia nimirum parua mo­<lb/>tione per temonem facta in eo &longs;itu, multo maius interual­<lb/>lum prora obliquè declinando percurrit, vt patere pote&longs;t <lb/>ex præcedenti figura <expan abbr="tantoq.">tantoque</expan> magis, quanto longior fuerit <pb pagenum="107" xlink:href="005/01/115.jpg"/>ip&longs;a nauis. </s> <s id="N1338C">Etenim idem, vel æqualis angulus, quo in­<lb/>ter longiores lineas continetur, eo maiorem ba&longs;im &longs;ubten­<lb/>dit, &longs;eu &longs;pectat, vt con&longs;tare etiam pote&longs;t per quartam propo­<lb/>&longs;itionem &longs;exti Euclidis. <!-- KEEP S--></s> <s id="N13396">Cum igitur longitudo nauis con&longs;i­<lb/>derata in priori &longs;itu, deinde in po&longs;teriori po&longs;t <expan abbr="motion&etilde;">motionem</expan> <expan abbr="cir-cular&etilde;">cir­<lb/>cularem</expan>, immota ferè manente cu&longs;pide puppis, <expan abbr="angulũ">angulum</expan> quen­<lb/>dam efficiat, vt BAE, cuius ba&longs;is EB: tanto maiorem ip&longs;a <lb/>prora veluti ba&longs;im tran&longs;mittet ad motionem temonis quan­<lb/>to longior fuerit ip&longs;a nauis. </s> <s id="N133AF">Quod quippe non contingeret <lb/>&longs;i alibi temo con&longs;titutus <lb/>fui&longs;&longs;et, <expan abbr="indeq">indeque</expan> talis motio <lb/><figure id="id.005.01.115.1.jpg" xlink:href="005/01/115/1.jpg"/><lb/>initium &longs;umeret. </s> <s id="N133BE">Quam­<lb/>obrem con&longs;entanea idem <lb/>Ari&longs;toteles protulit lib. de <lb/>motu animal. <!-- KEEP S--></s> <s id="N133C8">cap. 5. cum <lb/>ad explicandum quomo­<lb/>do parua permutatio, quæ <lb/>fit in principio, magnas, & <lb/>multas efficiat differentias <lb/>procul; exemplum adhi­<lb/>bens ait, vt temone pau­<lb/>lulum quid tran&longs;po&longs;ito, <lb/>multa proræ fit tran&longs;po­<lb/>&longs;itio. </s> </p> <p id="N133DD" type="main"> <s id="N133DF">Ex ijs autem ad aliam quæ&longs;tionem valde implexam. <lb/></s> <s id="N133E3">Ari&longs;toteles pertran&longs;it, cuius &longs;olutionem hic in&longs;erit, vt po­<lb/>&longs;tea ex ea melius præfata confirmet. </s> <s id="N133E8">Ait igitur ex ijs etiam <lb/>manife&longs;tum e&longs;&longs;e, quam ob cau&longs;am magis procedat naui­<lb/>gium antror&longs;um, quàm ip&longs;ius remi palmula mare reijciens <lb/>cædat retror&longs;um. </s> <s id="N133F1">Eadem enim (inquit) magnitudo, ij&longs;­<lb/>dem mota viribus, plus in aere progreditur, quàm in aqua; <lb/>eo &longs;cilicet, quod minorem in aere inueniat re&longs;i&longs;tentiam. <lb/></s> <s id="N133F9">Quod ip&longs;e quamuis ob&longs;curè propter defectum quorundam <lb/>verborum, ac fal&longs;itatem characterum, quibus figuram pro­<lb/>ponit, &longs;ic ferè explicat in propo&longs;ito. </s> <s id="N13400">Sit remus AB, &longs;cal-<pb pagenum="108" xlink:href="005/01/116.jpg"/><figure id="id.005.01.116.1.jpg" xlink:href="005/01/116/1.jpg"/><lb/>mus verò C, remi manubrium A, palmula in mari B. <lb/></s> <s id="N1340F">Si igitur manubrium A per aerem transferatur in D; vti­<lb/>que palmula B transferri non poterit per aquam in E. <lb/><!-- KEEP S--></s> <s id="N13416">Quandoquidem non po&longs;&longs;et cum maiori re&longs;i&longs;tentia æquale <lb/>&longs;patium pertran&longs;ire, quemadmodum e&longs;t &longs;patium BE ip&longs;i <lb/>AD. <!-- KEEP S--></s> <s id="N1341E">Quare palmula B retrocedet tantum v&longs;que ad F, <lb/><expan abbr="eritq.">eritque</expan> remus in DF, vbi &longs;patium retroce&longs;&longs;ionis palmulæ <lb/>con&longs;tituitur minus. </s> <s id="N13428">Nam &longs;i con&longs;iderentur duo trianguli, <lb/>AGD, & BGF; erunt &longs;imiles ex quarta propo&longs;itione <lb/>&longs;exti, ac propterea latera vnius, lateribus alterius erunt <lb/>proportionalia: Cumque latus GF minus &longs;i latere GD, <lb/>etiam latus BF, minus erit latere AD. <!-- KEEP S--></s> </p> <p id="N13434" type="main"> <s id="N13436">Addit præterea Ari&longs;toteles, quod inter i&longs;tos duos motus <lb/>contrarios id quod &longs;tabit, &longs;eu manebit, erit medium pun­<lb/>ctum vbi C, nempe vbi con&longs;tituitur &longs;calmus circa quem <lb/>remus conuertitur. </s> <s id="N1343F">Siquidem verè re&longs;pectu manubrij, ac <lb/>palmulæ, tanquam extremorum diametri circulariter du­<lb/>ctæ, &longs;calmus ip&longs;e tanquam <expan abbr="c&etilde;trum">centrum</expan> manebit. </s> <s id="N1344C">Quare &longs;calmus <lb/>C nunquam procederet ad partes D, nempe antror&longs;um, <lb/>ni&longs;i commoueretur nauigium, cui e&longs;t affixus, & eo transfer­<lb/>retur, vbi remi e&longs;t principium, cum &longs;emper nauigium per <lb/>impul&longs;um in ip&longs;a remigatione acceptum, &longs;equatur motum. <lb/></s> <s id="N13458">principij mouentis nempe manubrij à quo fertur antror­<lb/>&longs;um, & &longs;ic impo&longs;ito per motum manubrij ab A v&longs;que ad <lb/>D, &longs;calmus, qui erat in C, con&longs;tituetur in H, palmula re­<lb/>trocedente à B v&longs;que ad F. <!-- KEEP S--></s> </p> <p id="N13462" type="main"> <s id="N13464">Hæc paucis mutatis, vel adiunctis Ari&longs;toteles profert, <lb/>quæ &longs;anè licet probent maius e&longs;&longs;e &longs;patium AD, quod ma-<pb pagenum="109" xlink:href="005/01/117.jpg"/>nubrium conficit antror&longs;um; quam &longs;patium BF, quod pal­<lb/>mula tran&longs;mittit retror&longs;um; non tamen probant prout opus <lb/>erat, &longs;patium quoque CH, quod à &longs;calmo cum naui per­<lb/>curritur, maius e&longs;&longs;e, quàm &longs;patium, quod in contrarium pr&etail;­<lb/>terit palmula, vt BF, vel aliud &longs;imile. </s> <s id="N13476">Quare occa&longs;ionem <lb/>nobis tribuunt explicandi, num &longs;emper hoc accidat, vt ma­<lb/>gis in anteriora progrediatur nauigium, quàm ip&longs;ius remi <lb/>palmula retrocedat, an verò quandoque tantum, & qua. <lb/></s> <s id="N13480">ratione fiat. </s> </p> <p id="N13483" type="main"> <s id="N13485">Dicendum ergo e&longs;t, <expan abbr="aliquãdo">aliquando</expan> <expan abbr="nauigiũ">nauigium</expan> in <expan abbr="anterĩora">anterinora</expan> moue­<lb/>ri ab&longs;que eo, quod palmula retrocedat, aliquando verò tan­<lb/>tum prouehi nauigium, quantum palmula retroce&longs;&longs;erit; &longs;ed <lb/>vt plurimum, magis procedi nauigium, quàm palmula in. <lb/></s> <s id="N1349C">contrarium cædat. </s> </p> <p id="N1349F" type="main"> <s id="N134A1">Prima pars huius a&longs;&longs;ertionis in duobus ca&longs;ibus verifica­<lb/>tur. </s> <s id="N134A6">Prior e&longs;t, cum æquale &longs;patium pertran&longs;ierit nauigium, <lb/>ac remi manubrium motu proprio, quo &longs;cilicet circa &longs;cal­<lb/>mum conuertitur: tunc eorum palmula manet immota. <lb/></s> <s id="N134AE">Nam &longs;i exempli gratia nauigium pertran&longs;eat palmum &longs;pa­<lb/>tij, manubrium verò &longs;imul &longs;uo motu proprio alterum, iam, <lb/>in fine ip&longs;ius remigationis ip&longs;um manubrium per duos pal­<lb/>mos di&longs;tabit à loco priori vnde di&longs;ce&longs;&longs;erat. </s> <s id="N134B7">At palmula cum <lb/>per motum quidem nauigij anterius tran&longs;lata e&longs;&longs;et ad &longs;pa­<lb/>tium vnius palmi, per motum verò manubrij &longs;imul retro­<lb/>ce&longs;&longs;i&longs;&longs;et ad alium palmum (siquidem tantum retrocedit pal­<lb/>mula quantum antecedit manubrium motu proprio, &longs;uppo­<lb/>&longs;ito, quod æquè di&longs;tent à &longs;calmo) &longs;equitur verè ac &longs;implici­<lb/>ter ip&longs;am palmulam dimotam non fui&longs;&longs;e. </s> <s id="N134C6">Sicut homo qui <lb/>pari pa&longs;&longs;a graditur contra cur&longs;um nauigij à prora in pup­<lb/>pim, &longs;impliciter non mouetur, quia &longs;emper eandem &longs;eruat <lb/>di&longs;tantiam à punctis fixis, vt a terra, vel cælo. </s> </p> <p id="N134CF" type="main"> <s id="N134D1">Notandum tamen e&longs;t in ca&longs;u de&longs;cripto, nauigium non. <lb/></s> <s id="N134D7">moueri &longs;ola virtute eiu&longs;dem remigationis. </s> <s id="N134DA">Nam &longs;patium, <lb/>quod percurrit virtute illius, nec computari po&longs;&longs;et vltra il­<lb/>lud, quod &longs;imul percurrit manubrium motu proprio; nec <lb/>vnquam e&longs;&longs;et illi equale. </s> <s id="N134E3">Semper enim plus mouetur ma-<pb pagenum="110" xlink:href="005/01/118.jpg"/>nubrium, quam &longs;calmus eodem tempore ad impulsum il­<lb/>lius; nauis autem mouetur ad motum &longs;calmi. </s> <s id="N134ED">Quod clarius <lb/>patebit in &longs;ubiecta figura; in qua &longs;it remus AB, cuius ma­<lb/>nubrium A, pal­<lb/><figure id="id.005.01.118.1.jpg" xlink:href="005/01/118/1.jpg"/><lb/>mula B, &longs;calmus <lb/>verò &longs;it in pun­<lb/>cto medio vbi C. <lb/><!-- KEEP S--></s> <s id="N13502">Deinde promo-­<lb/>ueatur manubrium <lb/>A motu proprio <lb/>v&longs;que ad D, palmula manente in B. </s> <s id="N1350B">Scalmus verò C, <lb/>eodem tempore pertran&longs;eat &longs;patium CE, quod &longs;it æquale <lb/>ip&longs;i AD; <expan abbr="&longs;ubtendanturq.">&longs;ubtendanturque</expan> æquales rectæ ip&longs;is arcubus AD, <lb/>& CE, & con&longs;tituatur paralellogrammum DECA, &longs;u­<lb/>per ip&longs;um AB. <!-- KEEP S--></s> <s id="N1351B">Tunc dico &longs;calmum C vnà cum nauigio <lb/>tran&longs;latum non fui&longs;&longs;e v&longs;que ad E virtute &longs;ola eiu&longs;dem re­<lb/>migationis, &longs;eu proprij motus manubrij ab A v&longs;que ad D, <lb/>palmula manente in B. </s> <s id="N13524">Siquidem hoc &longs;olo motu remus <lb/>AB con&longs;titueretur in recta DB, cuius punctum medium <lb/>vbi &longs;calmus po&longs;itus e&longs;t e&longs;&longs;et in F, non autem in E, qua <lb/>pertran&longs;ire non pote&longs;t recta DB. </s> <s id="N1352D">Coincideret enim cum <lb/>linea DE paralella ip&longs;i AC; <expan abbr="proindeq.">proindeque</expan> per 35. definitio­<lb/>nem primi nunquam concurreret cum illa in punctum B, <lb/>vbi &longs;upponitur palmula. </s> <s id="N1353A">Cum autem linea CF minor &longs;it, <lb/>quàm CE, vel AD, quæ&longs;unt æquales: (Nam re&longs;pectu <lb/>vnius &longs;e habet tanquam pars ad totum, re&longs;pectu verò alte­<lb/>rius, con&longs;tituitur ba&longs;is anguli B, quæ per quartam propo­<lb/>&longs;itionem &longs;exti minor e&longs;t quam ba&longs;is AD, quæ longioribus <lb/>lineis continentibus &longs;ubtenditur eidem angulo B) &longs;equitur <lb/>per motum, quo manubrium ab A transfertur in D, &longs;cal­<lb/>mum cum naui pertran&longs;ire non po&longs;&longs;e ad æquale &longs;patium <lb/>v&longs;que ad E. <!-- KEEP S--></s> <s id="N1354E">Quod &longs;i illuc u&longs;que pertingat, id certè contin­<lb/>gere debet virtute alterius impul&longs;us aliunde incu&longs;&longs;i in <expan abbr="ipsũ">ipsum</expan> <lb/>nauigium. </s> <s id="N13559">Qua virtute <expan abbr="eod&etilde;">eodem</expan> tempore &longs;imul ac manubrium <lb/>motu proprio perueni&longs;&longs;et v&longs;que ad D, reperiatur in G; & <lb/>&longs;calmus qui e&longs;&longs;et in F, pertingat v&longs;que ad E; quod e&longs;t <pb pagenum="111" xlink:href="005/01/119.jpg"/>vtrumque, duplum &longs;patium percurrere re&longs;pectu illius, quod <lb/>virtute &longs;olius prædictæ remigationis percurri&longs;&longs;et. </s> </p> <p id="N1356B" type="main"> <s id="N1356D">Po&longs;terior verò ca&longs;us, in quo verificatur palmulam ad mo­<lb/>tum antror&longs;um nauigij <expan abbr="nõ">non</expan> retrocedere, e&longs;t cum celerius fer­<lb/>tur nauigium, quàm remi manubrium. </s> <s id="N13578"><expan abbr="Siquid&etilde;">Siquidem</expan> cum in tan­<lb/>tum palmula po&longs;&longs;it retrocedere, in quantum manubrium <lb/>motu proprio in anteriora amplius progreditur quàm naui­<lb/>gium, &longs;i celerius feratur nauigium quàm manubrium, ma­<lb/>iu&longs;que proinde &longs;patium percurrat, palmula nullo modo po­<lb/>terit retrocedere. </s> <s id="N13588">Etenim po&longs;ito, quod manubrium motu <lb/>proprio decurrat &longs;patium bipalmare, per totidem palmos <lb/>palmula retrocederet, &longs;i nauigium maneret immotum: At <lb/>&longs;i &longs;imul nauigium percurrat &longs;patium quadripalmare, nihil <lb/>palmula retrocedet. </s> <s id="N13593">Nam quo tempore retrocederet <expan abbr="vnũ">vnum</expan>, <lb/>duplum progrederetur in contrarium. </s> </p> <p id="N1359C" type="main"> <s id="N1359E">Secunda verò pars conclu&longs;ionis, videlicet tantum <expan abbr="quan-doq.">quan­<lb/>doque</expan> palmulam retrocedere, <expan abbr="quãtum">quantum</expan> prouehitur nauigium; <lb/>ex eo probatur. </s> <s id="N135AD">Nam &longs;i remi manubrium motu proprio, du­<lb/>plum confecerit &longs;patium, quam nauigium; vt verbi gratia <lb/>quadripalmare re&longs;pectu bipalmaris, palmula quidem per <lb/>totidem &longs;patij palmos retroce&longs;&longs;i&longs;&longs;et, ni&longs;i ob&longs;taret motus na­<lb/>uigij in contrarium: At non ob&longs;tat, ni&longs;i per dimidium, nem­<lb/>pe &longs;ecun dum &longs;patium bipalmare, quod certè nauigium &longs;imul <lb/>cum toto remo in anteriora percurrit: ergo per æquale &longs;pa­<lb/>tium bipalmare palmula retrocedet. </s> </p> <p id="N135BE" type="main"> <s id="N135C0">Tertia denique a&longs;&longs;ertionis pars, nempe magis, vt pluri­<lb/>mum prògredi nauigium, quàm palmulam in contrarium, <lb/>ex dictis ferè o&longs;tenditur aperti&longs;simè. </s> <s id="N135C7">Quia licet maius &longs;pa­<lb/>tium decurrat remi manubrium, quàm nauigium, quando <lb/>ip&longs;um nauigium mouetur &longs;olùm in virtute eiu&longs;dem remiga­<lb/>tionis, vt frequentius accidit: rarò tamen exce&longs;&longs;us ad dimi­<lb/>dium videtur pertingere, ita vt manubrium motu proprio <lb/>duplum conficiat &longs;patium, quàm nauigium. </s> <s id="N135D4">Cum autem <lb/>huiu&longs;modi exce&longs;&longs;us ad dimidium non pertingit, neque pal­<lb/>mula per æquale &longs;patium retrocedet, &longs;ed minus. </s> <s id="N135DB">Vnde &longs;i <lb/>manubrium progrediatur vt tria; nauigium vero vt duo, pal-<pb pagenum="112" xlink:href="005/01/120.jpg"/>mula retrocedet vt vnum: tantum &longs;cilicet quantum e&longs;t <lb/>&longs;patium, quo excedit illud, quod conficitur per motum <lb/>contrarium. </s> </p> <p id="N135E9" type="main"> <s id="N135EB">Quæ omnia Geometricè at que exactius con&longs;tare po&longs;&longs;unt <lb/>ex his, quæ Petrus Nonius acuti&longs;&longs;imè demon&longs;trat in &longs;ua <lb/>Annotatione &longs;uper hunc ip&longs;um locum Ari&longs;totelis. <!-- KEEP S--></s> <s id="N135F3">Quam­<lb/>uis non rectè videatur &longs;upponere, ip&longs;um Philo&longs;ophum, vni­<lb/>uer&longs;aliter a&longs;&longs;ump&longs;i&longs;&longs;e tantum &longs;patium conficere nauigium, <lb/>quantum remi manubrium. </s> <s id="N135FC">Forta&longs;&longs;e propter illa verba <lb/>ip&longs;ius Philo&longs;ophi: Non procederet autem vbi ex D, ni&longs;i <lb/>commoueretur nauigium, & eò transferretur, vbi remi e&longs;t <lb/>principium. </s> <s id="N13605">Quæ tamen verba in diuer&longs;um, ac veriorem <lb/>prolata &longs;unt &longs;en&longs;um, vt &longs;upra expo&longs;uimus. </s> <s id="N1360A">Solum enim per <lb/>ea intendit Philo&longs;ophus, quod non præcederet &longs;calmus an­<lb/>tror&longs;um ad partes D, quo tantum peruenit manubrium A; <lb/>ni&longs;i commoueretur nauigium ver&longs;us eandem partem, &longs;e­<lb/>quendo remi principium, à quo trahitur, vel à quo illuc fuit <lb/>impul&longs;um. </s> </p> <p id="N13617" type="main"> <s id="N13619">His tandem ita con&longs;titutis de motione remi, applican­<lb/>do Ari&longs;toteles eandem ob&longs;eruationem, non ab&longs;imile e&longs;&longs;e <lb/>docet, quod contingit in motione gubernaculi, ac temonis, <lb/>vt &longs;cilicet &longs;icut &longs;calmus, qui con&longs;tituitur medium inter ex­<lb/>trema ip&longs;ius remi, quæ mouentur in contrarium, illuc tran&longs;­<lb/>fertur vbi remi e&longs;t principium, nempe antror&longs;um, quo remi <lb/>manubrium pergit, ac nauem propellit: ita locus vbi ap­<lb/>plicatur gubernaculum, ac primo attingit temonem (qui <lb/>certè locus e&longs;t in linea cadenti, qua temo puppi adhæret in <lb/>cu&longs;pide, & vbi con&longs;tituitur etiam cardo) cum &longs;e habeat <lb/>tanquam medium inter duo extrema, quæ mouentur in <lb/>contrarium, videlicet manubrium gubernaculi, & alam te­<lb/>monis, qua mare propellitur, illuc intelligetur transferri, <lb/>quo ip&longs;um gubernaculi manubrium erat. </s> <s id="N13636">Quemadmodum <lb/>enim &longs;calmus, temo, ait Ari&longs;toteles, nempe &longs;ecundum præ­<lb/>dictam lineam circa quam qua&longs;i immotam, conuertitur la­<lb/>titudo ip&longs;ius temonis ex vna parte, & guberna culi manu­<lb/>brium ex alia, vt patet in hac prima figura; in qua cadens <pb pagenum="113" xlink:href="005/01/121.jpg"/>AB, <expan abbr="lineã">lineam</expan> o&longs;tendit <lb/><figure id="id.005.01.121.1.jpg" xlink:href="005/01/121/1.jpg"/><lb/>circa cuius prin­<lb/>cipium guberna-­<lb/>culum applicatur, <lb/>ac primo attingit <lb/>temonem, quæ li­<lb/>nea in motione <lb/>gubernaculi ma-­<lb/>net immota, &longs;icut <lb/>&longs;calmus in motio­<lb/>ne remi. </s> <s id="N13664">Pars ve­<lb/>rò AC &longs;ignat fa­<lb/>ciem dexteram <lb/>temonis; & AD <lb/>manubrium gu-­<lb/>bernaculi. </s> <s id="N13671">Quod <lb/>&longs;i extremum ma­<lb/>nubrij D, intelli­<lb/>gatur transferri in <lb/>E, vt cernere e&longs;t <lb/>in &longs;ecunda figura: <lb/>tunc ait Ari&longs;tote­<lb/>les, illuc transferri <lb/>etiam centrum A. <lb/><!-- KEEP S--></s> <s id="N13686">Nam D tran&longs;lato in E, &longs;imul C transferretur in F; <lb/>ac per impul&longs;um acceptum in latitudine AF nece&longs;&longs;ariò <lb/>A transferri deberet ad partes G. <!-- KEEP S--></s> <s id="N1368E">Cumque &longs;imul naui­<lb/>gium, cui temo e&longs;t alligatus, procedat antror&longs;um, ip&longs;um <lb/>A non con&longs;titueretur in G, &longs;ed in E, vbi prius erat ma­<lb/>nubrium gubernaculi. </s> <s id="N13697">Quare gubernaculum nihil naui­<lb/>gio ad id, quod in ante progredi e&longs;t, conferre ait Ari&longs;to­<lb/>teles, &longs;ed &longs;olum puppim in obliquum pellere, aliquantu­<lb/>lum &longs;cilicet ad latus, qua parua motione puppis, pro­<lb/>ra in contrarium vergit, nempe ad latus oppo&longs;itum, vt <lb/>ip&longs;emet Philo&longs;ophus docet, & con&longs;iderare licebit in hac <pb pagenum="114" xlink:href="005/01/122.jpg"/><figure id="id.005.01.122.1.jpg" xlink:href="005/01/122/1.jpg"/><lb/>figura nauiculæ, cuius <lb/>puppis A, prora D, <lb/><expan abbr="gubernaculũ">gubernaculum</expan> verò EF <lb/>obliquè con&longs;titutum; <lb/>Nam certè ad impul­<lb/>&longs;um aquæ in alam ob­<lb/>uer&longs;am FA, ip&longs;a pup­<lb/>pis A cum retrocede­<lb/>re non po&longs;&longs;it ob <expan abbr="pro-gre&longs;sũ">pro­<lb/>gre&longs;sum</expan> nauiculæ (dum­<lb/>modo aliquantulum cedere debeat impul&longs;ui) declinabit in <lb/>E, vbi erat gubernaculi manubrium, qua parua motione <lb/>puppis, ob rationes in principio po&longs;itas, prora ad contra­<lb/>rium verget, inquit Ari&longs;toteles, &longs;cilicet ad latus oppo&longs;itum, <lb/><expan abbr="proindeq.">proindeque</expan> con&longs;tituetur in H, ni&longs;i validum aliquod ventum <lb/>inde &longs;pirans <expan abbr="paruaq.">paruaque</expan> conuer&longs;io temonis non ob&longs;tet. </s> </p> <p id="N136DB" type="main"> <s id="N136DD">Quo ex principio intelligi pote&longs;t cur ex tran&longs;uer&longs;o per­<lb/>flante admodum vento, ac directè nihilominus nauigia <lb/>procedendo, tandem non pertingant, quo præcisè tende­<lb/>bant, &longs;ed inferius multo, &longs;eu ad partem vento magis oppo­<lb/>&longs;itam. </s> <s id="N136E8">Porro cum aliquantulum à latere vento perflante, <lb/>alam temonis illi &longs;atis obuer&longs;am nautæ con&longs;tituere tenean­<lb/>tur, validi&longs;simè ip&longs;am &longs;imul cum puppi fluctus repellunt, <lb/>quo &longs;anè repul&longs;o circumagerent totam nauim, ni&longs;i &longs;imul in <lb/>latus ver&longs;us proram inciderent, nam hinc inde coadæquato <lb/>repul&longs;u, ac gubernaculo moderante, dum nauis pergit an­<lb/>tror&longs;um &longs;emper eandem, quam prius in &longs;e po&longs;itionem, ac <lb/><expan abbr="direction&etilde;">directionem</expan> &longs;eruat. </s> <s id="N136FC">Cum <expan abbr="itaq;">itaque</expan> fluctus ip&longs;i nauem circumage­<lb/>re nequeant, <expan abbr="nauisq.">nauisque</expan> aliquid pati debeat ex ip&longs;o repul&longs;u, to­<lb/>ta &longs;imul cogitur &longs;en&longs;im declinare ad latus <expan abbr="v&etilde;to">vento</expan> oppo&longs;itum; <lb/>Vt exempli gratia data po&longs;itione, quam modo tenet de&longs;cri­<lb/>pta nauicula in AD, ac perflante vento ex tran&longs;uer&longs;o, vt <lb/>ex H, certè ad motum ip&longs;ius puppis ex A in E, prora <lb/>non conuerteretur à D in H, (ni&longs;i ob maiorem conuer­<lb/>&longs;ionem temonis, &longs;ed potius non nihil cedendo &longs;icut puppis, <pb pagenum="115" xlink:href="005/01/123.jpg"/>declinaret in I; Quare nauis à &longs;itu AD con&longs;tituta in EI, <lb/>eandem quippe &longs;eruaret po&longs;itionem, ac directionem, tran&longs;­<lb/>lata tamen e&longs;&longs;et inferius ver&longs;us partem vento oppo&longs;itam, <lb/>&longs;icque vlterius incedendo quamuis ab initio de&longs;tinatum &longs;i­<lb/>bi locum per proram in&longs;piceret, illuc tamen peruenire ne­<lb/>quiret, ni&longs;i altius, &longs;eu magis ad partem vnde ventus validè <lb/>&longs;pirat, proram direxerit, vt &longs;patium, quod coacta declinatio­<lb/>ne deperdit, compen&longs;etur anticipata &longs;itus po&longs;itione, ac di­<lb/>rectione. </s> </p> <p id="N1372E" type="main"> <s id="N13730">Demum illud, quod Ari&longs;toteles vltimo loco adiecit. </s> <s id="N13733">In <lb/>codem exi&longs;tente prora, totum transferri nauigium, (ni&longs;i li­<lb/>brariorum error irrep&longs;erit, vt potius con&longs;equenter ad &longs;upe­<lb/>rius dicta legendum &longs;it, in eodem exi&longs;tente puppi, eo quod <lb/>parua eius dimotio pro nihilo reputetur) ne cum doctrina <lb/>eiu&longs;dem Philo&longs;ophi hactenus tradita pugnet, intelligendum <lb/>e&longs;t, tum &longs;i quando per motum &longs;olius temonis tanquam remi <lb/>in cu&longs;pide puppis, tota nauis conuerteretur, vt explicuimus <lb/>in principio: tum etiam quando idip&longs;um contingit ad obli­<lb/>quam tantum modo po&longs;itionem temonis contra fluctus ad­<lb/>uenientes, po&longs;ito &longs;cilicet quod nauigium, nec velis, nec re­<lb/>mis, nec alio pacto feratur. </s> <s id="N1374C">Etenim &longs;i temo per &longs;ui con­<lb/>uer&longs;ionem, vel obliquam po&longs;itionem fluctus maris à dex­<lb/>tris excipiat, ab&longs;que dubio puppis ad &longs;ini&longs;tram declinabit, <lb/>prora manente ferè immota, eo quod impetus obliquè &longs;it <lb/>impre&longs;&longs;us, & illuc v&longs;que pertingere nequeat, vel ob &longs;uam <lb/>imbecillitatem ibi tandem langue&longs;cat. </s> <s id="N13759">Quod facilè con­<lb/>templari e&longs;t in &longs;ubiecta, quam delineauimus nauicula, cuius <lb/>linea AB refert gubernaculum cum temone affixo in ip&longs;a <lb/>cu&longs;pide puppis vbi C, ac prora con&longs;tituitur in G. <!-- KEEP S--></s> <s id="N13763">Nam <lb/>dato quod extremum temonis B, mare dextror&longs;um exci­<lb/>piens, aut propellens transferatur in D per motum guber­<lb/>naculi ab A in E, vtique cu&longs;pis puppis, quæ e&longs;t in C <lb/>transferetur &longs;ini&longs;tror&longs;um vnà cum tota nauicula ver&longs;us F, <lb/>prora ip&longs;a in eodem puncto manente, vel parum inde di­<lb/>mota, vt v&longs;que ad punctum H; ita vt nauicula, quæ erat <pb pagenum="116" xlink:href="005/01/124.jpg"/><figure id="id.005.01.124.1.jpg" xlink:href="005/01/124/1.jpg"/><lb/>in CG, con&longs;tituatur in FG, vel in <lb/>FH. </s> <s id="N1377F">Licet hoc non &longs;emper veri­<lb/>ficetur cum &longs;æpius impetus per <lb/>remonem incu&longs;&longs;us à mare in hu­<lb/>iu&longs;modi ca&longs;u &longs;uperare, ac tran&longs;­<lb/>ferre nequeat centrum grauitatis <lb/>totius nauis, quod e&longs;t circa me­<lb/>dium illius, <expan abbr="proindeq.">proindeque</expan> tota longi­<lb/>tudo nauis conuerti non po&longs;&longs;it <lb/>tanquam &longs;emidiameter circa ter­<lb/>minum prorae, tanquam circa cen­<lb/>trum, &longs;ed potius centrum huius <lb/>conuer&longs;ionis con&longs;tituatur in ip&longs;o centro grauitatis totius <lb/>nauis, vel in alio puncto lineæ per ip&longs;um ad centrum mundi <lb/>cadentis. </s> </p> <p id="N137A0" type="main"> <s id="N137A2">In prædictis ergo ca&longs;ibus, & cum explicata limitatione <lb/>loquendo de nauigio, quod nullo pacto fertur antror&longs;um <lb/>intelligitur verificari, quod docuit Ari&longs;toteles. <!-- KEEP S--></s> <s id="N137AA">In eodem <lb/>exi&longs;tente prora, totum transferri nauigium; Alioquin &longs;i &longs;er­<lb/>mo fui&longs;&longs;et de nauigio, quod plenis velis, aut remis mare <lb/>tran&longs;mittit, verificari certè non po&longs;&longs;et; cum talis ac tanta <lb/>&longs;it vis eiu&longs;dem cur&longs;us, quo recta in anteriora citi&longs;simè fer­<lb/>tur, vt non &longs;inat ip&longs;am puppim per occur&longs;um maris, quod <lb/>incidit in temonem à &longs;uo recto tramite admodum &longs;altem <lb/>diuerti, &longs;icut à puncto &longs;uæ quietis facilè ip&longs;a dimouetur cum <lb/>nauis quie&longs;cit. </s> <s id="N137BD">Licet enim promoto &longs;emel antror&longs;um naui­<lb/>gio, temo per obliquam &longs;ui con&longs;titutionem, & immediatum <lb/>repul&longs;um quem patitur, omnino re&longs;i&longs;tere nequeat occur­<lb/>rentibus fluctibus, <expan abbr="cogaturq.">cogaturque</expan> moueri, velut in gyrum circa <lb/>ip&longs;ius puppis extremum; vim tamen quam patitur transfun­<lb/>dit in longitudinem nauis, tanquam in alterum latus, cum <lb/>quo efficit angulum, vt in principio cum &longs;ua figura expre&longs;si­<lb/>mus: Vnde cum non &longs;olum ad motum vnius lateris in an­<lb/>gulo, moueatur alterum, &longs;ed facilius &longs;it, vtrumque latus cir­<lb/>culariter moueri, cu&longs;pide anguli tanquam centro manente <pb pagenum="117" xlink:href="005/01/125.jpg"/>immota ob aliquod <expan abbr="limpedimentũ">impedimentum</expan>, quàm <expan abbr="totũ">totum</expan> <expan abbr="angulũ">angulum</expan> &longs;imul <lb/>transferri; hinc e&longs;t, vt re&longs;i&longs;tentia nouis orta ex impetu indi­<lb/>rectum tendente, &longs;ufficiat vt cu&longs;pis prædicti anguli, quæ in <lb/>propo&longs;ito e&longs;t vbi puppis extremum; minimè dimoueatur à <lb/>tramite &longs;uper <expan abbr="qu&etilde;">quem</expan> fertur, <expan abbr="nõ">non</expan> <expan abbr="aut&etilde;">autem</expan> &longs;ufficiat quin prora <expan abbr="tanquã">tanquam</expan> <lb/>extremum alterius lateris moueatur ad motum lateris, quod <lb/>con&longs;tituitur à temone, ita vt temone ad leuam repul&longs;o lon­<lb/>gitudo nauis cum prora ad dexteram vergat. </s> <s id="N13805">Prouenit au­<lb/>tem maior hæc facilitas motus lateris vtriu&longs;que, circa pro­<lb/>priam cu&longs;pidem, tum ex facilitate motus circularis in vni­<lb/>uer&longs;um, tum ex ip&longs;a re&longs;i&longs;tentia, qua cu&longs;pis anguli, quem effi­<lb/>ciunt detinetur ab impul&longs;o in directum nè moueatur obli­<lb/>què in tran&longs;uer&longs;um. </s> <s id="N13812">Innititur enim ei tanquam fulcimento, <lb/>ip&longs;aque latera induunt rationem vectis cuiu&longs;dam angulo&longs;i <lb/>in medio fulti, qui &longs;anè facilius conuertitur circa fulcimen­<lb/>tum ad motum alterius extremi, quàm &longs;imul &longs;ecundum &longs;e <lb/>totum aliò transferatur. </s> <s id="N1381D">Antror&longs;um ergo naui promota, <lb/>ip&longs;e impetus promotionis, &longs;eu cur&longs;us impedit ne puppis ex­<lb/>tremum in tran&longs;uer&longs;um dimoueatur, non autem ob&longs;tat quin <lb/>ad motionem obliquam temonis, conuertatur &longs;ecum & <lb/>prora, cum propter vim illatam, quæ vrgentibus fluctibus, in <lb/>illam transfunditur; tum propter facilitatem conuer&longs;ionis <lb/>explicatam, con&longs;entaneè ad doctrinam &longs;upra traditam, <expan abbr="men-temq.">men­<lb/>temque</expan> Ari&longs;totelis aientis. </s> <s id="N13832">parua motione facta per temonem <lb/>in puppi, multo maius interuallum fieri in vltimo: Et alibi, <lb/>temone paululum quid tran&longs;po&longs;ito, multam fieri tran&longs;po&longs;i­<lb/>tionem proræ, <gap/>ibidem commonuimus. </s> </p> <p id="N1383D" type="main"> <s id="N1383F">Sed prætermi&longs;&longs;a Ari&longs;totelis doctrina, totius effectus quem <lb/>per v&longs;um temonis experimur in naui, cau&longs;am &longs;atis, ac bre­<lb/>uius explicari po&longs;&longs;e videtur &longs;i ad libram potius quàm ad ve­<lb/>ctem eam reuocauerimus. </s> <s id="N13848">Etenim nauis mari obuiando, <lb/>eiu&longs;que impul&longs;um æquabiliter à dextris, & à &longs;ini&longs;tris reci­<lb/>piendo, non aliter &longs;e habet, quàm libra in æquilibrio con&longs;ti­<lb/>tuta, in cuius brachijs æqualia pondera &longs;u&longs;tinentur. </s> <s id="N13851">Idem <lb/>enim e&longs;t vtrinque æqualia pondera &longs;u&longs;tinere, ac impetus <lb/>pariter æquales. </s> <s id="N13858">Cum autem à dextris, vel à &longs;ini&longs;tris ex na­<pb pagenum="118" xlink:href="005/01/126.jpg"/>ui lignum aliquod, vt temo, vel aliud non ab&longs;imile promi­<lb/>nuerit, cui mare obuians, maiorem impetum incutiat, iam <lb/>non e&longs;t amplius æqualis impetus vtrinque incu&longs;&longs;us. </s> <s id="N13864">Ac &longs;icut <lb/>libram cum ip&longs;a maius pondus altero brachio &longs;u&longs;tinet incli­<lb/>nari nece&longs;&longs;e e&longs;t, ac cedere &longs;ecundum illud brachium ex quo <lb/>maius pondus propendet: ita nauim inclinari oportet &longs;e­<lb/>cundum illam partem, in qua maiorem impetum excipit, <lb/>quod &longs;it per circumuer&longs;ionem totius longitudinis nauis ad <lb/>latus ip&longs;um vnde magis percutitur, prout paulò ante de&longs;cri­<lb/>p&longs;imus. </s> <s id="N13875">Licet hic dicendi modus, <expan abbr="ip&longs;umq,">ip&longs;umque</expan> fundamentum, <lb/>quo nititur verificari po&longs;&longs;it, tum &longs;i centrum motionis circu­<lb/>laris, quam experimur in naui con&longs;tituatur in cu&longs;pide pup­<lb/>pis, tum &longs;i con&longs;tituatur in prora, vt per &longs;e patet. </s> <s id="N1387E">Sed forta&longs;­<lb/>&longs;e multo melius &longs;i con&longs;tituatur in medio, &longs;eu in centro gra­<lb/>uitatis totius nauis, circa quod facilius e&longs;t intelligere ip&longs;am <lb/>nauis conuer&longs;ionem, &longs;iue inquiete, &longs;iue in motu. </s> <s id="N13887">Quomo­<lb/>docunque enim temo obliquè con&longs;titutus vim patiatur ab <lb/>aqua; Nimirum &longs;iue excipiendo illam fluentem, & obuian­<lb/>tem; &longs;iue impingendo in illam quie&longs;centem, &longs;emper dimo­<lb/>tio illa circularis intelligetur pertingere v&longs;que ad cen­<lb/>trum grauitatis totius nauis, cum qua temo vnum corpus <lb/>efficitur. </s> <s id="N13896">At in re tam occulta, quæ etiam dum ante ocu­<lb/>los ver&longs;atur, adhuc imaginationem comprehen&longs;ionemque <lb/>ob&longs;eruantis fugit, con&longs;ultius erit ab Ari&longs;totelis doctrina non <lb/>di&longs;cedere. </s> </p> <p id="N1389F" type="head"> <s id="N138A1">Quæ&longs;tio Sexta.</s> </p> <p id="N138A4" type="main"> <s id="N138A6">C<emph type="italics"/>vr quanto antenna &longs;ublimior fuerit, ij&longs;dem <lb/>velis, & vento eodem cæle, iùs feruntur na­<lb/>uigia? </s> <s id="N138B0">An quia malus quidem fit vectis, hy­<lb/>pomochlion verò mali &longs;edes, in qua colloca­<lb/>tur: pondus autem quod moueri debet, ip&longs;um <lb/>nauigium; mouens verò is, qui vela tendit, <lb/>&longs;piritus? </s> <s id="N138BB">Si igitur quando remotius fuerit hypomochlion,<emph.end type="italics"/><pb pagenum="119" xlink:href="005/01/127.jpg"/><emph type="italics"/>facilius eadem potentia, & citius idem mouet pondus, altius <lb/>sertè &longs;ublata antenna velum à mali &longs;ede, quæ hypomochlion <lb/>e&longs;t, remotius faciens, id efficiet.<emph.end type="italics"/></s> </p> <p id="N138CF" type="head"> <s id="N138D1">COMMENTARIVS.<!-- KEEP S--></s> </p> <p id="N138D5" type="main"> <s id="N138D7">Qværit hic Ari&longs;toteles cur <expan abbr="ij&longs;d&etilde;">ij&longs;dem</expan> pror&longs;us velis, <expan abbr="eod&etilde;q.">eodenque</expan> <lb/>vento perflante, celerius nauigia ferantur quando al­<lb/>tius &longs;ublimatur antenna. </s> <s id="N138E6"><expan abbr="Statimq.">Statimque</expan> re&longs;pondet, ex eo <lb/>id prouenire, quod malus in ventorum impul&longs;ionibus con&longs;ti­<lb/>tuitur vectis, cuius hypomochlion, &longs;eu fulcimentum e&longs;t ip&longs;a <lb/>mali &longs;edes in qua locatur; pondus autem quod moueri de­<lb/>bet, ip&longs;um nauigium, ac mouens ventum impellens. </s> <s id="N138F4">Etenim <lb/>cum huiu&longs;modi impul&longs;us velis quidem exceptus verè totus <lb/>refundatur in eam mali partem vbi alligatur antenna; quan­<lb/>tò &longs;ublimius illa fuerit alligata, tantò remotius à fulcimento <lb/>vis mouentis incutietur in malum, &longs;eu vectem. </s> <s id="N138FF">At virtus <lb/>mouentis beneficio vectis, eo magis augetur, quo remotius <lb/>ab eius fulcimento imprimitur: ergo cum &longs;ublimior fuerit <lb/>antenna, maior fiet virtus à ventis incu&longs;&longs;a, <expan abbr="validiusq.">validiusque</expan> proinde <lb/>mouebit nauigia. </s> <s id="N1390E">Diximus autem impetum velis exceptum <lb/>ferè totum, non ab&longs;olutè totum refundi in eam mali partem <lb/>vbi alligatur antenna; quia adhuc antennæ cornua, ac veli <lb/>pedes ex eodem impetu participant, dum per funes opife­<lb/>ros <expan abbr="propedesq.">propedesque</expan> nauim &longs;ecum trahunt atque proripiunt. </s> </p> <p id="N1391D" type="main"> <s id="N1391F">Sed vt firmius doctrina Ari&longs;totelis teneatur, ac difficulta­<lb/>tes omnes oppo&longs;itæ &longs;oluantur, notandum e&longs;t duplicem in <lb/>malo con&longs;iderari po&longs;&longs;e rationem vectis cum nauis per veli­<lb/>ficationem fertur antror&longs;um; vnam quæ illi competit ab&longs;o­<lb/>lutè prout <expan abbr="cõdi&longs;tinguitur">condi&longs;tinguitur</expan> à reliquis partibus nauis; Alteram <lb/>verò quæ coniunctim ei conuenit &longs;imul cum nauis carina, <lb/>&longs;ecundum cam partem, qua carina ver&longs;us puppim extendi­<lb/>tur. </s> <s id="N13934">Porrò malus ab&longs;olutè con&longs;ideratus in latione nauis, <lb/>virtute ventorum, fulcimentum obtinet circa profundam <lb/>&longs;edem vbi locatur in nauis carina, <expan abbr="eiq.">eique</expan> innititur per &longs;ui ex­<lb/>tremum infimum, qua parte, &longs;eu facie vergit ad puppim. <lb/></s> <s id="N13942">Onus autem &longs;eu nauem promouet per partem ip&longs;ius altio­<pb pagenum="120" xlink:href="005/01/128.jpg"/>rem ex ijs, quæ intra foramen continentur, vnde ip&longs;e malus <lb/>foris prodit in altum, tanquam arbor è terra; <expan abbr="vrgetq.">vrgetque</expan> &longs;ecun­<lb/>dum eam ip&longs;ius partis faciem, quæ ad proram re&longs;picit vbi <lb/>vltimo foramen de&longs;init. </s> <s id="N13954">Siquidem ibi tota ferè vis incuti­<lb/>tur naui ad progrediendum antror&longs;um, vt videre e&longs;t in hac <lb/>figura, in qua extremum mali fundo innixum &longs;it A, cuius <lb/>facies puppim <lb/>re&longs;piciens B; <lb/><figure id="id.005.01.128.1.jpg" xlink:href="005/01/128/1.jpg"/><lb/>pars verò ip­<lb/>&longs;ius mali, quæ <lb/><expan abbr="flãtibus">flantibus</expan> ventis <lb/>à tergo naui­<lb/>gium præmit, <lb/>vel vrget in an­<lb/>te, vbi C, è <expan abbr="cõ-&longs;pectu">con­<lb/>&longs;pectu</expan> pror&etail;; & <lb/>locus antennæ <lb/>in ip&longs;o malo, &longs;it <lb/>D; vbi tota pe­<lb/>nè virtus im­<lb/>pellentis &longs;piri­<lb/>tus refunditur, <lb/>vt diximus ra­<lb/>tione veli <expan abbr="illũ">illum</expan> <lb/>excipientis. </s> <s id="N13992"><expan abbr="Iã">Iam</expan> <lb/>igitur <expan abbr="cõ&longs;tat">con&longs;tat</expan> ex <lb/>hoc, malum <lb/>per &longs;e &longs;umptum propriè vectem con&longs;titui in ip&longs;a ventorum <lb/>impul&longs;ione, cum fulcimentum habeat in parte di&longs;tincta ab <lb/>ea, qua nauem promouet, & ab ea, qua mouetur à vento, vt <lb/>in &longs;imili commune e&longs;t omnibus vectibus; vnde quo altius <lb/>con&longs;tituetur antenna, vt verbi gratia &longs;i eleuaretur v&longs;que ad <lb/>E, eo celerius moueretur nauigium, quia virtutem impellen­<lb/>tem reciperet in parte à centro vectis di&longs;tantiori. </s> </p> <p id="N139AE" type="main"> <s id="N139B0">Altera verò vectis ratio, quæ con&longs;ideratur in malo con­<lb/>iunctim cum nauis carina, e&longs;t huiu&longs;modi. </s> <s id="N139B5">Quoniam vt rectè <pb pagenum="121" xlink:href="005/01/129.jpg"/>prænotat Baldus, e&longs;t quædam vectium &longs;pecies, cuius bra­<lb/>chia in angulum de&longs;inunt, <expan abbr="ip&longs;iusq.">ip&longs;iusque</expan> anguli cu&longs;pis in operatio­<lb/>ne con&longs;tituitur centrum, ac fulcimentum circa quod bra­<lb/>chia conuertuntur. </s> <s id="N139C7">Ad quam &longs;peciem reducitur ferreus <lb/>malleus prout eam partem continet, qua clauos reuellit. <lb/></s> <s id="N139CD">Etenim vt ob&longs;eruari pote&longs;t in hac figura, mallei manubrium <lb/>con&longs;tituit vnum brachium AB; alterum verò pars qua cla­<lb/>uos reuellit, nempe BC. <!-- KEEP S--></s> <s id="N139D5">Et ex vtri&longs;que fit angulus ABC, <lb/>ip&longs;o malleo in extractione clauorum <lb/>cu&longs;pidi innixo vbi B. </s> </p> <figure id="id.005.01.129.1.jpg" xlink:href="005/01/129/1.jpg"/> <p id="N139E1" type="main"> <s id="N139E3">Similiter ergo malus in naui con&longs;i­<lb/>derari pote&longs;t tanquam brachium ve­<lb/>ctis, quod alteri coniungatur, nempe <lb/>illi parti carin&etail;, qu&etail; vergit ad puppim, <lb/>& cum qua con&longs;tituit <expan abbr="angulũ">angulum</expan> in pun­<lb/>cto vbi de&longs;init altitudo ip&longs;ius mali. </s> <s id="N139F4"><expan abbr="Nã">Nam</expan> <lb/>impetu in <expan abbr="alterũ">alterum</expan> extremum ip&longs;ius ma­<lb/>li incu&longs;&longs;o, nempe circa locum vbi vr­<lb/>get antenna velo agitata à ventis, ip&longs;a <lb/>&longs;ummitas mali declinaret &longs;i po&longs;&longs;et ad <lb/>proram, tanquam per conuer&longs;ionem <lb/>circa punctum explicatum, in quo con&longs;tituitur angulus, <expan abbr="&longs;i-mulq.">&longs;i­<lb/>mulque</expan> eleuaretur &longs;i po&longs;&longs;et carina ex parte puppis. </s> <s id="N13A10">Quemad­<lb/><figure id="id.005.01.129.2.jpg" xlink:href="005/01/129/2.jpg"/><lb/>modum in propo&longs;ito an­<lb/>gulo ABC; &longs;i latus AB <lb/>declinaret in BD per <lb/>impul&longs;um acceptum in <lb/>A; latus etiam BC ele­<lb/>uaretur in BE. <!-- KEEP S--></s> <s id="N13A26">Quoniam <lb/>verò declinare non po­<lb/>te&longs;t malus, nec pars illa <lb/>carinæ per con&longs;equens <lb/>eleuari ab&longs;que immer­<lb/>&longs;ione proræ, totus impe­<lb/>tus incu&longs;&longs;us refunditur <lb/>in lationem antror&longs;um, eo quod mare cum &longs;it fluidum non <pb pagenum="122" xlink:href="005/01/130.jpg"/>re&longs;i&longs;tat lationi, &longs;icut ip&longs;ius proræ immer&longs;ioni, quæ contra <lb/>naturam ligni &longs;equeretur ex declinatione mali. </s> <s id="N13A3E">Accedit <lb/>quia neque pars carinæ, quæ e&longs;t à malo ad puppim po&longs;&longs;et <lb/>eleuari; tum propter grauitatem puppis, quæ &longs;e habet tan­<lb/>quam onus in extremo vectis, <expan abbr="ibiq.">ibique</expan> maximè præponderat <lb/>impul&longs;ui contrario; tum propter naturalem re&longs;i&longs;tentiam ca­<lb/>rinæ <expan abbr="totiusq.">totiusque</expan> fundi ne &longs;eparetur ab aqua, cui connaturalius <lb/>ligna præ&longs;ertim plana adhærent; vt patet ex difficultate, <lb/>qua &longs;upernatantes tabulæ extrahuntur ex aqua. </s> </p> <p id="N13A57" type="main"> <s id="N13A59">Secundum vtramque igitur vectis rationem, quam malus <lb/>participat, nauem promouet in anteriora, ab&longs;que eo, quod <lb/>ver&longs;us proram inclinetur, &longs;ed tantum præmat, eo pacto, quo <lb/>diximus, in &longs;itu vnde è foramine exit. </s> <s id="N13A62">Quare non rectè Bal­<lb/>dus &longs;ecundam vectis rationem in malo admittens, primam <lb/>ab Ari&longs;totele allatam impugnat. </s> <s id="N13A69">Ex eo quod &longs;i malus talis <lb/>vectis vim haberet, vento validè impellente, aut &longs;equeretur <lb/>fractio ip&longs;ius mali ad &longs;edem, aut inclinatio ver&longs;us proram <lb/>cum immer&longs;ione ip&longs;ius proræ, & eleuatione puppis: Siqui­<lb/>dem nec probat &longs;equelam, nec id ip&longs;um, quod damnat de­<lb/>uitat iuxta &longs;ecundam vectis rationem quam approbat, vt <lb/>per &longs;e patet. </s> <s id="N13A78"><expan abbr="Immeritoq.">Immeritoque</expan> proinde &longs;imul recurrit ad maio­<lb/>rem infe&longs;tationem ventorum, quam experimur in locis &longs;ubli­<lb/>mioribus, vt cau&longs;am afferat propter quam, cum &longs;ublimior <lb/>fuerit antenna, citius <expan abbr="nauigiũ">nauigium</expan> &longs;piritu flante moueatur. </s> <s id="N13A88">Nam <lb/>& cau&longs;am quam Ari&longs;toteles tradit manife&longs;tam habemus; & <lb/>non &longs;emper verum e&longs;t, quod ip&longs;e de vento a&longs;&longs;umit, maximè <lb/>in tam parua di&longs;tantia, & loco non minus expo&longs;ito. </s> </p> <p id="N13A91" type="main"> <s id="N13A93">Denique ex his expediri etiam pote&longs;t alia quæ&longs;tio, cur <lb/>nimirum fluctuante aliquantulum mare, ac minimè velis <lb/>munito, aut progrediente nauigio, quo altius &longs;ublimatur an­<lb/>tenna, minus ip&longs;um commoueatur; vt in &longs;tatione nauium at­<lb/>que triremium extra portum &longs;olet contingere. </s> <s id="N13A9E">Etenim <lb/>iuxta prædicta facilè re&longs;pondetur, tunc quoque malum, ve­<lb/>ctis rationem habere, altero in extremo &longs;uffulti prope na­<lb/>uis carinam: antennam verò oneris vicem &longs;ubire, ac mare <lb/>fluctuans, potentiæ mouentis, cuius virtus mediante naui-<pb pagenum="123" xlink:href="005/01/131.jpg"/>gio applicatur vecti inter fulcimentum, & onus; nempe vbi <lb/>malus ip&longs;e vltimo intra corpus nauigij continetur, vt paulo <lb/>ante de&longs;crip&longs;imus. </s> <s id="N13AB3">Dum enim iactatur &longs;imul cum nauigio <lb/>malus, ac propterea cogitur inclinari, ob&longs;tat quantum po­<lb/>te&longs;t antenna in &longs;uperiori eius parte alligata tanquam onus <lb/>incumbens, quod perpendiculariter ad mundi centrum gra­<lb/>uitans, re&longs;i&longs;tit inclinationi, ne contra propriam rectitudinem, <lb/>ac naturalem propen&longs;ionem à perpendiculo deuians, obli­<lb/>què ad latera vergat. </s> </p> <p id="N13AC2" type="main"> <s id="N13AC4">Magis autem, aut minus valet re&longs;i&longs;tere, iuxta maiorem, <lb/>aut minorem di&longs;tantiam, quam habet à &longs;ede mali, vbi con­<lb/>&longs;tituitur centrum ip&longs;ius motus circularis, quem ad commo­<lb/>tionem nauigij per varios arcus conficit malus. </s> <s id="N13ACF">Quo enim <lb/>plus à centro, &longs;eu fulcimento di&longs;ce&longs;&longs;erit onus, eo difficilius <lb/>dimouetur: di&longs;tabit autem tanto magis à &longs;ede mali, ac fun­<lb/>do nauis antenna, quantò altius &longs;ublimatur. </s> <s id="N13AD8">Accedit quia <lb/>&longs;imul magis di&longs;tabit à parte vbi vis incutitur malo in &longs;um­<lb/>mo foramine nauis hinc inde illum impellentis: potentia <lb/>verò remotius ab onere applicata, quàm à fulcimento ve­<lb/>ctis, minus illud mouere pote&longs;t quando fulcimentum con­<lb/>&longs;tituitur in altero vectis extremo: Vt &longs;i qui&longs;piam extremo <lb/>&longs;ari&longs;&longs;æ alicubi obfirmato, ac manu prope ip&longs;um extremum <lb/>illi admota, aliquod pondus altero extremo dimouere co­<lb/>netur. </s> <s id="N13AEB">Antenna ergo remoti&longs;&longs;imè à loco vbi virtus impul­<lb/>&longs;iua in malo refunditur collocata, difficillimè commouetur, <lb/><expan abbr="proindeq">proindeque</expan> &longs;imul cum illa totum nauigium cuius commotio­<lb/>ni magis valebit ob&longs;tare. </s> </p> <p id="N13AF4" type="main"> <s id="N13AF6">Quod &longs;anè verificatur in mediocri, vel modica fluctuum <lb/>eleuatione, vt con&longs;ultò innuimus; alioquin nimis extuante <lb/>mare, <expan abbr="nimisq.">nimisque</expan> obtume&longs;centibus vndis, dum validè iactatur <lb/>nauigium, oppo&longs;itum experimur. </s> <s id="N13B03">Tunc enim &longs;i antenna in <lb/>illo <expan abbr="di&longs;tãtiori">di&longs;tantiori</expan> &longs;itu con&longs;tituatur, ac &longs;emel cum nauigio admo­<lb/>dum inclinetur malus, ad totalem potius euer&longs;ionem con­<lb/>duceret. </s> <s id="N13B10">Quandoquidem linea perpendicularis, qua onus <lb/>antennæ mundi centrum petit ob talem inclinationem, non <lb/>caderet intra nauigium, &longs;ed foris à latere, quò propen&longs;ius <pb pagenum="124" xlink:href="005/01/132.jpg"/>tendendo antenna ip&longs;a non modo amplius inclinationi ni­<lb/>hil ob&longs;taret, &longs;ed vicem &longs;ubiret potentiæ inclinantis eundem <lb/>malum tanquam vectem, & cum illo totum nauigium cui <lb/>malus affigitur, eleuando &longs;cilicet alterum latus tanquam <lb/>onus impo&longs;itum, alterum comprimendo veluti hypomo­<lb/>chlion cui innititur, ex quo &longs;equeretur euer&longs;io, atque &longs;um­<lb/>mer&longs;io. </s> </p> <p id="N13B28" type="head"> <s id="N13B2A">Quæ&longs;tio Septima.