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<?xml version="1.0"?>

<!DOCTYPE archimedes SYSTEM "../dtd/archimedes.dtd" ><archimedes> <info> <author>Baldi, Bernadino</author> <title>In Mechanica Aristotelis problemata exercitationes</title> <date>1621</date>

<!DOCTYPE archimedes SYSTEM "../dtd/archimedes.dtd" >

<author>Baldi, Bernardino</author>

<title>In mechanica Aristotelis problemata exercitationes</title>

<place>Mainz</place>

<cvs_file>baldi_mecha_01_la_1621</cvs_file>

<cvs_version/>

</info> <text> <front> </front> <body> <chap> <pb/><pb id="p.0002"/>

<s>BERNARDINIBALDI VRBINATIS <lb/>GVASTALLÆ AB<lb/>BATIS <lb/><emph type="italics"/>IN<emph.end type="italics"/></s>

<place>Mainz</place> <translator></translator> <lang>la</lang> <cvs_file>baldi_mecha_01_la_1621.xml</cvs_file><cvs_version>1.11</cvs_version> <locator>0000000007</locator> </info> <text> <front> </front> <body> <chap> <pb/><pb id="p.0002"/>

<s>MECHANICA ARISTOTE <lb/>LIS PROBLEMATA <lb/>EXER CITATIONES:</s>

<s>BERNARDINI</s>

<s><emph type="italics"/>ADIECTA SVCCINCTA NAR<lb/>ratione de autoris vita & &longs;criptis.<emph.end type="italics"/></s><figure/>

<s>BALDI VRBINATIS <lb/>GVASTALLÆ AB<lb/>BATIS <lb/><emph type="italics"/>IN<emph.end type="italics"/></s>

<s><emph type="italics"/><gap/>NTIAE.<emph.end type="italics"/></s>

<s>MECHANICA ARISTOTE <lb/>LIS PROBLEMATA <lb/>EXER CITATIONES:</s>

<s>Typis & Sumptibus Viduæ Ioannis Albini.</s>

<s><emph type="italics"/>ADIECTA SVCCINCTA NAR<lb/>ratione de autoris vita & &longs;criptis.<emph.end type="italics"/></s><figure></figure>

<s><emph type="italics"/><gap/>NTIAE.<emph.end type="italics"/></s>

<s><emph type="italics"/>NOBILISSIMO AC GENE<lb/>ROSO DOMINO<emph.end type="italics"/>D. ADAMO PHILIP<lb/>PO BARONI A CRON<lb/>BERG, EQVITI, SACRÆ CÆSA<lb/>REÆ MAIESTATIS, ET SERENISSIMIPrincipis Archiducis Alberti Camerario intimo & c. <lb/></s>

<s>Typis & Sumptibus Viduæ Ioannis Albini.</s>

<s>Domino meo gratio&longs;i&longs;&longs;imo.</s>

<s>Opportune &longs;ub hoc ip&longs;um tem<lb/>pus, quo in Belgium ad Scre<lb/>ni&longs;&longs;imos Principes iter ador<lb/>nat.</s>

<s> Nobili&longs;&longs;ima & Genero&longs;a <lb/>Dom. </s>

<s> Nobili&longs;&longs;ima & Genero&longs;a <lb/>Dom. V.^{ra}, prodit no&longs;tris for<lb/>mis in publicum editus Com<lb/>mentarius Bernardini Baldi Vrbinatis Gua<lb/>&longs;tallæ Abbatis in Ari&longs;totelis Mechanica. </s>

<s>V.^{ra}, prodit no&longs;tris for<lb/>mis in publicum editus Com<lb/>mentarius Bernardini Baldi Vrbinatis Gua<lb/>&longs;tallæ Abbatis in Ari&longs;totelis Mechanica. </s>

<s>Is <lb/>virin omni &longs;cientiæ genere, at maxime inMa<lb/>thematicis di&longs;ciplinis fuit ver&longs;ati&longs;&longs;imus, quod <lb/>multa ab eo præclare &longs;crip ta te&longs;tantur opera, <lb/>ex quibus paucula edita, reliqua vero &longs;pera<pb/>mus &longs;uo temporein publicam luce<gap/> produ<lb/>cenda. </s>

<s> Cum vero nemini&longs;it ob&longs;curum Nobi<lb/>li&longs;&longs;imæ ac Genero&longs;æ Dom. </s>

<s> Cum vero nemini&longs;it ob&longs;curum Nobi<lb/>li&longs;&longs;imæ ac Genero&longs;æ Dom. V.^{ræ} id &longs;emper <lb/>extiti&longs;&longs;e familiari&longs;&longs;imum, vttum dome&longs;ticum <lb/>otium, tum maxime peregtinationes, quibus <lb/>totam pæne Europam &longs;umma cum laude <lb/>circum&longs;crip&longs;it, tum variarum linguarum per<lb/>fecto v&longs;u, tum Mathematicarum di&longs;ciplina<lb/>rum notitia & exercitio redderet <expan abbr="iuc&utilde;diores">iucundiores</expan>, <lb/>nulla me tenet dubitatio quin & Baldum Vr<lb/>binatem no&longs;tris typis loquentem in hoc iti<lb/>nere, quod à Deo felici&longs;&longs;imum Nobili&longs;&longs;imæ <lb/>acGenero&longs;æ Dom. V.^{ræ} precor, in &longs;uum comi<lb/>tatum ac tutelam beneuolo animo &longs;it admi&longs;<lb/>&longs;ura.</s>

<s>V.^{ræ} id &longs;emper <lb/>extiti&longs;&longs;e familiari&longs;&longs;imum, vttum dome&longs;ticum <lb/>otium, tum maxime peregtinationes, quibus <lb/>totam pæne Europam &longs;umma cum laude <lb/>circum&longs;crip&longs;it, tum variarum linguarum per<lb/>fecto v&longs;u, tum Mathematicarum di&longs;ciplina<lb/>rum notitia & exercitio redderet <expan abbr="iuc&utilde;diores">iucundiores</expan>, <lb/>nulla me tenet dubitatio quin & Baldum Vr<lb/>binatem no&longs;tris typis loquentem in hoc iti<lb/>nere, quod à Deo felici&longs;&longs;imum Nobili&longs;&longs;imæ <lb/>acGenero&longs;æ Dom. </s>

<s>V.^{ræ} precor, in &longs;uum comi<lb/>tatum ac tutelam beneuolo animo &longs;it admi&longs;<lb/>&longs;ura.</s>

<s> Id rogo humillime &longs;imulque precor, vt. <lb/></s>

<s>hanc meam typographiam plurimis iam re<lb/>tro annis de inclytæ familiæ Cronbergicæ tu<lb/>tela gloriantem, &longs;uo fauore pro&longs;equatur, vi<lb/>duæque afflictæ fortunis beneuole ad&longs;piret.</s>

<s> <lb/>Sic Deus Nobili&longs;&longs;. </s>

<s> <lb/>Sic Deus Nobili&longs;&longs;. & Genero&longs;am Dom. V.^{ram} <lb/>illu&longs;tret omnibus bonis, eamque R.^{mo} & Ill.^{mo} <lb/>Principiac Domino meo Clementi&longs;&longs;imo, D. <lb/>Ioanni Suicardo Archiepi&longs;copo Mogunti<lb/>no Principi Electori ac per <emph type="italics"/>G<emph.end type="italics"/>ermaniam Ar-<pb/>chicancellario &c. </s>

<s>& Genero&longs;am Dom. </s>

<s>V.^{ram} <lb/>illu&longs;tret omnibus bonis, eamque R.^{mo} & Ill.^{mo} <lb/>Principiac Domino meo Clementi&longs;&longs;imo, D. <lb/></s>

<s>Ioanni Suicardo Archiepi&longs;copo Mogunti<lb/>no Principi Electori ac per <emph type="italics"/>G<emph.end type="italics"/>ermaniam Ar-<pb/>chicancellario &c. </s>

<s>patruo &longs;uo optati&longs;&longs;imo <lb/>&longs;aluo florentique redhibeat &longs;aluum &longs;imili<lb/>ter florentem ac incolumem.</s>

<s> Moguntiæ è <lb/>typographeio Viduæ Albinianæ, honori No<lb/>bili&longs;&longs;imæ ac <emph type="italics"/>G<emph.end type="italics"/>enero&longs;æ Dom. </s>

<s> Moguntiæ è <lb/>typographeio Viduæ Albinianæ, honori No<lb/>bili&longs;&longs;imæ ac <emph type="italics"/>G<emph.end type="italics"/>enero&longs;æ Dom. Ve&longs;træ perpe<lb/>tuum dicato. </s>