</s> </p> <p id="N13B2D" type="main"> <s id="N13B2F">C<emph type="italics"/>vr quando ex puppi nauigare volue­<lb/>rint, non flante ex puppi vento, veli qui­<lb/>dem partem, quæ ad gubernatorem vergit, <lb/>con&longs;tringunt: illam verò quæ proram v<gap/>r&longs;us <lb/>e&longs;t, pedem facientes relaxant? </s> <s id="N13B3F">An quia re­<lb/>trahere quidem multò exi&longs;tente vento guber­<lb/>na culum non potest: pauco autem pote&longs;t, quem con&longs;tringunt? <lb/></s> <s id="N13B47">Propellit quidem igitur ip&longs;e ventus: in puppim verò illum <lb/>constituit gubernaculum retrahens, & mare compellens: &longs;i­<lb/>mul & nautæ ip&longs;i cum vento contendunt: in contrarium enim <lb/>&longs;e reclinant partem.<emph.end type="italics"/></s> </p> <p id="N13B52" type="head"> <s id="N13B54">COMMENTARIVS.<!-- KEEP S--></s> </p> <p id="N13B58" type="main"> <s id="N13B5A">Cau&longs;am hic inquirit Ari&longs;toteles cur nautæ ex puppi <lb/>antror&longs;um velo nauigare cupientes non flante ex <lb/>puppi vento, &longs;ed puta ex latere, &longs;eu ex tran&longs;uer&longs;o, <lb/>velo quidem in altero atque oppo&longs;ito nauis latere con&longs;titu­<lb/>to, partem eius, quæ ad puppim vergit vbi gubernator ad <lb/>clauum moderandum a&longs;&longs;i&longs;tit, quantum fieri pote&longs;t exten­<lb/>dunt, ac fune reducto eius extrema con&longs;tringunt: illam ve­<lb/>rò quæ proram ver&longs;us e&longs;t, ac tanquam inferiorem, pedem <lb/>ip&longs;ius veli con&longs;tituunt, altero fune producto relaxant, &longs;eu <lb/>laxiorem e&longs;&longs;e &longs;inunt. </s> <s id="N13B6F"><expan abbr="Docetq.">Docetque</expan> ex eo id fieri, nam &longs;uppo&longs;ito <lb/>quod gubernaculum cum temone, multum impellente ven-<pb pagenum="125" xlink:href="005/01/133.jpg"/>to inclinare non po&longs;&longs;it nauigium qua&longs;i in contrarium, &longs;icut cum <lb/>parum vel minus impellit; velo &longs;ic con&longs;tituto vt diximus, totus <lb/>penè impetus venti in eius partem, quæ ad puppim extenditur <lb/><expan abbr="tanquã">tanquam</expan> in &longs;inu excipitur atque colligitur, vbi propellit quidem <lb/>ex tran&longs;uer&longs;o, &longs;ed cum magis appropinquetur temoni, quo ob­<lb/>uiantibus fluctibus maris, nauis retrahitur in contrarium, minus <lb/>præualet, quàm &longs;i imprimeretur ver&longs;us proram, vel in totum ip­<lb/>&longs;um velum vniformiter ten&longs;um. </s> <s id="N13B8D"><expan abbr="Dumq.">Dumque</expan> nautæ mediante gu­<lb/>bernaculo, ac temone, cum vento contendunt, in contrariam <lb/>partem proram reclinando, medium iter tenet nauigium, <expan abbr="per-gitq.">per­<lb/>gitque</expan> antror&longs;um, quo ip&longs;emet de&longs;tinauerint nautæ. </s> </p> <p id="N13B9D" type="main"> <s id="N13B9F">Hæc ex Ari&longs;totele, quæ vt clarius dilucidentur, &longs;it nauis AB, <lb/>cuius puppis A, prora verò B, gubernaculum obliquè con&longs;ti­<lb/>tutum AC; temo &longs;imili­<lb/><figure id="id.005.01.133.1.jpg" xlink:href="005/01/133/1.jpg"/><lb/>ter AD, malus E, ac ve­<lb/>lum &longs;ecundum <expan abbr="infimã">infimam</expan> &longs;ui <lb/>oram, &longs;it curua linea FG, <lb/>lateraliter ventum exci­<lb/>piens ex parte dextera <lb/>vbi H. <!-- KEEP S--></s> <s id="N13BBD">Tunc qua&longs;i pugna <lb/><expan abbr="quædã">quædam</expan> <expan abbr="cõ&longs;ideretur">con&longs;ideretur</expan> inter <lb/><expan abbr="ventũ">ventum</expan>, ac temonem. </s> <s id="N13BCE"><expan abbr="Nã">Nam</expan> <lb/>flante vento ex H, <expan abbr="naui-giũ">naui­<lb/>gium</expan> transferri deberet in <lb/>oppo&longs;itum, hoc e&longs;t &longs;ini­<lb/>&longs;tror&longs;um ver&longs;us I per li­<lb/>neam HLI. </s> <s id="N13BE3">Incidentibus <lb/>autem fluctibus maris in <lb/>alam temonis AD, prora <lb/>ex B conuerti deberet in H, circa ip&longs;um <expan abbr="punctũ">punctum</expan> A <expan abbr="tanquã">tanquam</expan> cen­<lb/>trum talis motionis obliquæ, vt probatum e&longs;t. </s> <s id="N13BF6">Quoniam verò <lb/>neutrum præualet, nauis, medium cur&longs;um tenens, transfertur <lb/>antror&longs;um ver&longs;us K quo pergere, ac velificare cupiunt nautæ, <lb/>qui iccirco in tali po&longs;itione nauim cum velo con&longs;tituunt. </s> </p> <p id="N13BFF" type="main"> <s id="N13C01">Cau&longs;a verò cur neutrum præualeat hæc e&longs;t: Nam ex vno ca­<lb/>pite, licet temo, nauis <expan abbr="po&longs;ition&etilde;">po&longs;itionem</expan> immutet, ac inclinare eam va-<pb pagenum="126" xlink:href="005/01/134.jpg"/>leat obliquè, promouere tamen eam ip&longs;am nequit, quo proram <lb/>re&longs;picientem con&longs;tituit, <expan abbr="multoq.">multoque</expan> minus dum ventus inde validè <lb/>&longs;pirat. </s> <s id="N13C17">Quare in ca&longs;u propo&longs;ito, hoc tantum præ&longs;tat ala illa ob­<lb/>uer&longs;a temonis, quod e&longs;t, eandem nauis <expan abbr="po&longs;ition&etilde;">po&longs;itionem</expan> obliquam &longs;er­<lb/>uare contra impetum &longs;piritus, quo certè prora <expan abbr="nõ">non</expan> minus quàm <lb/>puppis ad latus retrocedere cogeretur, <expan abbr="pariterq.">pariterque</expan> in oppo&longs;itam <lb/><expan abbr="part&etilde;">partem</expan> abire. </s> <s id="N13C31">Ex alio verò capite licet ventus æquè incidat in to­<lb/>tum <expan abbr="velũ">velum</expan>, ac vehementer pellat ex tran&longs;uer&longs;o: nihilo minus pro­<lb/>pter explicatam veli po&longs;itionem totum ferè &longs;e confert in par­<lb/>tem ad puppim <expan abbr="vergent&etilde;">vergentem</expan>, quæ &longs;ublimior, ac latior e&longs;t, <expan abbr="&longs;inumq.">&longs;inumque</expan> <lb/>maiorem efficit, ex quo impetus qua&longs;i retortus refunditur in <lb/>latus ver&longs;us proram, vt in LB, quo proinde latere nauis fertur <lb/>antror&longs;um &longs;uper lineam E K. <!-- KEEP S--></s> </p> <figure id="id.005.01.134.1.jpg" xlink:href="005/01/134/1.jpg"/> <p id="N13C52" type="main"> <s id="N13C54">Retorqueri autem im­<lb/>pul&longs;um pr&etail;dictum ex eo <lb/>contingit, quia <expan abbr="tã">tam</expan> infima <lb/>veli ora ab E <expan abbr="v&longs;q;">v&longs;que</expan> ad G, <lb/>quàm <expan abbr="ant&etilde;na">antenna</expan> à loco vbi <lb/>malo alligatur v&longs;que ad <lb/><expan abbr="ceruchũ">ceruchum</expan>, &longs;eu cornu eius, <lb/>quod in <expan abbr="altũ">altum</expan> extollitur, <lb/>&longs;emper patitur magis à <lb/>vento perflante, quàm <lb/>pars tam veli; quàm an­<lb/>tennæ, quæ e&longs;t ab E in F <lb/>ver&longs;us <expan abbr="prorã">proram</expan>: nam inde <lb/>potius fugit <expan abbr="atq;">atque</expan> elabitur <lb/>ventus ob maiorem di­<lb/>rectionem, quam &longs;eruat <lb/>erga ip&longs;um ventum, quem non ita in faciem excipit, &longs;icut pars <lb/>concaua, quæ ad puppim vergit. </s> <s id="N13C94">Dum autem patitur, ac percu­<lb/>titur magis cum velo, antennæ pars, quæ e&longs;t à malo ad cornu, <lb/>verbi gratia in &longs;ini&longs;tra, tanquam &longs;i moueretur circa ip&longs;um <expan abbr="malũ">malum</expan> <lb/>veluti &longs;emidiameter circa centrum, vertere nititur nauigium in <lb/><expan abbr="contrariũ">contrarium</expan>, hoc e&longs;t dextror&longs;um, quia vim accipit à &longs;ini&longs;tra. </s> <s id="N13CA6">Vnde <lb/>impul&longs;us qua&longs;i retortus aliquantulum in gyrum, nauem ip&longs;am <pb pagenum="127" xlink:href="005/01/135.jpg"/>non quidem &longs;ini&longs;tror&longs;um, &longs;ed antror&longs;um præualet commouere. <lb/></s> <s id="N13CB1">Id quod clariùs hic licebit in&longs;picere in delineata figura ei&longs;dem <lb/>fermè litteris, quibus &longs;uperior con&longs;ignata. </s> </p> <figure id="id.005.01.135.1.jpg" xlink:href="005/01/135/1.jpg"/> <p id="N13CBB" type="main"> <s id="N13CBD">Cæterum ex his <lb/>patet, quàm rectè <lb/>Ari&longs;toteles docuerit <lb/>ex eo nautas veli <lb/>partem ver&longs;us <expan abbr="prorã">proram</expan> <lb/>pedem facere, ac re­<lb/>laxare, hoc e&longs;t ex eo <lb/>partem veli inferio­<lb/>rem <expan abbr="tanquã">tanquam</expan> pedem <lb/>ver&longs;us <expan abbr="prorã">proram</expan> collo­<lb/>care, ac funibus mi­<lb/>nus adducere; &longs;upe­<lb/>riorem verò quæ <expan abbr="lõ-gè">lon­<lb/>gè</expan> maior e&longs;t ver&longs;us <lb/>puppim retrahere, & <lb/>alligare, quia &longs;i vtramque partem veli &etail;quatame&longs;&longs;e paterentur, <lb/>malus vtrinque propul&longs;us æquè etiam propelleretur. </s> <s id="N13CF0">Cumque <lb/>propul&longs;us totus e&longs;&longs;et in directum à latere dextro, vel &longs;ini&longs;tro, <lb/>nauis per illam pergere non po&longs;&longs;et antror&longs;um. </s> <s id="N13CF7">Accedit quia <lb/>&longs;i æqualis, vel maior impetus incuteretur in proram, non tam <lb/>facilè temo illam po&longs;&longs;et retrahere in contrarium. </s> <s id="N13CFE">Siquidem <lb/>magis di&longs;taret à fulcimento, ac centro, quod con&longs;tituitur in <lb/>cu&longs;pide puppis. </s> <s id="N13D05">Vnde quo magis velum appropinquatur pup­<lb/>pi, eo magis temo præualet contra impul&longs;um ventorum ad <lb/>conuertendam nauim obliquè. </s> </p> <p id="N13D0C" type="main"> <s id="N13D0E">Quod autem ait Piccolomineus, in hac motione nauis cari­<lb/>nam vectis vicem obtinere, quæ centro grauitatis ip&longs;ius nauis <lb/>tanquam fulcimento innixa mare mouente, ac impellente te­<lb/>monem, ventum in prora &longs;u&longs;tineat tanquam onus, valde ambi­<lb/>guum e&longs;t. </s> <s id="N13D1A">Tum quia non minus ventus per velum, quàm ma­<lb/>re per temonem pote&longs;t habere rationem potentiæ mouentis. <lb/></s> <s id="N13D20">Tum etiam quia ventus præcipuè non &longs;u&longs;tinetur in prora, &longs;ed <lb/>potius in parte veli, quæ vergit ad puppim, vt dictum e&longs;t. </s> </p> <pb pagenum="128" xlink:href="005/01/136.jpg"/> <p id="N13D29" type="main"> <s id="N13D2B">Ex dictis etiam licebit duas alias veluti affines quæ&longs;tiones <lb/>diluere. </s> <s id="N13D30">Vna e&longs;t, cur flante ex latere vento, <expan abbr="veloq.">veloque</expan> cum malo <lb/>ad latus oppo&longs;itum inclinante, non &longs;equatur nauis &longs;ubmer&longs;io? <lb/></s> <s id="N13D3A">Quamuis enim nautæ cum cæteris nauigantibus ideo in latus <lb/>nauis, quod ver&longs;us ventum e&longs;t, &longs;e conferant, vt proprio onere <lb/>compen&longs;etur impetus veli, ac pondus mali in oppo&longs;itum incli­<lb/>nantis: Nihilominus hoc non videtur &longs;ufficere, attenta vehe­<lb/>mentia &longs;piritus impellentis, <expan abbr="magnaq.">magnaque</expan> vi quam exhibet malus <lb/>dum &longs;e conuertit, tanquam vectis ad latus illud quod deprimit. <lb/></s> <s id="N13D4C">Re&longs;pondetur tamen iuxta prædicta, quod malus licet incline­<lb/>tur ad latus præ&longs;criptum, non vrget &longs;ecundum ip&longs;am inclina­<lb/>tionem ver&longs;us idem latus directè, &longs;ed ver&longs;us proram, vel oram <lb/>lli propinquam, propter rationem adductam; eo &longs;cilicet, quod <lb/>&longs;inu veli obliquato non minus ex parte eiu&longs;dem lateris ventus <lb/>ibi collectus impellat, <expan abbr="modereturq.">modereturque</expan> proinde impetus in pedem <lb/>eiu&longs;dem antennæ ex alia parte, ne ad latus oppo&longs;itum malus <lb/>ip&longs;e omnino cogatur nauem inflectere. </s> </p> <p id="N13D61" type="main"> <s id="N13D63">Altera verò quæ&longs;tio e&longs;t, cur nauis hunc prout de&longs;crip&longs;imus <lb/>cur&longs;um &longs;eruando, &longs;ecurius incedat, <expan abbr="minusq.">minusque</expan> &longs;ubmer&longs;ioni &longs;it ob­<lb/>noxia, quàm cum ex puppi flante <expan abbr="v&etilde;to">vento</expan> recta procedit? </s> <s id="N13D72">Id quod <lb/>inexpertis <expan abbr="mirũ">mirum</expan> videri &longs;olet, <expan abbr="cũ">cum</expan> quippe talis inclinatio, qua &longs;æ­<lb/>pè <expan abbr="etiã">etiam</expan> mare intus excipitur, <expan abbr="&longs;ubmer&longs;ion&etilde;">&longs;ubmer&longs;ionem</expan> potius minetur, <expan abbr="quã">quam</expan> <lb/><expan abbr="&longs;ecuritat&etilde;">&longs;ecuritatem</expan> polliceatur. </s> <s id="N13D92">Contrà verò &longs;ecundis ventis <expan abbr="æquatisq.">æquatisque</expan> <lb/>velis <expan abbr="ab&longs;q.">ab&longs;que</expan> vlla nauis inclinatione <expan abbr="progredi&etilde;do">progrediendo</expan>, nullus appareat <lb/>ca&longs;us pertime&longs;cendus. </s> <s id="N13DA5">Sed facilis e&longs;t re&longs;pon&longs;io; <expan abbr="nã">nam</expan> velo ad pro­<lb/>ram laxato, <expan abbr="ventisq.">ventisque</expan> &longs;ecundis <expan abbr="obtume&longs;c&etilde;ti">obtume&longs;centi</expan>, plus <expan abbr="quandoq.">quandoque</expan> <expan abbr="cõ-tingit">con­<lb/>tingit</expan> &longs;e ad vnum, quam ad <expan abbr="alterũ">alterum</expan> latus inflectere, eo quod ne­<lb/>queat tam antenna, quàm velum exactè in duas partes &etail;quales <lb/>vtrinque ad malum di&longs;tribui. </s> <s id="N13DC8">Cumque in hac latione qua nauis <lb/>recta è puppi mouetur in proram, temo &longs;cindat quidem mare <lb/>obuium eodem pacto in <expan abbr="directũ">directum</expan>, &longs;ed illud non excipiat ad dex­<lb/>teram, aut &longs;ini&longs;tram, nec ideo vim alienam inferat naui circa <lb/>cur&longs;us <expan abbr="moderation&etilde;">moderationem</expan> per proræ <expan abbr="conuer&longs;ion&etilde;">conuer&longs;ionem</expan>: hinc fit, vt repen­<lb/>tino &longs;uperueniente impetu vehementi, atque in vnam magis <lb/>quàm in alteram veli partem incu&longs;&longs;o, ob aptiorem po&longs;itionem <lb/>illius, aut magnitudinem maiorem; facilè totum nauigium à re-<pb pagenum="129" xlink:href="005/01/137.jpg"/>ctitudine viæ deuiet, <expan abbr="moxq.">moxque</expan> &longs;e vnà cum malo ad latus, ad <lb/>quod pars illa maior vergerit, omnino declinando demer­<lb/>gat; ni&longs;i protinus ob&longs;tauerit gubernator per conuer&longs;ionem <lb/>temonis, compellendo proram, ac reclinando illam ver­<lb/>&longs;us eandem partem, in qua &longs;equeretur &longs;ubmer&longs;io, ac vn­<lb/>de deflexerat, vt ventus à tergo &longs;pirans, ex æquo velum fe­<lb/>riat in prora, <expan abbr="propellatq.">propellatque</expan> recta nauigium &longs;icut prius. </s> </p> <p id="N13DFE" type="head"> <s id="N13E00">Quæ&longs;tio Octaua.</s> </p> <p id="N13E03" type="main"> <s id="N13E05">C<emph type="italics"/>vr ex figurarum genere quæcunque rotun­<lb/>dæ &longs;unt, & circinatæ, facilius mouentur? <lb/></s> <s id="N13E0E">Trifariam autem circulum rotari contingit. <lb/></s> <s id="N13E12">Aut enim &longs;ecundum ab&longs;idem centro &longs;imul mo­<lb/>to, quemadmodum plau&longs;tri vertitur rota: aut <lb/>circa manens centrum, veluti trochleæ &longs;tante <lb/>centro, aut in pauimento manente centro, &longs;icut figuli rota con­<lb/>vertitur: an celerrima quidem huiu&longs;modi &longs;unt, quoniam par­<lb/>ia &longs;ui parte planum contingunt, veluti circulus &longs;ecundum <lb/>punctum, & quoniam non offen&longs;ant. </s> <s id="N13E21">A terra enim &longs;emotus e&longs;t <lb/>angulus. </s> <s id="N13E26">Præterea etiam cui obuiam fiunt corpori, id rur&longs;um <lb/>&longs;ecundum pu&longs;illum tangunt. </s> <s id="N13E2B">Si autem rectilineum e&longs;&longs;et, re­<lb/>ctitudine &longs;ua multum plani contingeret. </s> <s id="N13E30">Ad hæc quo nutat <lb/>pondus, eò motor mouet. </s> <s id="N13E35">Cùm igitur ad rectum &longs;uper plano <lb/>circuli fuerit diameter, planum &longs;ecundum punctum contin­<lb/>gente circulo æquale vtrinque pondus di&longs;terminat diameter. <lb/></s> <s id="N13E3D">Cùm autem mouetur plus illico, ad quod mouetur, ceri inde nu­<lb/>tans, ab impellente facilius in ante mouetur. </s> <s id="N13E42">Quo enim vnum­<lb/>quodque vergit, mouetur ex facili. </s> <s id="N13E47">Siquidem difficulter ad <lb/>contrarium nutus &longs;ui mouetur motum. </s> <s id="N13E4C">Praeterea nonnulli <lb/>autumant, quod circule linea in perpeti ver&longs;atur motu, quem­<lb/>admodum manentia propter contrarium nixum manent: &longs;icut <lb/>maioribus contingit circulis ad minores. </s> <s id="N13E55">Celeriùs enim ab <lb/>æquali mouentur potentia maiores circuli, <expan abbr="mouentq.">mouentque</expan> onera, <lb/>quoniam circuli maioris angulus ad minoris angulum, circu­<lb/>li nutum habet quendam: & &longs;icut diameter ad diametrum, <lb/>ita maior circulus ad minorem. </s> <s id="N13E64">Infiniti autem &longs;unt minores. <lb/></s> <s id="N13E68">Si autem ad alterum nutum habet circulus, &longs;imiliter e&longs;t benè <lb/>mobilis. </s> <s id="N13E6D">Et aliam &longs;anè habet inclinationem circulus, & <gap/>a<emph.end type="italics"/><pb pagenum="130" xlink:href="005/01/138.jpg"/><emph type="italics"/>quæ à circulo mouentur, licet planitiem ab&longs;ide non contingat, <lb/>&longs;ed aut iuxta planitiem, aut ueluti trochleæ. </s> <s id="N13E7D">Etenim hoc &longs;e <lb/>habentes modo facillimè mouentur, & onera commouent. </s> <s id="N13E82">An <lb/>quia parua &longs;ui portione cùm tangit, tum offen&longs;at circulus, &longs;ed <lb/>aliam ob cau&longs;am? </s> <s id="N13E89">ea autem e&longs;t, quæ dicta est prius, quod circu­<lb/>lus &longs;cilicet ex duabus effectus e&longs;t lationibus: quamobrem il­<lb/>larum alteram pro nutu &longs;emper habet, & veluti continuò mo­<lb/>tum illum moueat quicumque mouent, quando &longs;ecundum cir­<lb/>cumferentiam illum mouerint: latam enim ip&longs;am mouent. <lb/></s> <s id="N13E95">Eam quidem igitur, quæ in obliquum e&longs;t, motionem, ip&longs;um <lb/>impellit mouens: &longs;ecundum verò illam, quæ &longs;uper diametrum <lb/>est, &longs;e ip&longs;um mouet circulus.<emph.end type="italics"/></s> </p> <p id="N13E9E" type="head"> <s id="N13EA0">COMMENTARIVS.<!-- KEEP S--></s> </p> <p id="N13EA4" type="main"> <s id="N13EA6">Vt quæ&longs;tioni re&longs;pondeat Ari&longs;toteles cur corpora, <lb/>quæ rotundam, aut orbiculatam figuram obtinent, <lb/>&longs;ecundum illam facilius moueantur, triplicem mo­<lb/>dum di&longs;tinguit, quo ip&longs;a moueri rotando contingit. </s> <s id="N13EAF"><expan abbr="Pri-mumq.">Pri­<lb/>mumque</expan> e&longs;&longs;e docet, quo &longs;ecundum ab&longs;idem, &longs;eu extimam ip­<lb/>sorum curuaturam cientur, moto &longs;imul etiam centro, vt <lb/>plau&longs;trorum rotæ, quæ &longs;imul cum axe feruntur. </s> <s id="N13EBB">Secundum <lb/>verò modum, ait e&longs;&longs;e illum, quo circularia ip&longs;a corpora re­<lb/>cta quidem &longs;tantia, &longs;eu rectè ad horizontem con&longs;tituta mo­<lb/>uentur circa centrum immotum; veluti &longs;tantes trochlea­<lb/>rum rotulæ, quæ circa manentem axem, &longs;eu centrum ad di­<lb/>uer&longs;os v&longs;us conuertuntur. </s> <s id="N13EC8">Tertium denique modum e&longs;&longs;e <lb/>inquit, quo circa immotum pariter centrum mouentur, non <lb/>tamen &longs;tando, &longs;ed qua&longs;i pro&longs;trata iuxta planitiem &longs;oli, aut <lb/>pauimenti horizonti paralellam; &longs;icut rota figuli, quæ ad <lb/>impul&longs;um pedis illius conuertitur, ac circumagitur &longs;upra <lb/>axim pauimento perpendiculariter affixum, &longs;eruando &longs;em­<lb/>per eandem di&longs;tantiam ab horizonte. </s> </p> <p id="N13ED7" type="main"> <s id="N13ED9">Loquendo itaque de primo modo, pluribus ex cau&longs;is, ait <lb/>Ari&longs;toteles præfata corpora celerius, ac facilius moueri <lb/>quàm illa, quæ rectilineas adepta &longs;unt figuras, &longs;eu rectilineis <lb/>figuris terminantur, vt triangulari, vel quadrangulari, pirami-<pb pagenum="131" xlink:href="005/01/139.jpg"/>des, & cubi. </s> <s id="N13EE7">Prima e&longs;t, quia minima &longs;ui parte planum con­<lb/>tingunt hoc e&longs;t minori, quam cuiu&longs;libet alterius figuræ cor­<lb/>pora, re&longs;pectu, verbi gratia &longs;phæræ, quæ planum tangit in <lb/>puncto. </s> <s id="N13EF0">Secunda verò e&longs;t, quia hoc pacto non offendunt, aut <lb/>impingunt ni&longs;i &longs;cilicet rarius, ac difficilius; A terra enim &longs;e­<lb/>motus e&longs;t angulus, inquit Ari&longs;toteles, nimirum angulum <lb/>contingentiæ, &longs;eu contactus, quia po&longs;t punctum contingen­<lb/>tiæ, totum latus curuilineum ip&longs;orum corporum orbicula­<lb/>rium, quod cum plano con&longs;tituit huiu&longs;modi angulum, è ter­<lb/>ra eleuatur; ac propterea minus impingunt in offendicula, <lb/>quàm alia corpora, quorum latera <expan abbr="nõ">non</expan> &longs;tatim po&longs;t minimum <lb/>contactum eleuantur, &longs;ed ip&longs;i plano, &longs;eu terræ adhærent. <lb/></s> <s id="N13F08">Tertia cau&longs;a e&longs;t, nam huiu&longs;modi corpora cuicunque ob­<lb/>uient offendiculo, illud pariter nonni&longs;i &longs;ecundum pu&longs;illam <lb/>&longs;ui partem attingunt, eadem ratione, qua planum, &longs;eu &longs;olum <lb/>&longs;uper quod ip&longs;a mouentur, &longs;ecus, ac rectilineam figuram ha­<lb/>bentia, quæ &longs;emper &longs;ua rectitudine &longs;ecundum magnam, vel <lb/>&longs;altem maiorem partem contingunt. </s> </p> <p id="N13F15" type="main"> <s id="N13F17">Ad hæc quartam cau&longs;am addit Ari&longs;toteles. <!-- KEEP S--></s> <s id="N13F1B">Nam (inquit) <lb/>quò nutat pondus, eo motor mouet. </s> <s id="N13F20">Hoc e&longs;t, quia motor <lb/>dum huiu&longs;modi corpora rotunda, vel &longs;phærica &longs;ecundum <lb/>ab&longs;idem mouet, eo profectò impellit, quo &longs;tatim ip&longs;orum <lb/>pondus propendit &longs;iue inclinat. </s> <s id="N13F29">Etenim &longs;i con&longs;tituatur &longs;u­<lb/>per planum AB horizonti <lb/><figure id="id.005.01.139.1.jpg" xlink:href="005/01/139/1.jpg"/><lb/>paralellum erecta aliqua <lb/>rota, vt CDEF tanquam <lb/>circulus, eius diameter à <lb/>contactu plani vbi C per­<lb/>pendiculariter ad angulos <lb/>rectos per centrum &longs;upra <lb/>tra&longs;cendens ad D, totam <lb/>rotam eiu&longs;que pondus in <lb/>duas partes æquales di&longs;tri­<lb/>buet, nempe in DFC, & <lb/>DEC. <expan abbr="Eritq.">Eritque</expan> ip&longs;a rota in <pb pagenum="132" xlink:href="005/01/140.jpg"/>æquilibrio, quia non magis vna quam altera pars vtrinque <lb/>à perpendiculo DC grauitare pote&longs;t. </s> <s id="N13F55">Quod &longs;i impul&longs;us <lb/>quamuis perexiguus in ip&longs;am rotam à motore incutiatur, <lb/>vt ex parte E ver&longs;us F, &longs;tatim pars vbi F nutabit ac pro­<lb/>pendet ver&longs;us B; <expan abbr="&longs;uoq.">&longs;uoque</expan> nutu, totam rotam &longs;ecum trahet il­<lb/>luc. </s> <s id="N13F64">Nam quælibet vis pote&longs;t æquiponderantia ab æquili­<lb/>brio dimouere. </s> <s id="N13F69">Semel autem mota ip&longs;a rota, ni&longs;i impe­<lb/>diatur deinceps nutabit ad partem ver&longs;us quàm primò fuit <lb/>incitata; ideoque facilè vlterius atque vlterius mouebitur. <lb/></s> <s id="N13F71">Quo enim vnumquodque vergit, mouetur ex facili, &longs;ubdit <lb/>ip&longs;e Philo&longs;ophus, &longs;icut vice ver&longs;a difficulter in contrarium; <lb/>vt fu&longs;ius con&longs;tabit quæ&longs;t. </s> <s id="N13F78">31. </s> </p> <p id="N13F7B" type="main"> <s id="N13F7D">Atque hæc dicta intelliguntur de motu rotæ, aut &longs;phæræ <lb/>&longs;uper planum horizonti paralellum. </s> <s id="N13F82">Nam &longs;uper planum <lb/>quodlibet decliue, euidentius idem con&longs;tabit. </s> <s id="N13F87">Siquidem <lb/>demi&longs;&longs;a tantum rota, vel &longs;phæra &longs;uper illud, &longs;uo &longs;emper nu­<lb/>tu celerrimè deor&longs;um rotando &longs;e conferet, imò in præceps <lb/>quandoque decurret. </s> <s id="N13F90">Cum enim huiu&longs;cemodi corpora per <lb/>eam lineam maximè grauitent, quæ perpendiculariter ab <lb/>eorum centro tendit ad centrum mundi, &longs;i &longs;uper decliue <lb/>planum con&longs;tituantur, nequibunt &longs;ecundum eandem li­<lb/>neam fulciri, ac &longs;u&longs;tineri ab ip&longs;o plano. </s> <s id="N13F9B">Nam punctum cir­<lb/>cumferentiæ per quod ip&longs;a linea cadit ad centrum mundi, <lb/>& cui totum ferè onus incumbit, &longs;emper manebit &longs;u&longs;pen­<lb/>&longs;um &longs;upra planum ex parte inferiori ip&longs;ius, nec vnquam <lb/>planum ip&longs;um decliue continget. </s> <s id="N13FA6">Circulus enim vel glo­<lb/>bus non tangit planum, ni&longs;i in puncto in quod eius diame­<lb/>ter incidit ad angulos rectos; quo &longs;anè pacto cadere non <lb/>pote&longs;t perpendicularis tendens ad mundi centrum in pla­<lb/>num, quod non e&longs;t horizonti paralellum. </s> <s id="N13FB1">Cumque præ­<lb/>dictum punctum, cui poti&longs;&longs;imum onus incumbit, &longs;u&longs;tineri <lb/>non po&longs;&longs;it ab eo, quod non contingit; hinc fit, vt &longs;emper <lb/>ver&longs;us inferiores partes decliues propendat, ac nutet, de­<lb/>feratque propterea ip&longs;a orbiculata corpora quou&longs;que ab <lb/>alio fulciatur. </s> <s id="N13FBE">Vt per&longs;picuè apparebit in propo&longs;ita &longs;phæra <pb pagenum="133" xlink:href="005/01/141.jpg"/>vel rota ABC, &longs;i decliue <lb/><figure id="id.005.01.141.1.jpg" xlink:href="005/01/141/1.jpg"/><lb/>planum DE contingat in <lb/>C ad angulos rectos ip&longs;ius <lb/>diametri BC: linea verò <lb/>cadens per centrum ip&longs;ius <lb/>&longs;phæræ ad centrum mundi, <lb/>&longs;it AF. <!-- KEEP S--></s> <s id="N13FD9">Nam &longs;ic totum fe­<lb/>rè onus incumberet in pun­<lb/>cto G, quod cum fulciri <lb/><expan abbr="nõ">non</expan> po&longs;&longs;it in ip&longs;a DE, quam <lb/>nullo modo tangit, nece&longs;&longs;a­<lb/>riò <expan abbr="prop&etilde;det">propendet</expan> in F, <expan abbr="rapietq.">rapietque</expan> <lb/>&longs;ecum ad partes E totum <lb/>globum, qui deinceps rur­<lb/>&longs;us eadem ratione nutabit per aliud &longs;imile punctum, <expan abbr="infe-tiusq.">infe­<lb/>riusque</expan> citi&longs;&longs;imo cur&longs;u de&longs;cendet &longs;uccedentibus &longs;ibi ad inui­<lb/>cem punctis, ac partibus. </s> </p> <p id="N13FFF" type="main"> <s id="N14001">Ex hac autem maxima aptitudine, quam rotæ, vel &longs;imilia <lb/>orbiculata corpora habent ad motum, occa&longs;ionem &longs;ump&longs;i&longs;­<lb/>&longs;e videntur nonnulli arbitrandi, circuli periferiam nunquam <lb/>quie&longs;cere, &longs;ed perpetuo motu cieri, vt hic &longs;ubiungit Ari&longs;to­<lb/>teles. <!-- KEEP S--></s> <s id="N1400E">Quia &longs;cilicet circulus contrarium nixum non habet, <lb/>quo re&longs;i&longs;tat motui, aut motori &longs;icut corpora manentia, quæ <lb/>ex eo quie&longs;cunt, vel manent, quia habent, in quo contra ni­<lb/>tantur, & quo ob&longs;i&longs;tant motui, ac mouenti. </s> <s id="N14017">Vbi addendum <lb/>quippe fui&longs;&longs;et ab Ari&longs;totele, falsò eos ita putare; nam licet <lb/>circuli periferia nixum non habeat, quo retardetur, aut im­<lb/>pediatur à proprio motu; non tamen &longs;emper habet in &longs;e <lb/>principium proximum, ac formale &longs;ui motus, quod certè <lb/>cum &longs;it qualitas impetus impre&longs;&longs;i, hæc paulatim ex &longs;e re­<lb/>mittitur, ac tandem deficit, vt patet in proiectis, quæ iccirco <lb/>de&longs;i&longs;tunt à motu. </s> </p> <p id="N14028" type="main"> <s id="N1402A">Præterea Philo&longs;ophus doctrinam de mobilitate prædi­<lb/>ctorum corporum pro&longs;equendo, docet maiores circulos, <lb/>mobiliores e&longs;&longs;e minoribus. </s> <s id="N14031">Celerius enim (inquit) ab æqua­<lb/>li mouentur potentia, <expan abbr="mouentq.">mouentque</expan> onera. </s> <s id="N1403A"><expan abbr="Cau&longs;amq.">Cau&longs;amque</expan> eam e&longs;&longs;e <pb pagenum="134" xlink:href="005/01/142.jpg"/>&longs;ubnectit; quoniam &longs;emper angulus circuli maioris, nutum <lb/>quendam habet ad angulum circuli minoris (in eo &longs;cilicet <lb/>contenti circa idem centrum.) Et &longs;icut diameter ad diame­<lb/>trum, ita maior circulus, &longs;eu potius circumferentia ad mino­<lb/>rem: In quolibet autem circulo maiori, infiniti circuli mi­<lb/>nores continentur. </s> <s id="N1404F">Quo igitur maiores fuerint ip&longs;i circuli, <lb/><expan abbr="maioremq.">maioremque</expan> proinde nutum, &longs;eu inclinationem ad minores <lb/>contentos habuerint, eo facilius, ac celerius mouebuntur. </s> </p> <p id="N14059" type="main"> <s id="N1405B">Sed vt clarius hic Philo&longs;ophi di&longs;cur&longs;us innote&longs;cat, ob&longs;er­<lb/>uandum e&longs;t, per angulum circuli &longs;iue maioris, &longs;iue minoris, <lb/>non rectè intelligi &longs;ectorem, vt cum Piccolomineo inter­<lb/>pretatur Baldus. <!-- KEEP S--></s> <s id="N14065">Nam &longs;ector circuli maioris eundem an­<lb/>gulum con&longs;tituit cum &longs;ectore circuli minoris in eo conten­<lb/>ti; Ari&longs;toteles autem loquitur de angulo circuli maioris, ac <lb/>de angulo circuli minoris tanquam de diuer&longs;is, dum ait <expan abbr="vnũ">vnum</expan> <lb/>habere nutum ad alterum; alioquin perperam compara&longs;&longs;et <lb/>idem ad idem formaliter. </s> <s id="N14076">Quod &longs;i aliunde &longs;ectores ip&longs;i dif­<lb/>ferant inter &longs;e, vt reuera differunt in linearum longitudine, <lb/>ac &longs;patio intercepto, &longs;ecundum illam <expan abbr="ration&etilde;">rationem</expan> qua differunt, <lb/>& non &longs;ecundum angulum, in quo conueniunt Ari&longs;toteles <lb/>loquutus fui&longs;&longs;et ad probandam differentiam motus circuli <lb/>maioris re&longs;pectu minoris. </s> <s id="N14087">Nec per angulum circuli inter­<lb/>pretari po&longs;&longs;umus <expan abbr="cũ">cum</expan> Blancano ip&longs;ius &longs;ectoris arcum eo quod <lb/>opponatur angulo, qui e&longs;t in centro circuli. </s> <s id="N14092">Siquidem fru­<lb/>&longs;tra &longs;ignificaretur oppo&longs;itum per <expan abbr="nom&etilde;">nomen</expan> eius, cui opponitur, <lb/>cum vtrum que habeat &longs;uum vocabulum. </s> <s id="N1409D">Et eadem ratione <lb/>per angulum trianguli, po&longs;&longs;et intelligi latus illi oppo&longs;itum, <lb/>quod e&longs;&longs;et inuertere omnem proprietatem terminorum de <lb/>mente Ari&longs;totelis. <!-- KEEP S--></s> </p> <p id="N140A7" type="main"> <s id="N140A9">Potius ergo per angulum circuli, de quo hic loquitur Ari­<lb/>&longs;toteles, intelligi videtur angulus, qui ex diametro, vel &longs;e­<lb/>midiametro, ac portione circumferentiæ efficitur, quem an­<lb/>gulum Euclides vocat etiam angulum &longs;emicirculi in 16. <lb/>prop. tertij. </s> <s id="N140B4">Etenim iuxta hanc acceptionem angulus cir­<lb/>culi maioris non e&longs;t idem cum angulo circuli minoris, opti­<lb/>mèque intelligitur; & explicatur nutus, quem Philo&longs;ophus <pb pagenum="135" xlink:href="005/01/143.jpg"/>docet habere i&longs;tum ad illum. </s> <s id="N140C0">Hoc e&longs;t propen&longs;io, quam an­<lb/>gulus circuli maioris habet &longs;upra angulum circuli minoris <lb/>circa idem centrum de&longs;cripti, vt celerius, ac facilius cum. <lb/></s> <s id="N140C8">illo, ac toto circulo &longs;ecundùm ab&longs;idem moueatur. </s> </p> <p id="N140CB" type="main"> <s id="N140CD">E&longs;to enim circulus maior ABCD, minor verò EFGH, <lb/>circa idem centrum I &longs;upra planum KL. <!-- KEEP S--></s> <s id="N140D3">Diameter au­<lb/>tem maioris circuli &longs;it AC, minoris EG. </s> <s id="N140D8">Angulus item <lb/>maioris ACD; minoris ve­<lb/><figure id="id.005.01.143.1.jpg" xlink:href="005/01/143/1.jpg"/><lb/>rò EGH. <!-- KEEP S--></s> <s id="N140E6">Dicimus ergo an­<lb/>gulum ACD habere nu­<lb/>tum quendam, & inclina­<lb/>tionem &longs;upra angulum <lb/>EGH, qua, & &longs;e ip&longs;um, & <lb/>illum procliuiorem reddit <lb/>ad motum &longs;ecundum ab&longs;i­<lb/>dem &longs;uper planum KL, &longs;i <lb/>circulus ip&longs;e maior per im­<lb/>pul&longs;um motoris ver&longs;us L <lb/>moueatur. </s> <s id="N140FD">Porrò angulus <lb/>ACD, tam ex parte diametri, vel &longs;emidiametri, quàm ex <lb/>parte portionis circumferentiæ, ex quibus tanquam ex duo­<lb/>bus lateribus con&longs;tat, velocius, ac facilius pote&longs;t moueri, <lb/>quàm angulus EGH. <!-- KEEP S--></s> <s id="N14109">Ex parte quidem &longs;emidiametri, &longs;eu <lb/>lateris recti; quia extremum C magis elongatur à centro <lb/>I quàm G. <!-- KEEP S--></s> <s id="N14111">Ex parte verò portionis circunferentiæ, &longs;eu la­<lb/>teris curui; quia CD magis etiam di&longs;tat ab eodem centro, <lb/>ac minus curuatur, quàm GH; <expan abbr="minusq.">minusque</expan> proinde retrahitur <lb/>nè moueatur motu naturali, ad rectum &longs;cilicet magis ap­<lb/>propinquanti ideoque velocius ac facilius. </s> <s id="N14120">Sed angulus C <lb/>inclinari non pote&longs;t ver&longs;us L quin &longs;ecum rapiat angulum <lb/>G, quem intra &longs;e continet. </s> <s id="N14127">Igitur angulus ip&longs;e C, nutum, <lb/>& propen&longs;ionem habet ad angulum G, vt &longs;imul ac facilius <lb/>moueantur modo quo diximus ad quemlibet impul&longs;um <lb/>motoris. </s> <s id="N14130">Cumque infiniti &longs;int huiu&longs;modi anguli in explica­<lb/>tis circulis, hinc &longs;it, vt rectè ex illis concludat Ari&longs;toteles, <lb/>mobiliores e&longs;&longs;e circulos maiores, ac celerius moueri ab ea­<pb pagenum="136" xlink:href="005/01/144.jpg"/>dem, vel æquali potentia; &longs;icut celerius mouentur maiores <lb/>libræ, quàm minores ab eodem, vel æquali pondere. </s> <s id="N1413E">Non <lb/>enim aliter &longs;e habet circulus &longs;tans &longs;uper planum, quàm libra <lb/>&longs;upra fulcimentum in æquilibrio con&longs;tituta. </s> </p> <p id="N14145" type="main"> <s id="N14147">At Ari&longs;totelem per angulos circuli intelligere angulos <lb/>à nobis explicatos, illud confirmat, quod cum dixi&longs;&longs;et an­<lb/>gulum circuli maioris habere nutum ad angulum circuli <lb/>minoris, qua&longs;i id probans ait: Et &longs;icut diameter ad diame­<lb/>trum, ita circumferentia ad circumferentiam. </s> <s id="N14153">In quibus <lb/>verbis vtrumque ip&longs;orum angulorum latus comprehendit <lb/>nempe rectum, & <expan abbr="curuũ">curuum</expan>. </s> <s id="N1415E"><expan abbr="Idemq.">Idemque</expan> e&longs;t, ac dicere, quia <expan abbr="cũ">cum</expan> præ­<lb/>dicti anguli con&longs;tent ex huiu&longs;modi lateribus, &longs;icut latera ma­<lb/>iora, eo quod magis di&longs;tent à centro, velocius mouentur; ita <lb/>pariter angulus ex illis con&longs;titutus, velocius mouebitur; ma­<lb/>gis enim di&longs;tat à centro extremum diametri maioris, quàm <lb/>minoris, &longs;imiliter que portio maioris circumferentiæ ab illo <lb/>de&longs;criptæ, quàm minoris, vt per &longs;e patet. </s> </p> <p id="N14174" type="main"> <s id="N14176">Quod autem Baldus obijcit Ari&longs;toteli, prædictum nu­<lb/>tum, quem ip&longs;e gratis explicat per angulos sectores, nul­<lb/>lam arguere maiorem mobilitatem circuli maioris, eo quod <lb/>quantum vnus &longs;ector adiuuat de&longs;cen&longs;um ex vna parte, tan­<lb/>tum alter oppo&longs;itus retardet a&longs;cen&longs;um ex alia, nihil con­<lb/>uincit. </s> <s id="N14183">Nam idem dici po&longs;&longs;et de extremitate diametri lon­<lb/>gius à centro di&longs;tante, vt nihil conferat ad maiorem veloci­<lb/>tatem, eo quod altera extremitas tantundem debeat retar­<lb/>dare; Quod &longs;anè fal&longs;um e&longs;t, quoniam tam in illo, quàm in <lb/>i&longs;to motu &longs;upponitur impetus aliquis impre&longs;&longs;us, virtute cu­<lb/>ius motus ip&longs;e exerceatur, ac vna pars circuli, vel diametri <lb/>&longs;uperet aliam æqualem. </s> <s id="N14192">Alioquin &longs;icut &longs;ola maior di&longs;tan­<lb/>tia extremitatis diametri non &longs;ufficit ad motum illius; ita <lb/>nec maior nutus circuli maioris. </s> <s id="N14199">Vtrumque tamen confert <lb/>ad velocitatem &longs;uppo&longs;ito motu. </s> <s id="N1419E">Nam virtus illa impre&longs;&longs;a <lb/>nutu proprio ip&longs;ius circuli adiuta, efficacius operatur in ea <lb/>parte vbi imprimitur, vel in quam prius impre&longs;&longs;a fuerit à <lb/>motore. </s> </p> <p id="N141A8" type="main"> <s id="N141AA">Quod verò adducit ad probandum potius minores circu-<pb pagenum="137" xlink:href="005/01/145.jpg"/>los videri ad motum faciliores, eo quod maior e&longs;t angulus <lb/>contingentiæ ad planum, circumferentiæ minoris, quàm <lb/>maioris circuli, vt in &longs;ubiecta figura maior e&longs;t angulus ABC, <lb/>quàm DBC: probat quidem mi­<lb/><figure id="id.005.01.145.1.jpg" xlink:href="005/01/145/1.jpg"/><lb/>nores circulos minus offen&longs;are <lb/>propter maiorem eleuationem <lb/>ip&longs;ius anguli à terra, vt &longs;upra ex<lb/>plicuimus; &longs;ed non probat per &longs;e <lb/>facilius moueri; imò oppo&longs;itum. <lb/></s> <s id="N141C9">Nam quo curuior e&longs;t linea, eo re­<lb/>motior à motu recto, ac naturali, <lb/><expan abbr="ideoq.">ideoque</expan> tardius mouetur, vt cum <lb/>Ari&longs;totele pariter probauimus in <lb/>principio. </s> <s id="N141D7">Nec recurrere fas e&longs;t ad rotam materialem, quæ <lb/>&longs;i maior fit, maiore &longs;ui parte tangit planum, cum idip&longs;um <lb/>de&longs;truat eius a&longs;&longs;umptum, quod fundatur in eleuatione an­<lb/>guli contactus &longs;upra punctum B &longs;upponendo contactum <lb/>fieri in puncto ip&longs;o B, & non in parte diui&longs;ibili. </s> <s id="N141E2">Quod &longs;i di­<lb/>catur reuera fieri in parte diui&longs;ibili tanto maiore, quanto <lb/>maior fuerit circumferentia, tunc variatur &longs;uppo&longs;itio ante­<lb/>cedentis in con&longs;equenti, <expan abbr="nihilq.">nihilque</expan> propterea verè concluditur. </s> </p> <p id="N141EF" type="main"> <s id="N141F1">Iam verò lo quendo Ari&longs;toteles de duobus reliquis mo­<lb/>dis, quibus dixerat rotunda, vel orbiculata corpora circula­<lb/>riter moueri ab&longs;que eo, quod agitentur &longs;ecundum ab&longs;idem, <lb/>&longs;eu ab&longs;ide planum contingant, ait, his etiam modis iam ex­<lb/>plicatis facillimè ip&longs;a corpora moueri, ac alia ip&longs;is adiuncta <lb/>veluti onera commouere. </s> <s id="N141FE">Non quidem ex eo, quod parua <lb/>&longs;ui portione planum attingant, vel offen&longs;ent, vt dicebamus <lb/>de primo modo: &longs;ed alia ex cau&longs;a, quam initio huius operis <lb/>textu &longs;exto expo&longs;uimus. </s> <s id="N14207">Nimirum quia circulus cum ex <lb/>duabus efficiatur lationibus, vel cum &longs;i moueatur &longs;ecundum <lb/>circumferentiam, duabus feratur motionibus: altera obli­<lb/>qua, ac præter naturam; altera verò recta, ac &longs;ecundum na­<lb/>turam: ad hanc &longs;emper habet nutum, &longs;eu propen&longs;ionem. </s> <s id="N14212">Si­<lb/>cut verbi gratia quodlibet graue ad <expan abbr="motũ">motum</expan> deor&longs;um. </s> <s id="N1421B">Quam­<lb/>obrem qui mouent ip&longs;um circulum &longs;ecundum circumferen-<pb pagenum="138" xlink:href="005/01/146.jpg"/>tiam, parum aut nihil conantur re&longs;pectu huius lationis &longs;e­<lb/>cundum naturam; &longs;ed mouent ip&longs;um, veluti motum ab in­<lb/>trin&longs;eco propter explicatam propen&longs;ionem, quam habet <lb/>ad eandem lationem. </s> <s id="N1422B">Non &longs;ecus ac &longs;i mouerent onus deor­<lb/>&longs;um, quo ex &longs;e illud naturaliter tendit. </s> <s id="N14230">Solùm igitur impel­<lb/>lentes circulum conantur, ac mouent illum &longs;ecundum la­<lb/>tionem obliquam, quæ e&longs;t præter naturam, & ad quam ip&longs;e <lb/>circulus non habet nutum &longs;iue inclinationem. </s> <s id="N14239">Quod e&longs;t fa­<lb/>cillimè circularia ip&longs;a corpora à mouentibus moueri. </s> <s id="N1423E">Nam <lb/>&longs;impliciter loquendo de motione mi&longs;ta, quæ ex ijs duabus <lb/>lationibus re&longs;ultat, mouentur qua&longs;i à &longs;e ip&longs;is. </s> </p> <p id="N14245" type="main"> <s id="N14247">Vtitur autem Ari&longs;toteles illis verbis: &longs;ecundum verò il­<lb/>lam (&longs;cilicet motionem) quæ &longs;upra diametrum e&longs;t, &longs;e ip&longs;um <lb/>mouet circulus: ad connotandam ip&longs;am motionem mi&longs;tam, <lb/>ac circularem re&longs;ultantem ex duabus lationibus explicatis. <lb/></s> <s id="N14251">Quam quidem &longs;uper diametrum quadrilateri exemplifica­<lb/>uerat in principio, non &longs;eruata tamen eadem proportione <lb/>Quod non abs re fuerit in hac figura palam exprimere. </s> </p> <p id="N14258" type="main"> <s id="N1425A">Sit enim circulus ABCD <lb/><figure id="id.005.01.146.1.jpg" xlink:href="005/01/146/1.jpg"/><lb/>circa centrum E, cuius &longs;emi­<lb/>diameter EC. </s> <s id="N14267">A qua excite­<lb/>tur quadratum ECFD. <expan abbr="Sitq.">Sitque</expan> <lb/>diameter quadrati recta CD. <lb/><!-- KEEP S--></s> <s id="N14274">Dico igitur quod &longs;i punctum <lb/>C, quod e&longs;t extremum &longs;emi­<lb/>diametri, moueri debeat <expan abbr="v&longs;q;">v&longs;que</expan> <lb/>ad D, circa immotum <expan abbr="centrũ">centrum</expan> <lb/>E, nullo ferè conatu mouen­<lb/>tis mouebitur per arcum, cui <lb/>&longs;ubtenditur recta CD. <expan abbr="Eo-demq.">Eo­<lb/>demque</expan> tempore ip&longs;um D transferetur in A; &longs;icut etiam <lb/>A in B, & B vbi nunc e&longs;t punctum C: quod e&longs;t, totum <lb/>circulum nullo, aut paruo negotio, à mouente circulariter <lb/>moueri. </s> <s id="N14297">Cum enim punctum C per lationem &longs;ecundum <lb/>naturam, ad quam ex &longs;e habet nutum, & propen&longs;io­<lb/>nem, qualibet exigua vi moueatur ver&longs;us F; per latio-<pb pagenum="139" xlink:href="005/01/147.jpg"/>nem verò præter naturam retrahatur ver&longs;us centrum E; im­<lb/>pellente &longs;cilicet ip&longs;o mouente; vtique &longs;i pari proportione <lb/>ip&longs;orum laterum CF, & CE deduceretur, ip&longs;is duabus <lb/>lationibus proculdubio moueretur per diametrum CD, vt <lb/>cum Ari&longs;totele demon&longs;trauimus in principio. </s> <s id="N142AB">At cum non <lb/>&longs;eruetur eadem proportio inter lationem &longs;ecundum natu­<lb/>ram, ac præter naturam, vt ibi etiam explicuimus; hinc fit, vt <lb/>punctum C moueatur per arcum CD, cui diameter qua­<lb/>drati &longs;ubtenditur, & in quo nulla e&longs;t pars, &longs;uper quam di&longs;ce­<lb/>dendo à puncto C, non moueatur vtraque latione, nunc <lb/>magis; nunc minus &longs;e appropinquando puncto F, ac &longs;eruan­<lb/>do &longs;emper eandem di&longs;tantiam à centro E. <!-- KEEP S--></s> <s id="N142BD">Mouetur it a que <lb/>punctum C v&longs;que ad D, motione re&longs;ultante ex duabus <lb/>lationibus explicatis: at que adeo nulla alia adhibita vi, aut <lb/>impul&longs;u, qui corre&longs;pondeat ei &longs;icut illis, vt dictum e&longs;t. </s> <s id="N142C6">Et <lb/>&longs;ic verificatur, quod ait Ari&longs;toteles: &longs;ecundum hanc motio­<lb/>nem, quæ fit &longs;uper diametrum; (nempe per arcum, cui illa <lb/>&longs;ubtenditur) &longs;e ip&longs;um mouere circulum. </s> </p> <p id="N142CF" type="head"> <s id="N142D1">Quæ&longs;tio Nona.</s> </p> <p id="N142D4" type="main"> <s id="N142D6">C<emph type="italics"/>vr ea, quæ per maiores circulos tolluntur, & <lb/>trahuntur, facilius & citius moueri contin­<lb/>git, veluti maioribus trochleis, quàm mino­<lb/>ribus, & &longs;cytalis &longs;imiliter? </s> <s id="N142E2">An quoniam <lb/>quantò maior fuerit illa, quæ à centro e&longs;t, in <lb/>æquali tempore maius mouetur &longs;patium? <lb/></s> <s id="N142EA">Quamobrem æquali inexi&longs;tente onere, idem faciet: quemad­<lb/>modum diximus, maiores libras minoribus exactiores e&longs;&longs;e. <lb/></s> <s id="N142F0">Spartum enim in illis centrum e&longs;t: libræ autem vtrin que par­<lb/>tes, quæ ex centro &longs;unt, exi&longs;tunt.<emph.end type="italics"/></s> </p> <p id="N142F7" type="head"> <s id="N142F9">COMMENTARIVS.<!