<s>Ve&longs;træ perpe<lb/>tuum dicato. </s>

<s>Anno 1621.26.Martij. </s><pb/><figure></figure>

<s>Anno 1621.26.Martij. </s><pb/><figure/>

<s>PRAEFATIO.</s>

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<s>Pappus enim Heroneiunior, Athe<lb/>næus Archimediæqualis, vterque enim &longs;ub Mar<lb/>cello, cui Athenæus &longs;uum de bellicis Machinis <lb/><expan abbr="libell&umacr;">libellum</expan> dedicauit. </s>

<s>Archimedes verò circa CXL. <lb/></s>

<s>Archimedes verò circa CXL. <lb/></s>

<s>Olympiadem floruit, quamobrem po&longs;t Ari&longs;tote<lb/>lem Olympiadas XL. hoc est, annos ferè CLX. <lb/></s>

<s>Olympiadem floruit, quamobrem po&longs;t Ari&longs;tote<lb/>lem Olympiadas XL. hoc est, annos ferè CLX. <lb/></s>

<s>I&longs;thæc autem con&longs;iderantibus, facile e&longs;t cogno&longs;ce<lb/>refacultatis huius nobilitatem, atque dignit atem; <lb/>quippe quod &longs;ummus Philo&longs;ophus non modo eam <pb/>probauerit, &longs;cd etiam &longs;uis acutissimis lucubra<lb/>tionibus illu&longs;trauerit. </s>

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<s>Vitruuius Architecturæ <lb/>membrum, vt ita dicam, & portionem quan<lb/>dam facit, ait enim Architecturæ partes e&longs;&longs;e tres, <lb/>Ædificationem, Gnomonicam, Machinatio<lb/>nem. </s>

<s>Estautem Architectur â quideminferior, <lb/>paret enim Architecto Mechanicus; attamen &longs;i <lb/>cæteras artes &longs;pectes, Architectonica; hæc enim <lb/>omnesferè &longs;edentariæ, &longs;ellulariæue, quas banau<lb/>&longs;as Græci appellant, ordine &longs;ubijciuntur, & &longs;a<lb/>nè latissimos i&longs;ihæc habetfines; præcipuè autem <lb/>circa eam ver&longs;atur cognitionem, eamque inter <lb/>cæterasferè principem, quam dixere Centrobari<lb/>cam, quæ quidem ad Centri grauitatem, eiu&longs;que <lb/>&longs;peculationem pertinet: quà in &longs;pecie inter vete<lb/>res primum &longs;ibi vindicauit locum Archimedes, <lb/>mox Heron, deinde Pappus; inter neotericos au-<emph.end type="italics"/><pb/><emph type="italics"/>tem Commandinus, qui librum de Centro gra<lb/>uitatis &longs;olidorum &longs;crip&longs;it, & po&longs;t eum G. Vbal<lb/>dus è Marchion. Montis, qui non modò ab<lb/>&longs;olutissimum Mechanicorum librum cum maxi<lb/>maingenij &longs;ui laude con&longs;crip&longs;it, &longs;ed & Paraphra<lb/>&longs;in in librum Æqueponderantium Archimedis <lb/>egregiè concinnauit Centrobaricam hanc, igno<lb/>tam fui&longs;&longs;e Ari&longs;toteli, &longs;ætis patet. </s>

<s>Vbal<lb/>dus è Marchion. </s>

<s>Montis, qui non modò ab<lb/>&longs;olutissimum Mechanicorum librum cum maxi<lb/>maingenij &longs;ui laude con&longs;crip&longs;it, &longs;ed & Paraphra<lb/>&longs;in in librum Æqueponderantium Archimedis <lb/>egregiè concinnauit Centrobaricam hanc, igno<lb/>tam fui&longs;&longs;e Ari&longs;toteli, &longs;ætis patet. </s>

<s>nunquam enim <lb/>in Mechanicis demon&longs;trationibus, quod tamen <lb/>est potissimum, grauitatis centrum nominat, e<lb/>iu&longs;ue naturam atque vim &longs;peculatur. </s>

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<s>DE VITA ET SCRI<lb/>PTIS BERNARDINI <lb/>BALDI VRBINATIS</s>