-- KEEP S--></s> </p> <p id="N142FD" type="main"> <s id="N142FF">Maior e&longs;t difficultas, & controuer&longs;ia circa experien­<lb/>tiam hic <expan abbr="&longs;uppo&longs;itã">&longs;uppo&longs;itam</expan> ab Ari&longs;totele, dum quæ&longs;tionem <lb/>proponit, quam circa cau&longs;am ip&longs;ius adductam in <pb pagenum="140" xlink:href="005/01/148.jpg"/>&longs;olutione. </s> <s id="N1430F">Scribit enim facilius ac celerius tolli, ac trahi <lb/>pondera per maiores circulos, quàm per minores. </s> <s id="N14314">Con&longs;ti­<lb/>tuitque exemplum de trochleis, ac &longs;cytalis, quæ &longs;i maiores <lb/>&longs;int, aptius onera mouent. </s> <s id="N1431B">Quod fal&longs;um omnino e&longs;&longs;e cona­<lb/>tur o&longs;tendere Blancanus ex Guido Vbaldo. </s> <s id="N14320">Nam &longs;implex <lb/>trochlea per rotulam cui funis &longs;upernè inditur nullas addit <lb/>vires potentiæ mouenti, eo quod reducatur ad vectem, cu­<lb/>ius fultura e&longs;t in medio ip&longs;ius. </s> <s id="N14329">Vnde &longs;iue rotula illa magna <lb/>fuerit &longs;iue parua, &longs;emper eadem ratione nullam augere po­<lb/>te&longs;t facilitatem, aut velocitatem in hac motione. </s> <s id="N14330">Subdit que <lb/>Blancanus, experientia quoque con&longs;tare eodem labore <lb/>aquam hauriri, &longs;iue rotula illa magna fuerit &longs;iue parua. </s> </p> <p id="N14337" type="main"> <s id="N14339">Verum &longs;i hoc vniuer&longs;aliter demon&longs;traret experientia, fru­<lb/>&longs;tra pa&longs;&longs;im adhiberentur trochleæ ad leuanda, ac trahenda <lb/>pondera; nec e&longs;&longs;et cur iuxta maiorem ponderum grauita­<lb/>tem, maioribus rotis, ac trochleis <expan abbr="vter&etilde;tur">vterentur</expan> Architecti quan­<lb/>do minoribus vti po&longs;&longs;ent. </s> <s id="N14348">Quamuis igitur &longs;implex trochlea <lb/>&longs;upernè appen&longs;a nullam addat vim potentiæ motrici, &longs;icut <lb/>nec vectis, cuius fulcimentum non &longs;it propinquius oneri; <lb/>multam tamen affert commoditatem. </s> <s id="N14351">Vnde eadem quip­<lb/>pè vi, &longs;ed; non eodem labore eleuatur onus beneficio tro­<lb/>chleæ, aut vectis prædicti, quàm &longs;ine illis. </s> <s id="N14358">Commoditas enim <lb/>minuit laborem, ac &longs;i non auget potentiam, confert tamen <lb/>ad applicationem, & exercitium illius: id quod e&longs;t augere <lb/>facilitatem. </s> <s id="N14361">Rur&longs;us quæcumque &longs;it facilitas, qua rotis, vel <lb/>trochleis pondera leuantur, certum e&longs;t velocius ea leuari <lb/>maioribus, quàm minoribus rotis; &longs;ed hoc ip&longs;um e&longs;t faci­<lb/>lius mouere, quia licet non omnis facilitas includat veloci­<lb/>tatem, vt pater in pluribus machinis tractorijs, quæ facilius, <lb/>&longs;ed tardius mouent; nihilominus velocitas &longs;emper inuoluit <lb/>facilitatem; Ergo nihil contra experientiam a&longs;&longs;ump&longs;it Ari­<lb/>&longs;toteles, vt Blancanus contendit. </s> </p> <p id="N14372" type="main"> <s id="N14374">Baldus item ait non e&longs;&longs;e &longs;impliciter verum idip&longs;um, quod <lb/>Philo&longs;ophus a&longs;&longs;erit, vt &longs;cilicet quo maiores fuerint trochleæ, <lb/>eò facilius moueant. </s> <s id="N1437B">Quia tam maior, quàm minor trochlea <lb/>per eius centrum grauitatis diuiditur à perpendiculari ea-<pb pagenum="141" xlink:href="005/01/149.jpg"/>dente ad centrum mundi in duas partes æquales, & æquè <lb/>ponderantes, ac proinde &longs;emper e&longs;t eadem illarum pro­<lb/>portio inter &longs;e, & eadem ponderum ratio, ex qua prouenit <lb/>motus. </s> <s id="N1438B">Fatetur tamen hoc tantum procedere ab&longs;tractè lo­<lb/>quendo cum alioquin in trochleis, ac rotis materialibus ne­<lb/>gare non po&longs;&longs;it experientiam quam &longs;upponit Ari&longs;toteles. <lb/><!-- KEEP S--></s> <s id="N14394">Quare totam maiorem facilitatem, quam experimur in ip&longs;is <lb/>trochleis, ac rotis maioribus, ip&longs;e ad maiorem proportio­<lb/>nem, quam vt plurimum rota maior habet cum proprio axe <lb/>reducit. </s> </p> <p id="N1439D" type="main"> <s id="N1439F">Sed quidquid &longs;it de facilitate, aut difficultate &longs;imul <expan abbr="pro-ueni&etilde;te">pro­<lb/>ueniente</expan> ex hoc capite, quam certè admittimus, ac infra <expan abbr="etiã">etiam</expan> <lb/>explicabimus: &longs;i&longs;tendo in &longs;ola ratione maioris, aut minoris <lb/>ambitus rotæ prout hic &longs;upponit Ari&longs;toteles, cæteris &longs;cilicet <lb/>paribus; explorati&longs;&longs;imum e&longs;t, ac negari minimè pote&longs;t, quam <lb/>facilius adhuc &longs;eruata eadem proportione axis, &longs;eu cra&longs;&longs;itiei <lb/>illius ad ambitum rotæ, ferantur <expan abbr="põdera">pondera</expan>, &longs;i maioribus a&longs;por­<lb/>tentur, eleuentur; aut trahantur rotis; &longs;icut etiam &longs;cytalis, de <lb/>quibus hic eadem e&longs;t ratio. </s> <s id="N143BE">Loquitur autem Ari&longs;toteles <lb/>de illo genere <expan abbr="&longs;eytalarũ">&longs;cytalarum</expan>, quæ &longs;imiliter circa axim <expan abbr="coniunctũ">coniunctum</expan> <lb/>ad eleuanda pondera conuertuntur, appo&longs;ito in altera ex­<lb/>tremitate <expan abbr="illarũ">illarum</expan> ferreo quoddam manubrio, vt in &longs;pecie e&longs;t <lb/>in &longs;ubiecta figura. </s> <s id="N143D5">Scytala enim de &longs;e <expan abbr="tantũ">tantum</expan> &longs;ignificat lignum <lb/>quoddam <expan abbr="oblongũ">oblongum</expan>, ac teres <expan abbr="tanquã">tanquam</expan> <expan abbr="cylindrũ">cylindrum</expan>, cui <expan abbr="quandoq.">quandoque</expan> <lb/>alijs adiunctis diuer&longs;æ machinæ, ac in&longs;trumenta vectoria, &longs;i­<lb/>ue tractoria efficiuntur, quorum nonnulla adhuc &longs;cytalæ <lb/>vocantur, vt hæc de qua loquimur, & alia de qua infra quæ­<lb/>&longs;tione 11. </s> </p> <figure id="id.005.01.149.1.jpg" xlink:href="005/01/149/1.jpg"/> <p id="N143FB" type="main"> <s id="N143FD">His itaque &longs;ic &longs;e habentibus breuiter ac per&longs;picuè quæ­<lb/>&longs;tionem diluit Ari&longs;toteles, inquiens, maiorem hanc facilita­<lb/>tem, ac velocitatem motus procedere à maiori di&longs;tantia, <pb pagenum="142" xlink:href="005/01/150.jpg"/>quam à centro habet extremum diametri amplioris circu­<lb/>li, aut rotæ re&longs;pectu minoris, ob principium illud &longs;æpè re­<lb/>petitum, & à nobis pluries explicatum, quod iterum in libra <lb/>hic exemplificat. </s> <s id="N1440F">Quoniam (inquit) &longs;icut exactiores &longs;unt <lb/>maiores libræ, quam minores, <expan abbr="magisq.">magisque</expan> aut facilius mouen­<lb/>tur; ita maiores circuli, vel rotæ, æquali exi&longs;tente onere, <lb/><expan abbr="cæterisq.">cæterisque</expan> paribus, vt dictum e&longs;t: Cum rotæ ex totidem li­<lb/>bris, &longs;eu brachijs libræ videantur compactæ, quot &longs;unt dia­<lb/>metri ex quibus con&longs;tant. </s> </p> <p id="N14423" type="main"> <s id="N14425">Diximus autem cæteris paribus; nam vt rectè Baldus ad­<lb/>monuit, &longs;i rota maior corpulentiorem proportionaliter ha­<lb/>beat axem, quàm minor, non mouetur velocius. </s> <s id="N1442C">Siquidem <lb/>quo maior fuerit diameter rotæ re&longs;pectu diametri &longs;ui axis, <lb/>eò facilius mouebitur: quo verò minor, eò difficilius. </s> <s id="N14433">Magis <lb/>enim retardat, ac impedit axis cra&longs;&longs;ior, quam &longs;ubtilior. </s> <s id="N14438">Quod <lb/>adhuc (aliter tamen quàm ille) po&longs;&longs;umus probare; Nimirum <lb/>quia ambitus &longs;ubtilioris axis per minorem &longs;ui partem attin­<lb/>git rotam, quàm ambitus cra&longs;&longs;ioris: & &longs;ic minus impedit <lb/>circumuolutionem. </s> <s id="N14443">Itemque po&longs;t punctum, quod e&longs;t in <lb/>&longs;ummitate circumferentiæ, & cui poti&longs;&longs;imum onus rotæ in­<lb/>cumbit, partes vtrinque circulariter declinantes, decliuio­<lb/>res &longs;unt in axe &longs;ubtiliori; eo quod minor circumferentia <lb/>magis curuetur; &longs;icut è contra quæ amplior e&longs;t, rectius pro­<lb/>cedat, &longs;iue magis rectæ appropinquetur. </s> <s id="N14450">Cumque partes <lb/>decliuiores, minus valeant onus &longs;u&longs;tinere nè dilabatur, <lb/>quàm partes, quæ minus declinant; hinc fit, vt &longs;ubtilior <lb/>axis ex decliuioribus con&longs;titutus, minus retardet, aut impe­<lb/>diat rotæ circumuolutionem. </s> </p> <p id="N1445B" type="main"> <s id="N1445D">Cæterum data axium paritate, præter cau&longs;am ab Ari&longs;to­<lb/>tele a&longs;&longs;ignatam adhuc duplici ex capite reperiemus, maio­<lb/>res rotas citiùs, ac faciliùs quàm minores conuolui. </s> <s id="N14464">Primò <lb/>nimirum quia per maiores diametros tanquam per longio­<lb/>res vectes aptius &longs;uperatur impedimentum, quod experimur <lb/>tam ex parte axis, quàm ex parte foraminis rotæ vbi inditur <lb/>ip&longs;e axis, ad expeditum motum circumuolutionis illius, <lb/>dum propter vtriu&longs;que corporis a&longs;peritatem adinuicem co-<pb pagenum="143" xlink:href="005/01/151.jpg"/>guntur fricari, vnde non parum circumuolutio retardatur. <lb/></s> <s id="N14477">Secundo quia quæ minor e&longs;t rota, &longs;icut pluries, quàm ma­<lb/>ior debet conuolui ad eleuandum, vel trahendum aliquod <lb/>pondus, ita pluries e&longs;t illi &longs;uperanda huiu&longs;modi re&longs;i&longs;tentia, <lb/>&longs;eu impedimentum fricationis; <expan abbr="proindeq.">proindeque</expan> difficilius id præ­<lb/>&longs;tabit: &longs;icut è contra facilius, quæ maior e&longs;t, <expan abbr="paucioribusq.">paucioribusque</expan> <lb/>circumuolutionibus indiget. </s> <s id="N1448C">Quo fit, vt ex quatuor rotis <lb/>curruum, duæ anteriores, vt quæ minores &longs;int, ac &longs;æpius cir­<lb/>cumuoluantur, &longs;æpius etiam indigeant vnctione, ac facilius <lb/>conterantur; vt Aurigis &longs;atis e&longs;t notum. </s> <s id="N14495">Cum enim &longs;imul <lb/>eodem tempore æquale &longs;patium percurrere debeant, ac ro­<lb/>tæ maiores, quod ip&longs;is dee&longs;t extentionis ad <expan abbr="coadæquandũ">coadæquandum</expan> <lb/>&longs;e eidem &longs;patio, compen&longs;atur per multiplicationem, ac re­<lb/>petitionem circumuolutionis earum; non &longs;ecus ac qui bre­<lb/>uiori, &longs;ed frequentiori pa&longs;&longs;u &longs;imul gradiuntur cum ijs, qui <lb/>longiori, ac tardiori. </s> <s id="N144A8">Vt dicitur de Iulo cum Aenea patre <lb/>apud Maronem. </s> <s id="N144AD">Dextræ &longs;e paruus Iulus implicuit, <expan abbr="&longs;equi-turq.">&longs;equi­<lb/>turque</expan> patrem non p a&longs;&longs;ibus æquis. </s> </p> <p id="N144B6" type="head"> <s id="N144B8">Quæ&longs;tio Decima.</s> </p> <p id="N144BB" type="main"> <s id="N144BD">C<emph type="italics"/>vr facilius quando &longs;ine pondere e&longs;t, moue­<lb/>tur libra, quàm cùm pondus habet? </s> <s id="N144C5"><expan abbr="&longs;imiliq.">&longs;imilique</expan> <lb/>modo rota, & huiu&longs;modi quippiam, quod gra­<lb/>uius quidem e&longs;t, maius autem minore, & le­<lb/>uiore? </s> <s id="N144D1">An quia non &longs;olum in contrarium, <lb/>quod graue e&longs;t, &longs;ed in obliquum etiam diffi­<lb/>culter mouetur? </s> <s id="N144D8">In contrarium enim ei, ad quod vergit onus, <lb/>mouere difficile e&longs;t: quo autem vergit, e&longs;t facilè: in obliquum <lb/>autem haud quaquam vergit.<emph.end type="italics"/></s> </p> <p id="N144E1" type="head"> <s id="N144E3">COMMENTARIVS.<!-- KEEP S--></s> </p> <p id="N144E7" type="main"> <s id="N144E9">Dvo in vnum collecta quærit hic Ari&longs;toteles, nempe <lb/>cur facilius moueatur tàm libra ponderibus vacua <lb/>re&longs;pectu &longs;ui ip&longs;ius cum pondera &longs;u&longs;tinet; quàm ro-<pb pagenum="144" xlink:href="005/01/152.jpg"/>ta leuior re&longs;pectu grauioris, non &longs;olum æqualis magnitudi­<lb/>nis, &longs;ed etiam maioris, quam aliàs quæ&longs;tione præcedenti di­<lb/>xerat moueri facilius, ac velocius minore cæteris paribus. <lb/></s> <s id="N144FA"><expan abbr="Cau&longs;amq.">Cau&longs;amque</expan> &longs;ci&longs;citandi eam e&longs;&longs;e videtur, quoniam libra in <lb/>æquilibrio con&longs;tituta, &longs;icut etiam rota &longs;tans perpendicula­<lb/>riter &longs;uper planum, aut in axe &longs;uffulta, quæ &longs;imilem habet <lb/>rationem, cuiu&longs;cunque grauitatis fuerit, &longs;tatim atque ex ali­<lb/>qua parte impingatur, vel onus aliquod alteri eius extremo <lb/>&longs;uperaddatur; amplius manere non pote&longs;t in illo &longs;itu, aut <lb/>po&longs;itione, eo quod nece&longs;&longs;ariò æquilibrium auferatur per <lb/>additionem ponderis, vel impetum incu&longs;&longs;um in alteram eius <lb/>extremitatem; <expan abbr="proindeq.">proindeque</expan> &longs;iue ip&longs;a libra &longs;it ferrea, &longs;iue li­<lb/>gnea grauior, aut leuior, æquè facilè deberet moueri: idem­<lb/>que verificari de rota. </s> </p> <p id="N14518" type="main"> <s id="N1451A">Quæ&longs;tioni tamen re&longs;pondet Ari&longs;toteles, grauiora corpo­<lb/>ra difficilius moueri non modo directè contra proprium <lb/>nutum, quo tendunt deor&longs;um, vt cum rur&longs;um eleuantur; &longs;ed <lb/>etiam obliquè cum feruntur ad latera in tran&longs;uer&longs;um, quo <lb/>certè natura &longs;ua pondus non vergit. </s> <s id="N14525">Quamobrem hoc ip­<lb/>&longs;o, quod libra, vel rota dimoueri non po&longs;&longs;it ab æqui­<lb/>librio, quin obliquè circumferatur per motum mi&longs;tum, ac <lb/>præter naturalem circa proprium fulcimentum, vel axim; <lb/>quo grauior fuerit, eo difficilius mouebitur, <expan abbr="magisq.">magisque</expan> huic <lb/>motui repugnabit, grauior autem e&longs;t libra ponderibus onu­<lb/>&longs;ta, quàm vacua. </s> <s id="N14538"><expan abbr="Similiterq.">Similiterque</expan> rota ferrea, quàm lignea, vel <lb/>ferrea, aut lignea quadripalmaris diametri, quàm alia eiu&longs;­<lb/>dem materiæ, &longs;ed bipalmaris. </s> </p> <p id="N14542" type="main"> <s id="N14544">Nec retorqueri pote&longs;t hoc argumentum contra Ari&longs;tote­<lb/>lem, vt Baldus contendit ex eo, quod cum grauius pondus <lb/>violentius de&longs;cendat, maiori ni&longs;u deor&longs;um ferri deberet <lb/>pars illa rotæ, vel libræ per additionem ponderis, vel impul­<lb/>&longs;u aliquo mota. </s> <s id="N1454F">Nam licet grauius pondus &longs;i deor&longs;um fe­<lb/>ratur, violentius quidem de&longs;cendet, non tamen per hoc fa­<lb/>cilius à loco &longs;uo, vel quiete dimouetur. </s> <s id="N14556">Deinde quia &longs;icut <lb/>maius pondus auget procliuitatem ad motum perpendicu­<lb/>larem ver&longs;us mundi centrum; ita difficultatem auget re-<pb pagenum="145" xlink:href="005/01/153.jpg"/>&longs;pectu motus contrarij, vel obliqui, vt e&longs;t motus circularis <lb/>libræ, vel rotæ. </s> </p> <p id="N14564" type="main"> <s id="N14566">Rur&longs;umque nec &longs;ub&longs;i&longs;tit contradictio, quam Blancanus <lb/>Philo&longs;opho attribuit, qua&longs;i in præcedenti quæ&longs;tione di­<lb/>xerit, maiores trochleas, ac &longs;cytalas, minoribus facilius <lb/>moueri; hic autem a&longs;&longs;erat, maiorem rotam difficilius mo­<lb/>ueri, quam minorem. </s> <s id="N14571">Quandoquidem Ari&longs;toteles apertè <lb/>per minorem intelligit etiam leuiorem. </s> <s id="N14576">Ait enim, maius <lb/>autem minore, & leuiore. </s> <s id="N1457B">Quare &longs;en&longs;us e&longs;t, quod licet <lb/>rotæ maiores ratione magnitudinis, &longs;int mobiliores; ni­<lb/>hilominus quando grauiores &longs;unt minoribus, difficilius <lb/>commouentur. </s> </p> <p id="N14584" type="main"> <s id="N14586">Ex quibus patere etiam pote&longs;t &longs;olutio ad rationem <expan abbr="dubi-tãdi">dubi­<lb/>tandi</expan> in principio <expan abbr="po&longs;itã">po&longs;itam</expan>. </s> <s id="N14593">Nam e&longs;tò quolibet perexiguo pon­<lb/>dera in <expan abbr="alterã">alteram</expan> <expan abbr="part&etilde;">partem</expan> adiuncto, vel modico impetu in <expan abbr="illã">illam</expan> in­<lb/>cu&longs;&longs;o, re vera tollatur <expan abbr="æquilibriũ">æquilibrium</expan> tam leuioris, quàm grauio­<lb/>ris libra, aut rotæ con&longs;ideratæ in ab&longs;tracto, vt Guidus Vbal­<lb/>dus demon&longs;trat ex principijs Archimedis: id tamen &longs;en&longs;ibi­<lb/>liter non apparet in facto, nec propterea libra ip&longs;a, vel rota <lb/>mouetur, ni&longs;i exce&longs;&longs;us ponderis, vel impul&longs;us proportionem <lb/>quandam habeat cum grauitate partis oppo&longs;itæ, quam ex­<lb/>cedit; ita ut, quo grauior e&longs;t libra, vel rota &longs;ecundum vtran­<lb/>que partem in æquilibrio con&longs;titutam, eo maior &longs;it ip&longs;e ex­<lb/>ce&longs;&longs;us &longs;uperadditus in altera parte ad alteram &longs;uperandam. <lb/></s> <s id="N145BB">Quod totum procedit ex eo; nam hoc ip&longs;o, quod grauiora <lb/>corpora ægrius præter, vel contra proprium nutum feran­<lb/>tur, maior pariter virtus requiritur ad ea circumferenda <lb/>motu præternaturali, ac mi&longs;to, prout e&longs;t motus circularis. <lb/></s> <s id="N145C5">Sed ad concilianda principia Archimedis cum principijs <lb/>Ari&longs;totelis in propo&longs;ito di&longs;cur&longs;u explicandum &longs;uper e&longs;t, cur <lb/>quando libra, vel rota con&longs;ideratur &longs;u&longs;pen&longs;a per centrum <lb/>&longs;uæ grauitatis indiui&longs;ibiliter, non requiratur eadem propor­<lb/>tio inter exce&longs;&longs;um partis præponderantis, & grauitatem ma­<lb/>iorem, aut minorem alterius, &longs;ed &longs;ufficiat quilibet exce&longs;&longs;us. <lb/></s> <s id="N145D3">Siquidem etiam in i&longs;to ca&longs;u ab&longs;tracto maior grauitas partis <pb pagenum="146" xlink:href="005/01/154.jpg"/>eleuandæ, maiorem exce&longs;&longs;um ponderis, aut virtutis videre­<lb/>tur requirere in parte eleuante. </s> </p> <p id="N145DD" type="main"> <s id="N145DF">Dicimus ergo huiu&longs;modi di&longs;paritatem de&longs;umendam e&longs;&longs;e <lb/>ex propria conditione materiæ. </s> <s id="N145E4">Nam axis materialis circa <lb/>quem vertitur, cum non &longs;it indiui&longs;ibilis; nece&longs;&longs;ariò &longs;ecundum <lb/>plures &longs;ui partes, ac puncta corre&longs;pondet partibus, ac pun­<lb/>ctis incumbentibus ip&longs;ius rotæ, vel libræ, quam &longs;u&longs;tinet. <lb/></s> <s id="N145EE">Quare ad eleuandam verbi gratia partem &longs;ini&longs;tram libræ, <lb/>vel rotæ per depre&longs;&longs;ionem dexteræ inter quas mediat cen­<lb/>trum grauitatis, con&longs;equenter ob&longs;tabit pars illa axis corre­<lb/>&longs;pondens ip&longs;i dexteræ incumbenti, ac deprimendæ, eritque <lb/>veluti fulcimentum vectis ad eleuandam non modo partem <lb/>&longs;ini&longs;tram, &longs;ed etiam punctum medium, quod e&longs;t centrum <lb/>grauitatis tanquam præcipuum onus. </s> <s id="N145FD">Vnde licet propter <lb/>maximam approximationem <expan abbr="fulcim&etilde;ti">fulcimenti</expan> ad huiu&longs;modi onus, <lb/>facilè onus ip&longs;um, &longs;eu centrum grauitatis aliquantulum ele­<lb/>uetur; non per hoc tollitur, quin eo difficilius i&longs;te motus <lb/>exerceatur, quo maius fuerit pondus incumbens per ip&longs;um <lb/>centrum grauitatis; ac proinde maior virtus requiratur ad <lb/>&longs;uperandam ip&longs;am re&longs;i&longs;tentiam, ac maiorem difficultatem <lb/>Quod non ita contingeret &longs;i libra, vel rota &longs;u&longs;penderetur per <lb/>x<gap/>m indiui&longs;ibilem, ac centrum ip&longs;um grauitatis. </s> <s id="N14616">Nam hoc <lb/>æquè &longs;emper &longs;u&longs;tineretur, &longs;iue in motu, &longs;iue inquietè ip&longs;ius <lb/>libræ, vel rotæ. </s> <s id="N1461D">Imo &longs;emper quie&longs;ceret, nec vlla e&longs;&longs;et re&longs;i­<lb/>&longs;tentia partium axis explicata, &longs;iue pondus incumbens e&longs;&longs;et <lb/>grauius, &longs;iue leuius. </s> <s id="N14624">Ideoque nullo negotio ad quem­<lb/>libet exiguum impul&longs;um, vel modicam additio­<lb/>nem ponderis &longs;tatim ab æquilibrio, & à <lb/>quiete dimoueretur omnis quan­<lb/>tumuis ingens, & graui&longs;&longs;i­<lb/>ma libra, vel <lb/>rota. </s> </p> <pb pagenum="147" xlink:href="005/01/155.jpg"/> <p id="N14637" type="head"> <s id="N14639">Quæ&longs;tio Vndecima.<!-- KEEP S--></s> </p> <p id="N1463D" type="main"> <s id="N1463F">C<emph type="italics"/>vr &longs;uper &longs;cytalas facilius portantur one­<lb/>ra, quàm &longs;uper currus, cùm tamen ÿ ma­<lb/>gnas habeant rotas, illæ verò pu&longs;illas? </s> <s id="N14649">An <lb/>quoniam in &longs;cytalis nulla e&longs;t offen&longs;atio, in <lb/>curribus autem axis est, ad quem offen&longs;ant. <lb/></s> <s id="N14651">De&longs;uper enim illum premunt, & à lateri­<lb/>bus. </s> <s id="N14656">Quod autem e&longs;t in &longs;cytalis, ad i&longs;thæc duo mouetur, & <lb/>infernè &longs;ub&longs;trato &longs;patio, & onere &longs;uperimpo&longs;ito. </s> <s id="N1465B">In viri&longs;­<lb/>que enim ijs reuoluitur locis circulus, & motus impellitur.<emph.end type="italics"/></s> </p> <p id="N14662" type="head"> <s id="N14664">COMMENTARIVS.<!-- KEEP S--></s> </p> <p id="N14668" type="main"> <s id="N1466A">Scytalæ, de quibus hic loquitur Ari&longs;toteles non &longs;unt <lb/>eiu&longs;dem generis cum illis, quæ &longs;upra quæ&longs;tione no­<lb/>na commemorauerat. </s> <s id="N14671">Nam vltra communem for­<lb/>mam cylindricam, &longs;icut illæ axim, ac manubrium, &longs;ic <lb/>i&longs;tæ rotulas qua&longs;dam habent &longs;ingulas in ambis extremitati­<lb/>bus ex eodem ligno compactas; prominentiores quidem, <lb/>&longs;eu maioris ambitus, quàm &longs;it reliquum corpus teres, <lb/>quod intermediat, quodque axis vicem gerere videtur, <lb/>&longs;ed non ab eo &longs;eiunctas, quippe cum ad vnum, & idem <lb/>corpus continuatum pertineant, ac &longs;imul cum eo in latio­<lb/>ne &longs;uper planum circumuoluantur &longs;ecus ac illæ, quæ à <lb/>proprio axe &longs;unt &longs;eiunctæ. </s> <s id="N14686">Maximo autem adiumento hu­<lb/>iu&longs;modi &longs;cytalæ e&longs;&longs;e &longs;olent cum binæ, vel ternæ æquidi­<lb/>&longs;tantes oneribus &longs;upponuntur, vt ea facilius moueantur, <lb/>præ&longs;ertim &longs;uper &longs;olum &longs;atis con&longs;i&longs;tens, & æquatum, à <lb/>quo nulla vnquam &longs;upereminentia, aut cauitate rotarum <lb/>paruitas ab&longs;orbeatur. </s> <s id="N14693">Licet non minus imò frequentius <lb/>vtamur &longs;cytalis &longs;implicibus, ac non rotatis, quarum memi­<pb pagenum="148" xlink:href="005/01/156.jpg"/>nit Pappus lib. 8. Vtrarumque autem figuram hic erit in­<lb/>&longs;picere delineatam. </s> </p> <figure id="id.005.01.156.1.jpg" xlink:href="005/01/156/1.jpg"/> <p id="N146A4" type="main"> <s id="N146A6">Quærit igitur Ari&longs;toteles quid &longs;it in cau&longs;a, vt huiu&longs;modi <lb/>&longs;cytalis, quæ minores valde rotas obtinent, quàm currus, <lb/>facilius quàm ip&longs;is curribus onera a&longs;portentur cum quæ­<lb/>&longs;tione nona con&longs;titerit, maiores rotas facilius, ac celerius <lb/>onera mouere. </s> <s id="N146B1">Optimèque &longs;tatim re&longs;pondet, id ex eo con­<lb/>tingere, quòd cum &longs;cytalarum rotæ vnitum &longs;ibi axem, non <lb/>autem &longs;eiunctum, vt plau&longs;trorum rotæ &longs;ortiantur, nulla inter <lb/>ip&longs;as, & axem offen&longs;atio intercedit, &longs;icut in curribus, aut <lb/>plau&longs;tris. </s> <s id="N146BC">Axis enim currus duplici ex parte præmitur, <lb/>nempe de&longs;uper ab oneribus incumbentibus, & ex latere <lb/>dum ante, vel retro trahitur à mouentibus. </s> <s id="N146C3">Quare in dupli­<lb/>ci etiam & corre&longs;pondenti parte præmit rotas intra ip&longs;arum <lb/>modiolum, vbi cum rotæ &longs;eiunctæ ab eo &longs;int, ac di&longs;&longs;imili mo­<lb/>do moueantur, nece&longs;&longs;ario &longs;e&longs;e ad inuicem &longs;ecundum vtram­<lb/>que partem offen&longs;ant atque collidunt, eo quod diuer&longs;o &longs;ibi <pb pagenum="149" xlink:href="005/01/157.jpg"/>motu atque impul&longs;u occurrant. </s> <s id="N146D3">Quod non ita &longs;e habet in <lb/>&longs;cytalis, in quibus cum non &longs;it axis di&longs;tinctus, nec motus di­<lb/>uer&longs;us, & ab eodem pondere, quod &longs;u&longs;tinent ip&longs;æ anterius <lb/>&longs;uper planum impellantur, nullus fit in rotatione occur&longs;us <lb/>nullaque offen&longs;atio, &longs;eclu&longs;o omni offendiculo extrin&longs;eco, de <lb/>quo non loquimur. </s> <s id="N146E0">Pondus enim licet de &longs;e &longs;emper graui­<lb/>tet, ac præmat per lineam perpendicularem cadentem ad <lb/>mundi centrum; nihilominus po&longs;itum &longs;uper &longs;cytalas, tan­<lb/>quam &longs;uper &longs;tantes circulos; dum antror&longs;um impingitur, <lb/>totam præ&longs;sionem, ac impul&longs;um refundit in nutum, quem <lb/>auget in circulis &longs;ubiectis, & concitat, vt facilius mouean­<lb/>tur. </s> <s id="N146EF">Tollit namque explicatum æquilibrium illorum per <lb/>magnam additionem ponderis, aut virtutis in eam partem, <lb/>quam &longs;ucce&longs;siuè in illis deprimit, & ad rotandum impellit. <lb/></s> <s id="N146F7">Et &longs;ic corpus ip&longs;um cylindricum, quod in &longs;cytalis axis vi­<lb/>cem gerit, ac mediat inter duas vnitas &longs;ibi rotulas inter <lb/>pondus, & planum &longs;ub&longs;tratum reuoluitur tanquam circu­<lb/>lus inter duas &longs;uperficies, mutando &longs;emper locum ex par­<lb/>te vtriu&longs;que. </s> <s id="N14702">Nam & onus à motore impul&longs;um per &longs;ucce­<lb/>dentes iugiter &longs;ui partes impingit, & &longs;ub&longs;tratum planum <lb/>per nouas etiam partes corre&longs;pondentes &longs;cytalas ip&longs;as cum <lb/>onere &longs;u&longs;tinet. </s> </p> <p id="N1470B" type="head"> <s id="N1470D">Quæ&longs;tio Duodecima.</s> </p> <p id="N14710" type="main"> <s id="N14712">C<emph type="italics"/>vr longiùs feruntur mi&longs;&longs;ilia funda, quàm <lb/>manu mi&longs;&longs;a, cùm alioqui proiector manu <lb/>magis pondus comprehendat, quàm cùm il­<lb/>lud &longs;u&longs;pendit? </s> <s id="N1471E">Præterea &longs;ic quidem duo mo­<lb/>uet pondera, fundæ videlicet, & mi&longs;silis: illo <lb/>autem modo &longs;olum mi&longs;sile. </s> <s id="N14725">An quia in funda <lb/>quidem commotum mi&longs;sile funditor proijcit? </s> <s id="N1472A">Fundam enim <lb/>circulo, &longs;ubinde rotans, id iaculatur: ex manu autem, à quie­<lb/>te e&longs;t initium: omnia autem cùm in motu &longs;unt, quàm cùm <lb/>quie&longs;cunt, faciliùs mouentur. </s> <s id="N14733">An & eam ob cau&longs;am est, &longs;ed <emph.end type="italics"/><pb pagenum="150" xlink:href="005/01/158.jpg"/><emph type="italics"/>nec minus etiam, quia in fundæ v&longs;u manus quidem fit cen­<lb/>trum: funda verò, quod à centro exit? </s> <s id="N14741">Quanto autem pro­<lb/>ductius fuerit id, quod à centro e&longs;t, tantò citiùs mouetur. <lb/></s> <s id="N14747">Tactus autem, qui manu fit, fundæ re&longs;pectu breuis e&longs;t.<emph.end type="italics"/></s> </p> <p id="N1474C" type="head"> <s id="N1474E">COMMENTARIVS.<!-- KEEP S--></s> </p> <p id="N14752" type="main"> <s id="N14754">Dvas hic Aristoreles rationes dubitandi proponit, <lb/>vt explicet cau&longs;am cur longius ferantur mi&longs;silia <lb/>funda, quàm manu mi&longs;&longs;a. </s> <s id="N1475B">Prima e&longs;t, quia proie­<lb/>ctor melius mi&longs;&longs;ilia ip&longs;a manu comprehendit, quàm cum <lb/>funda &longs;u&longs;pendit: Quod autem melius comprehenditur, va­<lb/>lidius iacitur ac propterea longius mittitur: Potius itaque <lb/>manu mi&longs;&longs;a, quàm funda proiecta mi&longs;silia longius ferri de­<lb/>berent. </s> <s id="N14768">Secunda verò ratio e&longs;t, nam <expan abbr="cũ">cum</expan> funda quis proijcit; <lb/>duo &longs;imul mouet <expan abbr="põdera">pondera</expan>; fundá nempe <expan abbr="ipsã">ipsam</expan>, & mi&longs;sile, quod <lb/>proijcit; <expan abbr="ab&longs;q;">ab&longs;que</expan> autem funda <expan abbr="nõ">non</expan> mouet ni&longs;i proiectum: At am­<lb/>plius quilibet mouere valet quando <expan abbr="totã">totam</expan> eius vim applicat <lb/>in vnum, quàm cum di&longs;tribuit in plura: Ergo magis ac remo­<lb/>tius proiector manu mittet, ac proijciet, quàm funda. </s> </p> <p id="N1478D" type="main"> <s id="N1478F">Duplicem deinde cau&longs;am propo&longs;iti <expan abbr="experim&etilde;ti">experimenti</expan> a&longs;signat, <lb/>vna e&longs;t, quia per fundam agitatum atque commotum mi&longs;­<lb/>&longs;ile mittitur. </s> <s id="N1479A">Siquidem priu&longs;quam emittatur, ac è funda <lb/>elabatur, eadem funda circumagitur, ac rotatur; manu au­<lb/>tem non ni&longs;i quie&longs;cens proijcitur: ita vt &longs;tatim proiectio <lb/>po&longs;t quietem &longs;equatur, <expan abbr="&longs;umatq.">&longs;umatque</expan> initium à loco vbi mane­<lb/>bat, nempe ab ip&longs;a manu. </s> <s id="N147A9">Omnia autem cum in motu &longs;unt, <lb/>facilius vlterius per nouum impul&longs;um feruntur, quàm cum <lb/>quie&longs;cunt, ac tunc primò moueri coguntur. </s> </p> <p id="N147B0" type="main"> <s id="N147B2">Quocirca vt hæc doctrina iuxta rei veritatem clarius elu­<lb/>ce&longs;cat, ob&longs;eruandum e&longs;t, proiecta in rigore loquendo non <lb/>&longs;tatim po&longs;t quietem è manu iaculantis elabi; &longs;ed aliquan­<lb/>tulum &longs;altem prius manu ip&longs;a comitante moueri antequam <lb/>emittantur. </s> <s id="N147BD">Motus enim brachij iaculantis arcum quen­<lb/>dam &longs;emper de&longs;cribit, in cuius fine, non autem in principio <lb/>mi&longs;silia proijciuntur; & quò longius proijcienda &longs;unt eò <pb pagenum="151" xlink:href="005/01/159.jpg"/>maiorem arcum brachium ip&longs;um efficit; magis nimirum <lb/>prius retrocedendo, magi&longs;que po&longs;tea antror&longs;um &longs;e exten­<lb/>dendo, atque in fine exten&longs;ionis è manu mi&longs;silia dimitten­<lb/>do. </s> <s id="N147CF">Alioqui ni&longs;i manus imò etiam brachium &longs;imul cum il­<lb/>lis antea moueretur, nec impetum inferre, nec proijcere <lb/>ip&longs;a valeret. </s> <s id="N147D6">Quare cum ait Ari&longs;toteles, nullam antecede­<lb/>re commotionem in proiectione, quæ fit &longs;ola manu, intelli­<lb/>gendus non e&longs;t de commotione immediata coniuncta, & <lb/>qua&longs;i e&longs;&longs;entialiter pertinente ad eundem actum proiectio­<lb/>nis: &longs;ed de commotione di&longs;po&longs;itiua accidentali, & qua&longs;i re­<lb/>mota ad ip&longs;um actum iaculandi, vt e&longs;t præcedens illa irro­<lb/>tatio, & agitatio fundæ. </s> <s id="N147E5"><expan abbr="Congruuntq.">Congruuntque</expan> verba ip&longs;ius, nam <lb/>ad probandum, commotum mi&longs;sile proijci à funditore, ait: <lb/>funda enim circulo &longs;ubinde rotans id iaculatur. </s> </p> <p id="N147EF" type="main"> <s id="N147F1">Quod certè vim argumenti ip&longs;ius Ari&longs;totelis non labe­<lb/>factat, tum quia et&longs;i nunquam ab&longs;que comitante aliquo <lb/>motu proximo ip&longs;ius manus iaciantur proiecta, &longs;æpè tamen <lb/>iaciuntur ab&longs;que præuio motu remoto, quo nunquam ca­<lb/>rent mi&longs;silia, quæ funda mittuntur: tum etiam, quia eadem <lb/>&longs;altem procedit ratio à minori ad maius, nimirum vt quo <lb/>magis in motu e&longs;t aliquid, eò facilius adhuc vlterius alio &longs;u­<lb/>peraddito impul&longs;u procurrat. </s> <s id="N14802">Quare cum magis in motu <lb/>&longs;it mi&longs;sile, quod funda rotatur, quàm quod manu vnico, ac <lb/>breuiori arcu cietur, rectè concluditur longè facilius funda, <lb/>quàm manu vlterius mitti. </s> <s id="N1480B">Nec ob&longs;tat, funditores tardè po­<lb/>tius quàm citò fundam irrotare, ac brachio circumferre; <lb/>Nam id faciunt, vt aptius erga de&longs;tinatum &longs;itum ip&longs;a irrota­<lb/>tio dirigatur, aptiu&longs;que brachium paulatim procedendo di­<lb/>&longs;ponatur, antequam mi&longs;sile ab eo totis viribus proijciatur. </s> </p> <p id="N14816" type="main"> <s id="N14818">Altera verò cau&longs;a propo&longs;iti experimenti, quam Ari&longs;tote­<lb/>les a&longs;signat, eaque potior e&longs;t, quia in fundæ v&longs;u manus (&longs;eu <lb/>potius pars vbi brachium humero iungitur, vt optimè Bal­<lb/>dus adnotauit) con&longs;tituitur qua&longs;i centrum circuli de&longs;cripti <lb/>per eius motum, funda verò (&longs;cilicet &longs;imul cum brachio) <lb/>&longs;e habet tanquam linea, quæ à centro ad peripheriam ex­<lb/>tenditur. </s> <s id="N14827">Quanto autem productior, ac longior e&longs;t linea, <pb pagenum="152" xlink:href="005/01/160.jpg"/>quæ à centro ad periferiam tendit, vt illa, quæ ex brachio, & <lb/>funda con&longs;tituitur in rotatione; tanto velocius mouetur. <lb/></s> <s id="N14832">Cumque ex maiori velocitate i&longs;tius motus, maior impetus <lb/>producatur; hinc fit, vt quod funda iacitur, tanquam per <lb/>velociorem iaculationem, maiorem impetum à funditore <lb/>recipiat, quàm &longs;i manu mittatur, longiu&longs;que valde proinde <lb/>feratur. </s> <s id="N1483D">Iactus enim qui manu fit, inquit Ari&longs;toteles, breuis <lb/>e&longs;t re&longs;pectu &longs;cilicet eius, qui funda efficitur. </s> </p> <p id="N14842" type="main"> <s id="N14844">Ad primam igitur rationem dubitandi re&longs;ponderi pote&longs;t, <lb/>maiorem, aut minorem comprehen&longs;ionem proiecti, parum <lb/>aut nihil conferre ad vlteriorem eius emi&longs;sionem, &longs;ed po­<lb/>tius modum comprehendendi diuer&longs;um proportionatum, <lb/>in quantum &longs;cilicet ip&longs;a comprehen&longs;io ad commoditatem <lb/>pertinet iaculandi qua&longs;i artificiosè. </s> <s id="N14851">Vt &longs;i quis te&longs;tam, vel <lb/>complanatum lapillum eminus proijcere velit, inter pol­<lb/>licem, & indicem &longs;upra medium digitum collocat, vt ip­<lb/>&longs;o indice incu&longs;&longs;o impetu in latus po&longs;terius, ille per aera, ean­<lb/>dem po&longs;itionem &longs;eruando, feratur, qua cum facilius præeun­<lb/>te acie aerem &longs;cindat, vlterius quoque pergere valeat. </s> <s id="N1485E">Alio­<lb/>quin ad ab&longs;olutam proiecti emi&longs;sionem, &longs;atis illud com­<lb/>prehenditur funda, <expan abbr="ideoq.">ideoque</expan> nihil minor comprehen&longs;io ob­<lb/>&longs;tat, quominus funditor longius iaciat, cum hoc &longs;ibi vendi­<lb/>cet aliunde. </s> </p> <p id="N1486D" type="main"> <s id="N1486F">Ad &longs;ecundam re&longs;pondetur, grauitatem in&longs;trumenti nul­<lb/>lam, vt plurimum augere difficultatem in latione, aut <lb/>proiectione ponderis dummodo proportionem quandam <lb/>habeat cum potentia motrice, vt patere pote&longs;t inductio­<lb/>ne, tam in vectibus plurimis, ac rotis curruum, quàm in <lb/>in machinis bellicis, aut venatorijs, quibus mi&longs;silia iaciuntur. <lb/></s> <s id="N1487D">Quare cum grauitas fundæ, vel nullius momenti in &longs;e &longs;it, <lb/>vel ad &longs;ummum &longs;it grauitas in&longs;trumenti, nullam pariter &longs;u­<lb/>pra pondus proiecti augere pote&longs;t difficultatem, ad quam <lb/>&longs;uperandam maior conatus potentiæ requiratur, minu&longs;que <lb/>propterea funda, quàm &longs;ola manu, proiectum mittatur. </s> </p> <p id="N14888" type="main"> <s id="N1488A">Vna tamen adhuc &longs;upere&longs;t difficultas, quæ non mediocris <lb/>e&longs;t momenti; nimirum quo pacto motus circularis, quo <pb pagenum="153" xlink:href="005/01/161.jpg"/>funda circumducitur mi&longs;sile, antequam proijciatur, ad mo­<lb/>tum rectum proiectionis vim ac robur adijcere po&longs;sit; ita vt <lb/>impetus in circumlatione acqui&longs;itus, in impetum proie­<lb/>ctionis refundatur. </s> <s id="N1489A">Siquidem quilibet ex ijs duobus im­<lb/>pul&longs;ibus, natura &longs;ua ad <expan abbr="motũ">motum</expan> valde <expan abbr="diuersũ">diuersum</expan> videtur ordinari. </s> </p> <p id="N148A7" type="main"> <s id="N148A9">Sed pro &longs;olutione &longs;tabiliendum prius e&longs;t, qualitatem im­<lb/>petus corporibus impre&longs;&longs;am, varios quidem motus per ac­<lb/>cidens in illis po&longs;&longs;e cau&longs;are; per &longs;e tamen ac natura &longs;ua non <lb/>ni&longs;i ad motum rectum ordinari. </s> <s id="N148B2">Id quod ob&longs;eruatione faci­<lb/>lè comprobatur; Nam &longs;i attentè animaduertere quis velit, <lb/>nullum inueniet impetum per quem proiectum aliter quàm <lb/>recta tendat in terminum &longs;ui motus: ni&longs;i forta&longs;&longs;e aliqua ex <lb/>parte repercutiatur, aut impediatur. </s> <s id="N148BD">Vt cum proiecta pila <lb/>repercutiatur à loco in quem impulerit, ac reddere cogitur, <lb/>vel declinando à rectitudine propter impedimentum, obli­<lb/>què vlterius pergit. </s> <s id="N148C6">Aut certè cum corpori fune &longs;u&longs;pen&longs;o, <lb/>& alicubi alligato incutitur impul&longs;us, <expan abbr="illudq.">illudque</expan> non rectà quò <lb/>mittitur, &longs;ed in orbem mouetur, eo quod detineatur in cen­<lb/>tro ex quo per funem propendet. </s> <s id="N148D3">Nam &longs;i in eadem circum­<lb/>latione rumpatur funis, aut &longs;oluatur, videmus idem corpus <lb/>recta tendere, quò ver&longs;us per vltimum arcum &longs;uæ circum­<lb/>uolutionis re&longs;piciebat. </s> <s id="N148DC">Quod &longs;anè apertum indicium e&longs;t, <lb/>ab&longs;que impedimento per impul&longs;um impre&longs;&longs;um corpora <lb/>nonni&longs;i rectà moueri. </s> </p> <p id="N148E3" type="main"> <s id="N148E5">Quod &longs;i ignes mi&longs;siles &longs;ulphureo puluere artificio&longs;i&longs;simè <lb/>compactos videamus huc illuc variis <expan abbr="tortuo&longs;isq.">tortuo&longs;isque</expan> itineribus <lb/>di&longs;currere; id ex eo fit, quia &longs;ulphureus puluis, ita e&longs;t intra <lb/>cartaceos eorum anfractus artificiosè di&longs;po&longs;itus, vt accen­<lb/>&longs;us, diuer&longs;is ex lateribus vim inferat, ex quibus illi in oppo­<lb/>&longs;ita loca ferantur, ac veluti per obliquos calles &longs;erpendo <lb/>di&longs;currere videantur. </s> <s id="N148F8">Quod quippe tantum arguit mixtio­<lb/>nem ip&longs;ius motus procedentem à varia &longs;ituatione pulueris, <lb/>&longs;eu cau&longs;æ impellentis; cum alias etiam quilibet impetus ab <lb/>accen&longs;o puluere productus directè tendat, ac moueat ver&longs;us <lb/>eam partem in quam &longs;e&longs;e dilatando confert, & qua e&longs;t illi <lb/>additus, vt ex angu&longs;tia elabatur, ac foris erumpat. </s> </p> <pb pagenum="154" xlink:href="005/01/162.jpg"/> <p id="N14909" type="main"> <s id="N1490B">His ergo &longs;ic &longs;tabilitis, facilè &longs;oluetur difficultas propo&longs;i­<lb/>ta, nam impetus mi&longs;&longs;ili incu&longs;&longs;us dum funda circumageretur <lb/>non corrumpitur, nec de&longs;init e&longs;&longs;e per aduentum noui impe­<lb/>tus, quo recta illud proijcitur, cum neque natura &longs;ua, neque <lb/>po&longs;itione ei opponatur. </s> <s id="N14916">Siquidem in fine cuiu&longs;dam rotatio­<lb/>nis iacitur proiectum ver&longs;us eam partem in quam vltimò <lb/>vergebat, &longs;eu re&longs;piciebat vltimus arcus de&longs;criptus per cir­<lb/>cumductionem illius; ita vt motus obliquus circuitionis &longs;en­<lb/>&longs;im rectus euadat. </s> <s id="N14921">Quamobrem ip&longs;e impetus quo circum­<lb/>ducebatur facilè tran&longs;it in impetum, quo rectà illud rapitur, <lb/>vel addit &longs;e ei, qui de nouo illi per actum proiectionis incu­<lb/>titur. </s> </p> <p id="N1492A" type="head"> <s id="N1492C">Quæ&longs;tio Decimatertia.</s> </p> <p id="N1492F" type="main"> <s id="N14931">C<emph type="italics"/>vr circa idem iugum maiores collopes faci­<lb/>liùs, quàm minores mouentur: & item &longs;ucu­<lb/>læ, quæ graciliores &longs;unt, ab eadem vi, quàm <lb/>cra&longs;siores? </s> <s id="N1493D">An quia &longs;ucula quidem & iu­<lb/>gum, centrum est: prominentes autem longi­<lb/>tudines, eæ quæ &longs;unt à centro? </s> <s id="N14944">Celerius au­<lb/>tem & plus mouentur, quæ maiorum &longs;unt circulorum, ab ea­<lb/>dem vi, quàm quæ minorum. </s> <s id="N1494B">Ab eadem enim vi plus tran&longs;­<lb/>fertur id extremum, quod longius à centro distat. </s> <s id="N14950">Quamob­<lb/>rem ad iugum quidem in&longs;trumenta faciunt collopas, quibus <lb/>facilius ver&longs;ant: in gracilibus autem &longs;uculis plus fit id, quod <lb/>extra lignum est. </s> <s id="N14959">Hoc autem id efficitur, quod à centro exit.<emph.end type="italics"/></s> </p> <p id="N1495E" type="head"> <s id="N14960">COMMENTARIVS.<!-- KEEP S--></s> </p> <p id="N14964" type="main"> <s id="N14966">Cvm plura iugum de &longs;e po&longs;&longs;it &longs;ignificare, hoc loco &longs;u­<lb/>mitur ab Ari&longs;totele pro <expan abbr="in&longs;trum&etilde;to">in&longs;trumento</expan> quodam ligneo, <lb/>quo textores in machina textoria. </s> <s id="N14971">vtuntur, vt &longs;ta­<lb/>men <expan abbr="telasq.">telasque</expan> conuoluant. </s> <s id="N1497A">Oblongum itaque ac teres quod­<lb/>dam lignum e&longs;t &longs;uper tran&longs;uer&longs;a ip&longs;ius textrinæ locatum, <pb pagenum="155" xlink:href="005/01/163.jpg"/>bina circa <lb/><figure id="id.005.01.163.1.jpg" xlink:href="005/01/163/1.jpg"/><lb/><expan abbr="vtramq.">vtramque</expan> ex­<lb/>tremitatem <lb/><expan abbr="hab&etilde;s">habens</expan> fora­<lb/>mina, qui­<lb/>bus toti­<lb/>dem collo­<lb/>pes, &longs;eu fu­<lb/>&longs;tes infigun­<lb/>tur, vt faci­<lb/>liùs iugum ip&longs;um eorum beneficio cum opus fuerit conuer­<lb/>tatur, vt præ &longs;efert &longs;ub&longs;trata figura. <</s> </p> <p id="N149A6" type="main"> <s id="N149A8">Sucula item quamuis alia po&longs;&longs;it &longs;ignificare, hic tamen <lb/>machinam &longs;ignificat tractorij generis, quæ ex tereti ligno, <lb/>aut lignorum compagine con&longs;tat, adiuncto axe &longs;uffulta <lb/>æquidi&longs;tante à plano horizontis, duobus, vel pluribus col­<lb/>lopibus pari longitudine vtrinque immobiliter ad&longs;tantibus <lb/>tanquam rotæ radijs circa modiolum, quibus admota ma­<lb/>nu, &longs;ucula ip&longs;a circa proprium axem obuoluitur, <expan abbr="funeq.">funeque</expan> cir­<lb/>cumducto, pondera &longs;ubleuat, vt præ oculis hic e&longs;t videre <lb/>in eius figura. </s> </p> <p id="N149BF" type="main"> <s id="N149C1">Quærit igitur Ari­<lb/><figure id="id.005.01.163.2.jpg" xlink:href="005/01/163/2.jpg"/><lb/>&longs;toteles cur &longs;i lon­<lb/>giores fuerint collo­<lb/>pes facilius iugum <lb/>circumagatur, quam <lb/>&longs;i minores, ac bre­<lb/>uiores extiterint. <lb/></s> <s id="N149D7"><expan abbr="Itemq.">Itemque</expan> cur gracilio­<lb/>res &longs;ucculæ facilius <lb/>pariter ab <expan abbr="ead&etilde;">eadem</expan> po­<lb/>tentia circumuoluantur, quàm cra&longs;&longs;iores. </s> <s id="N149E7">Vtriu&longs;que &longs;ubin­<lb/>de cau&longs;am e&longs;&longs;e inquit, quod in vtraque machina quilibet <lb/>collops tanquam vectis &longs;e habet, cuius <expan abbr="centrũ">centrum</expan>, ac fulcimen­<lb/>tum e&longs;t in medio iugi, vel &longs;uculæ, &longs;iue in intimo axe coniun­<lb/>cto, aut &longs;altem in ip&longs;is concepto: potentia verò in extremi-<pb pagenum="156" xlink:href="005/01/164.jpg"/>tate, quæ extra ip&longs;um iugum, vel &longs;uculam prominet, vbi <lb/>manus communiter adhibetur: ac onus con&longs;tituitur in exti­<lb/>ma ip&longs;a vtriu&longs;que corporis &longs;uperficie, quam fortiter præ­<lb/>mendo vbi è foramine prodit, &longs;ecum conuoluit, ac ver&longs;at. <lb/></s> <s id="N14A02">Cuius quippe vectis &longs;imilitudinem, & operationem hacte­<lb/>nus etiam in malo expre&longs;simus loquendo de motione nauis <lb/>vento agitatæ. </s> <s id="N14A09">Cum itaque plus atque celerius transfera­<lb/>tur ab eadem potentia extremum &longs;emidiametri, quod ma­<lb/>gis à centro di&longs;tat in de&longs;criptione circuli, nec non plus, ac <lb/>facilius mouere valeat extremum vectis, quod longius à <lb/>fulcimento re&longs;pectu oneris leuandi protenditur, quò lon­<lb/>giores fuerint collopes, &longs;emidiametri, ac vectis rationem <lb/>adepti, <expan abbr="magisq.">magisque</expan> eorum extrema à fulcimento, &longs;eu centro <lb/>in &longs;uperficie conuoluenda di&longs;tauerint, eò faciliùs iugum, aut <lb/>&longs;uculam contorquendo ver&longs;abunt. </s> <s id="N14A20">Quoniam verò in omni <lb/>vecte maior, aut minor di&longs;tantia, quàm à centro, vel fulci­<lb/>mento habet extremum, in quo applicatur potentia, atten­<lb/>ditur &longs;olummodo re&longs;pectu di&longs;tantiæ, quam &longs;imul habet onus <lb/>ab eodem centro, vel fulcimento; hinc fit, vt in graciliori­<lb/>bus &longs;uculis, minore exi&longs;tente di&longs;tantia à centro ad circum­<lb/>ferentiam, &longs;eu extimam &longs;uperficiem conuexam vbi con&longs;ti­<lb/>tuitur onus, & vbi fit collopis præ&longs;sio, maior di&longs;tantia relin­<lb/>quatur v&longs;que ad alterum extremum eiu&longs;dem collopis, quod <lb/>e&longs;t extra; ac iuxta maiorem hanc proportionem, magis pa­<lb/>riter collops ip&longs;e mouere &longs;uculam valeat. </s> </p> <p id="N14A37" type="main"> <s id="N14A39">Quod &longs;i contra hanc expo&longs;itionem obijciatur, quòd Ari­<lb/>&longs;toteles palàm & ab&longs;olutè docuerit, tàm &longs;uculam, quàm iu­<lb/>gum <expan abbr="cõ&longs;titui">con&longs;titui</expan> centrum in collopum motione; ex quo a&longs;&longs;um­<lb/>pto minus concluderentur, quæ de ip&longs;ius mente relata &longs;unt; <lb/>Occurrendum e&longs;t, id &longs;ano modo e&longs;&longs;e intelligendum. </s> <s id="N14A48">Nam <lb/>eodem pacto præcedenti quæ&longs;tione apud ip&longs;um Philo&longs;o­<lb/>phum legimus, manum, non iuncturam brachij habere <lb/>rationem centri in motu circulari, quo circumuertitur fun­<lb/>da. </s> <s id="N14A53">Et tamen ibi vt vidimus &longs;icut hic omnino diuer&longs;us e&longs;t <lb/>&longs;en&longs;us, qui &longs;anè potius ex contextu aliorum omniumque <lb/>verborum, quàm ex vno tantum verbo fortè mendo&longs;o eli-<pb pagenum="157" xlink:href="005/01/165.jpg"/>ciendus e&longs;t. </s> <s id="N14A5F">Cum igitur vtrobique iuxta &longs;en&longs;um explica­<lb/>tum con&longs;onent reliqua verba, vi&longs;que argumenti non aliter <lb/>appareat, quàm quo expo&longs;uimus modo, &longs;eclu&longs;o omni con­<lb/>tentionis pruritu, nullus ambigendi locus relinquitur de <lb/>mente Ari&longs;totelis in his, quæ illum interpretando retuli­<lb/>mus. </s> </p> <p id="N14A6C" type="head"> <s id="N14A6E">Quæ&longs;tio Decimaquarta.</s> </p> <p id="N14A71" type="main"> <s id="N14A73">C<emph type="italics"/>vr eiu&longs;dem magnitudinis lignum faciliùs <lb/>genu. </s> <s id="N14A7B">frangitur, &longs;i qui&longs;piam æquè deductis <lb/>manibus extrema comprehendens fregerit, <lb/>quàm &longs;i iuxta genu: & &longs;i terræ illud appli­<lb/>cans pelle &longs;uperimpo&longs;ito, manu longè didu­<lb/>cta confregerit, quàm propè? </s> <s id="N14A86">An quia ibi <lb/>quidem genu centr<gap/> e&longs;t, bìs verò ip&longs;e pes. </s> <s id="N14A8D">Quantò autem <lb/>remotiùs à centro fuerit, faciliùs mouetur quodcunque. </s> <s id="N14A92">Mo­<lb/>ueri autem quod frangitur, nece&longs;&longs;e est.<emph.end type="italics"/></s> </p> <p id="N14A99" type="head"> <s id="N14A9B">COMMENTARIVS.<!-- KEEP S--></s> </p> <p id="N14A9F" type="main"> <s id="N14AA1">Qvoniam fracturus qui&longs;piam manibus, ac &longs;imul ge­<lb/>nu, aut pede aliquod lignum, dupliciter pote&longs;t ad <lb/>hoc præ&longs;tandum &longs;e gerere; nempe vel æquè dedu­<lb/>ctis manibus extrema ligni comprehendens, <expan abbr="genuq.">genuque</expan> aut pe­<lb/>de circa medium tanquam fulcimento adhibito, illa ad &longs;e <lb/>retrahendo: vel manibus non ni&longs;i iuxta genu àc prope me­<lb/>dium vtrinque admotis, vtrunque ip&longs;ius ligni dimidium in­<lb/>clinando: Quærit hic Ari&longs;toteles, cur facilius priori, quàm <lb/>po&longs;teriori modo &longs;equatur præruptio, etiam &longs;i eiu&longs;dem ma­<lb/>gnitudinis &longs;it lignum, <expan abbr="eademq.">eademque</expan> virtus in fractione adhibea­<lb/>tur. </s> <s id="N14AC0"><expan abbr="Idemq.">Idemque</expan> contingat &longs;i humi lignum ip&longs;um &longs;ub&longs;ternatur <lb/><expan abbr="pedeq.">pedeque</expan> circa medium &longs;uperimpo&longs;ito, manus ad tollendum <lb/><expan abbr="&longs;ur&longs;umq.">&longs;ur&longs;umque</expan> curuandum alterum, vel vtrumque eius extremum <lb/>admoueatur, vt &longs;cilicet quò longius à pede lignum com-<pb pagenum="158" xlink:href="005/01/166.jpg"/>prehenderit, eo facilius tollat atque confringat. </s> </p> <p id="N14AD7" type="main"> <s id="N14AD9">Huius igitur cau&longs;am eam e&longs;&longs;e, inquit Ari&longs;toteles. <!-- KEEP S--></s> <s id="N14ADD">Nam <lb/>explicatus motus, qui fit in fractione ligni, e&longs;t motus circu­<lb/>laris, cuius centrum con&longs;tituitur genu vel pes, &longs;eu punctum <lb/>ligni medium, quod &longs;uffultum illis quie&longs;cit. </s> <s id="N14AE6">Dimidia verò <lb/>ip&longs;ius ligni confringendi dum inclinantur &longs;e <expan abbr="hab&etilde;t">habent</expan> tanquam <lb/>duo &longs;emidiametri circulariter ducti angulum efficientes in <lb/>ip&longs;o centro circuli quem de&longs;cribunt. </s> <s id="N14AF3">Quanto autem remo­<lb/>tius à centro fuerit quodcumque circulariter moueri de­<lb/>bet, tanto facilius mouetur. </s> <s id="N14AFA">Facilius ergo manus dictum <lb/>motum perficient &longs;i longius, quàm &longs;i propius genu, vel <expan abbr="pe-d&etilde;">pe­<lb/>dem</expan>, lignum apprehenderint. </s> <s id="N14B05"><expan abbr="Cumq.">Cumque</expan> ex hac motione, & <lb/>inclinatione vtriu&longs;que dimidij procedat ip&longs;a fractio ligni, &longs;e­<lb/>quitur etiam facilius longè quàm propè diductis manibus <lb/>ip&longs;um lignum confringi. </s> </p> <p id="N14B11" type="main"> <s id="N14B13">Cur autem non ob&longs;tante prædicta di&longs;paritate in modo, <lb/>quo frangitur lignum, cæteris paribus difficilius <expan abbr="fuãgatur">frangatur</expan> <lb/>&longs;i cra&longs;sius ip&longs;um &longs;it, quàm &longs;i gracilius, non docet Ari&longs;tote­<lb/>les. <!-- KEEP S--></s> <s id="N14B23">Ex ip&longs;a <expan abbr="tam&etilde;">tamen</expan> rei natura qui&longs;que &longs;tatim intelliget ab&longs;que <lb/>eo, quod recurrat cum Baldo ad rationem illam angulati <lb/>vectis, quam dicit habere <expan abbr="vtrumq.">vtrumque</expan> dimidium ligni prærupti. <lb/></s> <s id="N14B33">Siquidem cum tota difficultas, quæ reperitur in fractione <lb/>ligni oriatur ex re&longs;i&longs;tentia partium &longs;eparandarum, eo quod <lb/>hæ inter &longs;e naturali nexu coniunctæ, nece&longs;&longs;ariò ob&longs;tent &longs;e­<lb/>parationi ab inuicem: quo plures fuerint ip&longs;æ partes, eo ma­<lb/>gis ob&longs;tabunt, <expan abbr="difficiliusq.">difficiliusque</expan> proinde per earum diui&longs;ionem <lb/>lignum quodlibet ex ip&longs;is compo&longs;itum confringetur. </s> </p> <p id="N14B44" type="main"> <s id="N14B46">Illud etiam hic quæri po&longs;&longs;et, quod Ari&longs;toteles prætermi­<lb/>&longs;it, cur prius ex parte &longs;uperiori, ac extra angulum, quem effi­<lb/>ciunt dimidia ligni inclinata, quàm ex parte inferiori in cu­<lb/>&longs;pide ip&longs;ius anguli vbi <expan abbr="c&etilde;trum">centrum</expan> motionis con&longs;tituitur, fractio <lb/>ip&longs;a ligni &longs;equatur. </s> <s id="N14B55">Facilisque erit re&longs;pon&longs;io &longs;i dicamus id <lb/>fieri, quia illæ partes continui in fractione prius ab inuicem <lb/>&longs;eparantur, quæ & citius & longius coguntur di&longs;cedere: In <lb/>fractione autem ligni per inclinationem, & complicationem <lb/>vtriu&longs;que dimidij, ex partibus cra&longs;sitiei, quæ ab inuicem di-<pb pagenum="159" xlink:href="005/01/167.jpg"/>uelluntur, illæ citius ac longius ab inuicem coguntur di&longs;ce­<lb/>dere, quæ magis di&longs;tant à puncto, quod con&longs;tituitur cen­<lb/>trum in hac motione; quia nimirum illæ di&longs;cedendo, maio­<lb/>rem &longs;emper arcum de&longs;cribunt eodem tempore, quam quæ <lb/>propinquiores &longs;unt centro. </s> <s id="N14B6D">Illæ igitur ip&longs;æ partes cra&longs;&longs;itiei <lb/>di&longs;tantiores a centro prius, ac citius ab inuicem &longs;eparantur, <lb/>ac proinde fractio non ab ip&longs;o centro, vel parte inferiori vbi <lb/>fulcitur, &longs;ed à parte &longs;uperiori, ac remotiori ab illo, initium <lb/>&longs;umere debet. </s> </p> <p id="N14B78" type="main"> <s id="N14B7A">Quod vt planius con&longs;tet, e&longs;to lignum, quod frangitur AB. <lb/><!-- KEEP S--></s> <s id="N14B7F">Centrum vbi fulcitur C, <expan abbr="&longs;intq.">&longs;intque</expan> fracta, vel frangenda dimi­<lb/>dia AD, & EB &longs;emicirculum de&longs;cribentia AFB circa <lb/><figure id="id.005.01.167.1.jpg" xlink:href="005/01/167/1.jpg"/><lb/>ip&longs;um C. <!-- KEEP S--></s> <s id="N14B91">Partes <lb/>verò quæ ab in­<lb/>uicem &longs;eparan­<lb/>tur &longs;int illæ, quæ <lb/>exi&longs;tunt in lineis <lb/>DC, & EC re­<lb/>pr&etail;&longs;entantes la­<lb/>titudinem, vel <lb/>cra&longs;sitiem ligni. <lb/></s> <s id="N14BA5">Dicimus ergo ex <lb/>huiu&longs;modi par­<lb/>tibus, quæ &longs;unt in ip&longs;is lineis DC, & EC, illas quæ magis <lb/>di&longs;tant à puncto C citius moueri, ac per maius interuallum <lb/>ab inuicem &longs;eparari: quod e&longs;t prius confringi, quàm quæ <lb/>propinquiores &longs;unt puncto C. <!-- KEEP S--></s> <s id="N14BB3">Siquidem ip&longs;um C non <lb/>modo con&longs;tituitur centrum in hac motione re&longs;pectu &longs;emi­<lb/>circuli AFB; &longs;ed etiam re&longs;pectu &longs;emicirculi GDEH, qui <lb/>efficitur à punctis DE, vt tandem DA po&longs;t ab&longs;olutam <lb/>complicationem ligni reperiatur in GI; & EB in HK. </s> <s id="N14BBE">Qua­<lb/>propter lineæ DC, & EC con&longs;tituuntur tanquam duo &longs;e­<lb/>midiametri, cuius partes quo remotiores fuerint à centro <lb/>C, eo velocius ab eadem potentia mouentur, <expan abbr="maiusq">maiusque</expan> &longs;pa­<lb/>tium in æquali tempore percurrunt, vt &longs;&etail;pius probatum e&longs;t. </s> </p> <p id="N14BC9" type="main"> <s id="N14BCB">Diximus autem prius &longs;eparari partes di&longs;tantiores à pun-<pb pagenum="160" xlink:href="005/01/168.jpg"/>cto C in ip&longs;is lineis DC, & EC, loquendo de illis prout <lb/>repræ&longs;entant materialem cra&longs;sitiem ligni, quæ non &longs;tatim <lb/>ac tota &longs;imul di&longs;rumpitur. </s> <s id="N14BD7">Nam ab&longs;tractè loquendo de ip­<lb/>&longs;is lineis, quæ ante diui&longs;ionem coincidebant in vnam, non <lb/>po&longs;&longs;et intelligi, prius &longs;eparari vnam partem illarum, quàm <lb/>aliam cum &longs;imul omnes, magis aut minus di&longs;tando di&longs;iungi <lb/>deberent con&longs;tituendo angulum DCE. </s> <s id="N14BE2">Alioquin non e&longs;­<lb/>&longs;ent rectæ, vt per &longs;e patet. </s> </p> <p id="N14BE7" type="head"> <s id="N14BE9">Quæ&longs;tio Decimaquinta.</s> </p> <p id="N14BEC" type="main"> <s id="N14BEE">C<emph type="italics"/>vr ea, quæ circa littora appellantur, crocæ, <lb/>rotunda &longs;unt figura, cùm alioqui à principio <lb/>ex magnis &longs;int lapidibus, ostreisvè? </s> <s id="N14BF8">An <lb/>quia, ea, quæ plus recedunt à medio in motio­<lb/>nibus: feruntur celeriùs? </s> <s id="N14BFF">Medium enim <lb/>fit centrum: interuallum verò ea, quæ à cen­<lb/>tro. </s> <s id="N14C06">Semper autem maior ab &etail;quali motione maiorem de&longs;cri­<lb/>bit circulum. </s> <s id="N14C0B">Quod autem maius in &etail;quali pertran&longs;it tem­<lb/>pore, celeriùs fertur. </s> <s id="N14C10">Qu&etail; autem celeriùs ex &etail;quali feruntur <lb/>&longs;patio, vebementius impetunt. </s> <s id="N14C15">Qu&etail; autem magis impetunt, <lb/>impetuntur & magis: quamobrem ea, qu&etail; plus à medio di­<lb/>&longs;tant, confringi nece&longs;&longs;e e&longs;t: id autem cùm patiantur, rotunda <lb/>fieri e&longs;t nece&longs;&longs;arium. </s> <s id="N14C1E">Crocis autem propter maris motum, <lb/>quoniam &longs;imul cum illo agitantur, in perpeti e<32>e accidit mo­<lb/>tione, <expan abbr="eòq.">eòque</expan> ver&longs;atas modo &longs;emper offen&longs;are. </s> <s id="N14C29">Id autem ip&longs;is <lb/>maximè extremis contingere partibus e&longs;t nece&longs;&longs;e.<emph.end type="italics"/></s> </p> <p id="N14C30" type="head"> <s id="N14C32">COMMENTARIVS.<!-- KEEP S--></s> </p> <p id="N14C36" type="main"> <s id="N14C38">Crocæ apud Græco sidem &longs;ignificant, ac apud Lati­<lb/>nos vmbilici, quorum meminit Cicero 2. de Orato­<lb/>re; <expan abbr="&longs;untq.">&longs;untque</expan> expoliti illi calculi, qui in littoribus repe­<lb/>riuntur continua maris agitatione attriti, ac in orbicularem, <lb/>vel rotundam figuram redacti, vt qui in glarea arenis vi&longs;un-<pb pagenum="161" xlink:href="005/01/169.jpg"/>tur admi&longs;ti. </s> <s id="N14C4C">De ijs igitur hic loquens Ari&longs;toteles, quærit, <lb/>qua de cau&longs;a rotundam potius quam aliam figuram per at­<lb/>tritionem ac perpetuam illam agitationem adipi&longs;cantur, <lb/>cum frequentius ex lapidibus, ac fragmentis alterius figuræ <lb/>efficiantur. </s> <s id="N14C57">Quod enim &longs;ecundum omnes &longs;ui partes paula­<lb/>tim conteritur, ac minuitur, vniformiter difformiter contun­<lb/>di debet, ac &longs;en&longs;im attenuari, eadem partium proportione <lb/>&longs;eruata, <expan abbr="eademq.">eademque</expan> proinde figura. </s> <s id="N14C64">Non igitur &longs;atis apparet <lb/>cur ex tot tanquam ex diuer&longs;is figuris te&longs;tarum o&longs;treorum <lb/><expan abbr="concarumq.">concarumque</expan> ac lapidum angularium non ni&longs;i rotundam, & <lb/>orbicularem formam eorum reliquiæ videantur &longs;eruare, <lb/><expan abbr="eiu&longs;demq.">eiu&longs;demque</expan> figuræ penè omnes euadant cuius non erant. </s> </p> <p id="N14C75" type="main"> <s id="N14C77">Huic autem quæ&longs;tioni Ari&longs;toteles re&longs;pondet, partes, quæ <lb/>magis à centro, &longs;eu puncto medio circumlati corporis rece­<lb/>dunt, cum celerius in eius circumuolutione ferantur (maius <lb/>videlicet in æquali tempore &longs;patium in rotatione conficien­<lb/>do) vehementius impetere, <expan abbr="vicinaq.">vicinaque</expan> corpora rotando per­<lb/>cutere, quàm partes centro propinquiores; velocitas enim <lb/>auget impul&longs;um: Quæ autem partes <expan abbr="vehem&etilde;tius">vehementius</expan> impetunt, <lb/>atque impingunt, &longs;i fragiles in &longs;e &longs;int, facilius etiam refran­<lb/>guntur. </s> <s id="N14C92">Cum igitur prominentiores partes crocearum &longs;int <lb/>huiu&longs;modi, vt celerius in &longs;uos orbes ruant, vehementiu&longs;que <lb/>propterea illidant, &longs;equitur facilius ip&longs;as contundi, <expan abbr="&longs;olumq.">&longs;olumque</expan> <lb/>propterea relinqui partes à centro æquidi&longs;tantes, ex quibus <lb/>re&longs;ultat orbicularis, ac rotunda figura, quam in ip&longs;is croceis <lb/>communiter cernimus. </s> </p> <p id="N14CA3" type="main"> <s id="N14CA5">Quod &longs;i ex hoc Ari&longs;totelis di&longs;cur&longs;u &longs;equatur maiores <lb/>croceas rotundiores fieri, quàm minores propter maiorem <lb/>à centro di&longs;tantiam, qua in rotatione prominentes partes <lb/>facilius contunduntur; id certè ab experientia non e&longs;t om­<lb/>nino alienum, vt Baldus arbitratur; &longs;icut nec ip&longs;as croceas <lb/>circa centrum conuerti, quamuis alijs, ac diuer&longs;is etiam mo­<lb/>tionibus agitentur. </s> <s id="N14CB4">Si enim in pluribus littoribus attentius <lb/>ob&longs;erua&longs;&longs;et, vidi&longs;&longs;et vtique fluctuum iactatione fluxu, ac re­<lb/>fluxu, non modo glareas, paruo&longs;que lapillos circa centrum <lb/>omnino conuolui, &longs;ed etiam maiores vmbilicos, & non me­<pb pagenum="162" xlink:href="005/01/170.jpg"/>diocria &longs;axa &longs;imiliter in orbem ruere, <expan abbr="&longs;e&longs;eq.">&longs;e&longs;eque</expan> collidere, quæ <lb/>ni&longs;i magna valde &longs;int, vt rotari minus commodè po&longs;sint, <lb/>mutua ip&longs;orum colli&longs;ione, orbiculata euadunt, vel ad orbi­<lb/>cularem figuram accedunt magis quàm minores lapilli, vel <lb/>te&longs;tæ. </s> <s id="N14CCE">Vnde lati&longs;simæ plagæ vi&longs;untur his tantum rotundis <lb/>lapidibus &longs;tratæ, nulla ferè admi&longs;ta arena, parua te&longs;ta, vel <lb/>glarea. </s> <s id="N14CD5">Quod verò non omnes lapides leuigatos, ac rotun­<lb/>dos tanquam torno fabrefactos &longs;e videantur o&longs;tendere; id <lb/>potius materiæ varietati tribuendum e&longs;t, qua non omnes <lb/>partes æquè fragiles con&longs;tituuntur, vt pariter po&longs;sint &longs;ua <lb/>volubilitate contundi. </s> <s id="N14CE0">Imò minores vmbilicos, vt plurimùm <lb/>fragiliorem adeptos e&longs;&longs;e materiam argumento e&longs;&longs;e pote&longs;t <lb/>ip&longs;a eorum paruitas. </s> <s id="N14CE7">Non enim ex magnis parui facti e&longs;&longs;ent, <lb/>ni&longs;i materia, ex qua con&longs;tant facilè cederet, ac cedendo vni­<lb/>formiter attenuaretur, ex quo prouenit leuitas. </s> </p> <p id="N14CEE" type="main"> <s id="N14CF0">Denique ratio, vel cau&longs;a ab Ari&longs;totele adducta non tollit <lb/>quin ex alia &longs;imul concau&longs;a idip&longs;um dicamus procedere, <lb/>quam tetigit Piccolomineus ac Baldus. <!-- KEEP S--></s> <s id="N14CF8">Quia nimirum vni­<lb/>uer&longs;aliter loquendo omnes eminentiæ, <expan abbr="omnesq.">omnesque</expan> anguli in <lb/>corporibus, natura &longs;ua infirmiores &longs;unt reliquis partibus in­<lb/>timioribus, quæ æquè di&longs;tant à centro. </s> <s id="N14D05">Minus enim cir­<lb/>cumfulciuntur ab illis dum prominent, <expan abbr="magisq.">magisque</expan> extrin&longs;ecis <lb/>offen&longs;ionibus &longs;unt expo&longs;iti atque obnoxij. </s> <s id="N14D10">Vnde faciliùs <lb/>læduntur, ac retunduntur. </s> <s id="N14D15">Sicut nares, ac digiti manu&longs;que <lb/>vel pedes in marmoreis &longs;tatuis, quæ propterea &longs;æpius mu­<lb/>tilatæ reperiuntur effo&longs;&longs;æ. </s> <s id="N14D1C">Cum igitur reliquiæ lapidum, <lb/>ac o&longs;trearum a&longs;sidua maris agitatione in littoribus vo­<lb/>lutentur, atque inuicem illidantur, extremas <lb/><expan abbr="eminentesq.">eminentesque</expan> earum partes retundi nece&longs;­<lb/>&longs;e e&longs;t, ob idque eas in orbicularem <lb/>formam redigi, vel ad ip­<lb/>&longs;am quantum fieri <lb/>pote&longs;t acce­<lb/>dere. </s> </p> <pb pagenum="163" xlink:href="005/01/171.jpg"/> <p id="N14D36" type="head"> <s id="N14D38">Quæ&longs;tio Decima&longs;exta.</s> </p> <p id="N14D3B" type="main"> <s id="N14D3D">C<emph type="italics"/>vr quantò longiora &longs;unt ligna, tantò imbe­<lb/>cilliora fiunt: & &longs;i tollantur, inflectuntur <lb/>magis, tamet&longs;i quod breue quidem e&longs;t, ceu <lb/>cubitum, fuerit tenue: quòd verò cubitorum <lb/>centum, cra&longs;&longs;um? </s> <s id="N14D4B">An quia & vectis, & onus, <lb/>& hypomochlion, in leuando ip&longs;a fit ligni <lb/>proceritas? </s> <s id="N14D52">Prior namque illius pars ceu hypomochlion fit: <lb/>quòd verò in extremo e&longs;t, pondus. </s> <s id="N14D57">Quamobrem quantò ex­<lb/>ten&longs;ius fuerit id, quod ab hypomochlio e&longs;t, tantò inflecti ne­<lb/>ce&longs;&longs;e e&longs;t magis. </s> <s id="N14D5E">Quo enim plus ab hypomochlio di&longs;tat, eò ma­<lb/>gis incuruari nece&longs;&longs;e e&longs;t. </s> <s id="N14D63">Nece&longs;&longs;ariò igitur extrema vectis ele­<lb/>uantur. </s> <s id="N14D68">Si igitur flexilis fuerit vectis, ip&longs;um inflecti magis <lb/>cum extollitur, nece&longs;&longs;e e&longs;t, quod longis accidit lignis: in bre­<lb/>uibus autem quod vltimum e&longs;t, quie&longs;centi hypomochlion de pro­<lb/>pe fit.<emph.end type="italics"/></s> </p> <p id="N14D73" type="head"> <s id="N14D75">COMMENTARIVS.<!-- KEEP S--></s> </p> <p id="N14D79" type="main"> <s id="N14D7B">Dvo quærit hic Ari&longs;toteles, quorum vnum pendet ex <lb/>alio. </s> <s id="N14D80">Primum e&longs;t cur quanto longiora &longs;unt ligna, <lb/>tanto imbecilliora fiant, etiam &longs;i &longs;int pariter cra&longs;&longs;io­<lb/>ra. </s> <s id="N14D87">Secundum verò e&longs;t cur longiora ip&longs;a ligna &longs;i ab aliquo <lb/>extremo tollantur, magis inflectantur quàm breuiora, atque <lb/>etiam &longs;imul graciliora, vt ha&longs;tæ, vel &longs;ari&longs;&longs;æ dum manu ab al­<lb/>tero extremo apprehenduntur, atque à terra eleuantur ad <lb/>lineam horizonti parallelam: Nam quo longiores extite­<lb/>rint, eò magis inclinantur, <expan abbr="minusq.">minusque</expan> rectitudinem, quam in <lb/>&longs;olo iacendo, vel &longs;tantes habebant, &longs;eruare queunt in aere <lb/>ita &longs;u&longs;pen&longs;æ. </s> </p> <p id="N14D9C" type="main"> <s id="N14D9E">Ex ijs autem duobus quæ&longs;itis, &longs;ecundo tantum <expan abbr="re&longs;põdet">re&longs;pondet</expan> <lb/>Ari&longs;toteles, cum ex eius &longs;olutione facilè patere po&longs;sit &longs;olu­<lb/>tio primi. </s> <s id="N14DA9">Ait igitur ex hoc procedere maiorem inflexio­<pb pagenum="164" xlink:href="005/01/172.jpg"/>nem ligni procerioris, quod cum lignum ita &longs;u&longs;pen&longs;um, &longs;i­<lb/>mul con&longs;tituatur vectis, & onus, fulcimentum habens prope <lb/>alterum extremum in manu à qua eleuatur; quanto exten­<lb/>&longs;ius fuerit id quod à fulcimento e&longs;t ver&longs;us alteram extremi­<lb/>tatem, quæ con&longs;tituitur pondus; tanto magis ip&longs;um inflecti <lb/>nece&longs;&longs;e e&longs;t, &longs;uppo&longs;ito quod vectis ip&longs;a &longs;eu lignum, ex &longs;e fle­<lb/>ctile &longs;it; id quod non contingit in breuibus lignis, aut vecti­<lb/>bus etiam &longs;i eadem &longs;eruetur proportio: Porrò extremum, <lb/>quod grauitat parum &longs;emper di&longs;tat à fulcimento. </s> <s id="N14DC1">Sit enim <lb/>&longs;ari&longs;&longs;a decem cubitorum longitudinis aliquantulum incli­<lb/><figure id="id.005.01.172.1.jpg" xlink:href="005/01/172/1.jpg"/><lb/>nata ip&longs;a AB, cuius manubrium A, cu&longs;pis B, &longs;uffulta di­<lb/>gitis vbi C, pollice præ mente in A tanquam potentia <lb/>eleuante. </s> <s id="N14DD2"><expan abbr="Eodemq">Eodemque</expan> pacto con&longs;tituatur gracilior &longs;urculus <lb/>bicubitus DE fultus in F. <!-- KEEP S--></s> <s id="N14DD9">Dico igitur &longs;ari&longs;&longs;am magis in­<lb/>clinari quàm &longs;urculum, eo quod licet vtrumque habeat ra­<lb/>tionem vectis &longs;imul & oneris; pondus tamen con&longs;titutus in <lb/>B magis di&longs;tat à fulcimento C, quàm quod <expan abbr="cõ&longs;tituitur">con&longs;tituitur</expan> in E <lb/>ab ip&longs;o F; <expan abbr="magisq.">magisque</expan> propterea grauitat, & inclinat deor&longs;um, <lb/>paulatim recedendo à rectitudine, quam &longs;tans, vel in &longs;olo <lb/>iacens habebat. </s> </p> <p id="N14DF0" type="main"> <s id="N14DF2">Quod non abs re fuerit aliundè etiam confirmare, ac vl­<lb/>terius declarare, notando prius ad inflexionem <expan abbr="cõtinui">continui</expan> duo <lb/>nece&longs;&longs;ario requiri. </s> <s id="N14DFD">Vnum e&longs;t determinata, ac proportiona­<lb/>ta quædam virtus &longs;iue ponderis, &longs;iue motricis potentiæ, ita <lb/>vt ab alia minori nulla cau&longs;ari po&longs;&longs;it talis inflexio. </s> <s id="N14E04"><expan abbr="Quõd">Quod</expan> <lb/>certè <expan abbr="cõmune">commune</expan> e&longs;t omnibus cau&longs;is naturalibus re&longs;pectu pro­<lb/>priorum effectuum, ad quos ordinantur. </s> <s id="N14E12">Alterum verò e&longs;t <pb pagenum="165" xlink:href="005/01/173.jpg"/>con&longs;tipatio quædam aliquarum partium, aliarumque laxa­<lb/>tio in corporibus flexibilibus tanquam conden&longs;atio, ac ra­<lb/>refactio. </s> <s id="N14E1E">Non enim po&longs;&longs;et continuum inflecti ni&longs;i partes il­<lb/>lius, quæ concauam &longs;uperficiem con&longs;tituunt vici&longs;&longs;im con&longs;ti­<lb/>parentur; illæ verò quæ conuexam, laxarentur; &longs;eu quo fie­<lb/>ri pote&longs;t extenderentur. </s> <s id="N14E27">Cumque &longs;en&longs;im natura ab vno ad <lb/>aliud in omnibus gradum faciat; hinc e&longs;t, vt non in qualibet <lb/>longitudine &longs;iue di&longs;tantia æquè fieri po&longs;&longs;it inflexio, &longs;ed lon­<lb/>gè facilius in ea, in qua paulatim procedendo, ita partes va­<lb/>lent curuari, vt &longs;ingulæ à rectitudine non videantur recede­<lb/>re. </s> <s id="N14E34">Vt ob&longs;eruare e&longs;t in portione, vel arcu alicuius magnæ <lb/>circumferentiæ, qui videtur à linea recta differre. </s> </p> <p id="N14E39" type="main"> <s id="N14E3B">His po&longs;itis duplici etiam ex capite dicemus contingere, <lb/>ligna quo longiora fuerint facilius inflecti. </s> <s id="N14E40">Primò namque <lb/>hoc ip&longs;o, quod longiora &longs;unt magis grauitant, <expan abbr="maiorq.">maiorque</expan> con­<lb/>&longs;tituitur vis à quo procedit inflexio. </s> <s id="N14E4B">E contra verò quo bre­<lb/>uiora extiterint, eo minor e&longs;t virtus huiu&longs;modi; quæ tandem <lb/>&longs;i minor &longs;it minima, quæ &longs;ufficere po&longs;sit ad motionem, nullo <lb/>pacto valet inflectere, vt patet in &longs;urculis calamis ac paleis, <lb/>quæ cum leuitate materiæ, tùm breuitate corporis, graui­<lb/>tare non po&longs;&longs;unt quantum &longs;ufficiat ad motum inflexionis. <lb/></s> <s id="N14E59">Quod &longs;i breuitas ligni compen&longs;etur magna cra&longs;&longs;itiei, ob&longs;ta­<lb/>bit ex alio capite ip&longs;amet eadem cra&longs;sities propter maio­<lb/>rem multitudinem partium, quarum aliæ con&longs;tipari, aliæ au­<lb/>tem laxari debent cum fit ip&longs;a inflexio. </s> <s id="N14E62">Secundo verò nam <lb/>quanto maior e&longs;t longitudo ip&longs;ius flexilis, tanto minor con­<lb/>&longs;tituitur laxatio, & con&longs;tipatio &longs;ingularum partium, quæ ar­<lb/>cum inflexionis efficiunt, meliu&longs;que valent &longs;en&longs;im inflecti. <lb/></s> <s id="N14E6C">Vice autem ver&longs;a, quò breuior e&longs;t longitudo illius, eò magis <lb/>&longs;ingulæ partes curuari debent, vt totius continui fiat infle­<lb/>xio. </s> <s id="N14E73"><expan abbr="Ideoq.">Ideoque</expan> difficilius curuantur, & inflectuntur etiam &longs;i gra­<lb/>cile &longs;it ip&longs;um lignum, quod debet inflecti. </s> </p> <p id="N14E7B" type="main"> <s id="N14E7D">Vtrum verò &longs;eruata eadem proportione cra&longs;sitiei ad lon­<lb/>gitudinem, æquè facilè inclinetur magnum, ac paruum, &longs;eu <lb/>longum, ac breue, non &longs;atis videtur con&longs;tare. </s> <s id="N14E84">Probabiliter <lb/>tamen dici pote&longs;t, &longs;pectandum primò e&longs;&longs;e qualitatem, ac di­<pb pagenum="166" xlink:href="005/01/174.jpg"/>&longs;po&longs;itionem materiæ, vt &longs;i grauior, aut leuior; den&longs;ior, aut <lb/>rarior; fortior, aut imbecillior in &longs;e &longs;it. </s> <s id="N14E90">Nam frequenter ex <lb/>ijs pendet, vt nonnulla corpora plus facilitatis ad &longs;e incli­<lb/>nandum acquirant ex maiori longitudine, quàm difficulta­<lb/>tis ex maiori cra&longs;&longs;itie: Alia verò contra. </s> <s id="N14E99">Deinde &longs;pectan­<lb/>dam e&longs;&longs;e ip&longs;am eandem proportionem cra&longs;&longs;itiei ad longitu­<lb/>dinem con&longs;iderando quænam illa &longs;it. </s> <s id="N14EA0">Etenim quamuis con­<lb/>&longs;tituatur eadem proportio, in vno atque in altero, non ta­<lb/>men omnis proportio eundem effectum in illis producit. <lb/></s> <s id="N14EA8">Eadem namque e&longs;t proportio cra&longs;&longs;itiei vnius digiti ad lon­<lb/>gitudinem vnius cubiti atque quinquaginta digitorum ad <lb/>quinquaginta cubitorum: & tamen virga ferrea, aut lignea <lb/>&longs;i digitalis cra&longs;&longs;itiei fuerit <expan abbr="longitudinisq.">longitudinisque</expan> vnius cubiti, non <lb/>tam facilè &longs;uo pondere flectetur, ac lignum, vel ferrum <lb/>quinquaginta digitorum cra&longs;sitiei, <expan abbr="totidemq.">totidemque</expan> cubitorum <lb/>longitudinis. </s> <s id="N14EBF">Quod &longs;i vnius palmæ fuerit cra&longs;situdo, longi­<lb/>tudo verò vnius cubiti nihil difficilius videretur inflecti, <lb/>quam &longs;i duarum palmarum con&longs;titueretur cra&longs;situdo in <lb/>longitudine bicubita. </s> <s id="N14EC8">Ad hæc proportio, quæ auget facili­<lb/>tatem, aut difficultatem inflexionis in vna &longs;pecie ligni, non <lb/>auget in alia &longs;icut non æquè in ligno, ac ferro plumbo, aut <lb/>calibe. </s> <s id="N14ED1">Quare nihil determinari pote&longs;t quo ad hoc ni&longs;i per­<lb/>&longs;pecta, vt diximus di&longs;po&longs;itione materiæ, <expan abbr="variaq.">variaque</expan> proportio­<lb/>ne, quæ diuer&longs;imodè iuxta maiorem, aut minorem corpo­<lb/>rum magnitudinem operatur. </s> </p> <p id="N14EDE" type="main"> <s id="N14EE0">Denique vt dictum e&longs;t de eleuatione, ac &longs;u&longs;pen&longs;ione li­<lb/>gni, vel alterius corporis oblongi &longs;umpti ab altera tantum <lb/>extremitate, vt exemplificauimus in &longs;ari&longs;&longs;a, idem dicendum <lb/>e&longs;t de eleuatione, ac &longs;u&longs;pen&longs;ione, quæ fit, vel ex ambabus <lb/>extremitatibus; vel ex medio inter illas: Nam &longs;i vtrinque ab <lb/>extremitatibus &longs;u&longs;pendatur aliquod lignum ad paralellum <lb/>horizonti, duo quidem in illo vectes fient in ip&longs;is extremita­<lb/>tibus fulti, <expan abbr="ponderaq">ponderaque</expan> in communi puncto intermedio gra­<lb/>uitabunt tanquam in remoti&longs;simo &longs;itu ab vtriu&longs;que fultura. <lb/></s> <s id="N14EF4">Quapropter ibidem fiet vtriu&longs;que vectis, &longs;eu totius ligni in­<lb/>flexio, &longs;uppo&longs;ita vt diximus flexibilitate materiæ, <expan abbr="ip&longs;aq.">ip&longs;aque</expan> ce-<pb pagenum="167" xlink:href="005/01/175.jpg"/>dente &longs;uomet ponderi. </s> <s id="N14F02">Alioquin lignum ip&longs;um, aut non <lb/>recederet à &longs;ua rectitudine, aut frangeretur. </s> <s id="N14F07">Quod &longs;i &longs;u­<lb/>&longs;pendatur ex medio, in ip&longs;o medio fulcietur vtrumque di­<lb/>midium, ceu duplex vectis vtrinque applicatus, extremita­<lb/>tibus vtrinque pariter grauitantibus, ac propendentibus <lb/>tanquam in remoti&longs;&longs;imo loco à communi centro &longs;iue fùlci­<lb/>mento. </s> <s id="N14F14">In quibus omnibus &longs;emper valet eadem ratio &longs;u­<lb/>pra explicata. </s> </p> <p id="N14F19" type="head"> <s id="N14F1B">Quæ&longs;tio Decima&longs;eptima.</s> </p> <p id="N14F1E" type="main"> <s id="N14F20">C<emph type="italics"/>vr à paruo existente cuneo magna &longs;cindun­<lb/>tur pondera, & corporum moles, <expan abbr="validaq.">validaque</expan> fit <lb/>impre&longs;sio? </s> <s id="N14F2E">An quia cuneus duo &longs;unt vectes, <lb/>&longs;ibi inuicem contrarii? </s> <s id="N14F33">vterque autem & <lb/>pondus habet, & hypomochlion; quod diuellit, <lb/>& comprimit. </s> <s id="N14F3A">Plagæ quin etiam ip&longs;ius latio <lb/>pondus, quod percutit, & mouet, magnum facit, & quoniam <lb/>motum mouet, ip&longs;a celeritate valentius fit. </s> <s id="N14F41">Paruo autem exi­<lb/>stente vectæ, magnæ illum con&longs;equuntur vires: quamobrem <lb/>vltra magnitudinis decentiam latet mouens. </s> <s id="N14F48">Sit cuneus vbi <lb/>ABC, quod verò cuneo &longs;cinditur DEFG. <!-- KEEP S--></s> <s id="N14F4E">Vectis igitur fit <lb/>ip&longs;a AB, pondus verò ip&longs;ius B inferior pars, hypomochlion <lb/>autem DG huic autem contrarius vectis BC. <!-- KEEP S--></s> <s id="N14F56">Percu&longs;&longs;a igi­<lb/>tur AC, vtroque illorum vtitur vecte &longs;cindit enim ip&longs;um B.<emph.end type="italics"/></s> </p> <p id="N14F5D" type="head"> <s id="N14F5F">COMMENTARIVS.<!-- KEEP S--></s> </p> <p id="N14F63" type="main"> <s id="N14F65">Celebrem non minus ac agitatam quæ&longs;tionem tam <lb/>parua in re hic in&longs;tituit Ari&longs;toteles. <!-- KEEP S--></s> <s id="N14F6B">Quippe cum <lb/>eius &longs;olutioni aliàs præclaræ, & ingenio&longs;æ, non om­<lb/>nes pr&etail;&longs;ertim recentiores pror&longs;us velint, aut valeant acquie­<lb/>&longs;cere. </s> <s id="N14F74">Quærit enim cur paruo exi&longs;tente cuneo, tam valida <lb/>eius adminiculo fiat virtutis impre&longs;sio, vt facilè magna &longs;cin­<lb/>dantur corpora, quæ alijs <expan abbr="maioribusq.">maioribusque</expan> adhibitis in&longs;trumen­<lb/>tis vix &longs;cindi aliquo modo po&longs;&longs;ent. </s> <s id="N14F81"><expan abbr="Soluitq.">Soluitque</expan> &longs;tatim, quia in <pb pagenum="168" xlink:href="005/01/176.jpg"/>cuneo, duo &longs;unt vectes &longs;ibi inuicem aduer&longs;i, quorum vter­<lb/>que & pondus habet, & fulcimentum, quod comprimens <lb/>diuellit; impul&longs;u &longs;cilicet accepto ab ip&longs;o motore, qui dum <lb/>cuneum malleo, vel alio corpore percutit, &longs;imul vtroque <lb/>vtitur vecte. </s> <s id="N14F94">Magna autem vis illi incutitur ex mallei per­<lb/>cu&longs;&longs;ione, eo quod malleus celerrimè motus moueat &longs;iue <lb/>percutiat. </s> <s id="N14F9B">Lationis enim celeritate validius ferit. </s> <s id="N14F9E">Ob vectis <lb/>igitur naturam, quam cuneus participat, & qua vires augen­<lb/>tur, validamque mallei percu&longs;&longs;ionem, magnas contingit <lb/>&longs;cindi, aut &longs;altem findi corporum moles, paruo adhibito <lb/>cuneo in rimula ip&longs;ius molis. </s> <s id="N14FA9">Quod adhuc &longs;chemate decla­<lb/>rans, hæc ferè &longs;ubnectit idem Ari&longs;toteles. <!-- KEEP S--></s> </p> <p id="N14FAF" type="main"> <s id="N14FB1">E&longs;to cuneus ABC, cuius apex, &longs;eu vertex B &longs;it ìntra <lb/>corpus &longs;cindendum DEFG. <!-- KEEP S--></s> <s id="N14FB7">Vectis autem vna con&longs;iderata <lb/>in ip&longs;o cuneo &longs;it AB, cuius pondus infra verticem B, nem­<lb/>pe ad partes ED, vt vbi H. <!-- KEEP S--></s> <s id="N14FBF">Fulcimentum verò I circa in­<lb/>gre&longs;&longs;um cunei, &longs;eu principium rimæ. </s> <s id="N14FC4">Huic autem vecti alius <lb/><figure id="id.005.01.176.1.jpg" xlink:href="005/01/176/1.jpg"/><lb/>oppo&longs;itus vectis <lb/><expan abbr="cõ&longs;tituatur">con&longs;tituatur</expan> BC, <lb/>cuius <expan abbr="põdus">pondus</expan> &longs;u­<lb/>pra verticem B <lb/>ad partes FG <lb/>vbi K, fulcimen­<lb/>tum verò in L. <lb/><!-- KEEP S--></s> <s id="N14FE4">Valde igitur per­<lb/>cu&longs;&longs;o cuneo in <lb/>AC, vectis AB fulta in I &longs;imul fulcimentum præmens, mo­<lb/>uebit ver&longs;us G; onus autem H ver&longs;us M. </s> <s id="N14FED">Vice autem ver­<lb/>&longs;a vectis CB, fulcimentum L mouebit ver&longs;us D: Onus ve­<lb/>rò K ver&longs;us N. <!-- KEEP S--></s> <s id="N14FF5">Quibus motibus dum partes molis ad <lb/>oppo&longs;ita impelluntur, molem ip&longs;am &longs;cindi nece&longs;&longs;e e&longs;t. </s> </p> <p id="N14FFA" type="main"> <s id="N14FFC">Huic autem Ari&longs;totelis doctrinæ, ac &longs;olutioni duo obijcit <lb/>Baldus. <!-- KEEP S--></s> <s id="N15002">Primum e&longs;t, quia &longs;i darentur explicati vectes in cu­<lb/>neo, eorum extremitates inuicem contendentes in puncto <lb/>B altera alteri ne quidquam operarentur e&longs;&longs;et impedimen­<lb/>to, vt late probat Guidus Vbaldus tractatu de cuneo. </s> <s id="N1500C">Se-<pb pagenum="169" xlink:href="005/01/177.jpg"/>cundum verò e&longs;t, quia in ip&longs;o &longs;ci&longs;&longs;ionis actu, facta aliqua di­<lb/>&longs;tractione partium molis adhuc non in totum di&longs;ci&longs;&longs;æ, ver­<lb/>tex cunei, quo pondera vtrinque diuelli, ac moueri debe­<lb/>rent, nihil vt plurimum tangit in rimula dum ip&longs;a vlterius <lb/>dilatatur. </s> </p> <p id="N1501C" type="main"> <s id="N1501E">Ad primum tamen re&longs;pondetur, &longs;i concipiamus in cuneo <lb/>vectes explicatos ex parte A vrgere ver&longs;us G, & ex parte <lb/>C vrgere ver&longs;us D; verticem verò non tran&longs;gredi punctum <lb/>B; &longs;ed in eo quie&longs;cere: tunc quidem &longs;equi, extrema ip&longs;orum <lb/>vectium &longs;ibi inuicem ob&longs;tare in puncto B, nè in contrarium <lb/>moueantur, moueantque adiacentia pondera modo de&longs;cri­<lb/>pto. </s> <s id="N1502D">At &longs;i concipiamus, vt re vera e&longs;t apicem ip&longs;um &longs;imul <lb/>pergere ad partes EF: tunc in ip&longs;o motu optimè intellige­<lb/>mus, concurrentiam extremorum vtriu&longs;que vectis in vni­<lb/>cum illud punctum terminatiuum verticis, nihil ob&longs;tare <lb/>quominus pars vectis, quæ &longs;equitur po&longs;t illud vbi K, impel­<lb/>lat aliam &longs;ibi corre&longs;pondentem in mole &longs;cindenda ver&longs;us <lb/>N: & pars vbi H, aliam &longs;imilem ver&longs;us M. </s> <s id="N1503C">Siquidem hoc <lb/>ip&longs;o, quod vertex vlterius pergit, partes illum vtrinque con­<lb/>&longs;equentes in proportionatum &longs;ibi locum &longs;uccedere non po&longs;­<lb/>&longs;ent, ni&longs;i prius inde <expan abbr="expeller&etilde;tur">expellerentur</expan> per &longs;ci&longs;&longs;ionem partes molis, <lb/>quæ eundem locum occupabant. </s> <s id="N1504B">Pars autem vbi K in <lb/>mole &longs;cindenda non expellitur inde virtute vectis AB; &longs;icut <lb/>nec H virtute vectis CB; cum nullam vim vtraque pati <lb/>po&longs;&longs;it à vecte ni&longs;i illa nitatur in contrariam partem. </s> <s id="N15054">Ergo ex­<lb/>pul&longs;io partis K fit virtute vectis CB, quæ contra nititur; & <lb/>expul&longs;io partis H, virtute vectis AB. <!-- KEEP S--></s> <s id="N1505C">Quod e&longs;t ip&longs;um ver­<lb/>ticem, &longs;eu apicem fungi officio extremorum vtriu&longs;que ve­<lb/>ctis ad remouendas vtrinque partes corporis &longs;cindendi tan­<lb/>quam ad leuanda pondera virtute impetus in contrarium <lb/>impre&longs;si in alterutro extremo, vt in AC vbi applicatur po­<lb/>tentia mouentis, &longs;eu percutientis. </s> <s id="N15069">Non igitur res ita e&longs;t con­<lb/>cipienda qua&longs;i vertex B tanquam extremum duorum ve­<lb/>ctium contra nitentium &longs;imul moueretur ad oppo&longs;ita ad <lb/>partes M, & N: Sed vt dum ip&longs;e vertex B mouetur &longs;u­<lb/>per lineam BO, partes cunei vtrinque &longs;equentes, ac paula-<pb pagenum="170" xlink:href="005/01/178.jpg"/>tim &longs;e dilatantes, & ab inuicem recedentes, nece&longs;&longs;ariò im­<lb/>pingant in partes molis, quas ab eodem loco di&longs;terminant, <lb/>vt ibidem ip&longs;æ &longs;uccedant. </s> <s id="N1507D">Non enim ab&longs;que impul&longs;u inde <lb/>po&longs;&longs;ent eas expellere, nec ab&longs;que expul&longs;ione in earum lo­<lb/>cum &longs;uccedere. </s> <s id="N15084">Cumque impul&longs;us fiat virtute impetus in <lb/>alterum vectis extremum impre&longs;&longs;i vbi adhibetur motoris <lb/>potentia; &longs;equitur verè extremitates ip&longs;as KH, partes mo­<lb/>lis &longs;ibi corre&longs;pondentes tanquam pondera &longs;cindendo di&longs;tra­<lb/>here, ac mouere, prout Ari&longs;toteles intendebat. </s> </p> <p id="N1508F" type="main"> <s id="N15091">Ad &longs;ecundum verò Baldi argumentum re&longs;pondetur, con­<lb/>cedendo &longs;æpè cu&longs;pidem cunei, nihil in &longs;ci&longs;&longs;ura contingere; <lb/>negando tamen propterea nullam ibi vectis rationem inter­<lb/>cedere. </s> <s id="N1509A">Porrò extremum quo vectis pondera mouet, vt <lb/>plurimum non e&longs;t vltimum punctum terminatiuum illius, <lb/>&longs;ed &longs;ufficit, vt &longs;it circa illud, vel &longs;altem po&longs;t fulcimentum, <lb/>quod intermediat inter pondus, & potentiam: Quare etiam <lb/>&longs;i vltimæ, & extremæ partes cunei, quæ verticem con&longs;e­<lb/>quuntur quandoque molem &longs;cindendam ob rimæ latitudi­<lb/>nem nullo pacto attingant: adhuc tamen explicata ratio du­<lb/>plicis vectis in illo procedit applicando nimirum, quæ dicta <lb/>&longs;unt de vltimis partibus terminantibus in vertice, ad alias <lb/>partes &longs;equentes, vbi primo fit contactus inter molem, & <lb/>cuneum. </s> </p> <p id="N150B1" type="main"> <s id="N150B3">Cæterum &longs;i quis vrgeat ex Guido Vbaldo, potius verti­<lb/>cem cunei e&longs;&longs;e commune <expan abbr="fulcimentũ">fulcimentum</expan> vtriu&longs;que vectis pon­<lb/>dera verò mediare inter fulcimentum, ac potentiam, ita vt <lb/>vectis AB fulta in ip&longs;o B moueat molis partem vbi e&longs;t I, <lb/>tanquam onus ver&longs;us G. <expan abbr="Similiterq.">Similiterque</expan> vectis CB ibidem <lb/>fulta, partem L ver&longs;us D. <!-- KEEP S--></s> <s id="N150C9">Occurrendum e&longs;t, hoc cum alijs, <lb/>quæ Guidus Vbaldus fusè pro&longs;equitur, probare quidem <lb/>talem pariter vectis rationem competere ip&longs;is AB & <lb/>CB; prout con&longs;tituuntur in cuneo: nihil tamen contra <lb/>Ari&longs;totelem concludere; cuius propterea di&longs;cur&longs;um refe­<lb/>rens Guidus Vbaldus minimè improbat. </s> <s id="N150D6">Nihil enim prohi­<lb/>bet, quominus idem numero vectis &longs;ecundum diuer&longs;as ra­<lb/>tiones ad duas, ac diuer&longs;as vectium &longs;pecies pertineat, vtriu&longs;-<pb pagenum="171" xlink:href="005/01/179.jpg"/>que &longs;cilicet vices gerendo atque exercendo: <expan abbr="idemq.">idemque</expan> cor­<lb/>pus &longs;imul po&longs;&longs;it e&longs;&longs;e fulcimentum, & onus quod mouetur <lb/>per vectem re&longs;pectu diuer&longs;orum, vt in &longs;imili &longs;upra explicui­<lb/>mus quæ&longs;t. </s> <s id="N150EC">3. Optime igitur &longs;ecundum vtranque vectis ra­<lb/>tionem dicere po&longs;&longs;umus, cuneum virtutis incrementum &longs;u­<lb/>mere à duplici vecte, quam continet, & ab ictu percu&longs;&longs;ionis, <lb/>qua validius omni alio impul&longs;u ip&longs;e adhibetur. </s> </p> <p id="N150F5" type="head"> <s id="N150F7">Quæ&longs;tio Decimaoctaua.</s> </p> <p id="N150FA" type="main"> <s id="N150FC">C<emph type="italics"/>vr &longs;i qui&longs;piam trochleas componens duas in <lb/>&longs;ignis duobus ad &longs;e inuicem iunctis contrario <lb/>ad trochleas moto circulo funem circumdu­<lb/>xerit, cuius alterum quidem caput &longs;ignorum <lb/>appendatur alteri, alterum verò trochleis &longs;it <lb/>innixum, & à funis initio trahere cœperit, <lb/>magna trahit pondera, licet imbecillium fuerit virium? </s> <s id="N1510E">An <lb/>quia idem pondus à minori potentia &longs;i mouetur, vecte medio <lb/>transfertur magis, quàm à manu? </s> <s id="N15115">Trochlea autem idem ve­<lb/>cti facit. </s> <s id="N1511A">Quamobrem &longs;i vna facilius trahet, & ab vnico <lb/>tractu multò grauius trahet, quàm facere po&longs;sit manus, idip­<lb/>sum duæ trochleæ plus quàm in dupla velocitate leuabunt. <lb/></s> <s id="N15123">Minus enim altera trahit, quàm &longs;i ip&longs;a per &longs;e ip&longs;am trahe­<lb/>ret, quando circa alteram iniectus fuerit funis, illa namque <lb/>minus etiam pondus effecit. </s> <s id="N1512A"><expan abbr="Pariq.">Parique</expan> modo &longs;i ad plures iniectus <lb/>fuerit funis in paucis trochleis, multa fit differentia, quamob­<lb/>rem à prima pondere quatuor minas trahente, ab vltima trahi <lb/>multò minus. </s> <s id="N15136">Et in re &etail;dificatoria faciliter magna mouent <lb/>pondera, traducunt enim ab una trochlea ad aliam, & rur&longs;us <lb/>ab illa ad &longs;uculas, & vectes. </s> <s id="N1513D">Hoc autem idem est, ac &longs;i mul­<lb/>tas facerent trochleas.<emph.end type="italics"/></s> </p> <p id="N15144" type="head"> <s id="N15146">COMMENTARIVS.<!-- KEEP S--></s> </p> <p id="N1514A" type="main"> <s id="N1514C">Svppo&longs;ita de&longs;criptione trochleæ, <expan abbr="eiusq.">eiusque</expan> multiplici di­<lb/>&longs;tinctione quam &longs;upra prima parte tex. <!-- REMOVE S-->8. Additione <lb/>prima tradidimus, illud in præ&longs;enti primò notandum <pb pagenum="172" xlink:href="005/01/180.jpg"/>occurrit, <expan abbr="Ari&longs;totel&etilde;">Ari&longs;totelem</expan> hic non agere ni&longs;i de trochlea, quæ vni­<lb/>cam, ac &longs;implicem rotulam contineat, quam pariter eodem <lb/>nomine trochleam appellat, ac di&longs;tinguit à tigno, &longs;eu ligno, <lb/>quod illam tanquam conceptaculum quoddam, aut cap&longs;u­<lb/>la in&longs;ertam continet; cum re vera communi acceptione <lb/>trochlea, vt diximus vtrumque &longs;imul &longs;ignificet, nempe, & <lb/>rotulam inditam &longs;iue orbiculum, & cap&longs;ulam continentem. <lb/></s> <s id="N1516F">Nec audiendus e&longs;t Piccolomineus dum ait tigna hic apud <lb/><expan abbr="Ari&longs;totel&etilde;">Ari&longs;totelem</expan>, non &longs;ignificare ligna prædicta, &longs;eu thecas ligneas, <lb/>rotulas continentes, &longs;ed trabes ad &longs;e inuicem iunctas, qui­<lb/>bus trochleæ cum pondere &longs;u&longs;tinentur. </s> <s id="N1517B">Quandoquidem &longs;i <lb/>hoc e&longs;&longs;et, Philo&longs;ophus <expan abbr="nõ">non</expan> dixi&longs;&longs;et, alterum extremum funis <lb/>ductarij, altero <expan abbr="tignorũ">tignorum</expan> appendi. </s> <s id="N1518A">Cum certum &longs;it, funem du­<lb/>ctarium nullo modo ad trabem aliquam appendi, &longs;ed ad ip­<lb/>&longs;um extremum trochleæ &longs;uperioris, &longs;eu ligni, quod rotulam <lb/>tegit, ac per axiculum regit, vt &longs;tatim patebit. </s> <s id="N15193">Præterea vbi <lb/>leonicus vertit in tignis duobus ad &longs;e inuicem iunctis, Græ­<lb/>cus textus habet <foreign lang="greek"><gap/>p\ dusi\ cu/lois sumba/llousin e(autoi_s e)nanti/ws</foreign>, <lb/>hoc e&longs;t in duobus lignis concurrentibus ad inuicem ex op­<lb/>po&longs;ito, quod propriè de&longs;ignat ip&longs;am &longs;ituationem cap&longs;ula­<lb/>rum rotulas continentium, &longs;eu trochlearum, quæ ex oppo­<lb/>&longs;ito &longs;e debent re&longs;picere, & qua&longs;i ad inuicem currere. </s> </p> <p id="N151A7" type="main"> <s id="N151A9">His ergo præmi&longs;&longs;is ad <expan abbr="nominũ">nominum</expan> dilucidationem, quæritur <lb/>hic ab Ari&longs;totele, qua de cau&longs;a <expan abbr="cõtingat">contingat</expan>, vt &longs;i quis duas tro­<lb/>chleas ad <expan abbr="inuic&etilde;">inuicem</expan> ex oppo&longs;ito componat, & fune ad <expan abbr="eorũ">eorum</expan> ro­<lb/>tulas circumducto, alterum eius caput alteri trochleæ, &longs;eu <lb/>ligno rotulam continenti appendat, alterum verò manu tra­<lb/>hat, magna eleuet pondera, quamuis imbecilla &longs;it virtus tra­<lb/>hentis. </s> <s id="N151C8"><expan abbr="Cau&longs;amq.">Cau&longs;amque</expan> mox reddit; quia nimirum facilius vel po­<lb/>tius vectis adiumento quàm &longs;ola manu, mouentur pondera <lb/>à minori potentia; rotula verò in trochlea vectis vicem obti­<lb/>net, &longs;eu vectis habet virtutem. </s> <s id="N151D4">Cumque in trochleis prædi­<lb/>cto modo applicatis, non tantum vna, &longs;ed duæ &longs;altem rotu­<lb/>læ tanquam totidem vectes adhibeantur, mirum non e&longs;t &longs;i <lb/><expan abbr="earũ">earum</expan> beneficio, celerius, ac facilius, <expan abbr="maioraq.">maioraque</expan> leuentur pon­<lb/>dera quàm &longs;it virtus <expan abbr="trah&etilde;tis">trahentis</expan>. </s> <s id="N151EA">Imò &longs;i vnius rotulæ adiumen-<pb pagenum="173" xlink:href="005/01/181.jpg"/>to plus <expan abbr="faciliusq.">faciliusque</expan> leuatur quàm &longs;ola manu, &longs;i duæ fuerint ro­<lb/>tulæ, plus ac celerius leuabitur, quàm in dupla proportione, <lb/>& &longs;ic deinceps tanto magis, &longs;eu maius pondus, quantò plu­<lb/>res extiterint rotulæ in ip&longs;is duabus, vel pluribus trochleis <lb/>adhibitæ; ita vt ex multiplicatione <expan abbr="totularũ">rotularum</expan>, intelligatur au­<lb/>geri virtutem trahentis, ac pondus imminui, cum certè plu­<lb/>ribus impertiatur tanquam diui&longs;um. </s> <s id="N15208">Quare inquit Ari&longs;tote­<lb/>les in re ædificatoria, multiplicatis trochleis &longs;uculis, ac ve­<lb/><figure id="id.005.01.181.1.jpg" xlink:href="005/01/181/1.jpg"/><lb/>ctibus magna <expan abbr="mou&etilde;tur">mouentur</expan> <expan abbr="põde">ponde</expan><lb/>ra non &longs;ecus ac multiplicatis <lb/>tantummodo trochleis, qu&etail; <lb/>vectis <expan abbr="vic&etilde;">vicem</expan> <expan abbr="gerũt">gerunt</expan> vt diximus. </s> </p> <p id="N1522B" type="main"> <s id="N1522D">Sed vt prædicta ad oculos <lb/>etiam pateant, &longs;int duæ tro­<lb/>chleæ ex oppo&longs;ito <expan abbr="cõ&longs;titutæ">con&longs;titutæ</expan>, <lb/>vna &longs;upernè ac &longs;tabiliter ap­<lb/>pen&longs;a vbi A; altera verò in­<lb/>fernè locata vbi B, cui pon<lb/>dus C &longs;it <expan abbr="religatũ">religatum</expan>, <expan abbr="habeatq.">habeatque</expan> <lb/><expan abbr="vtraq;">vtraque</expan> trochlea <expan abbr="&longs;uũ">&longs;uum</expan> <expan abbr="orbiculũ">orbiculum</expan> <lb/>inditum, cui funis ductarius <lb/><expan abbr="circũducatur">circunducatur</expan>; <expan abbr="alligeturq.">alligeturque</expan> al­<lb/>terum extremum ip&longs;ius funis <lb/>in parte inferiori &longs;uperioris <lb/>trochleæ vbi D. <!