<s><emph type="italics"/>EX LITERIS FABRITII SCHAR<lb/>loncini ad Illu&longs;trissimum & Reuerendissimum <lb/>Dominum Lælium Ruinum Epi&longs;copum Bal<lb/>neoregien&longs;em ex-Nuntium Apo&longs;tolicum <lb/>ad Poloniæ Regem & c.<emph.end type="italics"/></s>

<s>Natus e&longs;t Bern. Baldus Vrbini nobilibus <expan abbr="pa-r&emacr;tibus">pa<lb/>rentibus</expan> po&longs;tridie Non. </s>

<s>Natus e&longs;t Bern. </s>

<s>Baldus Vrbini nobilibus <expan abbr="pa-r&emacr;tibus">pa<lb/>rentibus</expan> po&longs;tridie Non. </s>

<s>Iunij anno MDLIII. <lb/></s>

<s>Genus traxit, quod me &longs;æpè ab eomemini <lb/>audire, à familia Cantagallina, quæ inter <lb/>Peru&longs;inas illu&longs;tris: hocautem cognomen, <lb/>Baldiaccepto, vtin varietate temporum fit, <lb/>Abauus reliquit, à teneris vnguiculis <expan abbr="pietat&emacr;">pietatem</expan> erga Deum <lb/>præ&longs;etulit; nam vt mater eius narrabat, &longs;anctorum imagi<lb/>nes & Altariola non cum lætitia &longs;olum, &longs;ed cum venera<lb/>tione anniculus intuebatur. </s>

<s>Præceptoribus in adole&longs;cen<lb/>tia v&longs;us fuit laudati&longs;&longs;imis Io. </s>

<s>Præceptoribus in adole&longs;cen<lb/>tia v&longs;us fuit laudati&longs;&longs;imis Io. And. Palatio, & Io. Antonio <lb/>Turoneo, qui altero doctior, & Paulo Manutio maxime <lb/>carus ob latinæ & græcæ linguæ peritiam propè &longs;ingula<lb/>rem: adillorum autem &longs;edulitatem tantum animi ardo<lb/>rem attulit, tantam ingenij aciudicij vim, vt non tantum <lb/>æqualis &longs;ed omnium vicerit expectationem. </s>

<s>Palatio, & Io. </s>

<s>Antonio <lb/>Turoneo, qui altero doctior, & Paulo Manutio maxime <lb/>carus ob latinæ & græcæ linguæ peritiam propè &longs;ingula<lb/>rem: adillorum autem &longs;edulitatem tantum animi ardo<lb/>rem attulit, tantam ingenij aciudicij vim, vt non tantum <lb/>æqualis &longs;ed omnium vicerit expectationem. </s>

<s>Puer adhuc <lb/>Aratiapparitiones Italico carmmered didit. </s>

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<s>Hîcin Ema<lb/>nuelis Margunij familiaritatem &longs;tatim venit, cui porro <pb/>fuit in amotibus. </s>

<s>Homeri Iliad. </s>

<s>Homeri Iliad. illo Doctore & interpre<lb/>te diligentius quam feci&longs;&longs;et antea, euoluit. </s>

<s>illo Doctore & interpre<lb/>te diligentius quam feci&longs;&longs;et antea, euoluit. </s>

<s>priuato autem <lb/>&longs;tudio Anacreonti, Pindaro, Æ&longs;chyli, Euripidi, Sophocli <lb/>operam dedit, &longs;ed præ cæteris Thcocriti Bucolica triuit, <lb/>ad quod &longs;criptionis genus natura magis ferri videbatur: <lb/>centenos græci alicuius poëtæver&longs;us memoriter tenebat, <lb/>&longs;æpeque habebat in ore, in oratoribus græcis ver&longs;andis <lb/>laborem &longs;ealiquem &longs;entire, in poëtis nullum. </s>

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<s>Pe&longs;tilentia ex co Gymna&longs;io exactus in Pa<lb/>triam redijt, vbi quin quennium integrum Federico <expan abbr="C&omacr;-mandino">Con<lb/>mandino</expan> affixus omnes Mathe&longs;eos partes perdidicit, cui <lb/>viro in delinean dis figuris ad Euclidis, Pappi, & Heronis <lb/>monumenta manum commodauit: ex eiu&longs;dem obitu do<lb/>lorem vix con&longs;olabilem &longs;u&longs;tinuit, &longs;u&longs;ceptoque eius vitam <lb/>&longs;cribendi con&longs;ilio, &longs;ubinde ad omnium Mathematicorum <lb/>vitas con&longs;cribendas animum adplicuit, quod & duode<lb/>cim annorum &longs;patio præ&longs;titit felici&longs;&longs;imè. </s>