-- KEEP S--></s> <s id="N15267">Alterum ve­<lb/>rò relinquatur <expan abbr="trah&etilde;ti">trahenti</expan> vbi E. <lb/><!-- KEEP S--></s> <s id="N15272">Tunc dicimus cum Ari&longs;tote­<lb/>le, quòd &longs;i quis manu trahat <lb/>funis caput vbi E, facilè au­<lb/>xilio ip&longs;arum trochlearum <lb/>eleuabit pondus C, eo quod <lb/>trochlearum orbiculi, vectis <lb/>vicem, ac virtutem &longs;ubeant. </s> </p> <p id="N15281" type="main"> <s id="N15283">Quod vt <expan abbr="palã">palam</expan> omnino fiat, <lb/><expan abbr="di&longs;tinguendũ">di&longs;tinguendum</expan> in primis e&longs;t in­<lb/>ter orbiculos &longs;uperioris, & <pb pagenum="174" xlink:href="005/01/182.jpg"/>inferioris trochleæ, <expan abbr="quandoquid&etilde;">quandoquidem</expan> <expan abbr="nõ">non</expan> <expan abbr="vterq.">vterque</expan> idem genus ve­<lb/>ctis exprimit, aut participat. </s> <s id="N152A4">Si igitur <expan abbr="orbiculũ">orbiculum</expan> trochleæ &longs;u­<lb/>perioris, hoc e&longs;t &longs;upernè appen&longs;æ con&longs;ideremus, eam ratio­<lb/>nem vèctis obtinere comperiemus, quam participat etiam <lb/>libra æqualium brachiorum, nempe, cuius fulcimentum in­<lb/>ter pondus, & potentiam collocatur. </s> <s id="N152B3">Porrò diameter or­<lb/>biculi orizonti parallela FG longitudinem vectis refert, <lb/>axiculus verò qui in centro e&longs;t vbi H, fulcimentum. </s> <s id="N152BA">Deinde <lb/>diametri extremum F à quo pondus cum inferiori trochlea <lb/>per funem propendet, vectis extremum exprimit, cui onus <lb/>e&longs;t alligatum. </s> <s id="N152C3">Alterum verò diametri extremum G, vectis <lb/>extremum de&longs;ignat, cui virtus mouentis applicatur. </s> </p> <p id="N152C8" type="main"> <s id="N152CA">At &longs;i orbiculum inferioris trochleæ con&longs;iderare velimus, <lb/>aliam in eo vectis ratione deprehendemus; illam vtique <lb/>cuius fulcimentum con&longs;tituitur in altero extremo, pondus <lb/>verò in medio, vt 1. par. </s> <s id="N152D3">tex. <!-- REMOVE S-->8. Additione 1 explicuimus. <lb/></s> <s id="N152D9">Etenim ex duobus eius diametri extremis IK, alterum nem­<lb/>pe K fulcitur à fune, cui veluti immobiliter innititur, eo <lb/>quod ip&longs;a &longs;u&longs;tineatur in D. <!-- KEEP S--></s> <s id="N152E1">Alterum verò extremum I &longs;ur­<lb/>&longs;um attollitur ver&longs;us F per motum eiu&longs;dem funis ibi vim <lb/>præcipuam imprimentis. </s> <s id="N152E8">Pondus denique C propendet ex <lb/>medio vbi L, <expan abbr="ibiq.">ibique</expan> propterea grauitat inter fulcimentum, & <lb/>potentiam attollentem. </s> <s id="N152F3">Ex quibus con&longs;tat, <expan abbr="vtriu&longs;q;">vtriu&longs;que</expan> trochleæ <lb/>orbiculos vectis rationem habere, &longs;ed non eandem. </s> </p> <p id="N152FC" type="main"> <s id="N152FE">Quod &longs;i quæras quæ nam ex his duabus trochleis maius <lb/>potentiæ mouenti auxilium præ&longs;tet. </s> <s id="N15303">Re&longs;pondetur, &longs;uperio­<lb/>rem trochleam non tam auxilium, quàm commoditatem, <lb/>ac facilitatem ad trahendum illi præbere. </s> <s id="N1530A">Vt enim patet ex <lb/>Guido Vbaldo de trochlea propo&longs;itione prima, beneficio <lb/>ip&longs;ius trochleæ &longs;uperioris &longs;upernè videlicet appen&longs;æ quan­<lb/>do potentia æqualis e&longs;t ponderi inferius alligato, nullatenus <lb/>eleuare illud poterit, cum ita &longs;e habeat, ac &longs;i aliud e&longs;&longs;et ap­<lb/>pen&longs;um pondus, æquale ponderi prædicto cum æquali di­<lb/>&longs;tantia à centro, &longs;iue axiculo, circa quem diameter orbiculi <lb/>non &longs;ecus ac libra conuertitur, vt clarius videre e&longs;t in hac <lb/>figura, in qua linea AB diametrum referat orbiculi ABC <pb pagenum="175" xlink:href="005/01/183.jpg"/>de&longs;cripta circa axiculum C, nam &longs;i funis ex vtroque dia­<lb/>metri extremo à centro æquidi&longs;tanti propendeat, & hinc <lb/>pondus D, illinc potentia E æqualiter præmat, idem erit, ac <lb/><figure id="id.005.01.183.1.jpg" xlink:href="005/01/183/1.jpg"/><lb/>&longs;i in libra æqualibus prædita <lb/>brachijs æqualia pondera ap­<lb/>pendantur, quorum vnum, alte­<lb/>rum per proprium de&longs;cen&longs;um <lb/>eleuare non po&longs;&longs;et, cum actio <lb/>debeat e&longs;&longs;e ab inæquali propor­<lb/>tione, vt docet idem Ari&longs;t. <!-- KEEP S--></s> </p> <p id="N1533B" type="main"> <s id="N1533D">Quare tota vis quæ adiungi­<lb/>tur potentiæ, pondus aliquod <lb/>eleuanti prædictarum trochlea­<lb/>rum beneficio, petenda e&longs;t ex <lb/>trochlea inferiori. </s> <s id="N15348">Etenim cum <lb/>alterum <expan abbr="extremũ">extremum</expan> funis orbicu­<lb/>lo huius trochleæ circumdu­<lb/>cti, in &longs;uperiori ligno firmiter &longs;u­<lb/>&longs;pen&longs;o &longs;it religatum; alterum <lb/>verò à potentia &longs;u&longs;tineatur, vel traha­<lb/>tur, pondus quod ex ip&longs;ius trochlea <lb/>pendet, qua&longs;i diui&longs;um, partim à ligno <lb/>&longs;uperiori, ac partim à potentia trahen­<lb/>te &longs;u&longs;tentatur, vt optimè demon&longs;trat <lb/>Guidus Vbaldus propo&longs;it. </s> <s id="N15363">2. & Baldus <lb/>in hac quæ&longs;t. </s> <s id="N15368"><expan abbr="videreq.">videreque</expan> e&longs;t in &longs;equenti <lb/>figura. </s> </p> <p id="N15370" type="main"> <s id="N15372">Quoniam &longs;i trochlea ABC &longs;u&longs;pen­<lb/>datur per funem eius orbiculo cir­<lb/>cumductum, cuius vnum <expan abbr="extremũ">extremum</expan> &longs;it <lb/>in D &longs;tabiliter alligatum, alterum verò <lb/>à potentia in E con&longs;tituta &longs;u&longs;tineatur; <lb/>ac pondus F ab ip&longs;a inferiori parte <lb/>trochleæ vbi B propendeat &longs;ubliga­<lb/>tum, pondus ip&longs;um <expan abbr="totũ">totum</expan>, non quidem <lb/>à &longs;ola potentia E, nec à &longs;olo &longs;u&longs;ten<pb pagenum="176" xlink:href="005/01/184.jpg"/>taculo D &longs;u&longs;tineri intelligetur, &longs;ed &longs;imul ab vtroque, ita <lb/>vt dimidium, alterutri re&longs;pondeat virtuti. </s> <s id="N15395">Quo fit vt cum <lb/>potentia ad pondus attollendum, ip&longs;a inferiori trochlea vti­<lb/>tur tanquam vecte non paruam virtutem ab ip&longs;a trochlea <lb/>mutuetur, <expan abbr="nõ">non</expan> &longs;ecus ac à vecte, cuius alterum extremum fir­<lb/>miter alicubi &longs;it innixum, ad eleuandum pondus, quod ex <lb/>eius medio pendeat, vt con&longs;tare pote&longs;t in de&longs;cripto vecte <lb/><figure id="id.005.01.184.1.jpg" xlink:href="005/01/184/1.jpg"/><lb/>ABC, cuius extre­<lb/>mum C fulciatur in <lb/>D, extremum verò <lb/>A &longs;it à <expan abbr="pot&etilde;tia">potentia</expan> ele­<lb/>uandum, & ex pun­<lb/>cto medio B <expan abbr="prop&etilde;-deat">propen­<lb/>deat</expan> onus <expan abbr="alligatũ">alligatum</expan>, <lb/>quod &longs;it ip&longs;um E. <lb/><!-- KEEP S--></s> <s id="N153CA">Nam & &longs;i pondus <lb/>potentiæ vires excederet, <expan abbr="duplamq.">duplamque</expan> ferè proportionem ha­<lb/>beret re&longs;pectu earum, omnino tamen beneficio vectis tolle­<lb/>retur, cum dimidium tantùm illius ip&longs;i potentiæ re&longs;ponde­<lb/>ret. </s> <s id="N153D9">Quod &longs;i plures orbiculi in ip&longs;a inferiori trochlea con­<lb/>tineantur, idem fiet, ac &longs;i totidem vectibus eiu&longs;dem rationis <lb/>idem pondus ab eadem potentia moueatur. </s> <s id="N153E0">Nam cum &longs;in­<lb/>gulis pariter onus leuandum impartiri debeat, quò plures <lb/>fuerint rotulæ &longs;icut vectes, eò minus potentiæ ad leuandum <lb/>propria virtute relinquitur, ac propterea minor, ac minor <lb/>virtus in trahente requiritur iuxta numerum rotularum. </s> </p> <p id="N153EB" type="main"> <s id="N153ED">Cæterum in qua &longs;igillatim proportione ad multiplicatio­<lb/>nem ip&longs;arum rotularum in inferioribus trochleis, augeatur <lb/>virtus mouentis, vel pondus imminuatur, &longs;umendum e&longs;t ex <lb/>codem Guido Vbaldo, & alijs, qui hac de re ex profe&longs;&longs;o, ac <lb/>fu&longs;iùs tractant; cum ad explicationem, & confirmationem <lb/>doctrinæ Ari&longs;totelis, &longs;ufficiat o&longs;tendi&longs;&longs;e, qua ratione, & via <lb/>id po&longs;&longs;it contingere. </s> <s id="N153FC">Et &longs;i quis multiplicatis trochleis, &longs;u­<lb/>culis, ac vectibus, vt hic idem Philo&longs;ophus ait, magna vide­<lb/>rit pondera eb exigua virtute moueri, aut eleuari, de&longs;inat <lb/>admirari. </s> <s id="N15405">Nam & ore tantum perflando vidi pondus tre-<pb pagenum="177" xlink:href="005/01/185.jpg"/>centorum quinquaginta axium, & eius loco hominem &longs;tan­<lb/>tem &longs;uper tabulam dimoueri, trochleis, ac &longs;cytalis, axeque <lb/>in paruo peritrochio adhibitis, quod idem vnciali pondere <lb/>præponderante contigerat, vt vtrumque cernere e&longs;t in <lb/>&longs;ub&longs;trata figura. </s> </p> <figure id="id.005.01.185.1.jpg" xlink:href="005/01/185/1.jpg"/> <p id="N1541A" type="head"> <s id="N1541C">Quæ&longs;tio Decimanona.</s> </p> <p id="N1541F" type="main"> <s id="N15421">C<emph type="italics"/>vr &longs;i quis &longs;uper lignum magnam imponat <lb/>&longs;ecurim, <expan abbr="de&longs;uperq.">de&longs;uperque</expan> illi magnum adijciat pon­<lb/>dus, ligni quippiam, quod curandum &longs;it, non <lb/>diuidit: &longs;i verò &longs;ecurim extollens percutiat, <lb/>illud &longs;cindit, cùm alioqui multò minus ha­<lb/>beat ponderis id, quod percutit, quàm id quod <lb/>&longs;uperiacet, & premit? </s> <s id="N15437">An quia omnia cum motu fiunt, & <lb/>graue ip&longs;um, grauitatis magis a&longs;&longs;umit motum dum mouetur, <lb/>quàm dum quie&longs;cit. </s> <s id="N1543E">Incumbens igitur connatam graui mo­<lb/>tionem non mouetur, motum verò & &longs;ecundum hanc moue­<lb/>tur, & &longs;ecundum eam, quæ est percutientis. </s> <s id="N15445">Præterea &longs;e-<emph.end type="italics"/><pb pagenum="178" xlink:href="005/01/186.jpg"/><emph type="italics"/>curis ip&longs;a efficitur cuneus. </s> <s id="N15451">Paruus autem exi&longs;tens cuneus <lb/>magna diuidit, cùm ex duobus &longs;it vectibus, contrario ad &longs;e in­<lb/>uicem modo constitutis.<emph.end type="italics"/></s> </p> <p id="N1545A" type="head"> <s id="N1545C">COMMENTARIVS.<!-- KEEP S--></s> </p> <p id="N15460" type="main"> <s id="N15462">Tam quæ&longs;tionis propo&longs;itio quàm dubitandi ratio <lb/>per &longs;e e&longs;t manife&longs;ta, ex quo nimirum contingat, vt <lb/>&longs;i quis &longs;uper lignum magnam imponat &longs;ecurim, <expan abbr="de-&longs;uperq.">de­<lb/>&longs;uperque</expan> ingens illi adijciat pondus, nihil con&longs;ideratione di­<lb/>gnum, aut alicuius momenti diuidat; &longs;i verò &longs;ecurim ip&longs;am <lb/>extollens percutiat, illud &longs;cindat, etiam &longs;i multo minus illa <lb/>habeat ponderis, quam id quod &longs;uperiacet, ac præmit. <lb/></s> <s id="N15476">Quod profecto ex eo euenire docet, quia cum omnia motu <lb/>fiant, & graue ip&longs;um maiorem grauitatem acquirat per mo­<lb/>tum, magis etiam mouet dum mouetur, quàm dum quie­<lb/>&longs;cit. </s> <s id="N1547F">Quare licet maior &longs;it grauitas innata totius incumben­<lb/>tis oneris quod præmit, nempe &longs;ecuris cum &longs;uperadiecto <lb/>pondere, quàm &longs;it &longs;olius motæ &longs;ecuris; nihilominus dum <lb/>prius elata &longs;ecuris deijcitur, non modò operatur per inna­<lb/>tam &longs;ibi grauitatem, &longs;ed per eam, quam in ip&longs;o motu acqui­<lb/>rit, & per impetum à percutiente impre&longs;&longs;um. </s> <s id="N1548C">Vnde mirum <lb/>non e&longs;t, &longs;i tune efficacius percutiat, ac ita percutiendo <lb/>&longs;cindat lignum, quod percutit. </s> <s id="N15493">Præ&longs;&longs;io namque oneris <lb/>ab vna tantum cau&longs;a grauitante &longs;ine locali motu proce­<lb/>dit; percu&longs;&longs;io verò &longs;ecuris à duplici, vel triplici cau&longs;a im­<lb/>pellente, à qua mixtus quidam, violenti&longs;simus efficitur <lb/>motus. </s> </p> <p id="N1549E" type="main"> <s id="N154A0">Quod autem motus penderi addat pondus, &longs;eu grauitas <lb/>augeatur in motu, ac propterea efficacius operetur, explo­<lb/>rati&longs;simum e&longs;t, non modo in ijs, quæ cadunt ex alto (nam <lb/>quò magis à principio motus di&longs;ce&longs;&longs;erint, eò velocius ip&longs;a <lb/>deor&longs;um ferri con&longs;picimus, <expan abbr="magisq.">magisque</expan> impellere non &longs;ecus ac <lb/>corpora grauiora;) &longs;ed in reliquis quoque motibus proie­<lb/>ctorum, quorum pondus magis operatur in motu, quam in-<pb pagenum="179" xlink:href="005/01/187.jpg"/>quiete, <expan abbr="magisq.">magisque</expan> in velociori motu, quàm in tardiori. </s> <s id="N154BC">Quam­<lb/>uis in rigore loquendo virtus illa grauium, quæ augetur in <lb/>motu, non &longs;it eadem propriè ip&longs;a grauitas per maiorem in­<lb/>tentionem &longs;ui ip&longs;ius, &longs;eu acqui&longs;itionem aliorum graduum <lb/>eiu&longs;dem qualitatis in &longs;pecie, &longs;ed potius &longs;it impetus ip&longs;orum, <lb/>grauium, vel à proijciente impre&longs;&longs;us, vel per ip&longs;am grauita­<lb/>tem de&longs;cendentis oneris in eodem onere productus dum <lb/>præceps fertur ad ima, ac &longs;ucce&longs;siuè in &longs;e impetum au­<lb/>get. </s> <s id="N154CF">Quamobrem in motu &longs;ecuris tendentis deor&longs;um ad <lb/>&longs;cindendum aliquod lignum, vterque impetus prædictus <lb/>concurrit, nempe & ille, qui à &longs;cindente fuit impre&longs;&longs;us, & <lb/>is qui ab ip&longs;a grauitate in de&longs;cen&longs;u producitur, ac &longs;ucce&longs;­<lb/>&longs;iuè &longs;emper augetur. </s> <s id="N154DA">Quod tamen non ita &longs;e habet dum <lb/>ligna non &longs;cinduntur per motum deor&longs;um, &longs;ed &longs;ur&longs;um ad­<lb/>mouendo, ac vibrando ip&longs;am &longs;ecurim, vt ad amputandum <lb/>ramum ex arbore; Nam tunc non intercedit ni&longs;i &longs;olus im­<lb/>petus admouentis; & iccirco diximus huiu&longs;modi motum <lb/>&longs;ecuris à duplici, vel triplici cau&longs;a procedere; cum gra­<lb/>uitas innata &longs;emper ad ip&longs;am percu&longs;sionem, aut inci&longs;io­<lb/>nem concurrat &longs;icut impetus impre&longs;&longs;us ab incidente; im­<lb/>petus verò à grauitate productus, vel auctus, tantum­<lb/>modo in de&longs;cen&longs;u, hoc e&longs;t cum ad &longs;cindendum tendit <lb/>deor&longs;um. </s> </p> <p id="N154F1" type="main"> <s id="N154F3">Omninò autem quilibet motus &longs;ecuris, prout mos e&longs;t <lb/>illam in &longs;cindendo adhibere, validi&longs;simus etiam con&longs;titui­<lb/>tur ex ip&longs;a circulatione quam efficit. </s> <s id="N154FA">Nam ex hac maior <lb/>velocitas, & ex maiori velocitate efficacior ictus proce­<lb/>dit. </s> <s id="N15501">Tanto enim fortius corpus quodlibet in aliud impin­<lb/>git, quantò celerius fertur, ac magis eius moles agitatur. <lb/></s> <s id="N15507">Celerius autem fertur &longs;ecuris per motum circularem, ma­<lb/>gi&longs;que agitatur, quàm quolibet alio motu; Alioquin &longs;i <lb/>rectà, verbi gratia moueretur &longs;imul cum manu, tantùm <lb/>&longs;pacij percurreret eodem tempore, quantum ip&longs;a manus; <lb/>vt &longs;i &longs;ecuris ex loco A &longs;imul ac manus manubrio appli­<lb/>cata ex loco B, rectà de&longs;cenderent ver&longs;us lineam CD <pb pagenum="180" xlink:href="005/01/188.jpg"/><figure id="id.005.01.188.1.jpg" xlink:href="005/01/188/1.jpg"/><lb/>paralellam ip&longs;i AB <lb/>ad <expan abbr="percuti&etilde;dum">percutiendum</expan> li­<lb/>gnum infra ip&longs;am <lb/>lineam collocatum <lb/>in E. <!-- KEEP S--></s> <s id="N1552C">Mouerentur <lb/>enim per latera op­<lb/>po&longs;ita <expan abbr="eiu&longs;d&etilde;">eiu&longs;dem</expan> <expan abbr="para-lellogrãmi">para­<lb/>lellogrammi</expan> ABCD, <lb/>quæ &longs;unt æqualia. <lb/></s> <s id="N15540">At &longs;i &longs;ecuris non <lb/>rectà, &longs;ed circulari­<lb/>ter moueatur, vt <lb/>mos e&longs;t illam à <lb/>&longs;cindentibus agitari, multò maius &longs;patium in eodem tem­<lb/>pore percurret quàm manus, eo quod magis di&longs;taret à <lb/>centro, circa quod ambæ conuerterentur. </s> <s id="N1554F">Etenim &longs;iue <lb/>centrum huius motionis circularis con&longs;tituatur in ver­<lb/>tebra vbi manus, &longs;eu palma iungitur cubito, &longs;iue in iunctura, <lb/>qua cubitus iungitur brachio, aut qua brachium iungitur <lb/>humero; &longs;emper tantum &longs;ecuris excedet di&longs;tantiam manus <lb/>à centro, quanta fuerit longitudo manubrij, in cuius extre­<lb/>mo ip&longs;a &longs;ecuris con&longs;tituitur; <expan abbr="proindeq.">proindeque</expan> tantundem &longs;patium, <lb/>quod percurrit &longs;ecuris, excedet &longs;patium eodem tempore <lb/>peragratum à manu. </s> <s id="N15566">Cum igitur quæ eadem vi commota <lb/>inæquali <expan abbr="t&etilde;pore">tempore</expan> maius <expan abbr="percurrũt">percurrunt</expan> <expan abbr="&longs;patiũ">&longs;patium</expan>, velocius <expan abbr="moueãtur">moueantur</expan>, <lb/>apertè <expan abbr="cõ&longs;equitur">con&longs;equitur</expan>, &longs;ecurim <expan abbr="ipsã">ipsam</expan> velocius ferri motu circula­<lb/>ri, quàm recto ab eadem vi percutientis <expan abbr="cõmotam">commotam</expan>: ac pro­<lb/>pterea vltra <expan abbr="impetũ">impetum</expan> ip&longs;i à percutiente impre&longs;&longs;um, magnam <lb/>&longs;ibi ad &longs;cindendum ex tali velocitate efficaciam vendicare. </s> </p> <p id="N15593" type="main"> <s id="N15595">Accedit, quia ip&longs;emet impetus aptius imprimitur per <lb/>motum circularem, <expan abbr="magisq.">magisque</expan> con&longs;eruatur in illo, vt ob&longs;erua­<lb/>re licet in rotis, quæ facilius mouentur, ac diu circumuol­<lb/>uuntur po&longs;t impul&longs;um acceptum; & in pilis, quæ longius <lb/>rotando feruntur, quàm corpora, quæ non mouentur in gy­<lb/>rum. </s> <s id="N155A6">Deinde aptius in particulari imprimitur impetus per <pb pagenum="181" xlink:href="005/01/189.jpg"/>circularem motum &longs;ecuris, quia in tali motu eius manu­<lb/>brium, vectis vicem &longs;ubit, cuius alterum extremum, quod <lb/>latet in manu, fulcitur vbi complicantur digiti minores in <lb/>ip&longs;i&longs;met digitis minoribus; alterum verò mouet ip&longs;am &longs;e­<lb/>curim tanquam pondus ei alligatum, & pars quæ inter pol­<lb/>licem, & indicem continetur, &longs;u&longs;cipit impul&longs;um ab eodem <lb/>indice tanquam à potentia monente. </s> <s id="N155BA">Vt videre e&longs;t in de­<lb/>&longs;cripto manubrio AB, cuius alterum extremum fulcitur <lb/><figure id="id.005.01.189.1.jpg" xlink:href="005/01/189/1.jpg"/><lb/>in A qua&longs;i tanquam in centro &longs;ui motus; alterum verò pro­<lb/>mouet &longs;ecurim in B: & pars vbi C, impul&longs;um recipit à <lb/>potentia motrice tendentem in D. <!-- KEEP S--></s> <s id="N155CC">Quo fit vt ip&longs;um manu­<lb/>brium tanquam vectis, ac &longs;emidiameter circulariter mouea­<lb/>tur, <expan abbr="efficiatq.">efficiatque</expan> arcum, &longs;eu lineam BE. <!-- KEEP S--></s> <s id="N155D8">Quamuis contingat <lb/>vltimum extremum A aliquantulum retrocedere ver&longs;us <lb/>F, eo quod fulcimentum non &longs;it omnino &longs;tabile, nec po&longs;sit <lb/>ei tam exactè ip&longs;um extremum manubrij applicari. </s> <s id="N155E1">Cum <lb/>itaque omnia, quæ vectis vicem obtinent, ac circulariter &longs;uo <lb/>innixa fulcimento cientur, apti&longs;simè virtutem, &longs;eu impul­<lb/>&longs;um à mouente recipiant, &longs;equitur vt hac etiam ratione &longs;e­<lb/>curis ip&longs;a per motum circularem magnam vim ad &longs;cinden­<lb/>dum adipi&longs;catur. </s> </p> <pb pagenum="182" xlink:href="005/01/190.jpg"/> <p id="N155F2" type="main"> <s id="N155F4">Rur&longs;us accedit, quod intra latitudinem &longs;patij, quo ma­<lb/>nus mouere pote&longs;t &longs;ecurim, illud maximum erit &longs;patium, <lb/>quod circumeundo ab ip&longs;a vnà cum &longs;ecuri complectitur. <lb/></s> <s id="N155FC">Cumque mobile quodlibet quanto maius &longs;patium percur­<lb/>rit, tanto maiorem &longs;ibi vindicet efficaciam &longs;ui motus, vt pro­<lb/>batum e&longs;t, dummodo impetus illi impre&longs;&longs;us non de&longs;inat ne­<lb/>que langue&longs;cat; hinc fit, vt efficacius per motum circula­<lb/>rem, quàm per alium &longs;ecuris mota impingat atque per­<lb/>cutiat. </s> </p> <p id="N15609" type="main"> <s id="N1560B">Cæterum Ari&longs;toteles aliam &longs;ubiungit cau&longs;am &longs;ci&longs;sionis, <lb/>quæ fit per &longs;ecurim. </s> <s id="N15610">Quia nimirum dum &longs;ecuris lignum &longs;cin­<lb/>dit, con&longs;tituitur veluti cuneus, vt ex propria eius figura, & <lb/>ex modo, quo intimè &longs;e&longs;e in&longs;inuando diuidit, pote&longs;t com­<lb/>prehendi. </s> <s id="N15619">E&longs;t enim &longs;ecuris, vt ait Baldus, vel malleus cu­<lb/>neatus, vel cuneus malleatus manubrio in&longs;ertus; <expan abbr="operaturq.">operaturque</expan> <lb/>&longs;icut cuneus cum manubrio motus. </s> <s id="N15624">Paruus autem exi&longs;tens <lb/>cuneus magnam diuidit molem, cum ex duobus &longs;it vecti­<lb/>bus compactus, contrario ad &longs;e&longs;e inuicem modo con&longs;titu­<lb/>tis, vt &longs;upra &longs;uo loco explicuimus quæ&longs;t. </s> <s id="N1562D">17. </s> </p> <p id="N15630" type="main"> <s id="N15632">Quæ autem dicta &longs;unt de &longs;ecuri, eadem accommodari <lb/>po&longs;&longs;unt ad malleum clauam en&longs;em, bipennem runcam, <expan abbr="cæ-teraq.">cæ­<lb/>teraque</expan> in&longs;trumenta, quæ impul&longs;o accepto percutiunt, diui­<lb/>dunt, &longs;cindunt, vel &longs;imilia munera obeunt. </s> <s id="N1563F">Maximè autem <lb/>omnium ad &longs;tipites loratos, qui communiter ad enuclean­<lb/>dum triticum in area ab agriculis adhibentur. </s> <s id="N15646">Hi enim im­<lb/>petu accepto per motum circularem incredibili vehemen­<lb/>tia ac virtute percutiunt. </s> <s id="N1564D">Porrò cum alter ex alterius extre­<lb/>mitate cui loris alligatur liberè pendeat, ac per ip&longs;um tan­<lb/>quam per manubrium &longs;atis procerum circulariter agitetur, <lb/>longè à centro, quod e&longs;t in iunctura lacerti cum humero <lb/>percutientis, &longs;uum qua&longs;i circulum perficit; <expan abbr="proindeq.">proindeque</expan> citi&longs;­<lb/>&longs;imè fertur, vnde & validi&longs;simè ferit, ac percutit. </s> <s id="N1565E">Iuxta <lb/>quam rationem colligitur, quod & experientia comproba­<lb/>tur prædicta omnia in&longs;trumenta maximam, ac præcipuam <lb/>virtutem &longs;ortiri in extremo, quod magis di&longs;tat à centro &longs;ui <lb/>motus. </s> </p> <pb pagenum="183" xlink:href="005/01/191.jpg"/> <p id="N1566D" type="main"> <s id="N1566F">Nec ob&longs;tat, quod Baldus adducit ad probandum ictum <lb/>ex en&longs;e, efficaciorem e&longs;&longs;e à parte, quæ e&longs;t circa medium, ex <lb/>eo quod ibi con&longs;tituatur centrum grauitatis, ac propterea <lb/>cu&longs;pis non ni&longs;i dimidium ponderis habeat re&longs;pectu illius. <lb/></s> <s id="N15679">Nam licet pondus cuiu&longs;libet in&longs;trumenti multum conducat <lb/>ad validiorem percu&longs;sionem, vt patet in malleo, & in claua, <lb/>cuius caput propterea efficitur maius: Nihilominus præ­<lb/>&longs;ertim in en&longs;e runca, & alijs procerioribus in&longs;trumentis, non <lb/>tam attenditur pondus ip&longs;ius partis ferientis, quàm di&longs;tan­<lb/>tia à centro &longs;ui motus, ex qua prouenit maior velocitas, & <lb/>efficacitas ictus ip&longs;ius. </s> <s id="N15688">Et planè &longs;i quæramus centrum gra­<lb/>uitatis in en&longs;e, nec circa medium en&longs;is illud reperire fas erit, <lb/>&longs;ed potius prope capulum, vel manubrium, vt ob&longs;eruanti <lb/>patebit, ex qua parte euidenti&longs;simum e&longs;t, non procedere <lb/>ictum validiorem. </s> </p> <p id="N15693" type="main"> <s id="N15695">Quod &longs;i en&longs;is ictus facilius euitetur, aut euadatur cum <lb/>quis en&longs;i obuiet ver&longs;us cu&longs;pidem, quàm cum in medio; hoc <lb/>prouenit ex eo quod pars illa cum magis di&longs;tet à centro, &longs;i­<lb/>cut facilius mouetur, &longs;ic etiam facilius diuertatur, tanquam <lb/>vectis, cuius fulcimentum centrum con&longs;tituitur in manu <lb/>gladiatoris. </s> <s id="N156A2">Deinde ob&longs;eruandum e&longs;t, non cedere <expan abbr="&longs;ecun-dũ">&longs;ecun­<lb/>dum</expan> propriam contrarietatem, ita vt facilè euitetur ictus de­<lb/>&longs;cendens per ictum a&longs;cendentem, aut re&longs;i&longs;tentiam illi ex di­<lb/>recto oppo&longs;itam; &longs;ed ex latere, remouendo ad latus ip&longs;am <lb/>cu&longs;pidem de&longs;cendentem, nempe dextror&longs;um, vel &longs;ini&longs;tror­<lb/>&longs;um. </s> <s id="N156B3">Quandoquidem impetus ita e&longs;t determinatus ad vnam <lb/>po&longs;itionem ex vi &longs;uæ impre&longs;sionis, vt non &longs;u&longs;cipiat contra­<lb/>rietatem ni&longs;i ab oppo&longs;ita. </s> <s id="N156BA"><expan abbr="Proindeq.">Proindeque</expan> idem ferè e&longs;t, moue­<lb/>re dextror&longs;um, vel &longs;ini&longs;tror&longs;um ip&longs;am cu&longs;pidem circumlati <lb/>en&longs;is de&longs;cendentem, & &longs;tantem, vel quie&longs;centem, eo quod <lb/>tali dimotio non apponatur directè ip&longs;i de&longs;cen&longs;ui, ad quem <lb/>impetus natura &longs;ua e&longs;t determinatus. </s> </p> <pb pagenum="184" xlink:href="005/01/192.jpg"/> <p id="N156CC" type="head"> <s id="N156CE">Quæ&longs;tio Vige&longs;ima.</s> </p> <p id="N156D1" type="main"> <s id="N156D3">C<emph type="italics"/>vr &longs;tatera qua carnes ponderantur, paruo ap­<lb/>pendiculo magna trutinat onera cùm alioqui <lb/>tota dimidiata exi&longs;tat libra<gap/>vbi enim onus im­<lb/>ponitur &longs;olùm &longs;u&longs;penditur lanx: in altera <lb/>verò parte &longs;ola est &longs;tatera. </s> <s id="N156E3">An quia &longs;imul li­<lb/>bra & vectem ip&longs;am contingit e&longs;&longs;e &longs;tateram? <lb/></s> <s id="N156E9">libram quidem, vbi &longs;partorum quodcumque &longs;tatera fit cen­<lb/>trum: in altera enim parte lancem, in altera autem pro lance <lb/>æquipondij appendiculum habet, quod libræ incumbit, ceu &longs;i <lb/>quis alteram apponeret lancem, & illi pondus imponeret. </s> <s id="N156F2">Ma­<lb/>nife&longs;tum enim quod tantundem trahit ponderis ei, quod in al­<lb/>tera iacet lance. </s> <s id="N156F9">Quemadmodum autem &longs;i vna libra multæ <lb/>&longs;int libræ, &longs;ic talia in&longs;unt &longs;parta multa in eiu&longs;modi libra, <lb/>quorum vniu&longs;cuiusque quod intrin&longs;ecus e&longs;t ad appendiculum, <lb/>&longs;tateræ e&longs;t dimidium: & omnino i&longs;thuc libra e&longs;t, vnam qui­<lb/>dem habens lancem, in qua pondus appenditur: alteram ve­<lb/>rò vbi id &longs;tatera æquipondium. </s> <s id="N15706">Quamobrem appendiculum <lb/>ad alteram &longs;ui partem e&longs;t &longs;tatera. </s> <s id="N1570B">Huiu&longs;modi autem exi­<lb/>&longs;tens multæ &longs;unt libræ, totque quot fuerint &longs;parta. </s> <s id="N15710">Semper <lb/>autem quod lanci propinquius e&longs;t &longs;partum, <expan abbr="appensòq.">appensòque</expan> oneri, <lb/>maius trahit pondus, quoniam fit quidem omnis &longs;tatera in­<lb/>uer&longs;us vectis<gap/>, hypornochlion namque vnumquodque &longs;par­<lb/>tum &longs;upernè exi&longs;tens, pondus verò id quod lanci ine&longs;t. </s> <s id="N15721">Quan­<lb/>tò autem productior vectis fuerit longitudo ab ip&longs;o hypomo­<lb/>chlio, tantò ibi quidem facilius mouet, hic autem æquilibrium <lb/>facit, pondu&longs;que &longs;tateræ trutinat, quod ad æquipondij vergit ap­<lb/>pendiculam.<emph.end type="italics"/></s> </p> <p id="N1572E" type="head"> <s id="N15730">COMMENTARIVS.<!-- KEEP S--></s> </p> <p id="N15734" type="main"> <s id="N15736">Cau&longs;am hic inquirit Ari&longs;toteles, ob quam in &longs;tatera <lb/>paruo appendiculo magna leuentur, ac trutinentur <lb/>pondera; Cum quippe &longs;tatera nonni&longs;i libra quæ­<lb/>dam e&longs;&longs;e videatur, licet qua&longs;i dimidiata, vtpotè quæ ex <lb/>altera tantum parte lancem pendentem habeat, ex altera <lb/>verò di&longs;currens quoddam appendiculum æquipondij. </s> <s id="N15743">Vt <pb pagenum="185" xlink:href="005/01/193.jpg"/>videre e&longs;t in de&longs;cripta &longs;tatera AB &longs;u&longs;pen&longs;a in C ex cuius <lb/>extremo A pendet lanx D, & ex B appendiculum E. <lb/><!-- KEEP S--></s> <s id="N1574F">Etenim &longs;icut libra æqualia duntaxat ponderibus onera le­<lb/><figure id="id.005.01.193.1.jpg" xlink:href="005/01/193/1.jpg"/><lb/>uat, ac trutinat; ita &longs;imiliter &longs;tatera, cum libra quædam <lb/>&longs;it, æqualia tantùm appendiculo onera videtur po&longs;&longs;e leua­<lb/>re; quod &longs;ecus experimur contingere. </s> <s id="N1575E">Nam paruæ molis <lb/>appendiculo, magna videmus onera extolli, ac men&longs;u­<lb/>rari. </s> </p> <p id="N15765" type="main"> <s id="N15767">Mox deinde cau&longs;am ip&longs;am in eo docet con&longs;i&longs;tere, quòd <lb/>&longs;tatera, libræ &longs;imul ac vectis rationem induat, ac vtriu&longs;que <lb/>vicem obtineat. </s> <s id="N1576E">Libræ nimirum, quia reuera e&longs;t veluti iu­<lb/>gum tran&longs;uer&longs;um, &longs;eu ha&longs;ta bilancis ex puncto qua&longs;i medio <lb/>&longs;u&longs;pen&longs;a, atque vtrinque ponderibus pendentibus librata <lb/>circa ip&longs;um punctum <expan abbr="intermediũ">intermedium</expan>. Quo &longs;u&longs;penditur tanquam <lb/>circa centrum, vel axem. </s> <s id="N1577F">Qamuis enim &longs;tatera con&longs;titua­<lb/>tur ex inæqualibus brachijs, & ex altero tantum lanx vna <lb/>propendeat; vel certè loco lancis vnci nonnulli demittan­<lb/>tur, qui mercibus, aut rebus ponderandis compacti, eas non <lb/>minus commodè &longs;u&longs;tinent, vt in &longs;ubiecta figura. </s> <s id="N1578E">Ex altero <pb pagenum="186" xlink:href="005/01/194.jpg"/>verò nonni&longs;i appendiculum æquipondij &longs;u&longs;pen&longs;um depen­<lb/>deat: Semper tamen ip&longs;a &longs;tatera libram refert, cum eius <lb/>axis, ac fulcimentum &longs;it inter onus, & æquipondium, <expan abbr="ip&longs;iusq.">ip&longs;iusque</expan> <lb/><figure id="id.005.01.194.1.jpg" xlink:href="005/01/194/1.jpg"/><lb/>æquipondij appendiculum, alterius lancis, vel vnci cum <lb/>pondere vicem &longs;ubeat; &longs;iue ip&longs;um fulcimentum, aut &longs;par­<lb/>tum con&longs;tituatur in puncto omnino medio, &longs;iue &longs;ecus, vnde <lb/>prouenit inæqualitas brachiorum, cum hæc libræ naturam <lb/>non auferat, nec immutet, vt diximus &longs;uo loco. </s> </p> <p id="N157AE" type="main"> <s id="N157B0"><expan abbr="Rur&longs;umq.">Rur&longs;umque</expan> vectis pariter naturam &longs;imul &longs;ortitur &longs;tatera, <lb/>quia fulcimentum habet vbi incumbit in axe, &longs;eu &longs;parto, <lb/>quod idem e&longs;t, ac punctum vnde &longs;u&longs;penditur, & circa quod <lb/>ip&longs;a conuertitur, <expan abbr="pondusq.">pondusque</expan> leuandum con&longs;tituitur merces <lb/>in lancem inuecta, vel vncis infixa; & potentia mouens, ip­<lb/>&longs;um appendiculum æquipondij. </s> <s id="N157C4">Cum igitur ea &longs;it vectis, ac <lb/>libræ natura <expan abbr="propriaq.">propriaque</expan> conditio,<gap/> cum alterum eius à ful­<lb/>cimento brachium longius protenditur, vt in &longs;tatera contin­<lb/>git, paruo in ip&longs;ius extremitate adhibito pondere, magnam <lb/>valeat molem ex altero breuiori brachio pendentem attol­<lb/>lere, iuxta proportionem vtriu&longs;que di&longs;tantiæ à centro, vt <pb pagenum="187" xlink:href="005/01/195.jpg"/>alibi demon&longs;trauimus; planum profecto relinquitur, qua <lb/>ratione, paruo appendiculo in &longs;tatera, magna leuari po&longs;&longs;int <lb/>pondera, vt intendebat Philo&longs;ophus. <!-- KEEP S--></s> </p> <p id="N157E1" type="main"> <s id="N157E3">Quoniam verò in præfato di&longs;cur&longs;u &longs;emel atque iterum <lb/>Ari&longs;toteles docuit, &longs;tateram e&longs;&longs;e veluti libram, in qua plures <lb/>&longs;int libræ, ac totidem quot fuerint &longs;parta, hinc Blancanus <lb/>conijcit, apud Pri&longs;cos, &longs;tateram ex multis trutinis, &longs;eu &longs;par­<lb/>tis compactam fui&longs;&longs;e, paribus interuallis per totam longi­<lb/>tudinem ip&longs;ius &longs;tateræ di&longs;&longs;eminatis; Ex quibus &longs;ingulis <lb/>prout pondus po&longs;tulabat, illa &longs;u&longs;penderetur, appendiculo <lb/>&longs;emper in extremitate &longs;ui brachij immoto manente; It aut <lb/>tantum mercis lanci imponeretur, quantum appendiculo <lb/>æquiponderaret, iuxta <expan abbr="&longs;ituation&etilde;">&longs;ituationem</expan> cuiu&longs;libet trutinæ. </s> <s id="N157FC"><expan abbr="Proin-deq.">Proin­<lb/>deque</expan> &longs;ingulæ trutinæ ad aliquod determinatum mercium <lb/>pondus trutinandum fuerint con&longs;titutæ. </s> <s id="N15806">Atque de hac ve­<lb/>teri &longs;tatera putat Ari&longs;totelem locutum fui&longs;&longs;e, de eaque &longs;o­<lb/>lum verificari, quod &longs;e habeat tanquam libra, quæ plures <lb/>contineat libras. </s> <s id="N1580F">Nam tot erunt libræ quot &longs;parta, quæ di­<lb/>uer&longs;as proportiones libræ con&longs;tituunt, atque adeo veluti <lb/>diuer&longs;as omnino libras. </s> </p> <p id="N15816" type="main"> <s id="N15818">Verumenimuerò non &longs;atis id colligitur ex Ari&longs;totele, nec <lb/>videtur nece&longs;&longs;arium ad verificandum dictum illud eiu&longs;dem <lb/>Philo&longs;ophi. </s> <s id="N1581F">Quandoquidem etiam &longs;tatera prout modò apud <lb/>no&longs;trates e&longs;t in v&longs;u, ex duplici &longs;altem trutina &longs;olet con&longs;tare, <lb/>vna quæ loco vnde lanx pendet e&longs;t propior, altera verò <lb/>quæ aliquantulum e&longs;t remotior, & in oppo&longs;ito, &longs;eu inuer&longs;o <lb/>&longs;tateræ latere locatur: Ac per propiorem vtique onera ma­<lb/>iora, per remotiorem verò minora con&longs;ueuerunt librari; li­<lb/>bero &longs;emper manente appendiculo, vt per reliquum &longs;tateræ <lb/>brachium iuxta exigentiam ponderis di&longs;currere valeat. <lb/></s> <s id="N15831">Quamobrem hac quoque in &longs;tatera contineri videntur plu­<lb/>res libræ, cum &longs;altem duplex in ea trutina reperiatur, quæ <lb/>tanquam duplex libra de&longs;eruit ad maiora, vel minora one­<lb/>ra aptius ponderanda, & vt eadem &longs;ecundum maiores, vel <lb/>minores differentias ponderum quando opus fuerit innote­<lb/>&longs;cant. </s> <s id="N15840">Et quidem cum Ari&longs;toteles ait: ac &longs;i vna libra multæ <pb pagenum="188" xlink:href="005/01/196.jpg"/>&longs;int libræ, eo quod in ea in&longs;int &longs;parta multa: forta&longs;&longs;e idem <lb/>intellexit per multa, vel multas, ac plura, vel plures; cum no­<lb/>men Græcum <foreign lang="greek">pollo\s</foreign> vtrumque &longs;ignificet, & à Cicerone <lb/><foreign lang="greek">w_olla\</foreign> in Timæo Platonis vertatur plures. </s> <s id="N15855">Ni&longs;i etiam cum <lb/>Baldo rectè dixerimus, &longs;tateram tot libras con&longs;titui, quot <lb/>&longs;unt tran&longs;lationes appendiculi de loco ad locum; quia toties <lb/>variatur proportio, <expan abbr="proindeq.">proindeque</expan> etiam libra. </s> <s id="N15862">Quare gratis ad <lb/>exponenda verba Ari&longs;totelis putat Blancanus &longs;tateræ ap­<lb/>pendiculum apud veteres fui&longs;&longs;e immobile, <expan abbr="ip&longs;amq.">ip&longs;amque</expan> &longs;tateram <lb/>ex tot &longs;partis, &longs;eu trutinis con&longs;ta&longs;&longs;e, quot erant metienda <lb/>pondera: Quamuis alioquin id non fuerit impo&longs;&longs;ibile, &longs;ed <lb/>laborio&longs;um duntaxat, & inutile. </s> </p> <p id="N15873" type="main"> <s id="N15875">Diximus, non impo&longs;&longs;ibile: Nam quolibet in lance onere <lb/>impo&longs;ito, e&longs;t adinuenire centrum grauitatis totius &longs;tateræ <lb/>&longs;ic con&longs;titutæ, ex quo &longs;i ip&longs;a per trutinam &longs;u&longs;pendatur, <lb/>&longs;tabit <expan abbr="æquiponderabitq.">æquiponderabitque</expan> appendiculum immobile ip&longs;i one­<lb/>ri in lance impo&longs;ito. </s> <s id="N15884">Vnde &longs;ingula puncta longitudinis &longs;ta­<lb/>teræ con&longs;titui po&longs;&longs;unt centra grauitatis re&longs;pectu diuer&longs;orum <lb/>onerum imponibilium, ac in quolibet illorum poterit truti­<lb/>na locari, quæ ad determinatum &longs;uum onus librandum de­<lb/>&longs;eruiat. </s> <s id="N1588F">Diximus tamen hoc e&longs;&longs;e laborio&longs;um, & inutile, <lb/>tum quia difficilius e&longs;t multiplicare trutinas, <expan abbr="ip&longs;amq.">ip&longs;amque</expan> totam <lb/>&longs;tateram diuer&longs;is ex punctis &longs;u&longs;pendere ad quamlibet oneris <lb/>differentiam digno&longs;cendam, cum &longs;ola appendiculi mobili­<lb/>tate, atque di&longs;cur&longs;u id con&longs;equi po&longs;&longs;it: tum etiam quia ad <lb/>pauciora onera libranda, <expan abbr="paucioresq.">paucioresque</expan> admodum ponderum <lb/>differentias percipiendas de&longs;eruire po&longs;&longs;et ip&longs;a huiu&longs;modi <lb/>&longs;tatera. </s> <s id="N158A8">Cum certè multiplicari trutinæ non valeant ad nu­<lb/>merum linearum, aut denticulorum, in quos modò diuer­<lb/>&longs;um e&longs;t brachium &longs;tateræ, & in quos di&longs;currens appendicu­<lb/>lum pro opportunitate transfertur, vt &longs;ingulis notis, &longs;eu li­<lb/>neis, &longs;ingula onera trutinentur, ac determinatè quodlibet <lb/>eorum pondus di&longs;tincti&longs;&longs;imè innote&longs;cat. </s> </p> <p id="N158B5" type="main"> <s id="N158B7">Addit autem Ari&longs;toteles quòd quantò propinquius one­<lb/>ri in lance, vel vncis appen&longs;o &longs;partum con&longs;tituitur, tanto <lb/>magis onus ip&longs;um, &longs;eu maius onus valet &longs;tatera leuare. </s> <s id="N158BE">Id <pb pagenum="189" xlink:href="005/01/197.jpg"/>quod experientia con&longs;tat, & ea ratione ab eodem Philo&longs;o­<lb/>pho probatur, quia cum <expan abbr="&longs;partũ">&longs;partum</expan> con&longs;tituatur hypomochlion, <lb/>&longs;eu fulcimentum talis vectis, nempe &longs;tateræ; <expan abbr="tantoq.">tantoque</expan> faci­<lb/>lius vectis beneficio onera leuentur, quantò productior fue­<lb/>rit vectis longitudo à fulcimento; hinc fit, vt &longs;parto magis <lb/>ad <expan abbr="locũ">locum</expan> vnde onus dependet appropinquato, maior vectis <lb/><expan abbr="lõgitudo">longitudo</expan> relinquatur <expan abbr="v&longs;q;">v&longs;que</expan> ad <expan abbr="appendiculũ">appendiculum</expan>, <expan abbr="faciliusq.">faciliusque</expan> propte­<lb/>rea ip&longs;um <expan abbr="appendiculũ">appendiculum</expan> valeat in maiori di&longs;tantia <expan abbr="æquipõde-rare">æquiponde­<lb/>rare</expan>, <expan abbr="maioraq.">maioraque</expan> onera trutinare: permutata videlicet <expan abbr="ponderũ">ponderum</expan>, <lb/>ac <expan abbr="brachiorũ">brachiorum</expan> proportione, vt ex Archimede lib. 1. æquipon­<lb/>derantium propo&longs;it.6. & &longs;equenti; necnon ex <expan abbr="eod&etilde;">eodem</expan> Ari&longs;to­<lb/>tele &longs;up. </s> <s id="N1590F">quæ&longs;t. </s> <s id="N15912">3. in vniuer&longs;um agendo de vecte retulimus. </s> </p> <p id="N15915" type="head"> <s id="N15917">Quæ&longs;tio Vige&longs;imaprima.</s> </p> <p id="N1591A" type="main"> <s id="N1591C">C<emph type="italics"/>vr medici facilius dentes extrahunt denti­<lb/>forcipis onere adiecto, quàm &longs;i &longs;ola vtantur <lb/>manu? </s> <s id="N15926">An quia ex mana magis, quàm ex den­<lb/>tiforcipe lubricus elabitur dens? </s> <s id="N1592B">An ferro id <lb/>potius accidit, quàm digitis, quoniam vndique <lb/>dentem non comprehendunt, quod mollis di­<lb/>gitorum facit caro, adhæret enim & complectitur magis. </s> <s id="N15934">An <lb/>quia dentiforcipes duo &longs;unt contrarij vectes, vnicum habentes <lb/>hypomochlion, eius &longs;cilicet in&longs;trumenti connexionem? </s> <s id="N1593B">Hoc <lb/>igitur ad extractionem vtuntur organo, vt facilius moueant. <lb/></s> <s id="N15941">Sit dentiforcipis alterum quidem extremum vbi e&longs;t A; alterum <lb/>autem quod extrahit, B, vectis autem vbi A D F, alter verò <lb/>vectis vbi BCE, hypomochlion autem CGD, connexio verò <lb/>vbi G, dens autem pondus. </s> <s id="N1594A">Vtroque igitur B & F &longs;imul com­<lb/>prehendentes mouent: quomodo autem commotus fuerit, faci­<lb/>lius manu trahitur, quàm instrumento.<emph.end type="italics"/></s> </p> <p id="N15953" type="head"> <s id="N15955">COMMENTARIVS.<!-- KEEP S--></s> </p> <p id="N15959" type="main"> <s id="N1595B">Qværitur in præ&longs;enti ab Ari&longs;totele, ex quo nam pro­<lb/>ueniat, vt facilius dentes extrahantur denti&longs;orcipis <lb/>adhibito in&longs;trumento, quàm &longs;ola manu, immediata <lb/>opera digitorum. </s> <s id="N15964">Ac primò ex eo, inquit videri po&longs;&longs;e, id or-<pb pagenum="190" xlink:href="005/01/198.jpg"/>tum habere, quòd cum dens lubricus in &longs;e &longs;it, magis for­<lb/>&longs;an è manu quæ leuis, & mollis e&longs;t, quàm ex rudi, ac tenaci<lb/>forcipe elabatur. </s> <s id="N15970"><expan abbr="Statimq.">Statimque</expan> hanc ip&longs;am rationem impugnat, <lb/>ac penitus euertit, inquiens, potius ferro, quàm digitis con­<lb/>tingere, vt dens ab illis apprehen&longs;us, propter &longs;ui lubricita­<lb/>tem aufugiat. </s> <s id="N1597C">Quandoquidem ferrum, &longs;eu ferrei dentiforci­<lb/>pes, minus quàm digiti <expan abbr="vndiq.">vndique</expan> dentem valent comprehen­<lb/>dere. </s> <s id="N15987">Mollis enim digitorum caro cedendo, ac flectendo <lb/>&longs;e&longs;e, adhæret, & complectitur magis quàm ferrum præ &longs;ua <lb/>duritie, ac in flexibilitate. </s> <s id="N1598E">Vnde perperam huiu&longs;modi Ari&longs;to­<lb/>telis verba intelligunt cum ij, qui ea tanquam in confirma­<lb/>tionem prioris rationis, aut &longs;olutionis dicta exponunt: tum <lb/>etiam qui ex oppo&longs;ito, ea ip&longs;a propo&longs;itam qu&etail;&longs;tionis &longs;uppo­<lb/>&longs;itionem arbitrantur de&longs;truere. </s> <s id="N15999">Etenim non &longs;uppo&longs;itioni, & <lb/>experientiæ a&longs;&longs;umptæ, &longs;ed priori duntaxat opponuntur &longs;olu­<lb/>tioni, vt vidimus, <expan abbr="rationemq.">rationemque</expan> dubitandi non mediocriter au­<lb/>gent, vt magis ea, <expan abbr="quã">quam</expan> traditurus e&longs;t vera &longs;olutio eluce&longs;cat. </s> </p> <p id="N159AA" type="main"> <s id="N159AC">Soluit igitur Ari&longs;toteles <expan abbr="quæ&longs;tion&etilde;">quæ&longs;tionem</expan> dicens, id ex eo con­<lb/>tingere, quòd in dentiforcipe duo continentur vectes &longs;ibi in­<lb/>uicem contrarij, videlicet ip&longs;a dentiforcipis brachia, quorum <lb/>vnicum e&longs;t commune hypomochlion, nempe ip&longs;a vtriu&longs;que <lb/>connexio, parisque alterius ad <expan abbr="alterũ">alterum</expan> inf<gap/>exio, qua <expan abbr="inuic&etilde;">inuicem</expan> ob­<lb/>uiantur. </s> <s id="N159C7">Proindeq, <expan abbr="horũ">horum</expan> <expan abbr="vectiũ">vectium</expan> virtute arctius, ac validius, <lb/>quàm digitis <expan abbr="dent&etilde;">dentem</expan> per&longs;tringi, <expan abbr="faciliusq.">faciliusque</expan> <expan abbr="cõ&longs;equenter">con&longs;equenter</expan> auelli. </s> </p> <p id="N159E0" type="main"> <s id="N159E2">Sit enim dentiforcipis in&longs;trumentum AB, quod dentem <lb/><expan abbr="quid&etilde;">quidem</expan> comprehen­<lb/>dat, & con&longs;tringat <lb/><figure id="id.005.01.198.1.jpg" xlink:href="005/01/198/1.jpg"/><lb/>per &longs;ui extremum <lb/>B. </s> <s id="N159F6">Vectis autem <lb/>vnus &longs;it brachium <lb/>BC. <!-- KEEP S--></s> <s id="N159FE">Alter verò <lb/>AD &longs;uffulti in con­<lb/>nexione qua&longs;i axe <lb/><expan abbr="vtriu&longs;q;">vtriu&longs;que</expan> vbi E. <!-- KEEP S--></s> <s id="N15A0B">Pon­<lb/>du&longs;que &longs;it ip&longs;um <lb/>dens F. <!-- KEEP S--></s> <s id="N15A13">Vtroque <pb pagenum="191" xlink:href="005/01/199.jpg"/>igitur vecte &longs;imul admoto per extrema BD ip&longs;um dentem <lb/>tanquam onus in contrarium repellendo, validi&longs;&longs;imè con­<lb/>&longs;tringent adhibita, &longs;cilicet manu in AC, qua extremum <lb/>A compellatur ver&longs;us C, & extremum C ver&longs;us A. <!-- KEEP S--></s> <s id="N15A22">Dens <lb/><expan abbr="aut&etilde;">autem</expan> ita con&longs;trictus facilè dimouetur, ac dimotus extrahi­<lb/>tur. </s> </p> <p id="N15A2C" type="main"> <s id="N15A2E">Hæc ferè Ari&longs;toteles, quæ tamen vt rectè Baldus ob&longs;er­<lb/>uat, con&longs;trictionem potius, quam dimotionem, & ab&longs;tractio­<lb/>nem dentis demon&longs;trant. </s> <s id="N15A35">Addendum ergo erit dentem <lb/>dentiforcipe con&longs;trictum, vnà cum ip&longs;o in&longs;trumento alium <lb/>quendam con&longs;tituere vectem, ac &longs;i e&longs;&longs;et vnum continuum, <lb/>cuius longitudo in præ&longs;enti erit ADF, vel CDF. </s> <s id="N15A3E">Si enim <lb/>attentè con&longs;ideretur, pr&etail;ter con&longs;trictionem, non datur alius <lb/>motus dentiforcipis ad dentem, &longs;eu re&longs;pectu dentis, &longs;ed &longs;i­<lb/>mul cum illo, nempe ambo tanquam vnicum corpus ad <lb/>modum vectis mouentur. </s> <s id="N15A49">Cuius fulcimentum e&longs;t in parte <lb/>gingiuæ vbi dens primò ex illa emergit, & in &longs;ua conuer&longs;io­<lb/>ne innititur, vt in D. <!-- KEEP S--></s> <s id="N15A51">Pondus verò con&longs;tituitur gingiuæ <lb/>pars re&longs;i&longs;tens ex oppo&longs;ito circa dentis radicem vbi B. </s> <s id="N15A56">Cum <lb/>igitur parua &longs;it di&longs;tantia à fulcimento D ad extremum F; <lb/>magna verò ab eodem fulcimento D ad alterum eiu&longs;dem <lb/>vectis extremum A, vel C: hinc fit, vt immoto manente <lb/>puncto D facilè ad motum circularem AC ver&longs;us G; ex­<lb/>tremum F moueatur in oppo&longs;itum etiam circulariter ver­<lb/>&longs;us B. </s> <s id="N15A65">Et &longs;ic dimota dentis radice ex proprio loco, dens <lb/>totus per dentiforcipem extrahatur. </s> <s id="N15A6A">Quod difficile e&longs;&longs;et <lb/>ab&longs;que illo &longs;ola manu præ&longs;tari. </s> <s id="N15A6F">Quippe cum digiti nec tam <lb/>tenaciter dentem apprehendere, nec ita vnum veluti corpus <lb/>oblongum, ac ten&longs;um cum eo po&longs;&longs;int componere; quod to­<lb/>tum vnius vectis rationem &longs;ubeat. </s> </p> <p id="N15A78" type="main"> <s id="N15A7A">Quocirca admittenda non erunt, quæ Baldus aliter Phi­<lb/>lo&longs;ophus hac in re profert, quamuis acutè fuerint excogita­<lb/>ta, cum ait, dentiforcipis partium, quibus dens apprehendi­<lb/>tur, eam quæ longior e&longs;t, potentiæ mouentis loco &longs;uccede­<lb/>re, breuiorem verò fulcimentum con&longs;titui: Quandoquidem <lb/>in v&longs;u dentiforcipis ad extrahendum dentem etiam prout <pb pagenum="192" xlink:href="005/01/200.jpg"/>ab ip&longs;o explicatur, fulcimentum non pote&longs;t con&longs;titui in ip&longs;a <lb/>breuiori dentiforcipis parte, qua apprehenditur dens; tum <lb/>quia hæc &longs;imul cum altera parte mouetur, licet per mino­<lb/>rem circulationem, quæ &longs;anè fit circa punctum illud gingi­<lb/>uæ, cui in ab&longs;tractione conuertendo &longs;e&longs;e innititur dens, & à <lb/>quo &longs;emper dentiforcipis extremum aliquantulum di&longs;tat, <lb/>eo quod nequeat ad illam v&longs;que partem gingiuæ interio­<lb/>rem, ac &longs;olidam vbi huiu&longs;modi fit nixus pertingere: tum, <lb/>etiam quia e&longs;to pars ip&longs;a breuior per &longs;ui extremum non, <lb/>moueretur ad motum alterius, &longs;ed quie&longs;ceret, non propte­<lb/>rea &longs;equeretur con&longs;titui fulcimentum huius motionis. </s> <s id="N15AA0">Nam <lb/>punctum cuiu&longs;libet vectis corre&longs;pondens puncto fulcimen­<lb/>ti cui innititur, penetratur cum illo, & &longs;imul cum illo quie­<lb/>&longs;cit in motione ip&longs;iusmet vectis; & tamen non pote&longs;t con­<lb/>&longs;titui fulcimentum &longs;uæ propriæ motionis. </s> <s id="N15AAB">Nimirum quia, <lb/>nihil in &longs;eip&longs;o pote&longs;t fulciri, &longs;ed &longs;emper inter fulcimentum, <lb/>& &longs;uffultum ea debet e&longs;&longs;e di&longs;tinctio, quæ e&longs;t inter mobile, <lb/>& immobile, vel commotum, & immotum. </s> <s id="N15AB4">Quare cum, <lb/>con&longs;titutum ex dente, ac forcipe &longs;e habeat per <expan abbr="modũ">modum</expan> vnius <lb/>vectis, non &longs;ecus ac &longs;i e&longs;&longs;et vnicum corpus continuum, <lb/>etiam &longs;i <expan abbr="&longs;ecundũm">&longs;ecundum</expan> punctum aliquod &longs;ibi intrin&longs;ecum quie­<lb/>&longs;ceret, ac circa illud &longs;ecundum reliquas &longs;ui partes circulari­<lb/>ter moueretur; Non propterea po&longs;&longs;et illi tanquam proprio <lb/>fulcimento in &longs;ua ip&longs;ius motione inniti. </s> <s id="N15ACB">Potius igitur fulci­<lb/>mentum con&longs;tituendum e&longs;t extrin&longs;ecum, in ea gingiuæ par­<lb/>te, quam de&longs;crip&longs;imus vbi dens ip&longs;e in auul&longs;ione fulcitur, ac <lb/>præmit, <expan abbr="doloremq.">doloremque</expan> infert non minus, quam vbi ex oppo&longs;ito <lb/>dimotæ eius radici re&longs;i&longs;titur. </s> </p> <p id="N15ADA" type="main"> <s id="N15ADC">In calce tandem huius quæ&longs;tionis Ari&longs;toteles &longs;ubnectit, <lb/>dentem commotum facilius manu &longs;ola quàm in&longs;trumento <lb/>&longs;imul auferri. </s> <s id="N15AE3">Quod &longs;anè intellexerim habita ratione ad <lb/>dolorem, quem in dentis ab&longs;tractione qui&longs;que vitare, aut <lb/>&longs;altem minuere intendit; ita vt facilitas ad commoditatem <lb/>patientis, non autem ad ab&longs;olutam effectus con&longs;ecutionem <lb/>referatur. </s> <s id="N15AEE">Quo &longs;en&longs;u id ex eo videtur probari, quoniam &longs;i <lb/>&longs;emel dens fuerit commotus, & à po&longs;itione &longs;uæ &longs;edis dimo-<pb pagenum="193" xlink:href="005/01/201.jpg"/>tus, non modò &longs;olis digitis poterit &longs;impliciter auelli, non, <lb/>minus ac &longs;imul adhibito in&longs;trumento; &longs;ed etiam commo­<lb/>dius, ac facilius, dolorem &longs;cilicet penitus, vel maiori ex par­<lb/>te vitando, eo quod digiti &longs;entire &longs;ecus, ac dentiforcipis <lb/>ferrum, & &longs;uperare magis valeant pro opportunitate ali­<lb/>qualem dentis re&longs;i&longs;tentiam. </s> <s id="N15B02">Alioquin ab&longs;olutè loquendo <lb/>nulla habita ratione ad dolorem, ip&longs;um dentiforcipis in&longs;tru­<lb/>mentum, &longs;icut maiorem præualet &longs;uperare dentis re&longs;i&longs;ten­<lb/>tiam firmiter inhærentis; ita & multo magis minorem, vt <lb/>cum iam ille à propria &longs;ede dimotus debiliter tantum gin­<lb/>giuæ inhæret. </s> </p> <p id="N15B0F" type="head"> <s id="N15B11">Quæ&longs;tio Vige&longs;ima&longs;ecunda.</s> </p> <p id="N15B14" type="main"> <s id="N15B16">C<emph type="italics"/>vr nuces ab&longs;que ictu facilè confringuntur in­<lb/>strumentis, qua ad eum fiunt v&longs;um. </s> <s id="N15B1E">Multum <lb/>enim aufertur virium, motionis &longs;cilicet & vio­<lb/>lentia. </s> <s id="N15B25">Praterea duro & graui comprimens in­<lb/>&longs;trumento citiùs confringet, quàm ligneo & <lb/>leui. </s> <s id="N15B2C">An quia &longs;ic vtrunque à duobus compri­<lb/>mitur vectibus ip&longs;a nux, à vecte autem facilè <lb/>diuelluntur onera? </s> <s id="N15B33">Id enim instrumentum ex duobus com­<lb/>ponitur vectibus, idem habentibus bypomochlion, connexio­<lb/>nem videlicet ip&longs;am, vbi est A, quemadmodum igitur fue­<lb/>ro diducta &longs;ecundum extrema molis CD, ip&longs;æ FE &longs;ic à par­<lb/>ua faciliter potentia conducuntur, quod igitur cum percu&longs;sio­<lb/>ne feci&longs;&longs;et pondus id valentiores illæ EC, & FD vectes effi­<lb/>eiunt. </s> <s id="N15B42">Eleuatione enim in contrarium elati, & comprimentes <lb/>frangunt vbi e&longs;t K. <!-- KEEP S--></s> <s id="N15B48">Hanc etiam ob cau&longs;am quanto vicinius <lb/>fuerit K ip&longs;um A, confringitur celerius. </s> <s id="N15B4D">Quantò enim ab bipo­<lb/>mochlio plus di&longs;tat vectis, facilius & plus mouet ab codem <lb/>potentia. </s> <s id="N15B54">E&longs;t igitur A quidem bipomochlion: ip&longs;a autem DAF <lb/>vectis, & item ip&longs;a CAE. </s> <s id="N15B59">Quantò igitur ip&longs;um K vicinius <lb/>fuerit angulo ip&longs;ius A, tantò vicinius fit connexioni, vbi est <lb/>A, hoc autem tpomochlion, ab eadem igitur potentia appli­<lb/>cante FE plus extolli nece&longs;&longs;e e&longs;t. </s> <s id="N15B62">Quamobrem quoniam ex <lb/>contario e&longs;t eleuatio, nece&longs;&longs;e e&longs;t magis comprimi, quod autem <lb/>comprimitur magis, citius frangitur.<emph.end type="italics"/></s> </p> <pb pagenum="194" xlink:href="005/01/202.jpg"/> <p id="N15B6F" type="head"> <s id="N15B71">COMMENTARIVS.<!-- KEEP S--></s> </p> <p id="N15B75" type="main"> <s id="N15B77">Præ&longs;ens quæ&longs;tio circa &longs;imile admodum in&longs;trumentum <lb/>ver&longs;atur, ac præcedens, quamuis ad diuer&longs;um om­<lb/>nino effectum natura &longs;ua ordinatum. </s> <s id="N15B7E">Quærit enim <lb/>Philo&longs;ophus quo fiat, vt nuces ab&longs;que ictu, facilè in&longs;tru­<lb/>mento ad id opus fabrefacto, confringantur: quod &longs;anè in­<lb/>&longs;trumentum forcipi &longs;imillimum, & ex ligneis regulis com­<lb/>pactum ip&longs;e videtur &longs;upponere. </s> <s id="N15B89">Eamque mox rationem <lb/>dubitandi affert; quia ab&longs;que ictu ac violenta aliqua per­<lb/>cu&longs;&longs;ione, remi&longs;&longs;ius ab&longs;olutè quam cum illa corpus compri­<lb/>mitur; impetus namque ictus aut percu&longs;&longs;ionis vires maxi­<lb/>mè auget in ip&longs;amet motione, ad comprimendum acrius <lb/>quod percutitur, vt hactenus explicuimus. </s> <s id="N15B96">Quare non tam <lb/>facilè præfato <expan abbr="in&longs;trum&etilde;to">in&longs;trumento</expan> ab&longs;que ictu nuces confringi po&longs;&longs;e <lb/>viderentur, &longs;icut cum malleo adacto impetu confringuntur. <lb/></s> <s id="N15BA2">Id quod præterea ex eo confirmat, quia graui ac duro in­<lb/>&longs;trumento, vt e&longs;t ferreus malleus, citius, con&longs;entaneum e&longs;t, <lb/>fieri confractionem quàm ligneo ac leui, quale hoc de quo <lb/>agimus in præ&longs;enti &longs;upponitur. </s> </p> <p id="N15BAB" type="main"> <s id="N15BAD">Attamen ip&longs;e Philo&longs;ophus huiu&longs;modi difficultatem ac <lb/>dubitationem exeodem principio, quo præcedentem quæ­<lb/>&longs;tionem &longs;oluerat, apti&longs;&longs;imè ac breui&longs;&longs;imè diluit, inquiens, <lb/>explicatum in&longs;trumentum duobus brachijs tanquam duo­<lb/>bus vectibus contrarijs, ad &longs;e&longs;e inuicem conuer&longs;is con&longs;tare, <lb/>vnico fulcimento innixis, quod e&longs;t vtriu&longs;que connexio ac <lb/>veluti axis: duorum autem vectium compre&longs;&longs;ione, vt potè <lb/>qui magnam vim habeant comprimendi, æquè facile nuces <lb/>amygdalas, vel id genus alia confringi, ac ictu vel percu&longs;&longs;io­<lb/>ne cum impetu. </s> <s id="N15BC2">Quod vt ad oculos etiam pateat, con&longs;ti­<lb/>tuatur primo in&longs;trumentum ABCD, cuius brachia &longs;int AD <lb/>& CB &longs;uffulta in connexione vtriu&longs;que vbi E. <!-- KEEP S--></s> <s id="N15BCA">Nux verò <lb/><expan abbr="confring&etilde;da">confringenda</expan> locetur inter A & C vbi F, nempe inter extre­<lb/>ma brachiorum ea parte qua minus di&longs;tant à fulcimento. <lb/></s> <s id="N15BD5">Potentia verò confringentis applicetur in extremis ecrun­<lb/>dem brachiorum ea parte, qua magis di&longs;tant a fulcimento, <pb pagenum="195" xlink:href="005/01/203.jpg"/><figure id="id.005.01.203.1.jpg" xlink:href="005/01/203/1.jpg"/><lb/>tanquam in manubrijs, <expan abbr="nimirũ">nimirum</expan> in BD. <!-- KEEP S--></s> <s id="N15BEA">Con&longs;ideretur dein­<lb/>de vtrum que brachium tanquam duplicem vectem moueri <lb/>circa immotum fulcimentum E; ita vt ad motum B ver&longs;us <lb/>D, alterum extremum nempe C appropinquetur ad A; & è <lb/>conuer&longs;o, ad motum D ver&longs;us B, ip&longs;um A appropinquetur <lb/>ad C. <!-- KEEP S--></s> <s id="N15BF8">Tunc dicimus nucem, qu&etail; quidem tanquam pondus <lb/>ab vtroque extremo duplicis vectis AC pellitur ac repelli­<lb/>tur, facilè comprimi, ac tandem nimia compre&longs;&longs;ione con­<lb/>fringi, &longs;iquidem dum magis ac magis ip&longs;a extrema AC ad <lb/>inuicem appropinquantur, nece&longs;&longs;ariò quæ inter ip&longs;a interci­<lb/>pitur, nucem comprimunt, & comprimendo confringunt. </s> </p> <p id="N15C05" type="main"> <s id="N15C07">Addit autem primò Ari&longs;toteles, quo <expan abbr="lõgiora">longiora</expan> fuerint bra­<lb/>chia huius in&longs;trumenti à connexione ip&longs;orum &longs;eu <expan abbr="fulcim&etilde;to">fulcimento</expan> <lb/>ad extrema, quibus applicatur potentia: & ex alia parte, quo <lb/>breuiora eadem brachia fuerint à conexione &longs;eu <expan abbr="fulcim&etilde;to">fulcimento</expan> <lb/>ad nucem, eo facilius confractionem fieri; ac proinde à mi­<lb/>nori potentia, ita vt id ip&longs;um quod cum percu&longs;&longs;ione feci&longs;&longs;et <lb/>pondus, præ&longs;tetur à binis explicatis vectibus in contrarium <lb/>&longs;e&longs;e conantibus, & comprimentibus ip&longs;am nucem; cuius <lb/>re&longs;i&longs;tentia gerit vicem ponderis. </s> </p> <p id="N15C26" type="main"> <s id="N15C28">Secundo verò addit Ari&longs;toteles, eò <expan abbr="maior&etilde;">maiorem</expan> fieri vectium <lb/>&longs;eu brachiorum dilatationem, <expan abbr="quõ">quom</expan> propinquius fulcimento, <lb/>&longs;eu angulo connexionis eorum nux confringenda con&longs;titua­<lb/>tur, quia nimirum vterque angulus ad verticem ab illis <expan abbr="cõ-&longs;titutus">con­<lb/>&longs;titutus</expan>, per talem appropinquationem dilatatur (nempe <lb/>AEC. & BED.) & cum angulo ip&longs;a quoque brachia, quæ <lb/>angulum con&longs;tituunt, ita vt magis tunc di&longs;tare oporteat in­<lb/>ter &longs;e extrema AC, &longs;icut & DB, <expan abbr="cũ">cum</expan> maius &longs;it latus, quod &longs;ub <pb pagenum="196" xlink:href="005/01/204.jpg"/>maiori angulo &longs;ubtenditur, vt con&longs;tat ex 18. primi ele­<lb/>ment. </s> <s id="N15C50">Dilatatur autem magis ip&longs;e angulus AEC, & con­<lb/>&longs;equenter alius ad verticem BED; Nam quò propinquius <lb/>ei acce&longs;&longs;erit nucis magnitudo, cum qua con&longs;tituit veluti <lb/><expan abbr="triangulũ">triangulum</expan> AEC, eò minora &longs;eu breuiora <expan abbr="euadũt">euadunt</expan> duo latera, <lb/>quibus ip&longs;e angulus E continetur, prædictamque magnitu­<lb/>dinem tanquam ba&longs;im &longs;ubtendit. </s> <s id="N15C64">Duo autem latera &longs;uper <lb/>eandem ba&longs;im quanto minora &longs;unt, tanto <expan abbr="maior&etilde;">maiorem</expan> angulum <lb/><expan abbr="cõ&longs;tituunt">con&longs;tituunt</expan>, vt patet per vige&longs;imam <expan abbr="primã">primam</expan> primi. </s> <s id="N15C76">Magis ergo <lb/>dilatatis brachijs &longs;eu vectibus cum angulo <expan abbr="cõnexionis">connexionis</expan> <expan abbr="eorũ">eorum</expan>, <lb/>propter <expan abbr="maior&etilde;">maiorem</expan> <expan abbr="approximation&etilde;">approximationem</expan> nucis ad ip&longs;um validius, ac <lb/>facilius, vt docet Ari&longs;tot. <!-- KEEP S--><!-- REMOVE S--><expan abbr="pot&etilde;tia">potentia</expan> qu&etail; in extremis manubrijs <lb/>adhibetur, comprimere, atque adeò <expan abbr="cõfringere">confringere</expan> intelligetur. </s> </p> <p id="N15C9B" type="main"> <s id="N15C9D">Quæ quidem con&longs;equentia duplici ex capite pote&longs;t pro­<lb/>bari. </s> <s id="N15CA2">Primo quia dilatatis brachijs, di&longs;tantioribu&longs;que ex­<lb/>tremis eorum ab inuicem con&longs;titutis, ob maiorem propin­<lb/>quitatem nucis ad centrum, velocior po&longs;tea con&longs;equitur <lb/>motus compre&longs;&longs;ionis eorum. </s> <s id="N15CAB">Siquidem maiorem arcum in <lb/>eodem tempore eadem potentia per talem <expan abbr="motũ">motum</expan> de&longs;cribet. <lb/></s> <s id="N15CB5">Licet enim eadem &longs;it exten&longs;io, quæ deperditur per com­<lb/>pre&longs;&longs;ionem ex parte corporis compre&longs;&longs;i, aut confracti vbi­<lb/>cunque fiat ip&longs;a compre&longs;&longs;io, &longs;emper tamen quò propriùs <lb/>centro fit, & amplius brachia dilatata &longs;upponit, eo maiorem <lb/>arcum extrema brachiorum, in quibus applicatur potentia <lb/>comprimendo percurrunt. </s> </p> <figure id="id.005.01.204.1.jpg" xlink:href="005/01/204/1.jpg"/> <p id="N15CC7" type="main"> <s id="N15CC9">Sint <expan abbr="namq;">namque</expan> tanquam <lb/>brachia dilatata duæ <lb/>diametri AD, & CB <lb/>in circulo ABCD &longs;e&longs;e <lb/>inuicem <expan abbr="bifariã">bifariam</expan> inter­<lb/>&longs;ecantes, & connecten­<lb/>tes in <expan abbr="c&etilde;tro">centro</expan> E. <!-- KEEP S--></s> <s id="N15CE5">Exten­<lb/>&longs;io verò corporis con­<lb/>fring <expan abbr="&etilde;di">endi</expan>, quæ per <expan abbr="com-pre&longs;&longs;ion&etilde;">com­<lb/>pre&longs;&longs;ionem</expan> deperditur, <lb/>&longs;it &longs;patium AF, quod <pb pagenum="197" xlink:href="005/01/205.jpg"/>primò con&longs;tituatur inter extrema AC eorundem brachio­<lb/>rum. </s> <s id="N15CFF">Et à puncto F per centrum E ducatur recta FG, quæ <lb/>locum, vel&longs;itum de&longs;ignat, in quo con&longs;tituendum e&longs;t bra­<lb/>chium AD po&longs;t ip&longs;am compre&longs;&longs;ionem, ita vt extremum A <lb/>transferatur in F, & extremum D transferatur in G. <lb/><!-- KEEP S--></s> <s id="N15D0A">Tunc certè ip&longs;um extremum D per huiu&longs;modi tran&longs;latio­<lb/>nem, æqualem arcum, aut lineam de&longs;criberet ip&longs;i &longs;patio <lb/>AF. <!-- KEEP S--></s> <s id="N15D12">Siquidem æquales anguli ad centrum circuli, æquali­<lb/>bus arcubus in&longs;i&longs;tunt, vt patet per 26. tertij. </s> <s id="N15D17">Anguli autem <lb/>con&longs;tituti ad centrum E per ip&longs;as rectas AD, & FG, nem­<lb/>pe AEF, & GED, &longs;unt æquales per 15. primi, eo quod <lb/>&longs;int ad verticem. </s> <s id="N15D20">Quando igitur corpus <expan abbr="confringendũ">confringendum</expan> col­<lb/>locatur inter extrema <expan abbr="brachiorũ">brachiorum</expan> præfati in&longs;trumenti longi&longs;­<lb/>&longs;ime a centro, <expan abbr="tantũ">tantum</expan> &longs;patium in fractione percurrunt ip&longs;a ex­<lb/>trema, <expan abbr="quantũ">quantum</expan> alia oppo&longs;ita in quibus applicatur potentia. </s> </p> <p id="N15D39" type="main"> <s id="N15D3B">Quod fi corpus confringendum collocetur propinquius <lb/>centro, &longs;eu connexioni brachiorum E, ita vt exten&longs;io eius <lb/>AF, quæ per confractionem deperditur, con&longs;tituatur exem­<lb/>pli gratia in HI, A tran&longs;lato in H &longs;uper eandem lineam, <lb/>AD, & F in I ver&longs;us lineam CB; & per ip&longs;um punctum <lb/>I, & centrum E excitetur alia diagonalis KL, quæ pa­<lb/>riter de&longs;ignet locum, ac fitum quo transferri debet idem <lb/>brachium AD po&longs;t confractionem: Tunc maiorem ar­<lb/>cum inueniemus de&longs;cribitura in ip&longs;a compre&longs;&longs;ione extrema <lb/>DA, quam &longs;it &longs;patium HI, quod deperditur per illam. <lb/></s> <s id="N15D51">Quandoquidem A transferetur in K, & D in L: Spatium <lb/>autem DL continet &longs;patium DG, &longs;icut &longs;patium AK con­<lb/>tinet &longs;patium AF æquale ip&longs;i HI, quo propterea maius e&longs;t <lb/>ip&longs;um AK, & DL, quæ per rationem &longs;uprafactam &longs;unt <lb/>æqualia. </s> <s id="N15D5C">Rur&longs;us verò &longs;i excitetur linea recta à puncto A <lb/>ad punctum K, & con&longs;iderentur i&longs;ta duo triangula, nempe <lb/>HEI, & AEK, inuenientur habere latera proportionalia <lb/>circa eundem angulum E; ba&longs;esq &longs;imilis rationis per quar­<lb/>tam propo&longs;. </s> <s id="N15D67">&longs;exti. </s> <s id="N15D6A">Cumque ba&longs;is AK longioribus lineis <lb/>&longs;ubtendatur ip&longs;i angulo E, maior erit, quàm ba&longs;is HI ei­<lb/>dem angulo &longs;ubten&longs;a breuioribus lineis EH, & EI. </s> </p> <pb pagenum="198" xlink:href="005/01/206.jpg"/> <p id="N15D75" type="main"> <s id="N15D77">Quod autem exempli&longs;icauimus in brachio, &longs;eu vecte AD, <lb/>idem etiam procedit de brachio CB. <!-- KEEP S--></s> <s id="N15D7D">Et quod de brachijs <lb/>in m dio ad inuicem connexis, ac bifariam &longs;e&longs;e inter&longs;ecan­<lb/>tibus dictum e&longs;t, accommodari pote&longs;t in alijs nonita &longs;e ha­<lb/>bentibus &longs;eu alibi connexis. </s> <s id="N15D86">Nam &longs;emper verificabitur ad <lb/>maiorem approximationem corporis confringendi ad cen­<lb/>trum connexionis eorum, &longs;eu fulcimentum, magis ip&longs;a bra­<lb/>chia dilatari, maiu&longs;que deinde &longs;patium eodem tempore, <lb/>comprimendo percurrere, quod e&longs;t velocius agere, vnde & <lb/>validius colligitur fiangere, vt dicebamus ex Ari&longs;totele. <!-- KEEP S--></s> </p> <p id="N15D94" type="main"> <s id="N15D96">Alio verò ex capite eadem con&longs;equentia probatur, quia <lb/>cum vectis beneficio eandem proportionem habeat po­<lb/>tentia ad pondus leuandum, aut deprimendum, quam habet <lb/>eius di&longs;tantia à fulcimento ad di&longs;tantiam ponderis ab eo­<lb/>dem fulcimento, vt quæ&longs;t. </s> <s id="N15DA1">3. ex Ari&longs;totele, & Archimede <lb/>probauimus: quanto magis corpus confringendum ad pun­<lb/>ctum connexionis, &longs;eu axem E, quo vterque vectis huius <lb/>in&longs;trumentifulcitur, appropinquabitur; tanto maior erit ex­<lb/>ce&longs;&longs;us di&longs;tantiæ ip&longs;ius potentiæ motricis digitorum in ex­<lb/>tremis BD applicatis, re&longs;pectu di&longs;tantiæ ip&longs;ius nucis, aut <lb/>alterius corporis confringendi ab eodem puncto E. <expan abbr="Proin-deq.">Proin­<lb/>deque</expan> tanto maior pariter erit vis eiu&longs;dem potentiæ ad de­<lb/>primendum, vel confringendum in tali &longs;itus proportione <lb/>præ&longs;ertim cum duo concurrant vectes duplicantes &longs;uas vi­<lb/>res, quod erat Philo&longs;ophi intentum. </s> </p> <p id="N15DBC" type="head"> <s id="N15DBE">Quæ&longs;tio Vige&longs;imatertia.</s> </p> <p id="N15DC1" type="main"> <s id="N15DC3">C<emph type="italics"/>vr &longs;i duo extrema in rhombo puncta duabus <lb/>ferantur lat onibus, baudquaquam æquale <lb/>vtrumque eorum pertran&longs;it rectam, &longs;ed multò <lb/>plus alterum? </s> <s id="N15DCF">Idem autem e&longs;t &longs;ermo, cur quod <lb/>&longs;uper latus fertur, minus pertran&longs;it quam <lb/>ip&longs;um latus? </s> <s id="N15DD6">Illud enim diametrum minorem <lb/>boc vero maius latus. </s> <s id="N15DDB">Et hoc quidem vnica. </s> <s id="N15DDE">Il­<lb/>lud verò duabus fertur lationibus. </s> <s id="N15DE3">Feratur enim ex ip&longs;a AB, A<emph.end type="italics"/><pb pagenum="199" xlink:href="005/01/207.jpg"/><emph type="italics"/>quidem ad <expan abbr="ipsũ">ipsum</expan> B, B verò ad <expan abbr="ipsũ">ipsum</expan> D eadem celeritate. </s> <s id="N15DF7">Feratur <lb/><expan abbr="aut&etilde;">autem</expan> & ip&longs;a AB in ip&longs;i AC iuxta CD <expan abbr="ead&etilde;">eadem</expan> celeritate <expan abbr="cũ">cum</expan> illis. <lb/></s> <s id="N15E08">Nece&longs;&longs;e igitur e&longs;t A quidem in ip&longs;a AD diametro ferri, B verò <lb/>in ip&longs;a BC, & vtranque &longs;imul pertran&longs;i&longs;&longs;e, & ip&longs;am AB <expan abbr="ip&longs;ũ">ip&longs;um</expan> <lb/>latus AC: latum enim &longs;it ip&longs;um A ip&longs;am AE, AB autem ip&longs;am <lb/>AF, & proiecta &longs;it FG iuxta ip&longs;um AB, & ab ip&longs;o E &longs;imiliter <lb/>repleatur. </s> <s id="N15E17">Similiter igitur fit quod <expan abbr="repletũ">repletum</expan> e&longs;t, ip&longs;i toti: æqualis <lb/>igitur AF ip&longs;i AE. <!-- KEEP S--></s> <s id="N15E21">Ip&longs;a autem AB ip&longs;am AF lata erit: in dia­<lb/>metro igitur erit &longs;ecundum K, & &longs;emper nece&longs;&longs;e e&longs;t ip&longs;um fer­<lb/>ri &longs;ecundum diametrum, & &longs;imul AB latus pertran&longs;it latus <lb/>AC, & ip&longs;um A diametrum pertran&longs;it AD. <!-- KEEP S--></s> <s id="N15E2B">Similiter etiam <lb/>demon&longs;trabitur & ip&longs;um B in ip&longs;a BC diametrum lato, æqua­<lb/>lis enim e&longs;t ip&longs;a BE ip&longs;i BG. <!-- KEEP S--></s> <s id="N15E33">Repleto igitur ab ip&longs;o G quod in­<lb/>tus e&longs;t, toti e&longs;t &longs;imile, & ip&longs;um B in ip&longs;a diametro erit &longs;ecun­<lb/>dum laterum connexionem. </s> <s id="N15E3A">Et &longs;imul latus pertran&longs;it latus, & <lb/>B ip&longs;um BC diametrum. </s> <s id="N15E3F">Simul igitur Amultò plus ip&longs;a AB <lb/>pertran&longs;it, & ip&longs;um latus minus latus eadem lata teleritate: <lb/>& ip&longs;um latus maiorem quàm B pertran&longs;iuit vna <expan abbr="latũ">latum</expan> latio­<lb/>ne. </s> <s id="N15E4C">Quantò enim acutior fuerit rbombus, diameter quidem <lb/>minor fit, AC autem maior; latus verò ip&longs;ius BC minus. </s> <s id="N15E51">Ab­<lb/>&longs;urdum e&longs;t enim (vt dictum e&longs;t) id quod duabus fertur latio­<lb/>nibus, aliquando ferri tardius illo, quo fertur vnica, & vtri&longs;­<lb/>que po&longs;itis æquali velocitate punctis, alterum pertran&longs;ire ma­<lb/>iorem Cau&longs;a autem e&longs;t quoniam ei, quod ab obtu&longs;o fertur an­<lb/>gulo, ambæ ferè contrariæ fiunt lationes, & illa &longs;ecundum <lb/>quam ip&longs;um fertur, & illa &longs;ecundum quam ip&longs;um à latere de­<lb/>fertur. </s> <s id="N15E62">Ei autem quod ab acuto fertur, accidit vt ad idem fe­<lb/>ratur. </s> <s id="N15E67">Coadiuuat enim quæ ip&longs;ius e&longs;t lateris,, illam quæ e&longs;t &longs;u­<lb/>per diametrum. </s> <s id="N15E6C">Et quantò bunc quidem acutiorem feceris, <lb/>illum verò obtu&longs;um magis: bæc quidem tardior erit, illa verò <lb/>celerior. </s> <s id="N15E73">Hæ quidem igitur magis contrariæ fiunt, quoniam <lb/>obtu&longs;ior fit angulus: illæ verò ad idem magis, quoniam lineæ <lb/>coarctantur. </s> <s id="N15E7A">Ip&longs;um enim A ferè ad idem fertur &longs;ecundum <lb/>ambas lationes. </s> <s id="N15E7F">Coadiuuatur igitur altera & quantò &longs;anè <lb/>acutior fuerit angulus, tantò magis ip&longs;um A ad contrarium, <lb/>ip&longs;um enim ad B fertur, latus autem defert ip&longs;um ad D. <!-- KEEP S--></s> <s id="N15E87">Et <lb/>quantò &longs;anè obtu&longs;ior fuerit angulus, magis contrartæ fiunt <lb/>lationes, rectior enim efficitur linea. </s> <s id="N15E8E">Si autem omnino recta <lb/>fieret penitus vtique e&longs;sent contrariæ. </s> <s id="N15E93">Latus verò &longs;ecundum <lb/>vnicam latam lationem à nullo præpeditur, rationabiliter igi­<lb/>tur maiorem pertran&longs;it.<emph.end type="italics"/></s> </p> <pb pagenum="200" xlink:href="005/01/208.jpg"/> <p id="N15EA0" type="head"> <s id="N15EA2">COMMENTARIVS.<!-- KEEP S--></s> </p> <p id="N15EA6" type="main"> <s id="N15EA8">Dvas hic peracutas difficultates proponit Ari&longs;tote­<lb/>les examinandas, <expan abbr="easq.">easque</expan> ingenio&longs;i&longs;&longs;imas, quas accu­<lb/>ratè admodum contemplari, ac diligenti&longs;&longs;imè pon­<lb/>derare operepretium e&longs;t, cum non parum confert ad mi&longs;to­<lb/>rum motuum naturam, <expan abbr="variamq.">variamque</expan> <expan abbr="proportion&etilde;">proportionem</expan> interno&longs;cen­<lb/>dam prout mechanicos maximè decet. </s> </p> <p id="N15EC1" type="main"> <s id="N15EC3">Prima difficultas e&longs;t, cur &longs;i duo puncta extrema vnius la­<lb/>teris in rhombo duabus &longs;imul ferantur lationibus cum ea­<lb/>dem velocitate, vnum maius, alterum minus &longs;patium per­<lb/>currit. </s> <s id="N15ECC">Ad cuius rei explieationem &longs;upponimus ex. </s> <s id="N15ECF">31. de­<lb/>finitione primi Euclidis Rhombum e&longs;&longs;e figuram quadrila­<lb/>teram quidem, & æquilateram, &longs;ed non rectangulam; quip­<lb/>pe quæ duos angulos habet acutos, duos verò obtu&longs;os. </s> <s id="N15ED8">Si <lb/><figure id="id.005.01.208.1.jpg" xlink:href="005/01/208/1.jpg"/><lb/>igitur in Rhombo ABCD, cuius <lb/>acuti anguli &longs;int A & D, obtu&longs;i <lb/>verò B & C, duo extrema pun­<lb/>cta lateris AB, nempe ip&longs;um A, & <lb/>ip&longs;um B, æqua velocitate duabus <lb/>ferantur lationibus, vna qua pun­<lb/>ctum A &longs;uper idem latus feratur <lb/>ver&longs;us B, & B feratur ver&longs;us A: <lb/>altera verò qua <expan abbr="dũ">dum</expan> ip&longs;a duo pun­<lb/>cta &longs;ibi obuiam procedunt, &longs;imul <lb/>cum toto latere AB, moueantur <lb/>ver&longs;us latus CD, ita vt &longs;emper la­<lb/>tus, &longs;eu linea AB, ip&longs;i CD &longs;it pa­<lb/>ralella, de&longs;cendatque per latera <lb/>AC, & BD quou&longs;que coincidat <lb/>cum eadem CD: Cum ex duabus lationibus, eadem &longs;em­<lb/>per laterum proportione &longs;eruata, recta quædam linea pro­<lb/>ducatur, vt &longs;upra demon&longs;tratum e&longs;t ex eodem Ari&longs;totele <lb/>1. par. </s> <s id="N15F0B">tex. <!-- REMOVE S-->6. vtraque puncta prædicta eandem laterum ip­<lb/>&longs;ius rhombi proportionem in &longs;uo motu &longs;eruando, propriam <pb pagenum="201" xlink:href="005/01/209.jpg"/>rectam lineam de&longs;cribent: A quidem lineam AD, B verò <lb/>BC: quæ nimirum erunt diametri eiu&longs;dem rhombi. </s> <s id="N15F19"><expan abbr="Cumq.">Cumque</expan> <lb/>in rhombo diametri non &longs;int æquales, &longs;ed quæ obtu&longs;is an­<lb/>gulis opponitur, vt AD maior &longs;it ea, quæ opponitur acutis, <lb/>vt BC: &longs;iquidem maius latus maiorem angulum &longs;ubtendit <lb/>per 18. primi; hin c e&longs;t, vt ex ip&longs;is duobus punctis AB, dua­<lb/>bus lationibus eodem tempore, <expan abbr="eademq.">eademque</expan> velocitate pro­<lb/>motis, vnum quippe maius &longs;patium, nempe maiorem dia­<lb/>metrum, alterum verò minus, &longs;eu minorem diametrum per­<lb/>currat. </s> <s id="N15F33">Quod mirum proculdubio omnibus cau&longs;am igno­<lb/>rantibus videri &longs;olet. </s> </p> <p id="N15F38" type="main"> <s id="N15F3A">Verùm quod linea recta, quam de&longs;cribere diximus pun­<lb/>ctum A, &longs;it ipfa diameter AD; quam verò punctum B, <lb/>&longs;it diameter BC, facilè demon&longs;tratur ex eo. </s> <s id="N15F41">Nam &longs;i pun­<lb/>ctum A, proprio motu delatum fuerit exempli gratia v&longs;que <lb/>ad punctum E medium ip&longs;ius lineæ AB, & linea tota <lb/>AB eodem tempore, æquale &longs;patium pertran&longs;ierit ver&longs;us <lb/>CD, ita vt alterum eius extremum peruenerit ad punctum <lb/>F, medium lateris AC; alterum verò ad punctum G, me­<lb/>dium lateris BD: quoniam AF æqualis e&longs;t ip&longs;i AE, &longs;i com­<lb/>pleatur figura &longs;imilis toti, productis lineis EH, & FG per <lb/>punctum medium K, nempe rhombus AEKF, &longs;imilis <lb/>rhombo maiori ABCD per 24. &longs;exti elementorum; erit <lb/>recta FK æqualis oppo&longs;itæ AE, & AF ip&longs;i EK; proin­<lb/>deque punctum A cum duabus tran&longs;latum &longs;it lationibus <lb/>&longs;emper proportionalibus iuxta rationem æqualitatis; quam <lb/>latera rhomborum habent inter &longs;e, vtique tran&longs;latum erit <lb/>&longs;uper rectam AK in ip&longs;um K, quod e&longs;t punctum medium <lb/>diametri AD; Cuius reliquum dimidium conficiet, tum <lb/>ex motu &longs;uo ab E v&longs;que ad B, tum ex alieno ab F v&longs;que <lb/>ad C, ita vt tandem perueniat ad punctum D. <!-- KEEP S--></s> </p> <p id="N15F67" type="main"> <s id="N15F69">Eodem pacto, quod dictum e&longs;t de puncto A, applica­<lb/>ri pote&longs;t in puncto B. </s> <s id="N15F6E">Nam &longs;i hoc cum eadem velocitate <lb/>moueatur ver&longs;us A, &longs;icut linea AB ver&longs;us CD, quo tem­<lb/>pore per proprium motum percurri&longs;&longs;er v&longs;que ad E, alieno <lb/>motu perueni&longs;&longs;et v&longs;que ad G; <expan abbr="æqualesq.">æqualesque</expan> forent lineæ BE, <pb pagenum="202" xlink:href="005/01/210.jpg"/>& BG; producti&longs;que lateribus, EH, & GF, rhombus <lb/>EBGK per illa con&longs;titutus, &longs;imilis e&longs;&longs;et rhombo continen­<lb/>ti ABCD: Ideoque GK æqualis oppo&longs;itæ BE, & BG <lb/>æqualis EK. </s> <s id="N15F86">Quare punctum B vtroque motu<gap/> tran&longs;la­<lb/>tum cum eadem proportione æqualitatis, mouebitur motu <lb/>mixto &longs;uper diametrum ip&longs;ius rhombi, & quo tempore <lb/>transferri deberet in E & in G, transfertur in K, quod e&longs;t <lb/>punctum medium diametri BC; cuius reliquum dimidium <lb/>conficiet per motum proprium ab E v&longs;que ad A, & alie­<lb/>no à G v&longs;que ad D; ita vt tandem reperiatur in C. <!-- KEEP S--></s> <s id="N15F98">Cum <lb/>igitur &longs;patium BC, vt dicebamus, minus &longs;it quam &longs;patium <lb/>AD eodem tempore peragratum à puncto A, difficile vi­<lb/>detur qua ratione id po&longs;&longs;it contingere, po&longs;tquam ita rem <lb/>&longs;e habere con&longs;titerit. </s> </p> <p id="N15FA3" type="main"> <s id="N15FA5">Huius tamen euentus cau&longs;am &longs;oluendo primam partem <lb/>quæ&longs;tionis, <expan abbr="primamq.">primamque</expan> difficultatem, eam e&longs;&longs;e inquit Ari&longs;to­<lb/>teles, quia cum in rhombo duo &longs;int obtu&longs;i anguli, duo verò <lb/>acuti, lationes illæ, quibus fertur punctum, quod ab obtu&longs;o <lb/>angulo di&longs;cedit, vt in propo&longs;ita figura e&longs;t punctum B, &longs;unt <lb/>inter &longs;e omnino ferè contrariæ, cum vna, verbi gratia &longs;ur­<lb/>&longs;um penè tendat ver&longs;us A, altera verò deor&longs;um ver&longs;us D: <lb/>Quo fit vt mutuo præpediantur, ac retardentur. </s> <s id="N15FBA">Lationes <lb/>verò quibus fertur punctum, quod ab acuto angulo di&longs;cedit <lb/>vt A; quamuis diuer&longs;æ in &longs;e &longs;int, nullo tamen modo con­<lb/>&longs;tituuntur contrariæ, cum ad eandem ferè partem pergere <lb/>teneantur, <expan abbr="parumq.">parumque</expan> aut minus &longs;emper di&longs;tent inter &longs;e termi­<lb/>ni ad quos tendunt. </s> <s id="N15FCB">Quare potius ip&longs;æ ad inuicem iuuan­<lb/>tur, quàm aliquo modo impediantur. </s> <s id="N15FD0">Rationi autem con­<lb/>&longs;entaneum e&longs;t, vt punctum contrarijs ferè lationibus &longs;e&longs;e <lb/>impedientibus latum, minori interuallo in eodem tempore <lb/>feratur, quàm punctum, quod duabus lationibus &longs;e&longs;e mutuo <lb/>adiuuantibus a&longs;portatur; mitumque propterea non e&longs;&longs;e &longs;i <lb/>hoc maiorem diametrum, illud verò minorem eodem tem­<lb/>pore percurrat. </s> <s id="N15FDF">Vnde etia n &longs;equitur, vt quò acutiores <lb/>con&longs;tituantur anguli A, & D, <expan abbr="proindeq.">proindeque</expan> obtu&longs;iores B, <lb/>& C; tardius ac minori interuallo feratur ip&longs;um B; cele-<pb pagenum="203" xlink:href="005/01/211.jpg"/>rius verò ac maiori &longs;patio ip&longs;um A. <!-- KEEP S--></s> <s id="N15FF0">Quandoquidem ex ma­<lb/>iori angu&longs;tia angulorum magis. </s> <s id="N15FF5">vniuntur latera, magis <expan abbr="q.">que</expan> ad <lb/>vnum, & idem terminum appropinquantur. </s> </p> <p id="N15FFE" type="main"> <s id="N16000">Quam Ari&longs;totelis &longs;olutionem pluribus euerrere conatur <lb/>Baldus, quæ &longs;ummatim in hoc tantum redigi po&longs;&longs;unt, quòd <lb/>ex ea &longs;equeretur, idem &longs;imiliter dicendum e&longs;&longs;e de duo­<lb/>bus punctis v<gap/> ius lateris in quadrato, &longs;i duabus &longs;imul latio­<lb/>nibus mouerentur eo pacto quo in rhombo Philo&longs;ophus <lb/>de&longs;crip&longs;it; vt &longs;cilicet punctum, quod duabus lationibus fer­<lb/>tur, ambabus deor&longs;um tendentibus &longs;uper de&longs;cendentem <lb/>diametrum ip&longs;ius quadrati, velocius feratur, quàm punctum, <lb/>quod duabus lationibus fertur, vna deor&longs;um tendente, alte­<lb/>ra verò &longs;ur&longs;um &longs;uper diametrum tran&longs;uer&longs;am. </s> <s id="N16017">Id quod per <lb/>&longs;e fal&longs;um e&longs;&longs;e con&longs;tat; cum æquali tempore; æquale &longs;patium <lb/>vtrumque punctum conficeret Siquidem in quadrato vtra­<lb/>que diameter alteri ad inuicem &longs;emper e&longs;t æqualis. </s> <s id="N16020"><expan abbr="Idemq.">Idemque</expan> <lb/>confirmat: in rhombo inuer&longs;o. </s> <s id="N16028">Nam &longs;equeretur, punctum <lb/>duabus lationibus latum deor&longs;um per minorem diametrum, <lb/>citius ferri, quàm punctum, quod duabus lationibus, vna <lb/>&longs;ur&longs;um: altera deor&longs;um tendente: pertran&longs;iret diametrum <lb/>tran&longs;uer&longs;am, nempe maiorem, Quod quippe ab&longs;urdum e&longs;­<lb/>&longs;e liquet. </s> </p> <p id="N16035" type="main"> <s id="N16037">Verumenimuerò Baldus in his propriam potius appre­<lb/>hen&longs;ionem, quam Ari&longs;totelis &longs;olutionem euertit. </s> <s id="N1603C">Porrò <lb/>hæc non fundatur in eo, quod e&longs;t &longs;ur&longs;um, aut deor&longs;um pun­<lb/>cta ip&longs;a duabus lationibus ferri, vt ip&longs;e &longs;upponit, quamuis ad <lb/>explicationem præ dicti motus, <expan abbr="doctrinæq.">doctrinæque</expan> Ari&longs;totelis, om­<lb/>nes vtamur exemplo diuer&longs;arum po&longs;itionum, vt &longs;ur&longs;um, aut <lb/>deor&longs;um: &longs;ed ab&longs;trahendo à quacumque po&longs;itione, tota <lb/>&longs;olutionis ratio ab Ari&longs;totele con&longs;tituitur in maiori vnione, <lb/>&longs;eu propinquitate laterum acutranguli, & in maiori &longs;epara­<lb/>none, &longs;eu di&longs;tantia laterum anguli obtu&longs;i. </s> <s id="N16053">Nam per ip&longs;a <lb/>latera anguli obtu&longs;i; punctum in diuer&longs;as longè partesra­<lb/>pitur, qua&longs;i omnino contrario motu: per latera verò anguli <lb/>acuti, in vnam ferè partem, qua&longs;i per eundem motum, qui <lb/>propterea velocior con&longs;tituitur, vt dictum e&longs;t. </s> </p> <pb pagenum="204" xlink:href="005/01/212.jpg"/> <p id="N16062" type="main"> <s id="N16064">Deinde propria Baldi &longs;olutio, quam ex proprijs cau&longs;is <lb/>ip&longs;e ait e&longs;&longs;e de&longs;umptam, nullam cau&longs;am affert propo&longs;iti effe­<lb/>ctus ad diluendam difficultatem, &longs;eu rationem dubitandi, <lb/>&longs;ed rur&longs;us noua cluntaxat via idip&longs;um demon&longs;trat, quod Ari­<lb/>&longs;totelis argumento demon&longs;tratum e&longs;t de veritate ip&longs;ius ef­<lb/>fectus, nempe punctum A per longiorem diametrum AD, <lb/>illis duabus lationibus ferri eodem tempore, quo punctum <lb/>B fertur &longs;uper minorem diametrum BC; quod e&longs;t citius <lb/>moueri: nihil attingens de cau&longs;a cur id contingat, &longs;eu ob <lb/>quam punctum A, eodem tempore maiorem valeat li­<lb/>neam pertran&longs;ire, <expan abbr="proindeq.">proindeque</expan> velocius moueri; id quod opti­<lb/>mè fecit Ari&longs;toteles vt vidimus. </s> </p> <p id="N16081" type="main"> <s id="N16083">Secunda autem difficultas, quam Philo&longs;ophus hac in <lb/>quæ&longs;tione proponit, e&longs;t, cur in eodem rhombo punctum B, <lb/>quod vt diximus &longs;ua &longs;ponte fertur &longs;uper latus BA, <expan abbr="totamq.">totamque</expan> <lb/>eius longitudinem percurrit; minus quippe pertran&longs;eat &longs;pa­<lb/>tium, quàm totum ip&longs;ummet latus BA, in quo fertur ver&longs;us <lb/>CD; imò quàm &longs;it ip&longs;ummet latus BA, quod percurrit. <lb/></s> <s id="N16095">Quandoquidem punctum B non conficit ni&longs;i&longs;patium BC: <lb/>totum autem latus BA conficit &longs;patium BD, &longs;eu AC, <lb/>quod maius e&longs;t quàm BC. <!-- KEEP S--></s> <s id="N1609D">Sicut ip&longs;um latus BA maius <lb/>con&longs;tituitur, quàm diameter BC in rhombo propo&longs;ito. <lb/></s> <s id="N160A3"><expan abbr="Totaq.">Totaque</expan> ratio difficultatis in eo &longs;ita e&longs;t, quoniam punctum <lb/>B, duplici fertur latione, latus verò AB, vnica, & <lb/>vtrunque pari velocitate: Quamobrem potius punctum <lb/>B, quàm latus BA, &longs;equeretur maius &longs;patium pertran&longs;i­<lb/>re. </s> <s id="N160B1">Accedit quia punctum B verè totum latus BA, in <lb/>quo fertur percurrit eodem tempore, quo vehitur cum ip­<lb/>&longs;omet latere ve<gap/>&longs;us CD; ideoque &longs;atis arduum videtur, <lb/>minus ip&longs;um B &longs;patium pertran&longs;ire quàm &longs;it latus BA, in <lb/>quo fertur. </s> </p> <p id="N160BE" type="main"> <s id="N160C0">Sed vnde hæc dubitandi ratio de&longs;umpta e&longs;t, inde pariter <lb/>ade&longs;t ratio difficultatem &longs;oluendi. </s> <s id="N160C5">Etenim hoc ip&longs;o, quod <lb/>punctum B feratur duplici latione explicata &longs;uper diame­<lb/>trum BC, latus verò BA vnica vel &longs;implici motione <lb/>vehatur ver&longs;us CD, hoc quidem à nullo motu contrario <pb pagenum="205" xlink:href="005/01/213.jpg"/>præpeditur, illud verò contrarijs ferè lationibus detinetur <lb/>ne velocius eodem tempore moueatur, maiu&longs;que proin­<lb/>de &longs;patium valeat peragrare. </s> <s id="N160D7">Quod per&longs;picuè ex dictis <lb/>iam pote&longs;t patere. </s> </p> <p id="N160DC" type="head"> <s id="N160DE">Quæ&longs;tio Vige&longs;imaquarta.</s> </p> <p id="N160E1" type="main"> <s id="N160E3">D<emph type="italics"/>vbitatvr, quam ob cau&longs;am maior cir­<lb/>culus æqualem minori circulo conuoluitur li­<lb/>neam, quando circa idem centrum fuerint po­<lb/>&longs;iti: Seor&longs;um autem reuoluti, quemadmodum <lb/>alterius magnitudo ad magnitudinem &longs;e. </s> <s id="N160F1">ha­<lb/>bet alterius, &longs;ic & illorum ad &longs;e inuicem fiunt <lb/>lineæ. </s> <s id="N160F8">Præterea vno etiam & eodem vtri&longs;que <lb/>existente centro, aliquando quidem tanta fit linea, quam con­<lb/>uoluuntur, quantum minor per &longs;e conuoluitur circulus, <expan abbr="quan-doq.">quan­<lb/>doque</expan> verò quantam maior. </s> <s id="N16105">Quod quidem igitur maiorem con­<lb/>uoluitur maior, manifestum est, angulus enim &longs;en&longs;u videtur <lb/>e&longs;se cuiu&longs;que circum ferentia propriæ diametri, maioris circuli <lb/>maior, minoris minor, quamobrem eandem habebunt proportio­<lb/>nem &longs;ecundum &longs;en&longs;um ad &longs;e lineæ, &longs;ecundum quas fuerint <lb/>conuoluti. </s> <s id="N16112">V erumenimuerò quod etiam æqualem conuoluun­<lb/>tur, quando circa idem fuerint po&longs;iti centrum, manife&longs;tum <lb/>e&longs;t, & &longs;ic fiunt aliquando quidem æquales lineæ, &longs;ecundum <lb/>quam maior conuoluitur circulus, aliquando verò &longs;ecundum <lb/>quam minor. </s> <s id="N1611D">Sit enim circulus maior quidem, vbi DFC, mi­<lb/>nor verò vbi EGB, vtria&longs;que autem centrum A. <!-- KEEP S--></s> <s id="N16123">Et quam qui­<lb/>dem magnus per &longs;e conuoluitur, &longs;it vbi FI, quam veròper &longs;e <lb/>minor, vbi GK, æqualis AF. <!-- KEEP S--></s> <s id="N1612B">Si igitur minorem mouero, idem <lb/>mouens centrum vbi A, maior autem &longs;it annexus: quando <lb/>igitur AB fuerit recta ad ip&longs;am GK, &longs;imul & AC fit recta <lb/>ad ip&longs;am FI: quamobrem æqualem &longs;emper translata erit, ip­<lb/>&longs;am quidem GK, vbi e&longs;t GB circumferentia, ip&longs;am verò <lb/>FL, quæ est vbi FC. </s> <s id="N16138">Si autem quarta pars æqualem conuol­<lb/>uitur, manife&longs;tum e&longs;t, quod totus circulus toti circulo æqualem <lb/>conuoluetur. </s> <s id="N1613F">Quare quando BG linea ad ip&longs;um peruenerit <lb/>K, & ip&longs;a FC circumferentia erit in ip&longs;a CL & vniuer&longs;us <lb/>erit conuolutus circulus. </s> <s id="N16146"><expan abbr="Similiq.">Similique</expan> modo &longs;i magnum mouero, <lb/>illi paruum annectens, eodem existente centro, &longs;imul cum AC <lb/>ip&longs;a AB perpendiculum & recta erit: hac quidem ad ip&longs;am<emph.end type="italics"/><pb pagenum="206" xlink:href="005/01/214.jpg"/><emph type="italics"/>FI, illæ verò ad GM. </s> <s id="N16159">Quamobrem quando bæc quidam <lb/>ip&longs;i GM pertran&longs;iuerit, illa verò ip&longs;i FI, & rur&longs;um facta <lb/>fuerit recta ip&longs;a FA ad ip&longs;am FL, & ip&longs;a AG rur&longs;um re­<lb/>cta, velut à principio erant in ip&longs;is MI. </s> <s id="N16162">Hoc autem neque <lb/>alia intercedente mora maioris ad minorem, vbi &longs;eilicet per <lb/>aliquod temporis &longs;patium &longs;taret in eodem puncto, neque tran&longs;i­<lb/>liente minore aliquod punctum, maiorem quidem æqualem mi­<lb/>nori p<gap/>rtran&longs;ire, bunc autem maiori, ab&longs;urdum e&longs;t. </s> <s id="N1616F">Præterea <lb/>vnica etiam &longs;emper existente motione, centrorum motum inter­<lb/>dum quidem magnam, nonnunquam verò minorem conuerti, <lb/>admirandum est. </s> <s id="N16178">I dem enim celeritate eadem latum æqualem <lb/>natum boc e&longs;t pertran&longs;ire: eadem autem celeritate vtroque <lb/>modo æqualem licet mouere. </s> <s id="N1617F">Principium autem &longs;umendum <lb/>est circa i&longs;torum cau&longs;am, quod eadem potentia, & æqualit <lb/>bans quidem tardius mouet magnitudinem, illam verò cel<gap/>­<lb/>rius. </s> <s id="N1618A">Si enim fuerit quippiam, quod à &longs;eip&longs;o moueri, natum <lb/><gap/>n &longs;it, &longs;i &longs;imul & illud mouerit, quod natum e&longs;t mouert, tar­<lb/>dius mouebitur, quàm &longs;i ip&longs;um per &longs;e moueretur. </s> <s id="N16192">Et &longs;iquidem <lb/><gap/>atum fuerit moueri, non &longs;imul autem moueatur, &longs;imiliter <lb/>&longs;e habebit. </s> <s id="N1619A">Et impo&longs;&longs;ibile certè e&longs;t, plus moueri quàm mouem, <lb/><gap/>on enim &longs;uam ip&longs;ius mouetur motionem. </s> <s id="N161A0">Sit igitur e reu'us <lb/>maior vbi A, minor autem vbi B, &longs;i minor maiorem impel­<lb/>let non reuolutum ex &longs;e, manife&longs;tum e&longs;t, quod tantum ip&longs;ius <lb/>rectæ maior pertran&longs;it, quantum e&longs;t impul&longs;us. </s> <s id="N161A9">T antum autem <lb/>e&longs;t impul&longs;us, quantum paruus est motus æqualem igitur ip&longs;ius <lb/>rectæ pertran&longs;iuerunt. </s> <s id="N161B0">Nece&longs;ie igitur e&longs;t &longs;i reuolutus minor <lb/>maiorem impellet, reuoluti &longs;imul cum impul&longs;ione; tantum <lb/>autem, quantum minor reuolutus e&longs;t, &longs;i nibil ip&longs;e &longs;ui ip&longs;ius <lb/>motione mouetur. </s> <s id="N161B9">Quomodo enim & quantum mouit, tantum <lb/>motum e&longs;&longs;e nece&longs;&longs;e e&longs;t, quod mouetur ab illo. </s> <s id="N161BE">Sed profectò par­<lb/>uus circulus tantum jeip&longs;um circulariter mouit, quantum est <lb/>pedalis quantitas (tantum enim &longs;it id, quod motus e&longs;t) & ma­<lb/>gnus igitur tantum motus erit. </s> <s id="N161C7"><expan abbr="Similiq.">Similique</expan> modo &longs;i magnus par­<lb/>uum mouebit, motus erit paruus quemadmodum maior. </s> <s id="N161CF">Per <lb/>&longs;e autem motus illorum vtrumlibet, &longs;iue celeriter, &longs;eu tardè <lb/>eadem velocitate, statim quando maior natus e&longs;t circumferri <lb/>lineam, quod difficultatem facit, quod non &longs;imiliter faciunt <lb/>quando fuerint connexi. </s> <s id="N161DA">Hoc autem e&longs;t, &longs;i alter ab altero mo­<lb/>ueatur, non quam natus e&longs;t, neque peculiarem motionem: nibil <lb/>enim refert cireumponere, & annectere, aut <expan abbr="eõiungere">eoniungere</expan> vtrum­<lb/>libet alteri. </s> <s id="N161E7">Similiter enim quando bic quidem mouet, ille ve­<lb/>rò mouelur ab isto, quantum vtique mouerit, alt<gap/>r, tantum<emph.end type="italics"/><pb pagenum="207" xlink:href="005/01/215.jpg"/><emph type="italics"/>alter mouebitur. </s> <s id="N161F7">Quandoquidem igitur adiacens mouerit, aut <lb/>propen&longs;us, non &longs;emper conuoluitur, quando verò circa idem <lb/>po&longs;iti fuerint centrum, alterum ab illo &longs;emper conuolui nece&longs;­<lb/>&longs;e est. </s> <s id="N16200">Sed nihileminus non &longs;uam ip&longs;ius motionem mouetur al­<lb/>ter, &longs;ed velut nullam baberet motionem: & &longs;i babuerit, illa <lb/>autem non vtatur, tantundem accidit. </s> <s id="N16207">Quandoquidem igitur <lb/>magnus mouerit &longs;ibi <expan abbr="alligatũ">alligatum</expan> paruum, paruus mouetur quan­<lb/>tum ille: quando autem paruus, rur&longs;us magnus quantum i&longs;te, <lb/>&longs;eparatus autem vterque &longs;eip&longs;um mouet. </s> <s id="N16214">Quod autem eodem <lb/>exi&longs;tente centro, & mouente eadem velocitate, accidit inæqua­<lb/>lem illos pertran&longs;ire lineam, paralogi&longs;mo &longs;opbi&longs;ticè vtitur is, <lb/>qui dubitat: idem enim ambobus e&longs;t centrum, verùm per acci­<lb/>dens, veluti mu&longs;icum, & album. </s> <s id="N1621F">E&longs;&longs;e enim vtriu&longs;que circuli <lb/>centro non eodem vtitur. </s> <s id="N16224">Quandoquidem igitur mouens fue­<lb/>rit paruus, vt illius centrum, & principium: quando verò <lb/>magnus, vt illius. </s> <s id="N1622B">Non igitur idem &longs;impliciter mouet, &longs;ed e&longs;t <lb/>quo modo.