<s>cum vero Ma<lb/>thematicarum di&longs;ciplinarum amore torqueretur, ami&longs;&longs;o <lb/>Commandino Præceptore, amicum nactus fuit præ&longs;tan<lb/>ti&longs;&longs;imum & &longs;ymmy&longs;tam Guidum Vbaldum è Marchioni<lb/>bus Montis, in cuius &longs;e con&longs;uetudinem daret: quantum <lb/>profeci&longs;&longs;et, o&longs;tendunt ij commentarij quos anno 1582. in <lb/>Ari&longs;t. </s>

<s>Mechanica &longs;crip&longs;it. </s>

<s>Vt po&longs;tea à grauioribus &longs;tudijs <lb/>ad am&oelig;niora animum abduceret, de re nautica poëma I<lb/>talicè <gap/>onfecit. </s>

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<s>Cum Ferrando hero &longs;uo obueni&longs;&longs;et nece&longs;&longs;i<lb/>tas Hi&longs;panias adeundi, illud iter &longs;ine Baldo facere &longs;e po&longs;<lb/>&longs;e non putabat, non tam vt haberet, qui erudito cloquio <lb/>viæ tæ dium leuaret, quam cui po&longs;&longs;et arcana committere, <lb/>atque adeo à quo iuuaretur con&longs;ilio. </s>

<s>Vix viæ &longs;e dederant <lb/>cum Baldus grauem in morbum delap&longs;us itinere cogitur <lb/>de&longs;i&longs;tere: Mediolanum proinde diuertit, vbi à S. </s>

<s>Vix viæ &longs;e dederant <lb/>cum Baldus grauem in morbum delap&longs;us itinere cogitur <lb/>de&longs;i&longs;tere: Mediolanum proinde diuertit, vbi à S. Carolo <lb/>Borromæo & benignè exceptus, & tamdiu detentus do<lb/>necvaletudinem recuperaret. </s>

<s>Carolo <lb/>Borromæo & benignè exceptus, & tamdiu detentus do<lb/>necvaletudinem recuperaret. </s>

<s>Gua&longs;tallam po&longs;tea &longs;e re<lb/>cepit, vbi cum ab&longs;ente Domino liberiori otio fruerctur, <lb/>libros &longs;ex de Aula eruditi&longs;&longs;imos methodo analytica con<lb/>&longs;crip&longs;it. </s>

<s>alios non commemoro, quod cum otium erit, o<lb/>mnium &longs;yllabum dabo. </s>

<s>Anno 1586. ip&longs;o nihil po&longs;tulante <lb/>eligitur Gua&longs;tallæ Abbas, à quo tempore Iuri Can. </s>

<s>Anno 1586. ip&longs;o nihil po&longs;tulante <lb/>eligitur Gua&longs;tallæ Abbas, à quo tempore Iuri Can. </s>

<s>Con<lb/>cilijs, & SS.Patribustotum &longs;e dedit. </s>

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<s>Anno 1593. no<lb/>uæ Gnomonices libros quinque compo&longs;uit. </s>

<s>in&longs;equenti <lb/>Chaldæam Onkeli paraphra&longs;in in Pentateuchum vertit <lb/>& commentarios adiunxit; quo exantlato labore in Iob <lb/>ex Heb. </s>

<s>in&longs;equenti <lb/>Chaldæam Onkeli paraphra&longs;in in Pentateuchum vertit <lb/>& commentarios adiunxit; quo exantlato labore in Iob <lb/>ex Heb. fonte paraphra&longs;in texuit, quam & &longs;cholijs illu<lb/>&longs;trauit. </s>

<s>fonte paraphra&longs;in texuit, quam & &longs;cholijs illu<lb/>&longs;trauit. </s>

<s>Tabulam Etru&longs;cam Eugubinam interptetatus <pb/>fuit:in ca autem diuinatione, vt aiebat, &longs;ubci&longs;iuas vnius <lb/>men&longs;is horas con&longs;ump&longs;it. </s>