<emph.end type="italics"/></s> </p> <p id="N16232" type="head"> <s id="N16234">COMMENTARIVS.<!-- KEEP S--></s> </p> <p id="N16238" type="main"> <s id="N1623A">Qvæ&longs;tio hæc admirabilem complectitur difficulta­<lb/>tem, vtpotè in&longs;tituta circa rem, quæ vix credi po&longs;&longs;et, <lb/>ni&longs;i ante oculos ob&longs;eruaretur: Vnde inter cæteras <lb/>præcipua ac omnium difficillima exi&longs;timatur, <expan abbr="multumq.">multumque</expan> pa­<lb/>riter &longs;icut præcedens ad mixti motus naturam exploran­<lb/>dam conducit. </s> <s id="N1624B">Cau&longs;am igitur &longs;ci&longs;citatur Ari&longs;toteles, cur <lb/>duo circuli alter altero maior circa idem centrum &longs;imul an­<lb/>nexi, & coaptati, &longs;i &longs;ecundùm ab&longs;idem volutentur (vt plau­<lb/>&longs;trorum progredientium rotæ) ambo æquale pertran&longs;eant <lb/>&longs;patium: &longs;eor&longs;um verò &longs;eparati, &longs;i eodem pacto circum­<lb/>uoluantur, non ita &longs;ed maior circulus maiorem lineam, mi­<lb/>nor verò minorem percurrat iuxta proportionem circumfe­<lb/>rentiæ vnius ad circumferentiam alterius? </s> <s id="N1625C">Quod vt di&longs;tin­<lb/>ctius ob&longs;eruetur addit Ari&longs;toteles, cir culos ip&longs;os circa idem <lb/>centrum coniunctos, <expan abbr="quandoq.">quandoque</expan> in circumuolutione tantam <lb/>lineam &longs;patij pertran&longs;ire, quantam &longs;eor&longs;um pertran&longs;iret cir­<lb/>culus minor: quandoque verò quantam eodem pacto per­<lb/>curreret circulus maior. </s> <s id="N1626D">Etenim, vt quilque experiri po-<pb pagenum="208" xlink:href="005/01/216.jpg"/>te&longs;t, &longs;i ex ip&longs;is duobus circulis &longs;imul circa idem centrum <lb/>coniunctis volutetur minor &longs;ecundum ab&longs;idem &longs;uam &longs;uper <lb/>aliquod planum, ad motum ip&longs;ius conuoluetur &longs;imul & ma­<lb/>ior &longs;uper aliud planum; &longs;ed vtraque linea ab ip&longs;is de&longs;cripta, <lb/>æqualis erit ei quam de&longs;criberet ip&longs;emet circulus minor &longs;i <lb/>&longs;olus per &longs;e ac &longs;eor&longs;um volutaretur. </s> <s id="N1627F">E contra verò &longs;i &longs;uper <lb/>planum eodem pacto volutetur &longs;ecundum ab&longs;idem &longs;uam <lb/>circulus maior, & ad motum ip&longs;ius circumuoluatur etiam <lb/>circulus minor, vtraque linea recta ab ip&longs;is de&longs;cripta æqua­<lb/>lis erit ei quam per &longs;e volutatus de&longs;criberet idemmet circu­<lb/>lus maior. </s> </p> <p id="N1628C" type="main"> <s id="N1628E">Manife&longs;tum autem e&longs;&longs;e, ait Ari&longs;toteles, circulum maio­<lb/>rem &longs;eor&longs;um reuolutum, maius <expan abbr="&longs;paciũ">&longs;pacium</expan>, &longs;eu maiorem lineam <lb/>pertran&longs;ire, quàm pertran&longs;eat circulus minor. </s> <s id="N16299">Idque ex eo, <lb/>nam &longs;icut &longs;en&longs;u con&longs;tat, ambitum cuiu&longs;que circuli e&longs;&longs;e, at­<lb/>que con&longs;titui per ip&longs;am circumferentiam, &longs;eu circumuolu­<lb/>tionem propriæ cliametri eiu&longs;dem circuli, maioris quidem <lb/>maiorem, minoris verò minorem: ita &longs;en&longs;u pariter digno&longs;ci­<lb/>tur eandem inter &longs;e proportionem habere lineas, quæ per <lb/>circumuolutionem ip&longs;orum circulorum de&longs;cribuntur in <lb/>plano; vt&longs;cilicet linea de&longs;cripta à maiori circumferentia <lb/>&longs;it maior, quæ verò à minori de&longs;cribitur, &longs;it minor. </s> <s id="N162AC">Vbi <lb/>autem v&longs;i &longs;umus nomine (ambitus) textus habet (angulus) <lb/>cuius propria &longs;ignificatio difficile cohæret cum &longs;en&longs;u ip&longs;ius <lb/>orationis, <expan abbr="proindeq.">proindeque</expan> non paruam &longs;u&longs;picionem præbuit er­<lb/>roris librariorum, qui forta&longs;&longs;e angulum pro ambitu &longs;crip&longs;e­<lb/>runt: Cum alioquin vox ambitus contextui planè coh&etail;reat, <lb/><expan abbr="explicetq.">explicetque</expan> magis ac breuius quod auctor intendit. </s> </p> <p id="N162C2" type="main"> <s id="N162C4">Veruntamen &longs;i &longs;en&longs;um eiu&longs;dem textus prout &longs;onat ip&longs;a <lb/>vox (angulus) explicare velimus, non incongrue ad hoc to­<lb/>tus Ari&longs;totelis di&longs;cur&longs;us pote&longs;t reduci, vt dicat, &longs;en&longs;u con&longs;ta­<lb/>re, angulum cuiu&longs;que circuli (con&longs;titutum &longs;cilicet ex cir­<lb/>cumferentia propriæ diametri, & ex ip&longs;a diametro) e&longs;&longs;e <lb/>quidem maiorem &longs;i circulus &longs;it maior, minorem verò &longs;i cir­<lb/>culus &longs;it minor. </s> <s id="N162D3">Atque ex hoc fieri, vt ip&longs;a circumferentia, <lb/>&longs;eu ambitus circuli maioris &longs;it pariter maior, minoris verò, <pb pagenum="209" xlink:href="005/01/217.jpg"/>&longs;it minor, iuxta maiorem, vel minorem remotionem ip&longs;ius <lb/>ab altero latere nempe diametro, cum qua con&longs;tituit an­<lb/>gulum. </s> <s id="N162E1">Ac propterea in circumuolutione ip&longs;orum circu­<lb/>lorum, etiam ad &longs;en&longs;um con&longs;tare, eandem inter &longs;e propor­<lb/>tionem habere lineas, quas ip&longs;i circuli &longs;uper planum de&longs;cri­<lb/>bunt, vt &longs;cilicet linea de&longs;cripta à maiori iuxta maiorem cir­<lb/>cumferentiam &longs;it maior, quæ verò à minori de&longs;cribitur iux­<lb/>ta propriam circumferentiam &longs;it minor. </s> <s id="N162EE">Sump&longs;imus autem <lb/>angulum circuli de mente Ari&longs;totelis &longs;ecundum præfatam <lb/>acceptionem, quam latius explicuimus quæ&longs;t. </s> <s id="N162F5">8. nè maxi­<lb/>ma ei tribuatur improprietas locutionis explicando angu­<lb/>lum pro Sectore, vt Baldus, vel pro arcu qui &longs;ubtenditur <lb/>angulo, vt Blancanus: Cum vnumquodque i&longs;torum, pro­<lb/>prium habeat vocabulum, quod Ari&longs;toteles non ignorabat, <lb/><expan abbr="eoq.">eoque</expan> v&longs;us fui&longs;&longs;et, &longs;i idip&longs;um per illud &longs;ignificare volui&longs;&longs;et </s> </p> <p id="N16305" type="main"> <s id="N16307">Vlterius verò quod prædicti circuli quando &longs;unt &longs;imul <lb/>coniuncti circa idem centrum, æquale ambo pertran&longs;eant <lb/>&longs;patium, &longs;iue maius illud &longs;it, vt rotando &longs;ecundum ab&longs;idem <lb/>circuli maioris, &longs;iue minus &longs;ecundum ab&longs;idem minoris, hoc <lb/>ferè pacto probat Philo&longs;ophus. <!-- KEEP S--></s> </p> <figure id="id.005.01.217.1.jpg" xlink:href="005/01/217/1.jpg"/> <p id="N16318" type="main"> <s id="N1631A">Sint circa <lb/>idem <expan abbr="pũctum">punctum</expan> <lb/>A ip&longs;i duo cir­<lb/>culi <expan abbr="coniũcti">coniuncti</expan>, <lb/>maior <expan abbr="quid&etilde;">quidem</expan> <lb/>BCDE, minor <lb/>verò FGHI. <lb/></s> <s id="N16336">Sintque dia­<lb/>metri maioris <lb/>BD, & EC; <lb/>minoris verò <lb/>FH, & IG &longs;e&longs;e <lb/>inuicem inter&longs;ecantes ad angulos rectos in cenrro A. <!-- KEEP S--></s> <s id="N16344">Ideo­<lb/>que quadrans circuli maioris &longs;it CD, minoris verò GH. <lb/></s> <s id="N1634A">Deinde con&longs;tituamus vtrunque circulum ad dexteram &longs;i­<lb/>mul moueri cum &longs;uo communi centro, rotando alterum <pb pagenum="210" xlink:href="005/01/218.jpg"/>quidem per &longs;e &longs;uper rectam lineam DK, alterum verò ad <lb/>motum illius, de&longs;cribendo aliam rectam huic parallelam, <lb/>quæ &longs;it HL. </s> <s id="N16358">Rur&longs;us con&longs;tituamus, maiorem circulum per <lb/>&longs;e moueri &longs;ecundum ab&longs;idem quadrantis CD &longs;uper lineam <lb/>DK, ita vt aliquando punctum C perueniat in M, percur­<lb/>rendo &longs;patium DM æquale ip&longs;i CD. <!-- KEEP S--></s> <s id="N16362">Tunc &longs;emidiame­<lb/>ter AC con&longs;titueretur perpendicularis ip&longs;i DK, <expan abbr="e&longs;&longs;etq.">e&longs;&longs;etque</expan> <lb/>vbi NM, puncto C tran&longs;lato in M, & puncto A tran&longs;­<lb/>lato in N. <!-- KEEP S--></s> <s id="N16370">Cumque punctum G circuli minoris, &longs;it in <lb/>linea AC, nece&longs;&longs;ariò po&longs;t huiu&longs;modi quadrantis rotatio­<lb/>nem con&longs;titueretur in loco vbi O, ita vt &longs;emidiameter AG <lb/>circuli minoris transferatur in NO. </s> <s id="N16379">Ad reuolutionem igi­<lb/>tur vtriu&longs;que circuli &longs;ecundum ab&longs;idem maioris, quadrans <lb/>ip&longs;ius maioris circuli conficiet &longs;patium DM; quadrans ve­<lb/>rò minoris circuli, quod &longs;imul cogitur conuolui, percurret <lb/>&longs;patium HO, quod æquale e&longs;t ip&longs;i DM per 34. primi ele­<lb/>ment. </s> <s id="N16386">Idemque quod de quadrantibus dictum e&longs;t verificari <lb/>poterit de totis ip&longs;is eorum circulis. </s> <s id="N1638B">Con&longs;tat ergo mino­<lb/>rem circulum eodem tempore ad motum maioris circa <lb/>idem centrum conuolutum, æqualem lineam peragrare ip&longs;i <lb/>rectæ quam maior circulus per &longs;e motus pertran&longs;it. </s> </p> <p id="N16394" type="main"> <s id="N16396">Sed nec minus con&longs;tabit è contra ad <expan abbr="rotation&etilde;">rotationem</expan> propriam <lb/>minoris circuli &longs;ecundum ab&longs;idem, maiorem circulum ei <lb/>annexum, æquale pariter &longs;patium, & non amplius percurre­<lb/>re. </s> <s id="N163A3">Rotetur enim motu proprio minoris circuli quadrans <lb/>GH &longs;uper rectam HL, ita vt punctum G aliquando per­<lb/>ueniat in P, percurrendo &longs;patium HP, æquale ip&longs;i GH; <lb/>& centrum A con&longs;equenter con&longs;tituatur in Q, exi&longs;ten­<lb/>te &longs;patio A Q æquale ip&longs;i HP. </s> <s id="N163AE">Tum excitetur linea <lb/>QPR, perpendicularis ip&longs;is planis HL, & DK; <expan abbr="eritq.">eritque</expan> <lb/>punctum C in R, &longs;icut punctum G in P, & punctum <lb/>A in <expan abbr="q.">que</expan> Siquidem hæc tria puncta &longs;unt in eadem recta, <lb/>vel &longs;emidiametro circuli maioris. </s> <s id="N163C1">Iam igitur po&longs;t huiu&longs;mo­<lb/>di rotationem, quo tempore quadrans minoris circuli con­<lb/>fecit &longs;patium HP; quadrans maioris circuli conuoluti ad <lb/>motum illius, confecit &longs;patium. </s> <s id="N163CA">DR, quod æquale e&longs;t ip&longs;i <pb pagenum="211" xlink:href="005/01/219.jpg"/>HP. pereandem 34 primi. </s> <s id="N163D2">Quod & de tota circumferen­<lb/>tia vtriu&longs;que circuli demon&longs;trari pote&longs;t, non ab&longs;que magna <lb/>omnium admiratione, quibus forta&longs;&longs;e videretur, maiorem <lb/>circulum, &longs;emper maiorem lineam de&longs;cribere, quàm circu­<lb/>lus minor in ip&longs;a rotatione. </s> </p> <p id="N163DD" type="main"> <s id="N163DF">Admirationis autem ratio ex eo maximè augetur apud <lb/>ip&longs;um Philo&longs;ophum, quòd cum circulus maior minorem <lb/>lineam pertran&longs;it, quàm &longs;it eius peripheria, nulla vel mini­<lb/>ma intercedit mora, in qua ip&longs;e quie&longs;cat. </s> <s id="N163E8">Ac vice ver&longs;a <lb/>cum circulus minor maiorem lineam de&longs;cribit, nullam tran­<lb/>&longs;iliat, vel modicam partem, quam percurrendo non attin­<lb/>gat. </s> <s id="N163F1">Præterea quòd vnica exi&longs;tente motione vtriu&longs;que cir­<lb/>culi connexi, centrum commune commotum, interdum <lb/>quidem maiorem, interdum verò minorem lineam percur­<lb/>rat iuxta ab&longs;idem, &longs;cilicet maioris, aut minoris circuli &longs;e­<lb/>cundum quam mouetur: cum tamen idem eadem celerita­<lb/>te latum, æqualem lineam regulariter debeat pertran&longs;ire. </s> </p> <p id="N163FE" type="main"> <s id="N16400">Pro &longs;olultione igitur quæ&longs;tionis ad explicandam cau&longs;am <lb/>tam mirifici effectus, duo &longs;upponit Ari&longs;toteles fundamenta. <lb/></s> <s id="N16406">Vnum e&longs;t eandem, vel æqualem potentiam, tardius quidem <lb/>mouere vnam magnitudinem, quàm aliam. </s> <s id="N1640B">Licet enim illæ <lb/>æquè ex &longs;e mobiles &longs;int, &longs;i tamen vna &longs;imul cum alia ad <lb/>motum inepta vel difficili reperiatur coniuncta, tardius mo­<lb/>uebitur, quàm illa, quæ reperitur &longs;oluta, vel quam ip&longs;amet <lb/>&longs;eor&longs;um moueretur ab eadem potentia. </s> <s id="N16416">Quod &longs;i magni­<lb/>tudo, quæ moueri debet ad motum alterius, cui reperi­<lb/>tur connexa, mobilis quidem facilè ex &longs;e &longs;it, nihil tamen <lb/>ex &longs;e moueatur, vel ad motum alterius conferat, perin­<lb/>de e&longs;t, ac &longs;i minimè apta e&longs;&longs;et ad motum: vnde & altera, <lb/>quæ &longs;imul cum ip&longs;a moueri debet, tardius non minus mo­<lb/>uebitur. </s> </p> <p id="N16425" type="main"> <s id="N16427">Alterum verò fundamentum à Philo&longs;opho &longs;uppo&longs;itum <lb/>illud e&longs;t, quòd impo&longs;&longs;ibile profectò exi&longs;timandum &longs;it aliquid <lb/>plus moueri, quàm mouens à quo mouetur; Siquidem non <lb/>&longs;ua, &longs;ed illius motione cietur, <expan abbr="nullaq.">nullaque</expan> propria vtitur mobili­<lb/>tate intrin&longs;eca, & actiua, qua motus po&longs;&longs;it augeri. </s> </p> <pb pagenum="212" xlink:href="005/01/220.jpg"/> <p id="N1643A" type="main"> <s id="N1643C">Quibus po&longs;itis Ari&longs;toteles quæ&longs;tionem &longs;oluendo prædi­<lb/>ctum effectum ex eo inquit contingere. </s> <s id="N16441">Nam &longs;i circulus ma­<lb/>ior non moueatur ni&longs;i ad motum minoris cui e&longs;t annexus, <lb/>tantum &longs;patium poterit pertran&longs;ire, quantum delatus fuerit <lb/>ex impullu illius: tantum autem deferri poterit quantum <lb/>minor ip&longs;e circulus ex &longs;e motus impulerit, & non amplius. <lb/></s> <s id="N1644D">Quomodo enim & quantum ex &longs;e motus fuerit mouens, <lb/>tantundem nece&longs;&longs;e e&longs;t moueri, qui mouetur ab illo. </s> <s id="N16452">Aequa­<lb/>lem igitur viam vterque circulus rotando conficiet dum <lb/>maior mouetur ad motum minoris. </s> <s id="N16459"><expan abbr="Idemq.">Idemque</expan> infert contin­<lb/>gere &longs;i minor circulus moueatur ad motum maioris &longs;ibi an­<lb/>nexi, & eodem pacto &longs;ecundum ab&longs;idem lati. </s> <s id="N16463">Nam tantum <lb/>ip&longs;e minor circulus, & non minus moueri poterit, quantum <lb/>à maiori deportabitur. </s> <s id="N1646A">Rapitur enim iugiter ab illo in &longs;ua <lb/>rotatione v&longs;que ad vltimum terminum, <expan abbr="æqualemq.">æqualemque</expan> propte­<lb/>rea lineam rectam <expan abbr="cũ">cum</expan> illo de&longs;cribet, quamuis minorem pe­<lb/>ripheriam obtineat. </s> <s id="N1647B">Quod &longs;i vtrumlibet ip&longs;orum circulo­<lb/>rum &longs;eor&longs;um ex &longs;e &longs;ecundum propriam ab&longs;idem eadem ve­<lb/>locitate moueatur, tunc maior circulus maiorem rectam, <lb/>minor verò minorem &longs;ua volutatione conficiet iuxta men­<lb/>&longs;utam &longs;ecundum quam natus e&longs;t circumferri. </s> </p> <p id="N16486" type="main"> <s id="N16488">Cæterum eam, ac profectò <expan abbr="arduã">arduam</expan> difficultatem &longs;ibi obij­<lb/>cit Philo&longs;ophus. <!-- KEEP S--></s> <s id="N16492">Nam quæ dicta &longs;unt, rectè ac facilè intel­<lb/>ligerentur procedere, &longs;i circulus qui mouetur ad motum al­<lb/>terius, non e&longs;&longs;et cum illo concentricus, &longs;ed alio modo com­<lb/>pactus, <expan abbr="eiq.">eique</expan> connexus. </s> <s id="N1649F">Siquidem moueri non po&longs;&longs;et circa <lb/>proprium centrum, nec proinde peculiarem, ac proportio­<lb/>natam &longs;ibi motionem vendicare, &longs;ed tantum circa alienum <lb/>centrum ip&longs;ius circuli deferentis conuerti: Non &longs;ecus ac <lb/>quælibet alia magnitudo adiacens eidem circulo deferenti, <lb/>vel ei extra centrum quoquo modo appen&longs;a; tantum &longs;cili­<lb/>cet &longs;patium tran&longs;mittendo, quantum ip&longs;e circulus, ad cuius <lb/>motum defertur, pertran&longs;ierit. </s> <s id="N164B0">Verùm cum hic &longs;ermo &longs;it <lb/>de duobus circulis concentricis, qui nimirum circa idem <lb/>commune <expan abbr="centrũ">centrum</expan> &longs;imul conuertuntur, non videntur præfa­<lb/>ta, & ab ip&longs;o Philo&longs;opho adducta rectè procedere, autcon-<pb pagenum="213" xlink:href="005/01/221.jpg"/>cludere. </s> <s id="N164C2">Quoniam &longs;icut circulus delatus, non minus ac de­<lb/>ferens conuoluitur circa proprium centrum, ac &longs;imul cum <lb/>illo progreditur modo &longs;ibi connaturali; ita nec minus pro­<lb/>portionatum &longs;ibi interuallum rotando videtur po&longs;&longs;e tran&longs;­<lb/>mittere, de&longs;cribendo lineam rectam æqualem &longs;uæ periphe­<lb/>riæ &longs;eu ab&longs;idi &longs;ecundum quam conuoluitur. </s> </p> <p id="N164CF" type="main"> <s id="N164D1">Huic tamen difficultati occurrit Philo&longs;ophus re&longs;ponden­<lb/>do, quòd licet ip&longs;i circuli &longs;upponantur concentrici, vtpotè <lb/>circa idem pariter centrum coniuncti, ac reuoluti, non pro­<lb/>pterea &longs;equitur, quod ambo debeant connaturali modo &longs;ua <lb/>propria motione moueri. </s> <s id="N164DC">Nam qui ab altero fertur, moue­<lb/>tur ad motionem illius, non &longs;ecus ac &longs;i nullam ad talem mo­<lb/>tum, &longs;eu rotationem circa idem centrum propriam aptitu­<lb/>dinem obtineret quemadmodum reuera obtinet; quippe <lb/>cum illa non vtatur: Vnde tantum poterit moueri, quan­<lb/>tum mouebitur is, à quo fertur, & cui e&longs;t alligatus. </s> <s id="N164E9"><expan abbr="Ideoq.">Ideoque</expan> <lb/>inquit rectè concludi, inæquales circulos circa idem cen­<lb/>trum connexos æquale &longs;patium in &longs;ua rotatione tran&longs;mitte­<lb/>re, &longs;i vnus moueatur ad motum alterius. </s> </p> <p id="N164F5" type="main"> <s id="N164F7">Po&longs;tremò illud hic adnotat Ari&longs;toteles, quòdlicet vter­<lb/>que circulus circa idem centrum reuoluatur, non tamen <lb/>&longs;impliciter idem e&longs;t vtriu&longs;que circuli centrum; &longs;ed vnius <lb/>quidem per &longs;e, nempe deferentis, alterius verò per accidens, <lb/>nempe delati. </s> <s id="N16502">Quandoquidem deferens ex &longs;e vtitur pro­<lb/>prio centro dum circa illud mouetur, <expan abbr="ip&longs;umq.">ip&longs;umque</expan> &longs;ecum rapit <lb/>dum ad vlteriora &longs;uper planum rectà progreditur: delatus <lb/>verò per accidens circa illud conuertitur; &longs;icut per accidens <lb/>etiam progreditur ad motum deferentis. </s> <s id="N16511">Quamobrem &longs;o­<lb/>phi&longs;ticè ac deceptiua ratiocinatione inquit argumentari <lb/>eos, qui ab&longs;olutè, idem ambobus circulis e&longs;&longs;e centrum do­<lb/>cent, eo quod ambo circa idem reuoluantur, ac inde infe­<lb/>runt, vtrumlibet proportionato, & connaturali motu cir­<lb/>cumferri debere: Quod e&longs;t vnumquemque illorum æqua­<lb/>lem rectam &longs;uæ peripheriæ rotando de&longs;cribere; nempe ma­<lb/>iorem circulum rectam maiorem, minorem verò minorem, <lb/>&longs;ecus quàm de facto accidit propter cau&longs;as explicatas. </s> </p> <pb pagenum="214" xlink:href="005/01/222.jpg"/> <p id="N16528" type="main"> <s id="N1652A">Hucu&longs;que ex mente, ac doctrina Ari&longs;totelis, qui tamen <lb/>mul<gap/>orum iudicio non videtur obiectam &longs;ibi difficultatem <lb/>&longs;atis infringere, vt quæ adhuc magna ex parte maneat in &longs;uo <lb/>robore. </s> <s id="N16535">Nam hoc quod e&longs;t proprio, vel alieno motu cieri, <lb/><expan abbr="centrumq.">centrumque</expan> circuli deferentis per accidens e&longs;&longs;e etiam cen­<lb/>trum circuli delati, non tollit, vtrunque circulum &longs;ecun­<lb/>dum ab&longs;idem codem pacto rotari, ac propriam lineam <lb/>rectam in &longs;uo plano de&longs;cribere: vnde videtur inferri eodem <lb/>etiam pacto vtramque lineam de&longs;criptam propriæ periphe­<lb/>riæ à qua de&longs;cribitur debere commen&longs;urari. </s> <s id="N16547">Parum enim <lb/>refert, circulum per &longs;e rotari circa proprium centrum ad <lb/>impul&longs;um axis immediatè, vel per accidens mediante alio <lb/>circulo, dummodo eodem pacto per circumuolutionem &longs;u&etail; <lb/>ab&longs;idis circa idem centrum lineam de&longs;cribat, cui illa debeat <lb/>commen&longs;urari. </s> <s id="N16554">Sphæra namque &longs;uper planum rotando &longs;i­<lb/>ue proprio nutu, &longs;iue alieno impul&longs;u, tardius, aut velocius, <lb/>&longs;icut omnes plani partes, per quas tran&longs;it debet attingere; <lb/>ita per totidem partes &longs;uas illis debet corre&longs;pondere, & ad <lb/>æqualitatem in tran&longs;itu adaptari. </s> <s id="N1655F">Ratio verò vtriu&longs;que e&longs;&longs;e <lb/>pote&longs;t, quia non datur in&longs;tans, in quo ab&longs;is ip&longs;a, vel periphe­<lb/>ria &longs;iue maioris, &longs;iue minoris circuli per nouum punctum <lb/>proprium, vlterius non attingat nouum punctum lineæ re­<lb/>ctæ &longs;uper quam fertur; nec tempus in quo noua eius pars <lb/>nouæ parti illius non commen&longs;uretur. </s> <s id="N1656C">Quapropter cum <lb/>peripheria minoris circuli, vel non habeat tot partes, quot <lb/>habet recta &longs;uper quam fertur motu maioris circuli; vel cer­<lb/>tè partes ip&longs;æ, quas habet non &longs;int æqualis dimen&longs;ionis, &longs;ed <lb/>proculdubio minoris; non videtur quomodo ad contactum <lb/>partis po&longs;t partem mediantibus punctis, po&longs;&longs;it maior linea, <lb/>vt e&longs;t recta, ip&longs;i minori, vt e&longs;t circumferentia minoris circuli <lb/>adæquari, ni&longs;i alia via, ac ratione id comprobetur, & o&longs;ten­<lb/>datur. </s> <s id="N1657F"><expan abbr="Idemq.">Idemque</expan> è conuer&longs;o applicari pote&longs;t in contactu pe­<lb/>ripheriæ maioris circuli cum recta breuiori, quam conficit <lb/>ad motum minoris circuli &longs;uper ab&longs;idem per &longs;e lati. </s> </p> <p id="N16589" type="main"> <s id="N1658B">Ad diluendam igitur omnino prædictam difficultatem, <lb/>quæ multorum quippe vexauit ingenia, & pene in&longs;uperabi-<pb pagenum="215" xlink:href="005/01/223.jpg"/>lis apud aliquos extimatur, liceat aliunde totum negocium <lb/>au&longs;picari, nouumque aliquid in medium affere in eiu&longs;dem <lb/>Ari&longs;totelis, ac veterum Philo&longs;ophorum princip<gap/>s funda <lb/>tum. </s> <s id="N1659D">Ac primò quidem &longs;tabiliatur, motum cuiu&longs;libet circu­<lb/>li &longs;ecundum ab&longs;idem, e&longs;&longs;e motum quendam mixtum ex du­<lb/>plici latione; vna qua circumuoluitur, &longs;eu circa proprium <lb/>centrum fertur in gyrum; altera verò qua ad motum axis <lb/>rectà fertur &longs;uper planum quo ver&longs;us tendit ip&longs;emet axis. <lb/></s> <s id="N165A9">Etenim &longs;i circulus &longs;tans ab&longs;que &longs;ui rotatione raperetur &longs;u­<lb/>per <expan abbr="planũ">planum</expan>, verè moueretur motu recto, ac per vnicum pun­<lb/>ctum totam plani longitudinem &longs;uper quam fertur attinge­<lb/>ret. </s> <s id="N165B6">Si verò circumuolueretur ab&longs;que progre&longs;&longs;u, aut latio­<lb/>ne axis, verè moueretur circulariter ac per omnes partes, <lb/><expan abbr="punctaq.">punctaque</expan> &longs;uæ peripheriæ, eandem plani partem, vel punctum <lb/>in quo &longs;i&longs;tebat attingeret. </s> <s id="N165C2">Cum itaque ad motum axis re­<lb/>ctà &longs;uper planum trahitur, ac &longs;imul rotatur, ex vtraque la­<lb/>tione mixtus quidam motus producitur, per quem tota <lb/>circumferentia toti longitudini &longs;uper quam fertur ada­<lb/>ptatur. </s> </p> <p id="N165CD" type="main"> <s id="N165CF">Deinde verò &longs;tabiliatur lineam, quæ à circulo, prædicto <lb/>modo de&longs;cribitur &longs;uper planum, ab&longs;trahendo à rotatione <lb/>&longs;pontanea, vel coacta ad motum alterius, ex natura &longs;ua non <lb/>de&longs;cribinisi luxta men&longs;uram lationis, &longs;eu motus recti, qui &longs;imui <lb/>cum axe conficitur in anteriora, & cuius virtute de&longs;cribitur. <lb/></s> <s id="N165DB">Etenim ip&longs;a de&longs;cribi po&longs;&longs;et ab eodem circulo etiam &longs;ine ro­<lb/>tatione, per vnicum punctum vt diximus, non autem &longs;ine re­<lb/>cta aliqua latione. </s> <s id="N165E2">Quamobrem in de&longs;criptione ip&longs;ius lineæ <lb/>rectæ &longs;uper planum, per &longs;e, & ab&longs;olutè loquendo, non habe­<lb/>tur ratio de motu circulari, nec de &longs;patio circulariter pera­<lb/>grato ab ip&longs;o circulo, &longs;ed de motu recto, ac &longs;patio, quod ip­<lb/>&longs;e circulus &longs;imul <expan abbr="cũ">cum</expan> axe percurrit, & ad cuius &longs;emper men­<lb/>&longs;uram ip&longs;a recta linea excitatur. </s> <s id="N165F3">Quamuis per accidens con­<lb/>tingat, circulum deferentem, vel alium ex &longs;e, ac &longs;eor&longs;um ro­<lb/>tando, tantum &longs;patium &longs;imul cum axe recta tran&longs;inittere, <lb/>quantum ip&longs;emet circulariter eodem tempore peragrare <lb/>valuerit. </s> <s id="N165FE">Quia &longs;cilicet cum tota progre&longs;&longs;io à &longs;ua ip&longs;ius ro­<pb pagenum="216" xlink:href="005/01/224.jpg"/>tatione dependeat, &longs;icut motus rectus progre&longs;&longs;ionis nece&longs;­<lb/>&longs;ariò proportionatur motui circulari à quo pendet, ita <lb/>etiam linea de&longs;cripta per talem motum proportionari, & <lb/>adæquari debet lineæ de&longs;criptæ, &longs;eu peragratæ per circui­<lb/>tionem. </s> </p> <p id="N1660E" type="main"> <s id="N16610">His itaque &longs;ic &longs;tabilitis, atque &longs;uppo&longs;itis tanquam certis, <lb/>& cuidentibus, ad primam partem quæ&longs;tionis &longs;imul, ac dif­<lb/>ficultatis propo&longs;itæ re&longs;pondetur, circulum delatum &longs;emper <lb/>æquale &longs;patium, ac circulum deferentem &longs;uper planum ro­<lb/>tando, rectà tran&longs;initrere, &longs;iue maior eo fuerit, &longs;iue minor; <lb/>quia illud non tran&longs;mittit ex vi &longs;uæ rotationis, ac iuxta <lb/>men&longs;uram &longs;uæ circumferentiæ, &longs;ed ex vi &longs;ui raptus, & a&longs;por­<lb/>tationis. </s> <s id="N16621">Siquidem tantum rectà progreditur, quantum à <lb/>deferente rapitur, & a&longs;portatur, licet aliàs eodem tempore <lb/>maiorem, aut minorem &longs;imul peragrat circuitum, de quo <lb/>nulla per &longs;e haberi debet ratio, vt præmonuimus. </s> <s id="N1662A">Vnde nec <lb/>requiritur, vt cius motus circumuolutionis &longs;it æqualis mo­<lb/>tui recto, nec vt linea recta, quam percurrit &longs;it æqualis cir­<lb/>cunferentiæ &longs;ecundum quam rotando conuoluitur. </s> </p> <p id="N16633" type="main"> <s id="N16635">Ad &longs;ecundam verò partem quæ&longs;tionis re&longs;pondetur, cir­<lb/>culum deferentem, vel alium, qui &longs;eor&longs;um per &longs;e &longs;uper pla­<lb/>num circumuoluatur, quò maior ip&longs;e fuerit, maius &longs;patium <lb/>rectà in &longs;ua reuolutione percurrere, quò verò minor, minus. <lb/></s> <s id="N1663F">Quia cum tota eius progre&longs;&longs;io fiat ex vi propriæ rotationis, <lb/>non ni&longs;i æqualem &longs;uæ peripheriæ lineam in plano pote&longs;t de­<lb/>&longs;cribere; tantum &longs;cilicet cum &longs;uo axe rectà progrediendo, <lb/>quantum rotatur; ac tantundem &longs;patium percurrendo, quan­<lb/>tum fuerit circumuolutus. </s> <s id="N1664A">Quæ re&longs;pon&longs;io ad vtramque <lb/>difficultatis, &longs;eu quæ&longs;tionis partem, e&longs;t omnino ad mentem <lb/>Ari&longs;totelis, vt patere pote&longs;t ex eius propria, cui hæc maxi­<lb/>mè congruit, licet aliunde vim, ac di&longs;tinctionem obtinuerit. </s> </p> <p id="N16653" type="main"> <s id="N16655">Adhuc tamen ex ei&longs;dem principijs <expan abbr="re&longs;põderi">re&longs;ponderi</expan> pote&longs;t, præ­<lb/>fata nos experiri, quia minor circulus quando mouetur ad <lb/>motum alterius maioris motu mixto iam explicato, magis <lb/>participat de latione recta, quàm circulari; citius videlicet <lb/>progrediendo quàm rorando. </s> <s id="N16664">Cogitur enim rectà progre-<pb pagenum="217" xlink:href="005/01/225.jpg"/>di iuxta progre&longs;&longs;um axis, ac circuli maioris, <expan abbr="&longs;imulq.">&longs;imulque</expan> tardius <lb/>rotari quàm ille, minus &longs;patium eodem tempore tran&longs;init­<lb/>tendo in &longs;ua minori circumuolutione: <expan abbr="proindeq.">proindeque</expan> per talem <lb/>rotationem, rectam quandam lineam de&longs;cribit maiorem, <lb/>quam &longs;it eius circunferentia propria. </s> <s id="N1667C">E contra verò, nam <lb/>cum circulus maior mouetur ad motum minoris, magis par­<lb/>ticipat de latione circulari, quàm recta. </s> <s id="N16683">Siquidem, cogitur <lb/>citius moueri circulariter quàm rectà, cum eodem tempo­<lb/>re maiorem ambitum, quàm circulus minor, æqualemque <lb/>rectam debeat percurrere: <expan abbr="ideoq.">ideoque</expan> minorem rectam in &longs;ua <lb/>circumuolutione de&longs;cribit, quàm &longs;it eiu&longs;inet circum&longs;erentia­<lb/>qua illam attingit. </s> <s id="N16694">Demum quia &longs;i circulus ex &longs;e, & inde­<lb/>pendenter ab alio duplici hac latione feratur, &longs;iue maior &longs;it, <lb/>&longs;iue minor, &longs;emper æquè de vtraque participat. </s> <s id="N1669B">Etenim tan­<lb/>tum rectà progreditur quantum rotatur, nec aliunde rapi­<lb/>tur, aut detinetur, vt magis vna quàm altera latione dimo­<lb/>ueatur. </s> <s id="N166A4">Quo fit vt linea quam &longs;uper planum de&longs;cribit, æqua­<lb/>lis &longs;it propriæ circumferentiæ eique &longs;ecundum omnes par­<lb/>tes commen&longs;urata. </s> </p> <p id="N166AB" type="main"> <s id="N166AD">Verum vt non &longs;olum cau&longs;a tam admirabilis effectus, &longs;ed <lb/>etiam modus quo ip&longs;e ab illa procedit expre&longs;&longs;ius innote­<lb/>&longs;cat, ac difficultas vltimò propo&longs;ita ex directo penitus eua­<lb/>datur, vlterius dicendum e&longs;t, circulum delatum non minus <lb/>ac deferentem, omnia ac &longs;ingula puncta, quæ &longs;unt in linea re­<lb/>cta &longs;uper quam fertur per totidem puncta propria &longs;ucce&longs;&longs;i­<lb/>uè attingere; ita vt in quolibet in&longs;tanti per nouum punctum <lb/>&longs;<gap/>æ peripheriæ attingat nouum punctum plani. </s> <s id="N166C0">Etenim cum <lb/>planum à circulo attingatur per puncta, quæ &longs;unt extremita­<lb/>tes diametrorum, & vterque circulus ex infinitis diametris <lb/>con&longs;tet; imò diametri cir culi maioris includant diametros <lb/>minoris; tot erunt puncta terminatiua diametrorum in cir­<lb/>culo minori, quot &longs;unt in maiori, &longs;iue delato per quæ &longs;imili­<lb/>ter omnia puncta &longs;ui plani valebit attingere. </s> </p> <p id="N166CF" type="main"> <s id="N166D1">Rur&longs;us dicendum e&longs;t tam circulum deferentem, quàm <lb/>circulum delatum omnes, ac &longs;ingulas partes diui&longs;ibiles, qu&etail; <lb/>&longs;unt in eadem linea plani per totidem partes &longs;uas &longs;ucce&longs;&longs;iuè <pb pagenum="218" xlink:href="005/01/226.jpg"/>attingere: hoc tamen di&longs;crimine, quod circulus deferens <lb/>illas attingit commen&longs;uratiuè, & adæquatè, circulus verò <lb/>delatus nonni&longs;i inadæquatè. </s> <s id="N166E1">Sicut enim circulus deferens <lb/>&longs;iue maior &longs;it, &longs;iue minor con&longs;tat ex infinitis partibus inde­<lb/>terminatis, quæ mediant inter infinita puncta, ita etiam cir­<lb/>culus delatus, per ea&longs;que non minus attingere poterit infi­<lb/>nitas partes, quæ &longs;unt in plano. </s> <s id="N166EC">Diximus tamen attingere <lb/>inadæquatè. </s> <s id="N166F1">Nam contactus adæquatus, & commen&longs;ura­<lb/>tus duarum quantitatum, fit per æqualem applicationem <lb/>partium æqualium vtriu&longs;que quantitatis ad coexi&longs;tendum <lb/>&longs;imul in eodem &longs;patio loci: partes autem æqualiter appli­<lb/>carinon po&longs;&longs;ant per lationes inæquales, nam ea e&longs;t inæqua­<lb/>litas in applicatione, quæ e&longs;t in ip&longs;is lationibus, &longs;iue lationes <lb/>cadant in vtramque quantitatem, &longs;iue in alteram tantùm. <lb/></s> <s id="N16701">Quapropter cum tota applicatio partium circumferentiæ <lb/>ad attingendas partes plani &longs;uper quod rotatur, fiat tum ex <lb/>vi ip&longs;ius rotationis, qua &longs;ucce&longs;&longs;iuè ip&longs;æ partes inclinantur <lb/>ad illas, tum ex vi motus recti quo &longs;ucce&longs;&longs;iuè etiam progre­<lb/>diendo ad ca&longs;dem perueniunt: hinc fit, vt &longs;i lationes ip&longs;æ <lb/>æqualiter procedant, quemadmo dum in motu mixto circuli <lb/>deferentis, aut alterius per &longs;e &longs;eor&longs;um rotantis, æqualiter <lb/>etiam alterius quantitatis partes, ad partes alterius appli­<lb/>centur, ac &longs;e tangendo ad inuicem commen&longs;urentur, & <lb/>adæquentur: E contra verò &longs;i non procedant æqualiter ip­<lb/>&longs;æ lationes, &longs;ed vna alteram excedat in velocitate, aut tardi­<lb/>tate, vt in motu mixto cuiu&longs;libet circuli delati, inæqualiter <lb/>etiam partes ip&longs;ius ad partes plani applicentur, ac inadæ­<lb/>quatè adinuicem commen&longs;urentur. </s> </p> <p id="N1671E" type="main"> <s id="N16720">Quod &longs;i non po&longs;&longs;it coexi&longs;tere in &longs;patio, exempli gratia <lb/>bipalmari cum linea recta bipalmari arcus circumferentiæ <lb/>paimaris, vel tripalmaris, quacunque rotatione ad inuicem <lb/>applicentur; hoc profectò intelligitur in quiete, atque in <lb/>termino ip&longs;ius motus: alioquin in tran&longs;itu, ac &longs;ucce&longs;siuè id <lb/>nullo modo repugnat, &longs;icutnec punctum globirectà &longs;uper <lb/>planum delati po&longs;t punctum ip&longs;ius plani, attingere partem <lb/>diui&longs;ibilem eiu&longs;dem plani, eique coexi&longs;tendo inadæquatè <pb pagenum="219" xlink:href="005/01/227.jpg"/>& &longs;ucce&longs;siuè commen&longs;urari, vt omnes penè Philo&longs;ophi fa­<lb/>tentur. </s> <s id="N16738">Maior enim vel minor velocitas atque &longs;ucce&longs;sio in <lb/>tran&longs;itu, & in partium applicatione, ex vi alterius lationis <lb/>æquipollet maiori, vel minori exten&longs;ioni ip&longs;ius quantitatis <lb/>ad replendum æquale &longs;patium ei, quod occupatur ab alia <lb/>quantitate in eodem tempore, qua ratione dicuntur coexi­<lb/>&longs;tere, ac inter &longs;e coaptari. </s> </p> <p id="N16745" type="main"> <s id="N16747">Res itaque &longs;ic e&longs;t concipienda, vt in reuolutione circuli <lb/>minoris ad motum maioris &longs;emper pars minor ip&longs;ius attin, <lb/>gat partem plani maiorem, quia velocius tran&longs;it per illam <lb/>motu recto, quàm rotando æqualem <expan abbr="dimen&longs;ion&etilde;">dimen&longs;ionem</expan> proptiam <lb/>po&longs;sit exponere, atque &longs;ecundum ip&longs;am &longs;e applicare. </s> <s id="N16756">Vnde <lb/>quod illi dee&longs;t exten&longs;ionis compen&longs;atur velociori &longs;ucce&longs;sio­<lb/>ne, & applicatione &longs;ecundum lationem rectam ad coaptan­<lb/>dum &longs;e parti majori. </s> <s id="N1675F">Quod certè non e&longs;t intelligendum <lb/>fieri per raptationem, qua&longs;i per vnicum delati circuli pun­<lb/>ctum plura plani puncta, vel per <expan abbr="eand&etilde;">eandem</expan>. </s> <s id="N1676A">omnino circuli par­<lb/>tem, plures plani partes attingerentur; &longs;ed per propriam, <lb/>rotationem. </s> <s id="N16771">Quia ita rapitur, ac fertur &longs;uper illud motu re­<lb/>cto, vt &longs;imul quamuis tardius feratur latione circulari per <lb/>quam partes, ac puncta ip&longs;ius peripheriæ iugiter mutantur. <lb/></s> <s id="N16779">Cumque numerus in&longs;inities in&longs;initus punctorum, ac indeter­<lb/>minatarum partium vtriu&longs;que circuli &longs;ufficiat ad mutatio­<lb/>nem ip&longs;am continuam, & corre&longs;pondentiam, quam præ&longs;ta­<lb/>re debet infinitis punctis, ac partibus plani, nullum relinqui­<lb/>tur inconueniens, minorem circumferentiam maiori &longs;pario, <lb/>plani ob di&longs;parem lationem, & applicationem inadæquatè <lb/>in tran&longs;itu coaptari. </s> <s id="N16788">Idemque è conuer&longs;o dici pote&longs;t in re­<lb/>uolutione circuli maioris ad <expan abbr="motũ">motum</expan> minoris, vt &longs;cilicet &longs;em­<lb/>per pars maior ip&longs;ius co re&longs;pondeat parti minori in plano <lb/>&longs;uper quod fertur, quia tardius tran&longs;it per illam motu recto, <lb/>quàm rotando æ qualem &longs;ibi dimen&longs;ionem po&longs;&longs;it attingere. <lb/></s> <s id="N16798">Siquidem velocius rotando, quàm progrediendo, nequit at­<lb/>tingere tantam dimen&longs;ionem in plano, quantam ip&longs;e exhi­<lb/>bet per circumuolutionem. </s> <s id="N1679F">Vnde quod ei &longs;upere&longs;t exten­<lb/>&longs;ionis circularis compen&longs;atur tardiori &longs;ucce&longs;&longs;ione, & appli-<pb pagenum="220" xlink:href="005/01/228.jpg"/>cationem &longs;ecundum lationem rectam ad proportionandum <lb/>&longs;e parti minori. </s> <s id="N167AB">Atque hæc in re tam ambigua &longs;i minus <lb/>demon&longs;tra&longs;&longs;e, &longs;altem indica&longs;&longs;e, vel tenta&longs;&longs;e &longs;ufficiat. </s> </p> <p id="N167B0" type="main"> <s id="N167B2">Ad exactius denique percipiendam naturam mi&longs;torum <lb/>motum, non abs re fuerit affinem aliam quæ&longs;tionem diluere, <lb/>quæ forta&longs;&longs;e non minus admirabilem, ac ferè incredibilem <lb/>&longs;upponit experientiam. </s> <s id="N167BB">Nimirum cur in prædicta latione <lb/>duorum circulorum circa idem centrum &longs;ecundùm ab&longs;idem <lb/>circuli maioris, aliqua puncta circumferentiæ maioris, mi­<lb/>nus progrediantur, quàm corre&longs;pondentia &longs;ibi puncta cir­<lb/>cumferentiæ minoris; aliqua verò magis. </s> <s id="N167C6">In maiori enim <lb/>circulo puncta vnius &longs;emicirculi minus progrediuntur, quam <lb/>puncta &longs;emicirculi corre&longs;pondentis in circulo minori. </s> <s id="N167CD">Con­<lb/>tra verò, puncta alterius &longs;emicirculi magis progrediuntur in <lb/>circulo maiori, quàm in minori, vt de motu particulari Epi­<lb/>cyclorum docere &longs;olent A&longs;tronomi. <!-- KEEP S--></s> <s id="N167D7">Quod maximè vide­<lb/>tur admirandum <expan abbr="cū">cum</expan> vterque circulus &longs;impliciter, ac &longs;ecun­<lb/>dum &longs;e totum ad motum axis progrediendo, æquale &longs;pa­<lb/>rium percurrat, vt vidimus, ac probatum e&longs;t in præcedenti­<lb/>bus. </s> <s id="N167E6">Ita tamen rem &longs;e habere &longs;ic o&longs;tenditur. </s> </p> <figure id="id.005.01.228.1.jpg" xlink:href="005/01/228/1.jpg"/> <p id="N167EE" type="main"> <s id="N167F0">E&longs;to exempli gratia circulus maior ABCD, minor verò <lb/>EFGH circa commune centrum I &longs;uper planum KL. <expan abbr="Sintq.">Sintque</expan> <lb/>duo diametri maioris ad angulos rectos &longs;e&longs;e inter&longs;ecantes <lb/>AC, & BD; minoris verò in ip&longs;is contenti EG, & FH; ita <pb pagenum="221" xlink:href="005/01/229.jpg"/>vt BD &longs;it perpendicularis ip&longs;i KL. <!-- KEEP S--></s> <s id="N16803">Rotetur autem vterque <lb/>circulus &longs;imul &longs;ecundum <expan abbr="ab&longs;id&etilde;">ab&longs;idem</expan> maioris dextror&longs;um quou&longs;­<lb/>que punctum C perueniat, verbi gratia in L, ac &longs;emidiame­<lb/>ter IC con&longs;tituatur in ML perpendicularis ip&longs;i KL: ac <lb/>per con&longs;equens IG in MN; ita vt punctum G reperia­<lb/>tur in N. <!-- KEEP S--></s> <s id="N16815">Dicimus ergo punctum C in hac reuolutione <lb/>minus dextror&longs;um promoueri, quàm punctum G. <!-- KEEP S--></s> <s id="N1681B">Demit­<lb/>tatur enim à puncto C linea CO perpendicularis pariter <lb/>ip&longs;i KL, & à puncto G alia perpendicularis GP: & tunc <lb/>apparebit punctum C dextror&longs;um peragra&longs;&longs;e &longs;patium CM, <lb/>vel OL, quæ &longs;unt latera oppo&longs;ita, ac proinde æqualia re­<lb/>ctanguli CMLO, vt pater per 34. propo&longs;it. </s> <s id="N16828">primi. </s> <s id="N1682B">Pun­<lb/>ctum verò G con&longs;tabit peragraffe &longs;patium GM, &longs;eu PL <lb/>æquale huic. </s> <s id="N16832">At GM maior e&longs;t, quàm CM, eo quod <lb/>illam contineat, &longs;icut PL maior e&longs;t ip&longs;a OL propter ean­<lb/>dem rationem. </s> <s id="N16839">Ergo per talem circumuolutionem minus <lb/>dextror&longs;um progreditur punctum C, quod e&longs;t extremum <lb/>diainetri circuli maioris, quàm punctum G extremum <lb/>diametri contenti cit culi minoris. </s> </p> <p id="N16842" type="main"> <s id="N16844">Rur&longs;us verò dicimus punctum D eiu&longs;dem circuli maio­<lb/>ris, minus pariter dextror&longs;um progredi, quam punctum H, <lb/>quod illi corre&longs;pondet in circulo minori. </s> <s id="N1684B">Etenim po&longs;t præ­<lb/>dictam reuolutionem centro I tran&longs;lato in M, ac C in <lb/>L, punctum D erit in linea AM vbi Q, (nempe in loco, <lb/>qui tantum &longs;anè di&longs;ter à puncto M, quantum di&longs;tat extre­<lb/>mum D ip&longs;ius &longs;emidiametri DI ab ip&longs;o centro I,) pun­<lb/>ctum verò H &longs;imiliter erit in R; ita vt &longs;emidiameter IHD <lb/>reperiatur in <expan abbr="MRq.">MRque</expan> Quapropter &longs;i ex duobus punctis QR <lb/>demittantur duæ perpendiculares in planum DL, quæ &longs;int <lb/>QS, & RT, &longs;patium progre&longs;&longs;ionis ip&longs;ius puncti D, erit <lb/>linea IQ, æqualis ip&longs;i DS: Spatium verò progre&longs;&longs;ionis <lb/>puncti H, erit linea IR, &longs;iue DT. C<gap/> lgitur minor &longs;it linea <lb/>DS ip&longs;a DT, &longs;iquidem continetur in illa, remanet vt pun­<lb/>ctum D circuli maioris, minus. </s> <s id="N1686C">dextror&longs;um promoueatur <lb/>quàm punctum H &longs;ibi corre&longs;pondens circuli minoris. </s> </p> <p id="N16871" type="main"> <s id="N16873">E contra tamen dicimus punctum A circuli maioris am-<pb pagenum="222" xlink:href="005/01/230.jpg"/>plius dextror&longs;um progredi, quàm punctum E circuli mino­<lb/>ris quo illi corre&longs;pondet. </s> <s id="N1687D">Po&longs;ita namque eadem reuolu­<lb/>tione, I exi&longs;tente in M, ac C in L, A erit in V: con­<lb/>&longs;titueretur enim tota diameter AIC in VML, in qua etiam <lb/>linea e&longs;&longs;et punctum E, nempe in X. <!-- KEEP S--></s> <s id="N16887">Quod &longs;i compleatur <lb/>rectangulum AV, ac rectangulum EX, erit &longs;patium <lb/>peragratum à puncto A dextror&longs;um idem, quod linea <lb/>AM, vt deducitur ex eadem 34. propo&longs;itione primi. </s> <s id="N16890">Spa­<lb/>tium verò &longs;imiliter peragratum à puncto E, erit EM, quod <lb/>continetur in illo. </s> <s id="N16897">Magis ergo progreditur A, quàm E. <!-- KEEP S--></s> </p> <p id="N1689B" type="main"> <s id="N1689D">Id ip&longs;um tandem demon&longs;tratur de puncto B, quod cer­<lb/>tè magis progreditur quàm F. <!-- KEEP S--></s> <s id="N168A3">Quandoquidem in de&longs;cri­<lb/>pta reuolutione &longs;emidiarneter IB con&longs;titueretur in MY in <lb/>qua cum contineatur &longs;emidiameter IF, ip&longs;um F con&longs;titue­<lb/>retur in Z: completi&longs;que rectangulis BY, & BZ, erit &longs;pa­<lb/>tium dextror&longs;um peragratum à B quantum IY; peragra­<lb/>tum verò ab F; quantum IZ contentum in ip&longs;o IY, quod <lb/>propterea maius e&longs;t. </s> <s id="N168B2">Erunt igitur duo puncta circuli maio­<lb/>ris, quæ minus dextror&longs;um progrediuntur, quàm puncta &longs;ibi <lb/>corre&longs;pondentia circuli minoris: alia verò duo quæ magis. <lb/></s> <s id="N168BA">Quod etiam demon&longs;trari poterit de reliquis punctis eiu&longs;­<lb/>dem &longs;emicirculi cum &longs;uo corre&longs;pondenti in vtroque circulo <lb/>&longs;i vterque bifariam &longs;ecetur per diametrum 3, 4, cuius extre­<lb/>mitates nempe 3, & 4, in circulo maiori medient inter A, <lb/>& D, ac inter B & C. <!-- KEEP S--></s> <s id="N168C6">Sicut in circulo minori extremita­<lb/>tes 5, 6. medient inter E, & H, ac inter F, & G. <!-- KEEP S--></s> <s id="N168CC">Nam <lb/>puncta omnia &longs;emicirculi inferioris 3 DC 4 in circulo <lb/>maiori, minus progredi <expan abbr="reperi&etilde;tur">reperientur</expan>, quàm puncta &longs;emicircu­<lb/>li inferioris 5 HG 6 &longs;ibi corre&longs;pondentis in circulo mino­<lb/>ri. </s> <s id="N168DB">E contra verò omnia puncta &longs;emicirculi &longs;uperioris 3 <lb/>AB 4 magis progredi, quàm puncta corre&longs;pondentis &longs;emi­<lb/>circuli 5 EF 6 in circulo minori. </s> <s id="N168E2">Ip&longs;a tamen puncta ex­<lb/>trema diametri 3, 4 in circulo maiori, nec magis, nec mi­<lb/>nus, &longs;ed æquè progredi con&longs;picientur, ac extrema diametri <lb/>5, 6 in circulo minori. </s> <s id="N168EB">Sicut enim per quàm facilè id po­<lb/>terit eadem ratione qua &longs;upra demon&longs;trari, ita hic de-<pb pagenum="223" xlink:href="005/01/231.jpg"/>mon&longs;tra&longs;&longs;e, inutile, ac prolixum extimaretur. </s> </p> <p id="N168F5" type="main"> <s id="N168F7">Eiu&longs;modi ergo euentus cau&longs;am reddere nullo negocio <lb/>qui&longs;que poterit &longs;uppo&longs;ita expo&longs;itione mixti motus, quam <lb/>&longs;upra tradidimus: cum planè ex illa pateat, puncta CD, &longs;i­<lb/>cut & puncta GH duabus lationibus ferri, vna dextror&longs;um, <lb/>&longs;imul cum toto circulo ad motum rectum axis I ver&longs;us M: <lb/>altero verò &longs;ini&longs;tror&longs;um ad proprium rotationis motum quo <lb/>obliquè puncta omnia &longs;emicirculi inferioris CDA, &longs;icut & <lb/>GHE retrocedunt ver&longs;us partes AK. </s> <s id="N16908">Hinc namque fit, vt <lb/>tantum de recta eorum latione dextror&longs;um &longs;ubtrahatur, <lb/>quantum per motum circularem obliquè retroce&longs;&longs;erint. <lb/></s> <s id="N16910">Cumque minus contingat retrocedere punctum G, &longs;i­<lb/>cut & punctum H, quàm ip&longs;a puncta CD iuxta mino­<lb/>rem &longs;uum motum, <expan abbr="minoremq.">minoremque</expan> &longs;emicirculum, quem per il­<lb/>lum percurrunt; &longs;equitur, vt ip&longs;a puncta GH, magis quàm <lb/>puncta CD participent de latione recta qua tendunt dex­<lb/>tror&longs;um. </s> <s id="N16921">At loquendo de punctis AB, ac de EF, contraria <lb/>e&longs;t ratio. </s> <s id="N16926">Nam huiu&longs;modi quatu or puncta &longs;icut & ip&longs;i toti <lb/>&longs;emicirculi &longs;uperiores, nempe ABC, & EFG, vtraque la­<lb/>tione feruntur dextror&longs;um. </s> <s id="N1692D">Quo fit, vt illud punctum ma­<lb/>gis progrediatur, quod celerius mouetur latione propria, <lb/>&longs;eu maius &longs;patium eodem tempore virtute circumuolutio­<lb/>nis tran&longs;mi&longs;erit. </s> <s id="N16936">Cum igitur puncta AB, hoc ip&longs;o, quod &longs;int <lb/>puncta circuli maioris, velocius ferantur, <expan abbr="maioremq.">maioremque</expan> ambi­<lb/>tum rotando percurrant, quàm puncta EF in circulo mino­<lb/>ri; magis etiam dextror&longs;um progredientur. </s> </p> <p id="N16943" type="main"> <s id="N16945">Quod &longs;i puncta, quæ &longs;unt in arcubus 4 C, & 6 G dex­<lb/>tror&longs;um vtraque pariter latione ferantur, &longs;icut reliqua pun­<lb/>cta, quæ &longs;unt in &longs;emicirculis ABC, & EFG; & tamen pun­<lb/>cta inter 4 C circuli maioris minus progrediantur, quàm <lb/>&longs;ibi corre&longs;pondentia in 6 G circuli minoris; hoc quidem <lb/>fit; nam cum ip&longs;i arcus maximè declinent deor&longs;um, parum <lb/>ambo progrediuntur ad dexteram virtute &longs;uæ circumuolu­<lb/>tionis; <expan abbr="multumq.">multumque</expan> virtute motus recti, & a&longs;portantis ad mo­<lb/>tum axis. </s> <s id="N1695C">Cumque ratione &longs;itus, terminus à quo incipit mo­<lb/>ueri prædictus arcus circuli minoris, magis di&longs;tet à termino, <pb pagenum="224" xlink:href="005/01/232.jpg"/>à quo incipit moueri arcus maioris, quàm &longs;it exce&longs;&longs;us pto­<lb/>gre&longs;&longs;ionis ip&longs;ius arcus maioris ratione termini, ad quem <lb/>po&longs;tea pertingit, &longs;equitur ab&longs;olutè loquendo, magis progre­<lb/>di dextror&longs;um prædictum arcum circuli minoris, quàm ar­<lb/>cum circuli maioris. </s> <s id="N1696E"><expan abbr="Idemq.">Idemque</expan> è conuer&longs;o applicari pote&longs;t in <lb/>arcubus 3 A, 5 E ad o&longs;tendendum, cur puncta arcus <lb/>3 A circuli maioris, magis progrediantur quàm puncta ar­<lb/>cus 5 E circuli minoris. </s> <s id="N1697A">Nam licet vterque arcus per mo­<lb/>tum circularem retrocedat, ac retrocedendo velocius mo­<lb/>ueatur arcus maioris, quàm minoris; nihilominus ratione <lb/>&longs;itus, ac termini à quo, <expan abbr="cũ">cum</expan> minor &longs;it exce&longs;&longs;us retroce&longs;&longs;ionis, <lb/>quàm antece&longs;&longs;ionis virtute motus rect, eo quod à remotio­<lb/>ri termino arcus maioris promoueatur; hinc pariter fit, vt <lb/>maior &longs;it progre&longs;&longs;us dextror&longs;um maioris, quàm minoris ar­<lb/>cus prædicti, &longs;icut & totius &longs;emicirculi 3 AB 4, quàm 5 <lb/>EF 6, vt dicebamus. </s> </p> <p id="N16991" type="head"> <s id="N16993">Quæ&longs;tio Vige&longs;imaquinta.</s> </p> <p id="N16996" type="main"> <s id="N16998">C<emph type="italics"/>vr lectulorum &longs;pondas &longs;ecundum duplam fa­<lb/>ciunt proportionem, hanc quidem &longs;ex pedum, <lb/>vel paulò ampliorem, illam verò trium? </s> <s id="N169A2">Curvè <lb/>non &longs;ecundum diametcum illos restibus exten­<lb/>dunt? </s> <s id="N169A9">An tantos quidem magnitudine faciunt, <lb/>vt corporibus &longs;int proportionem babentes? <lb/></s> <s id="N169AF">fiunt enim &longs;ic &longs;ecundum &longs;pondas dupli, longitudine quidem <lb/>cubitorum, latitudine verò duorum. </s> <s id="N169B4">Extendunt autem illos <lb/>non &longs;ecundum diametrum, &longs;ed ex oppo&longs;ito, vt & ligna <lb/>minus di&longs;trabantur. </s> <s id="N169BB">Celerrimè enim &longs;cinduntur &longs;ecundum na­<lb/>turam diui&longs;a, & eodem modo distenta laborant maximè. </s> <s id="N169C0">Am­<lb/>plius quonia n opus e&longs;t, vt re&longs;tes pondus ferre po&longs;sint, &longs;i certè <lb/>pondere impo&longs;ito minus <expan abbr="laborabũt">laborabunt</expan>, &longs;i tran&longs;uer&longs;im, quàm &longs;i obli­<lb/>què extendantur. </s> <s id="N169CD">Præterea hoc etiam modo minus ab&longs;umitur <lb/>restium. </s> <s id="N169D2">Sit enim lectulus AFGK, & bifariam diuidatur ip­<lb/>&longs;a FG &longs;ecundum B: æqualia certè foramina &longs;unt in ip&longs;a <lb/>FA: latera enim &longs;unt æqualia, nam totum FG duplum est. <lb/></s> <s id="N169DA">Extendunt autem, vt de&longs;criptum e&longs;t, ab ip&longs;o A ad ip&longs;um B: ita <lb/>vbi e&longs;t C ita e&longs;t D, ita vbi H, po&longs;tea vbi E, & <expan abbr="eod&etilde;">eodem</expan> &longs;emper mo-<emph.end type="italics"/><pb pagenum="225" xlink:href="005/01/233.jpg"/><emph type="italics"/>do, donee ad angulum peruenerint <expan abbr="aliũ">alium</expan>. </s> <s id="N169F0">Duo enim anguli restis <lb/>babent capita: æquales autem &longs;unt re&longs;tes &longs;ecundum curuatu­<lb/>ras, videlicet AB, & BC, ip&longs;is CD, & DH: & aliæ &longs;imi­<lb/>li &longs;e babent modo, quoniam eadem demon&longs;tratio: ip&longs;a enim <lb/>AB æqualis est ip&longs;i HE, æqualia enim &longs;unt latera &longs;patÿ BG, <lb/>MA, & foramina æquè distant. </s> <s id="N169FD">Ip&longs;a autem BG æqualis e&longs;t <lb/>ip&longs;i MA. </s> <s id="N16A02">Angulus enim B æqualis e&longs;t angulo G. <!-- KEEP S--></s> <s id="N16A06">In æquali­<lb/>bus enim hic quidem intus, ille verò extra, & B quidem est <lb/>&longs;emirectus. </s> <s id="N16A0D">Est enim FB æqualis ip&longs;i FA. </s> <s id="N16A10">Et angulus vbi <lb/>F, rectus e&longs;t, B autem angulus æqualis ei, vbi e&longs;t G quo­<lb/>niam quadratum altera parte longius, duplum e&longs;t: & ad me­<lb/>dium e&longs;t curuatura, quamobrem AD ip&longs;i EG e&longs;t æqualis, bui<gap/><lb/>verò ip&longs;a HM. <expan abbr="Similiq.">Similique</expan> modo demon&longs;trantur aliæ, quoniam <lb/>æquales &longs;unt duæ, quæ &longs;ecundum euruaturas &longs;unt, duabus. <lb/></s> <s id="N16A23">Quare manifestum e&longs;t, quod tot &longs;unt re&longs;tes in lectulo, quot <lb/>&longs;unt quatuor, &longs;icut AB. <!-- KEEP S--></s> <s id="N16A29">Quanta autem foraminum e&longs;t mul­<lb/>titudo in ip&longs;o FG laters, & in eius dimidio FB e&longs;t medietas. <lb/></s> <s id="N16A2F">Quamobrem in dimidiato lectulo tantæ re&longs;tium magnitudines <lb/>erunt, quantum e&longs;t AB, multitudine verò tot, quot in BG &longs;unt <lb/>foramina. </s> <s id="N16A36">Hoc autem nihil refert dicere, quàm quot &longs;unt in <lb/>ip&longs;is AF, & BF &longs;imul &longs;umptis. </s> <s id="N16A3B">Si autem &longs;ecundum diame­<lb/>trum extendantur re&longs;tes, quemadmodum &longs;e babet in lectulo <lb/>ABCD: dimidia non tot &longs;unt, quot amborum latera FAFG, <lb/>æqualia autem quot in ip&longs;is FB, FA, &longs;unt foramina. </s> <s id="N16A44">Maio­<lb/>res autem &longs;unt ip&longs;æ AF, BF, duæ exi&longs;tentes, quam AB. <!-- KEEP S--></s> <s id="N16A4A">Qua­<lb/>re re&longs;tis in tantùm maior, quantùm ambo latera diametro &longs;unt <lb/>maiora.<emph.end type="italics"/></s> </p> <p id="N16A53" type="head"> <s id="N16A55">COMMENTARIVS.<!-- KEEP S--></s> </p> <p id="N16A59" type="main"> <s id="N16A5B">Vt ex re nullius difficultatis, atque momenti, inge­<lb/>nioiam, ac perdifficilem apud multos excitet dubi­<lb/>tationem, quærit hic primò Ari&longs;toteles, cur lectulo­<lb/>rum &longs;pondæ &longs;ecundum duplam proportionem longitudinis <lb/>ad latitudinem eorum efficiantur, ita vt quæ lectulorum <lb/>longitudinem con&longs;tituunt &longs;ex pedum exi&longs;tant, quæ verò la­<lb/>titudinem, trium. </s> <s id="N16A6A"><expan abbr="Statimq.">Statimque</expan> id con&longs;ueui&longs;&longs;e docet, vt huma­<lb/>norum corporum ratio habeatur, <expan abbr="lectuliq.">lectulique</expan> illis proportio­<pb pagenum="226" xlink:href="005/01/234.jpg"/>nentur ad cubantium commoditatem. </s> <s id="N16A7B">Loquitur autem. <lb/></s> <s id="N16A7F">Philo&longs;ophus de lectulis minoribus cum qui ad vnum dum­<lb/>taxat capiendum hominem cubantem efficiuntur, tum qui <lb/>re&longs;tibus, &longs;eu funibus quibu&longs;dam ad &longs;u&longs;tinendam culcitram <lb/>&longs;uper quam ille iaceat &longs;unt intexti, quemadmodum adhuc <lb/>in Italia licet rarò, frequentius tamen in Gallia, atque Hi&longs;pa­<lb/>nia con&longs;piciuntur in v&longs;um traducti. </s> </p> <p id="N16A8C" type="main"> <s id="N16A8E">Hinc itaque rur&longs;us qu<gap/>rit cur in huiu&longs;modi lectulis mu­<lb/>niendis, re&longs;tes per tran&longs;uer&longs;um, & ex oppo&longs;ito, non autem <lb/>per diametrum extendantur. </s> <s id="N16A97"><expan abbr="Aitq.">Aitque</expan> triplici ex cau&longs;a id fieri; <lb/>vel pariter in con&longs;uetudinem abij&longs;&longs;e. </s> <s id="N16A9F">Primò nimirum, vt <lb/>&longs;pondarum ligna ab ip&longs;is re&longs;tibus minus di&longs;trahantur atque <lb/>&longs;cindantur; quandoquidem &longs;ci&longs;&longs;ioni magis obnoxia &longs;unt cum <lb/>per diametrum in eis funes inditi fuerint, ac di&longs;tenti. </s> <s id="N16AA8">Nam <lb/>tunc qua&longs;i per longum iuxta naturales venulas, ac rimulas, <lb/>quibus ob&longs;equendo facilè &longs;equitur &longs;ci&longs;sio, ligna ip&longs;a vim pa­<lb/>terentur, ac veluti &longs;ecarentur; &longs;ecus ac &longs;i per tran&longs;uer&longs;um, <lb/>ac &longs;ecundum latitudinem terebrata &longs;int, funesq per ip&longs;a <lb/>foramina <expan abbr="traducãtur">traducantur</expan>. </s> <s id="N16AB9">Quia &longs;emper lignorum tramites tran&longs;­<lb/>uer&longs;i funium pre<gap/>&longs;&longs;ioni magis re&longs;i&longs;tunt. </s> </p> <p id="N16AC0" type="main"> <s id="N16AC2">Secundo id fieri docet ex eo quod &longs;ic funes traducti, mi­<lb/>nus laborant, pondus &longs;uperimpo&longs;itum &longs;u&longs;tinendo. </s> <s id="N16AC7">Quo enim <lb/>per breuiores lineas exten&longs;i fuerint, eò fortiores euadunt. <lb/></s> <s id="N16ACD">Sic è contra cum per longiores, debiliores fiunt, ac facilius <lb/>in parte ab extremis remoti&longs;&longs;ima di&longs;rumpuntur: longiores <lb/>autem lineæ &longs;unt diametrales in quadrangulari, ac rectan­<lb/>gula figura de qua loquimur, vt per &longs;e patet. </s> </p> <p id="N16AD6" type="main"> <s id="N16AD8">Tertio denique id ip&longs;um iccirco v&longs;ui e&longs;&longs;e inquit, vt in ip­<lb/>&longs;a lectulorum textura minus re&longs;tium, &longs;eu funium ab&longs;umatur. <lb/></s> <s id="N16ADE">Quod licet implexè admodum videatur probare ob textus <lb/>corruptionem; Satis tamen &longs;en&longs;us probationis tenctur, at­<lb/>que optimè à Piccolomineo dilucidatur. </s> </p> <p id="N16AE5" type="main"> <s id="N16AE7">Summatim verò ad hoc, vt clarius probatio ip&longs;a perci­<lb/>piatur, &longs;upponimus primò cum ip&longs;o Ari&longs;torele, quod lectu­<lb/>lus &longs;uis re&longs;tibus per tran&longs;uer&longs;um intextus exempli gratia <pb pagenum="227" xlink:href="005/01/235.jpg"/><figure id="id.005.01.235.1.jpg" xlink:href="005/01/235/1.jpg"/><lb/>&longs;it <expan abbr="rectãgulũ">rectangulum</expan> IGAO, <lb/><expan abbr="eiusq.">eiusque</expan> <expan abbr="lõgiores">longiores</expan> <expan abbr="&longs;põ-dæ">&longs;pon­<lb/>dæ</expan>, nempe &longs;ex <expan abbr="pedũ">pedum</expan> <lb/>&longs;int IG, & AO; bre­<lb/>uiores verò <expan abbr="triũ">trium</expan> pe­<lb/>dum IA, & GO, &longs;in­<lb/>gulæ in totidem pe­<lb/>des diui&longs;æ per &longs;ua <lb/>foramina, quibus re­<lb/>&longs;tes indantur, prout <lb/>hic litteris con&longs;ignantur. </s> <s id="N16B24">Deinde &longs;upponimus ex eodem, <lb/>hoc pacto re&longs;tes ip&longs;os per tran&longs;uer&longs;um extendi. </s> <s id="N16B29">Sumitur ini­<lb/>tium re&longs;tis, & obfirmatur in A, tunc re&longs;tis ip&longs;a ducitur ad B, <lb/>ex quo po&longs;tea per C flectitur in D; hinc per E ad F; exinde <lb/>verò per G ad H: ex H autem rur&longs;us ducitur in I, & ex I per <lb/>K in L; vnde per M ad N; & ex N per B, <expan abbr="tand&etilde;">tandem</expan> peruenitur <lb/>in O; vbi &longs;imiliter <expan abbr="alterũ">alterum</expan> re&longs;tis caput de&longs;inendo obfirmatur. </s> </p> <p id="N16B3E" type="main"> <s id="N16B40">Quibus po&longs;itis ad <expan abbr="comprehendendã">comprehendendam</expan> huiu&longs;modi re&longs;tium <lb/>quantitatem &longs;ic ferè procedit Ari&longs;toteles, vel &longs;altem ob&longs;cu­<lb/>riu&longs;culè æquiualentia profert. </s> <s id="N16B4B">Cum enim triangulus BGO <lb/>ex con&longs;tructione &longs;it rectangulus, quadrata laterum BG, & <lb/>GO, per 47. primi, æqualia &longs;unt quadrato lateris BO. </s> <s id="N16B52">Cum­<lb/>que latus BG, &longs;icut & latus GO trium exi&longs;tant pedum, ac <lb/>ternarij quadratus numerus, &longs;int nouem; hinc fit, vt ex vtro­<lb/>que quadrato, &longs;cilicet lateris BG, & lateris GO, con&longs;ti­<lb/>tuatur numerus 18. totidem pedes contineat quadratum <lb/>lateris BO duobus illis æquale, proindeque vt latus ip­<lb/>&longs;um BO &longs;it radix quadrata numeri 18. nempe quatuor <lb/>pedum circiter cum quarta. </s> <s id="N16B63">At in lectulo non &longs;unt ni&longs;i <lb/>octo re&longs;tes æquales, <expan abbr="eiu&longs;demq.">eiu&longs;demque</expan> dimen&longs;ionis, ac latus BO, <lb/>vt patet per 33. primi. </s> <s id="N16B6E">Ergo omnes ip&longs;i re&longs;tes &longs;imul &longs;um­<lb/>pti, ac per tran&longs;uer&longs;um intexti erunt qua&longs;i triginta quatuor <lb/>pedum: quibus &longs;i addantur (vt rectè notat Baldus) &longs;ex alij <lb/>pedes re&longs;tium qui cadunt extra, nempe à B in C, & à D in <lb/>E, & &longs;ic in reliquis, erit re&longs;tis totius longitudo pedum qua­<lb/>draginta cum dimidio, vel paulò amplius. </s> </p> <pb pagenum="228" xlink:href="005/01/236.jpg"/> <p id="N16B7F" type="main"> <s id="N16B81">Quod &longs;i re&longs;tes extendantur &longs;ecundum diametrum, vt in <lb/>de&longs;cripto lectulo ABCD, plus re&longs;tium ab&longs;umi, inquit Phi­<lb/><figure id="id.005.01.236.1.jpg" xlink:href="005/01/236/1.jpg"/><lb/>lo&longs;ophus; & eadem <lb/>qua &longs;upra ratioci­<lb/>natione poterit de­<lb/>mon&longs;trari. </s> <s id="N16B94"><expan abbr="Nã">Nam</expan> &longs;in­<lb/>gulis <expan abbr="quibusq.">quibusque</expan> re­<lb/>&longs;tibus, tanquam la­<lb/>teribus trianguli re­<lb/>ctanguli con&longs;idera­<lb/>tis per 47. prop. <lb/></s> <s id="N16BA9">primi, & per extractionem radicis quadratæ, inueniemus, <lb/>eos omnes &longs;imul &longs;umptos quadraginta pedum cum dimi­<lb/>dio obtinere dimen&longs;ionem, quibus &longs;i alios &longs;eptem, qui ex­<lb/>tra cadunt adijciamus, erit tota longitudo re&longs;tis pedum 47. <lb/>cum dimidio. </s> <s id="N16BB4">Quod &longs;anè ad rei, de qua agitur intelligen­<lb/>tiam &longs;ufficit indica&longs;&longs;e, cum exactior &longs;upputatio fru&longs;trà ac <lb/>prolixius quàm par e&longs;t, &longs;ermonem protraheret. </s> </p> <p id="N16BBB" type="head"> <s id="N16BBD">Quæ&longs;tio Vige&longs;ima&longs;exta.</s> </p> <p id="N16BC0" type="main"> <s id="N16BC2">C<emph type="italics"/>vr diffi ilius e&longs;t longa ligna ab extremo &longs;upe<gap/><lb/>humeros ferre, quàm &longs;ecundum medium, <lb/>æquali existente pondere? </s> <s id="N16BCD">An quia vibrato li­<lb/>gno ip&longs;um extremum prohibet ferre, vibratio­<lb/>ne magis retrahens lationem? </s> <s id="N16BD4">An quoniam li­<lb/>cet nihil inflectatur, neque multam habeat lon­<lb/>gitudinem, difficilius tamen ad ferendum e&longs;t <lb/><gap/> extremo, quoniam facilius ex medio eleuatur, quàm ab ex­<lb/>tremo, & ideo &longs;ic ferre e&longs;l facilius. </s> <s id="N16BE0">Cau&longs;a autem quoniam <lb/>&longs;ecundum medium quidem eleuato ligno &longs;emper &longs;e&longs;e inuicem <lb/>&longs;u&longs;pendunt extrema, & altera pars alteram bene &longs;ubleuat. <lb/></s> <s id="N16BE8">Medium enim veluti centrum fit, vbi babet is qui eleuat, <lb/>aut fert. </s> <s id="N16BED">Extremorum igitur vtrumque deor&longs;um vergens, <lb/>&longs;ur&longs;um &longs;u&longs;penditur. </s> <s id="N16BF2">Quod &longs;i ab extremo eleuetur, aut fe­<lb/>ratur, non &longs;anè facit: &longs;ed vniuer&longs;um pondus ad vnum ver­<lb/>git medium, quo eleuatur, aut fertur. </s> <s id="N16BF9">Sit medium vbi A, <lb/>extrema B, C. <!-- KEEP S--></s> <s id="N16BFF">Eleuato igitur aut portato &longs;ecundum A,<emph.end type="italics"/><pb pagenum="229" xlink:href="005/01/237.jpg"/><emph type="italics"/>ip&longs;um quidem B deor&longs;um nutans, &longs;ur&longs;um eleuat C, ip&longs;um au­<lb/>tem C aeor&longs;um nutans, B &longs;ur&longs;um eleuat, ambo autem &longs;ur&longs;um <lb/>eleuata hoc faciunt.<emph.end type="italics"/></s> </p> <p id="N16C11" type="head"> <s id="N16C13">COMMENTARIVS.<!-- KEEP S--></s> </p> <p id="N16C17" type="main"> <s id="N16C19">Dvplicem Ari&longs;totel<gap/>cau&longs;am affert, ob <expan abbr="quã">quam</expan> difficilius <lb/>procera ligna ab extremo &longs;uper <expan abbr="humerũ">humerum</expan> ge&longs;tantur, <lb/>quàm è medio, æquali exi&longs;tente pondere, à quo to­<lb/>ta ge&longs;tandi difficultas na&longs;ci videretur. </s> <s id="N16C2C">Vna e&longs;t, quia procera <lb/>ligna, vt plurimùm ex &longs;e flexibiliora &longs;unt, ac vibrationi, & flu­<lb/>ctuationi magis obnoxia, quàm breuiora. </s> <s id="N16C33">Quapropter &longs;i to­<lb/>ta ferè longitudo ligni &longs;uper humerum ge&longs;tati, à tergo po­<lb/>natur, parte tantum ante relicta qua manu &longs;u&longs;tineatur, cre­<lb/>&longs;cit cum ip&longs;a longitudine flexibilitas: vnde magis agitatio­<lb/>ne ip&longs;a portantis fluctuando vibratur: vibratio autem non <lb/>parum ge&longs;tationem impedit, retrahendo quodammodo la­<lb/>tionem, dum frequenti&longs;&longs;imo motu &longs;ur&longs;um, ac deor&longs;um vi­<lb/>brati ligni extremitas tendit, <expan abbr="proindeq.">proindeque</expan> non ad partes ante­<lb/>riores, iuxta motum progre&longs;&longs;iuum ferentis. </s> <s id="N16C4A">De quo vibra­<lb/>tionis effectu iterum redibit &longs;ermo quæ&longs;tione &longs;equenti vbi <lb/>fu&longs;iùs, ac luculentiùs declarabitur. </s> <s id="N16C51">Interim concluditur ex <lb/>Ari&longs;totele, propter maiorem huiu&longs;modi fluctuationem, ac <lb/>vibrationem difficilius procera ligna ab extremo &longs;uper hu­<lb/>merum ge&longs;tari, quàm &longs;i è medio &longs;u&longs;tinerentur, atque a&longs;por­<lb/>tarentur, cum hoc pacto, minus ab humero, feu fulcimen­<lb/>to producta, minus vibrationi e&longs;&longs;ent obnoxia. </s> </p> <p id="N16C5E" type="main"> <s id="N16C60">Quoniam verò cau&longs;a hæc vniuer&longs;alis non e&longs;t, nec adæ­<lb/>quata, &longs;iquidem nec omnia ligna quantumuis procera fle­<lb/>xibilia &longs;unt, aut vibrari po&longs;&longs;unt; nec difficultas ge&longs;tationis <lb/>à &longs;ola vibratione <expan abbr="interced&etilde;te">intercedente</expan> procedit; hinc e&longs;t, quod Ari&longs;to­<lb/>teles alteram propo&longs;itæ difficultatis cau&longs;am, tanquam vni­<lb/>uer&longs;aliorem in medium afferat. </s> <s id="N16C71">Ea autem e&longs;t, quia quæ­<lb/>cumque difficilius eleuantur, difficilius pariter po&longs;tquam <lb/>eleuata fuerint &longs;u&longs;tinentur, aut ge&longs;tantur, cum tàm latio, <lb/>quàm &longs;u&longs;tentatio &longs;it veluti continuata quædam eleuatio ob <pb pagenum="230" xlink:href="005/01/238.jpg"/>longa autem ligna difficilius ab extremo eleuantur, quam <lb/>ex medio, &longs;iquidem eleuato ligno ab eius medio &longs;emper <lb/>&longs;e&longs;e inuicem &longs;u&longs;tentant extrema, & altera pars alteram &longs;ub­<lb/>leuat, ait ip&longs;e <gap/>hilo&longs;cphus. </s> <s id="N16C87">Medium enim qua&longs;i centrum <lb/>con&longs;tituitur, quod fulcitur in manu eleuantis, aut in humero <lb/>deferentis. </s> <s id="N16C8E">Quapropter ad depre&longs;sionem alterius extremi, <lb/>alterum eleuatur, & &longs;ic vici&longs;sim mutuo &longs;u&longs;tolluntur. </s> <s id="N16C93">At &longs;i <lb/>ab extremo idem lignum eleuetur, vel deferatur, vniuer&longs;o <lb/>pondere deor&longs;um vergente, nulla e&longs;&longs;et pars, quæ ad graui­<lb/>tationem alterius eleuatetur, proindeque laborio&longs;a magis <lb/>e&longs;&longs;et ge&longs;tatio. </s> </p> <p id="N16C9E" type="main"> <s id="N16CA0">Verùm contra huiu&longs;modi di&longs;cur&longs;um, ac doctrinam Ari­<lb/>&longs;totelis illud obijci po&longs;&longs;et, quod tamet&longs;i extrema proceri <lb/>ligni è puncto medio delati &longs;e&longs;e inuicem &longs;u&longs;tollant vtrum <lb/>libet alterum &longs;uperando: nihilominus ip&longs;a &longs;imul &longs;umpta <lb/>cum toto ligno &longs;emper eodem modo grauitant re&longs;pectu <lb/>deferentis, &longs;iue in &etail;quilibrio, &longs;iue &longs;ecus con&longs;tituantur. </s> <s id="N16CAD">Quan­<lb/>doquidem deferens tam excedens, quàm exce&longs;&longs;um &longs;u&longs;ti­<lb/>net, ac defert: proindeq pondus ip&longs;ius ligni, non minus gra­<lb/>uitare concluditur cum lignum ip&longs;um è medio &longs;u&longs;tollitur, ac <lb/>cum ab extremo. </s> </p> <p id="N16CB8" type="main"> <s id="N16CBA">Huic tamen obiectioni occurritur di&longs;tinguendo grauita­<lb/>tionem procedentem ab ip&longs;o pondere ligni delati &longs;ecun­<lb/>dum &longs;e &longs;umpto ab ea, quæ procedit ratione di&longs;tantiæ à ful­<lb/>cimento quò &longs;u&longs;tinetur. </s> <s id="N16CC3">Nulli namque dubium e&longs;t grauita­<lb/>tionem procedentem à naturali pondere ip&longs;ius ligni, ean­<lb/>dem &longs;emper e&longs;&longs;e, &longs;iue lignum ex medio, &longs;iue ab extremo &longs;u­<lb/>&longs;tollatur. </s> <s id="N16CCC">Nihilque conducere po&longs;itionem extremorum in <lb/>æquilibrio ad diminutionem ponderis naturalis. </s> <s id="N16CD1">Vnde non <lb/>minus grauitat lignum &longs;i è medio &longs;u&longs;pendatur tanquam iu­<lb/>gum alicuius libræ, ac &longs;i ab extremo perpendiculariter ad <lb/>horizontem erectum &longs;u&longs;tineatur. </s> <s id="N16CDA">At loquendo de grauita­<lb/>tione, quæ procedit ex di&longs;tantia grauitatis a fulcimento pr&etail;­<lb/>dicto, non ita res &longs;e habet. </s> <s id="N16CE1">Quandoquidem hæc augetur ad <lb/>augmentum di&longs;tantiæ, ac minuitur per approximationem; <lb/>imò omninò deperditur per <expan abbr="æquilibration&etilde;">æquilibrationem</expan>. </s> <s id="N16CEC">Porrò brachia <pb pagenum="231" xlink:href="005/01/239.jpg"/>libræ, &longs;iue magis &longs;iue minus protendantur, dummodo &etail;qua­<lb/>lia inter &longs;e &longs;int, nihil ponderis, aut grauitationis augent, vel <lb/>minuunt; &longs;ecus autem &longs;i alterum &longs;it protentius, licet æqualis <lb/>ponderis naturalis. </s> <s id="N16CFA">Nam libram vertet per exce&longs;&longs;um &longs;uæ <lb/>di&longs;tantiæ à fulcimento, vt &longs;upra quæ&longs;t. </s> <s id="N16CFF">prima explic uimus. </s> </p> <p id="N16D02" type="main"> <s id="N16D04">Rectè igitur argumentatur Philo&longs;ophus, dum ex mutua <lb/>victoria, ac &longs;ubleuatione extremorum ligni in medio fulti, <lb/>minorem difficultatem, &longs;eu grauitationem infert, quàm &longs;i <lb/>ab extremo &longs;u&longs;tolleretur, ac in &longs;itu &longs;imili &longs;u&longs;tentaretur per <lb/>lineam horizonti paralellam, &longs;eu qua&longs;i paralellam. </s> <s id="N16D0F">Etenim <lb/>in hac &longs;ituatione lignum grauitaret tum iuxta pondus natu­<lb/>rale, tum etiam iuxta di&longs;tantiam alterius extremi à fulci­<lb/>mento; in illa verò non ni&longs;i iuxta grauitatem naturalem. <lb/></s> <s id="N16D19">Quo &longs;it vt &longs;ari&longs;&longs;a, aut lancea perpendiculariter ad planum <lb/>horizontis erecta, facilè ab extremo &longs;u&longs;tineatur, difficilè <lb/>verò per lineam horizonti paralellam con&longs;tituta. </s> <s id="N16D20">Vnde ad <lb/>facilius, præ&longs;tandum manubrium in lancea non quidem in <lb/>ip&longs;o extremo, &longs;ed prope extremum con&longs;tituitur, nec non <lb/>extremum ip&longs;um cra&longs;sius, grauiu&longs;que propterea efficitur <lb/>ad compen&longs;andam grauitatem ortam ex longitudine, qua <lb/>illa cu&longs;pidem ver&longs;us protenditur. </s> <s id="N16D2D">Imò ex hoc etiam ip&longs;a <lb/>productior pars lanceæ cum primò cra&longs;&longs;e&longs;cit, &longs;triari con&longs;ue­<lb/>uit v&longs;que ad manubrium, vt ip&longs;is excauata &longs;trijs, vel &longs;ulcis, <lb/>leuior euadat, & ad planum horizontis vergens, facilius va­<lb/>leat manu ge&longs;tari. </s> <s id="N16D38">Hinc pariter qui viribus pollent ad o&longs;ten­<lb/>tandum robur brachij, atque lacerti, dum ad confrin­<lb/>gendam lanceam in de&longs;tinatum locum procur­<lb/>runt, ab extremo &longs;ubtus manubrium eam <lb/>procumbentem in ip&longs;o cur&longs;u &longs;u&longs;ten­<lb/>tant. </s> <s id="N16D45">Quæ omnia &longs;atis con­<lb/>firmantur ex di­<lb/>ctis <expan abbr="q.">que</expan> 3. ac <lb/>16. </s> </p> <pb pagenum="232" xlink:href="005/01/240.jpg"/> <p id="N16D56" type="head"> <s id="N16D58">Quæ&longs;tio Vige&longs;ima&longs;eptima.</s> </p> <p id="N16D5B" type="main"> <s id="N16D5D">C<emph type="italics"/>vr &longs;i valde procerum fuerit idem pondus, dif­<lb/>ficilius &longs;uper humeros gestatur, etiam&longs;i me­<lb/>dium qui&longs;piam illud ferat, quàm &longs;i breuius <lb/>&longs;it? </s> <s id="N16D69">Quod enim dudum dictum e&longs;t, cau&longs;a non <lb/>e&longs;t, &longs;ed vibratio nunc est cau&longs;a. </s> <s id="N16D6E">Quando enim <lb/>productius fuerit, vibrantur extrema, quam­<lb/>obrem contingit portantem difficilius ge&longs;tare. </s> <s id="N16D75">Vibrationis au­<lb/>tem cau&longs;a e&longs;t, quoniam ab eadem motione magis transferuntur <lb/>extrema; quanto proceriu<gap/> fuerit lignum. </s> <s id="N16D7E">Humerus quidem <lb/>&longs;it centrum vbi A manet enim is; ip&longs;æ autem A B, A C, quæ <lb/>&longs;unt ex centro, quantò autem maius fuerit id, quod ex centro <lb/>e&longs;t, &longs;iuè A B, &longs;eu A C, plus transfertur &longs;patÿ. </s> <s id="N16D87">Demon&longs;tratum <lb/>autem e&longs;t boc prius.<emph.end type="italics"/></s> </p> <p id="N16D8E" type="head"> <s id="N16D90">COMMENTARIVS.<!-- KEEP S--></s> </p> <p id="N16D94" type="main"> <s id="N16D96">Qvamuis idemmet lignum, vel aliud graue corpus <lb/>oblongum facilius ex medio &longs;u&longs;tineatur, ac defera­<lb/>tur, quam ab extremo, vt in præcedenti quæ&longs;t. </s> <s id="N16D9D">di­<lb/>ctum e&longs;t: nihilominus cum hoc etiam pacto delatum, quò <lb/>procerius illud fuerit, eò difficilius ge&longs;tetur, quærit hic Ari­<lb/>&longs;toteles vnde maior hæc difficultas oriatur. </s> <s id="N16DA6">Concluditque, <lb/>vibrationem huius rei cau&longs;am e&longs;&longs;e. </s> <s id="N16DAB">Nam quanto produ­<lb/>ctius fuerit lignum, tantò imbecillius redditur, ac vibrationi <lb/>obnoxius: magis enim in&longs;lectitur, vt quæ&longs;t. </s> <s id="N16DB2">16. probatum <lb/>e&longs;t magi&longs;que eius extrema iactantur tanquam à centro re­<lb/>motiora. </s> <s id="N16DB9">Magis autem iactatis, ac vibratis extremis, diffi­<lb/>cilior euadit ge&longs;tatio; Idque duplici ex capite, vt rectè Bal­<lb/>dus ob&longs;eruat. </s> <s id="N16DC0">Tum &longs;cilicet quia motus vibrationis, vt præ­<lb/>cedenti quæ&longs;t. </s> <s id="N16DC5">docuerat Ari&longs;toteles, morum progre&longs;sionis, <lb/>&longs;ur&longs;um ac deor&longs;um tendendo impedit, ac quod ammodo <lb/>prohibet, retrahendo ip&longs;um delatum, quod in anteriora fer­<lb/>tur: tum etiam quia impetum quendam producit quo vltra <pb pagenum="233" xlink:href="005/01/241.jpg"/><expan abbr="põdus">pondus</expan> grauatus humerus <expan abbr="defer&etilde;tis">deferentis</expan>. </s> <s id="N16DDA">Etenim extrema ip&longs;ius <lb/>ligni valde ab eius medio, &longs;eu centro remota, dum inferius, <lb/>quantum ex &longs;e e&longs;t, vibrando flectuntur ip&longs;ummet centrum, <lb/>&longs;eu medium &longs;ecum rapere, ac detrahere conantur. </s> <s id="N16DE3">Quam­<lb/>obrem humerus, qui medio &longs;upponitur, non modo totius li­<lb/>gni &longs;u&longs;tinet pondus, quod in ip&longs;o grauitatis centro coacer­<lb/>uatur, &longs;ed impetum quoque per eandem extremorum in­<lb/>flexionem ei illatum. </s> <s id="N16DEE">Tamet&longs;i hoc totum intelligatur non <lb/>iugiter, &longs;ed per interualla tantum contingere, vt idem Bal­<lb/>dus animaduertit; Quandoquidem impetus ex ip&longs;o motu <lb/>vibrationis acqui&longs;itus quemadmodum deor&longs;um tendendo <lb/>deprimit, ita &longs;ur&longs;um attollens ip&longs;a extrema, portantem alle­<lb/>uiat, humerumq aliquanti&longs;per nonnihil exonerat, vt milites <lb/>&longs;ari&longs;&longs;am in humero ge&longs;tantes pa&longs;sim experiuntur. </s> </p> <p id="N16DFD" type="head"> <s id="N16DFF">Quæ&longs;tio Vige&longs;imaoctaua.</s> </p> <p id="N16E02" type="main"> <s id="N16E04">C<emph type="italics"/>vr iuxta puteos celonia faciunt eo, quo <lb/>vi&longs;untur modo? </s> <s id="N16E0C">Ligno enim plumbi adiun­<lb/>gunt pondus, cùm alioqui vas ip&longs;um & ple­<lb/>num, & vacuum pondus habeat. </s> <s id="N16E13">An quo­<lb/>niam duobus temporibus hauriendi diui&longs;o ope­<lb/>re (intingere enim oportet, & id &longs;ur&longs;um <lb/>trahere) continget demittere quidem vacuum faciliter, <lb/>trahere verò plenum difficulter. </s> <s id="N16E1E">Commodum igitur est pau­<lb/>lò tardius illud demittere, cùm multò leuiùs effectum &longs;u&longs;tol­<lb/>latur pondus: id autem facit in extremo celonio adiunctum: <lb/>plumbum, aut lapis. </s> <s id="N16E27">Demittendi quidem maius &longs;it pon­<lb/>dus, quàm &longs;i &longs;olummodò vacuum oporteret demittere: <lb/>cùm verò plenum fuerit &longs;ur&longs;um id rapii plumbum, aut quic­<lb/>quid illi ponderis inerit. </s> <s id="N16E30">Quamobrem faciliora boc modo <lb/>ambo &longs;unt, quàm illo.<emph.end type="italics"/></s> </p> <pb pagenum="234" xlink:href="005/01/242.jpg"/> <p id="N16E3B" type="head"> <s id="N16E3D">COMMENTARIVS.<!-- KEEP S--></s> </p> <p id="N16E41" type="main"> <s id="N16E43">Celonium quod & Tellenon apud Latinos appella­<lb/>tur, machina quædam e&longs;t ad commodius haurien­<lb/>dam aquam ex puteis, vt frequenter vi&longs;itur in hor­<lb/>tis. </s> <s id="N16E4C">Con&longs;tat autem ex tigno quodam prægrandi, quod iux­<lb/>ta puteos erigitur, ac validè obfirmatur, & ex tran&longs;uer&longs;ario <lb/>quodam alio ligno tenuiori, quod &longs;uperiori parti illius tan­<lb/>quam furculæ per &longs;ui qua&longs;i medium incumbens, in altero <lb/>extremo funem habet appen&longs;um <expan abbr="cũ">cum</expan> aquario va&longs;e; in altero <lb/>verò, appo&longs;ito pondere prægrauatur, vt &longs;ur&longs;um, ac deor&longs;um <lb/>facili negocio pro olitoris arbitrio valeat commoueri. </s> <s id="N16E5F">V&longs;us <lb/><expan abbr="namq;">namque</expan> huius machinæ e&longs;t, vt manu funis <expan abbr="appreh&etilde;&longs;us">apprehen&longs;us</expan> vnà <expan abbr="cũ">cum</expan> <lb/>va&longs;e, quod &longs;u&longs;tinet, in puteum demittatur quou&longs;que vas in <lb/><expan abbr="aquã">aquam</expan> immergatur, reclinato &longs;cilicet ligni extremo cui funis <lb/>alligatur. </s> <s id="N16E78">Deinde pu&longs;illa vi adhibita ob <expan abbr="præponderantiã">præponderantiam</expan> al­<lb/>terius extremi, quod onere pre&longs;&longs;um de&longs;cendit, ac <expan abbr="alterũ">alterum</expan> co­<lb/>git a&longs;cendere, ip&longs;ummet vas aqua plenum &longs;u&longs;tollatur, & ex­<lb/>trahatur. </s> <s id="N16E89">Quamuis enim vas ip&longs;um aqua <expan abbr="repletũ">repletum</expan>, <expan abbr="de&longs;criptoq.">de&longs;criptoque</expan> <lb/>ab extremo propendens ex &longs;e æquiponderare &longs;oleat oneri, <lb/>quod alteri extremo adiungitur, vix tamen vel modicè ma­<lb/>nu adiuuante eleuatum &longs;tatim ab onere prædicto vincitur, <lb/>ac &longs;uperatur: non &longs;ecus ac lanx libræ in æquilibrio con&longs;titu­<lb/>tæ ab æquali pondere alterius lancis, &longs;i vel tenuiter manu <lb/>aliqua &longs;u&longs;tollatur. </s> </p> <p id="N16EA0" type="main"> <s id="N16EA2">His itaque non aliter &longs;e habentibus, quærit hic Ari&longs;tote­<lb/>les, cur ad huiu&longs;modi machinam facilius promouendam, & <lb/>& aquam eius motione exhauriendam, onus oneri adiunga­<lb/>tur, plumbum nimirum, aut lapidem apponendo in alte­<lb/>ro extremo tran&longs;uer&longs;arij ligni, cum alioquin tota ip&longs;a ma­<lb/>china &longs;it per &longs;e grauis, ac præ&longs;ertim idemmet tran&longs;uer­<lb/>&longs;arium lignum, quod adhuc prægrauatur pondere va&longs;is ap­<lb/>pen&longs;i, &longs;iue vacui, &longs;iue repleti. </s> <s id="N16EB3">Difficilius namque e&longs;t mo­<lb/>uere machinam grauiorem, quàm leuiorem. </s> <s id="N16EB8">Quamob­<lb/>rem &longs;it in de&longs;cripta Tellenonis figura A B C D tignum <pb pagenum="235" xlink:href="005/01/243.jpg"/>arrectarium &longs;uper <lb/><figure id="id.005.01.243.1.jpg" xlink:href="005/01/243/1.jpg"/><lb/>planum <expan abbr="erectũ">erectum</expan> AB: <lb/>tran&longs;uer&longs;arium ve­<lb/>rò CD; ac funis <lb/>propendens DE, <lb/>in cuius ima extre­<lb/>mitate vbi E, alli­<lb/>gata &longs;it vrna, vel &longs;i­<lb/>tula, aut &longs;imile <lb/>aliud vas <expan abbr="aquariũ">aquarium</expan>: <lb/><expan abbr="Puteusq.">Puteusque</expan> &longs;ubiectus, <lb/>&longs;it vbi F. <!-- KEEP S--></s> <s id="N16EEA">Tunc in­<lb/>quam &longs;i in extremo <lb/>C tran&longs;uer&longs;arij li­<lb/>gni adiungatur <expan abbr="põ-dus">pon­<lb/>dus</expan> lapidis, aut <expan abbr="plũ-bi">plun­<lb/>bi</expan>, vt in figura refertur, manus funi admota ad demittendum <lb/>vas aquarium, difficilius deprimet extremum D, vnde fu­<lb/>nis ip&longs;e propendet, cum vltra propriam grauitatem ligni <lb/>AC, &longs;uperare, ac eleuare etiam debeat pondus illi adiun­<lb/>ctum. </s> <s id="N16F07">Quare ex huiu&longs;modi ponderis additione, potius vi­<lb/>detur, motionem ip&longs;am explicatæ machinæ retardari, quàm <lb/>facilius con&longs;equi, & expediri. </s> </p> <p id="N16F0E" type="main"> <s id="N16F10">Nihilominus re&longs;pondet idem Philo&longs;ophus, omnemque <lb/>dubitandi rationem exterminat, quoniam hauriendi opus <lb/>duobus di&longs;tributum temporibus perficitur. </s> <s id="N16F17">Primo nimirum <lb/>vas demittendo vacuum, vt aquæ immergatur: deinde il­<lb/>lud extrahendo plenum. </s> <s id="N16F1E">Nullo autem addito pondere <lb/>in extremo C, facilius quidem vas vacuum demittendum <lb/>fore, quia nihil ob&longs;taret; difficilius tamen extrahi po&longs;&longs;et, <lb/>quia pondus aquæ, magnopere a&longs;cen&longs;ui repugnaret, nec ha­<lb/>beret à quo &longs;u&longs;tolleretur &longs;imul cum parte tran&longs;uer&longs;arij li­<lb/>gni AD, quæ tanquam productior, ac prægrauata ponde­<lb/>re va&longs;is pleni, vinci non po&longs;&longs;et à parte eiu&longs;dem ligni AC, <lb/>breuiori, ac omni exonerata pondere. </s> <s id="N16F2F">Quoniam verò ma­<lb/>gis expedit, vt tardius ac difficilius vas demittatur, dum-<pb pagenum="236" xlink:href="005/01/244.jpg"/>modò facilius extrahatur; plumbum vel &longs;imile aliud onus <lb/>&longs;uperimponitur ip&longs;i extremo C, vt eo depre&longs;&longs;o, eleuetur <lb/>alterum extremum D, per conuer&longs;ionem ip&longs;ius ligni CD, <lb/>tanquam vectis &longs;uper fulcimentum A; & ad eleuationem <lb/>ip&longs;ius extremi D, vas ex eo pendens, pariter euehatur, & è <lb/>puteo extrahatur. </s> <s id="N16F43">Expedit autem facilitas potius in va&longs;is <lb/>extractione, quàm in demi&longs;&longs;ione; <expan abbr="idq.">idque</expan> tam ex parte poten­<lb/>tiæ, quàm ex parte ponderis. </s> <s id="N16F4E">Ex parte quidem potentiæ, <lb/>quia laborio&longs;us e&longs;t cum difficultate extrahere, quàm cum <lb/>difficultate demittere. </s> <s id="N16F55">Nam corpus humanum dum ex­<lb/>trahendo inclinatur, &longs;uo præpeditur pondere, ne expeditiùs <lb/>erigatur, <expan abbr="funemq.">funemque</expan> paulatim reducat, & per eam vas ip&longs;um <lb/>&longs;ubleuet. </s> <s id="N16F62">Contra verò dum ad vas demittendum, & immer­<lb/>gendum, funis cum ligni extremo D trahitur deor&longs;um, illi <lb/>naturali quodam nutu incumbit, commodiu&longs;que vires <lb/>exerit, ac difficultatem omnem euincit; vt experiri etiam e&longs;t <lb/>in v&longs;u trachleæ ad exhauriendam aquam, vel &longs;u&longs;tollendum <lb/>quodlibet aliud pondus per funis detractionem. </s> <s id="N16F6F">Deinde <lb/>ex parte ponderis, quia minor e&longs;t difficultas demi&longs;sionis, <lb/>quàm extractionis prædictæ. </s> <s id="N16F76">Siquidem pondus lapidis, aut <lb/>plumbi, quod &longs;uperari debet in va&longs;is mi&longs;sione, æquale e&longs;t <lb/>ponderi &longs;olius aquæ hauriendæ ip&longs;o eodem va&longs;e, vt dictum <lb/>e&longs;t: pondus autem quod &longs;uperandum e&longs;t in extractione, <lb/>non &longs;olum e&longs;t pondus aquæ hauriendæ, &longs;ed etiam <lb/>va&longs;is, ac funis, ideoque maius con&longs;tituitur, <lb/>ac difficilius &longs;uperatur. </s> <s id="N16F85">Con&longs;ultius ergo <lb/>e&longs;t, maiori difficultati &longs;uccur­<lb/>rere ip&longs;o machinæ bene­<lb/>ficio, ac ponde­<lb/>re adie­<lb/>cto <lb/>in altero extremo, vt <lb/>aiebat Philo&longs;o­<lb/>phus. </s> </p> <pb pagenum="237" xlink:href="005/01/245.jpg"/> <p id="N16F9C" type="head"> <s id="N16F9E">Quæ&longs;tio Vige&longs;imanona.</s> </p> <p id="N16FA1" type="main"> <s id="N16FA3">C<emph type="italics"/>vr quando &longs;uper ligno, aut huiu&longs;modi quo­<lb/>piam duo portauerint homines æquale pondus <lb/>non &longs;imiliter præmuntur, &longs;i ad vnum non de­<lb/>clinet pondus, &longs;ed magis quanti vicinius fue­<lb/>rit gestantibus? </s> <s id="N16FB1">An quoniam vectis quidem <lb/>lignum efficitur: pondus verò hypomochlion: <lb/>qui autem propior e&longs;t ponderi ex ÿs, qui illud ge&longs;tant, id qua­<lb/>re mouetur: alter vero portantium, quod mouet? </s> <s id="N16FBA">Quantò igitur <lb/>plus di&longs;tat à pondere, tanto facilius mouet, & alterum premit <lb/>magis inferius, velut contranitente pondere impo&longs;ito quod hy­<lb/>pomochlion factum e&longs;t, &longs;i autem in medio inerit pondus, nihilo <lb/>magis alter alteri fit pondus, aut mouet: &longs;ed eodem modo alteri <lb/>alter fit pondus.<emph.end type="italics"/></s> </p> <p id="N16FC9" type="head"> <s id="N16FCB">COMMENTARIVS.<!-- KEEP S--></s> </p> <p id="N16FCF" type="main"> <s id="N16FD1">Cau&longs;am hic inquirit Ari&longs;toteles cur duo baiuli idem <lb/>pondus &longs;uper lignum, vel quidpiam aliud &longs;imile fe­<lb/>rentes, <expan abbr="nõ">non</expan> æquè grauentur, atque <expan abbr="pr&etail;mãtur">pr&etail;mantur</expan> &longs;i in <expan abbr="eo-rũ">eo­<lb/>rum</expan> medio <expan abbr="nõ">non</expan> extiterit ip&longs;um pondus, &longs;ed magis præmatur is, <lb/>cui ip&longs;um proximius con&longs;tituitur. </s> <s id="N16FEC"><expan abbr="Eamq.">Eamque</expan> mox e&longs;&longs;e ait, quo­<lb/>niam huiu&longs;modi lignum in ip&longs;a a&longs;portatione efficitur vectis, <lb/>cuius fulcimentum con&longs;tituitur ip&longs;ummet pondus quod ge­<lb/>&longs;tatur: Onus verò baiulus, qui ponderi e&longs;t propinquior, ac <lb/>veluti potentia mouens, baiulus, qui e&longs;t ab illo remotior. <lb/></s> <s id="N16FFB">Etenim cum onus quodlibet, vecte adhibito, tanto facilius <lb/>moueatur, quanto proximius fuerit centro, &longs;eu fulcimen­<lb/>to locatum, ac motrix potentia remotius fuerit applicata, <lb/>vt &longs;upra o&longs;ten&longs;um e&longs;t quæ&longs;t. </s> <s id="N17004">3. hinc fit, vt baiulus, qui one­<lb/>tis loco &longs;uccedit, hoc ip&longs;o, quod pr<gap/>pinquius centro con­<lb/>&longs;tituitur, quàm alter qui potentiæ vices obtinet, magis <lb/>præmatur, contranitente pondere impo&longs;ito, tanquam fulci­<lb/>mento validè obfirmato, cui vectis innititur in ip&longs;o motu. <pb pagenum="238" xlink:href="005/01/246.jpg"/><figure id="id.005.01.246.1.jpg" xlink:href="005/01/246/1.jpg"/><lb/>Quod vt præ ocu­<lb/>lis habeatur e&longs;to <lb/>lignum AB, pon­<lb/>dus C appen&longs;um <lb/>in D proximius <lb/>ip&longs;i A; baiulorum <lb/>verò alter hume­<lb/>rum, vel manum <lb/>&longs;upponat in A; al­<lb/>ter in B. </s> <s id="N1702E">Dicimus ergo cum Ari&longs;totele, lignum ip&longs;um AB, <lb/>vectem con&longs;titui &longs;uffultum in D, tanquam fulcimento in­<lb/>uer&longs;o ad deprimendum humerum a&longs;portantis in A, per mo­<lb/>tum a&longs;portantis in B, qui baiulando, &longs;emper eleuare cona­<lb/>tur extremitatem &longs;ibi incumbentem in B. </s> <s id="N17039">Quandoquidem <lb/>punctum D, quod con&longs;tituitur centrum in motione ip&longs;ius <lb/>vectis, ita à pendente pondere præmitur, & figitur, ac &longs;i im­<lb/>mobile omnino e&longs;&longs;et ad fulciendum ip&longs;um vectem. </s> <s id="N17042">Quod <lb/>ueidentius fiet &longs;i eundem vectem inuer&longs;o modo con&longs;idere­<lb/><figure id="id.005.01.246.2.jpg" xlink:href="005/01/246/2.jpg"/><lb/>mus, in &longs;equenti fi­<lb/>gura; Nimirum vt <lb/>&longs;i vectis A B &longs;u­<lb/>&longs;pendatur in C ex <lb/>puncto intermedio <lb/>vbi D, ad eleuan­<lb/>dum onus impo­<lb/>&longs;itum in extremo A <lb/>per depre&longs;sionem alterius extremi B. </s> <s id="N1705F">His namque po­<lb/>&longs;itis ad primam figuram redeuntes facilè intelligitur cur <lb/>baiulus ge&longs;tans in A magis grauetur à pondere C, <lb/>quàm ge&longs;tans in B. </s> <s id="N17068">Quanto enim longior e&longs;t pars vectis <lb/>DB, ip&longs;a DA, eo facilius ge&longs;tans in B eleuat, vel &longs;u&longs;ti­<lb/>net ip&longs;um extremum B re&longs;pectu &longs;u&longs;tinentis in A tanquam <lb/>in loco centro vectis propinquiori quàm &longs;it ip&longs;um B. </s> </p> <p id="N17071" type="main"> <s id="N17073">Quod autem cum Ari&longs;totele explicuimus per rationem <lb/>vnius vectis, Piccolomineus explicat per rationem duplicis <pb pagenum="239" xlink:href="005/01/247.jpg"/>vectis, ita vt idem lignum AB rationem &longs;ubeat vtriu&longs;que <lb/>vectis, vnius nempe per quem ge&longs;tans in A prematur ad <lb/>motum ge&longs;tantis in B: alterius verò per quem ge&longs;tans in <lb/>B, prematur ad motum ge&longs;tantis in A, eodem &longs;emper exi­<lb/>&longs;tente fulcimento D. <!-- KEEP S--></s> <s id="N17086">Siquidem ambo ge&longs;tantes eleuare <lb/>conantur &longs;ua extrema, & ambo deprimuntur adinuicem, <lb/>ita vt alter alteri con&longs;tituatur onus, ac mouens potentia; li­<lb/>cetille magis moueat, minu&longs;que grauetur, qui longius di&longs;tat <lb/>à fulcimento. </s> <s id="N17091">Quæ profectò explicatio à mente Ari&longs;totelisc <lb/>tradita doctr