<s>De Firmamento & aquis egre<lb/>gic &longs;crip&longs;it. </s>

<s>Oeconomiam Tropologicam in S.Matthæum <lb/>Card. </s>

<s>Oeconomiam Tropologicam in S.Matthæum <lb/>Card. Baronius, qui non alia Baldi vidit, vehementer pro<lb/>babat. </s>

<s>Baronius, qui non alia Baldi vidit, vehementer pro<lb/>babat. </s>

<s>Romæ dum viueret, fere ne&longs;ciuit quid gereretur <lb/>in Aulis: Arabicæ enim linguæ cum Io. Bapti&longs;ta Raimon<lb/>do diligenti&longs;&longs;ime &longs;tuduit, & arcana indu&longs;tria Slauonicæ, <lb/>quam perfecte callebat. </s>

<s>Romæ dum viueret, fere ne&longs;ciuit quid gereretur <lb/>in Aulis: Arabicæ enim linguæ cum Io. </s>

<s>Bapti&longs;ta Raimon<lb/>do diligenti&longs;&longs;ime &longs;tuduit, & arcana indu&longs;tria Slauonicæ, <lb/>quam perfecte callebat. </s>

<s>Ex Arabico vertit Hortum Geo<lb/>graphicum Anonymi, quem ante &longs;excentos annos flo<lb/>rui&longs;&longs;e arbitrabatur. </s>

<s>Hunc vero extru&longs;i&longs;&longs;et, vtalios Baldi <lb/>libros, Marcus Vel&longs;erus IIvir Aug. </s>

<s>Hunc vero extru&longs;i&longs;&longs;et, vtalios Baldi <lb/>libros, Marcus Vel&longs;erus IIvir Aug. &longs;i eo paulo longior <lb/>huius lucis v&longs;ura contigi&longs;&longs;et. </s>

<s>&longs;i eo paulo longior <lb/>huius lucis v&longs;ura contigi&longs;&longs;et. </s>

<s>Compo&longs;uit & Dictionarium <lb/>Arabicum. </s>

<s>Compo&longs;uit & Dictionarium <lb/>Arabicum. </s>

<s>atque cum beati&longs;&longs;imam illam vbertatem in<lb/>genij a&longs;&longs;idue diffundi nece&longs;&longs;e e&longs;&longs;et, anno 1603. orbem vni<lb/>uer&longs;um de&longs;eribere aggre&longs;&longs;us fuit; atque ita quidem, vt <lb/>tam quæ ad Hi&longs;toriam, quam quæ ad Geographiam per<lb/>tinerent complecteretur: Neque illu&longs;trare &longs;olum voluit <lb/>quæ nouerunt antiqui, quemadmodum vi&longs;um Ortelio, <lb/>&longs;ed vel oppidula omnia & pagos, de quibus aliquain po<lb/>&longs;tremis &longs;criptoribus mentio. </s>

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<s>qua<lb/>tuor aut ni fallor quinque tantum Tomi fuerunt ordine <lb/>Alphabetico di&longs;po&longs;iti:&longs;upere&longs;&longs;ent &longs;eptem aut octo di&longs;po<lb/>nendi, quantum ex chartarum & fa&longs;ciculorum mo<gap/>e con<lb/>ijcere licet. </s>

<s>Anno 1617. quarto Idus Octob. </s>

<s>Anno 1617. quarto Idus Octob. </s>

<s>po&longs;teaquam <lb/>dies 40. vehementi de&longs;tillatione vexatus fui&longs;&longs;et, &longs;piritum <lb/>Deo reddidit Sacramentis Eccle&longs;iæ omnibus rite muni<lb/>tus. </s>

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<s>Sermo modicus ei fuit, <lb/>itemque cultus. </s>

<s>Nullos vnquam honores petijt, qui à <lb/>Clem. </s>

<s>Nullos vnquam honores petijt, qui à <lb/>Clem. </s>

<s>8. ampli&longs;&longs;imi promi&longs;&longs;i fuerant; nullum emolumen<lb/>tum quæ&longs;iuit &longs;uo ceniu contentus. </s>

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<s>SYLLABVS LIBRORVM</s>

<s>omnium B.Abb.Baldi.</s>

<s>omnium B.Abb.Baldi.</s>

<s>Arati apparitiones è gr.in Ital. </s>

<s>vertit. </s>

<s>Arati apparitiones è gr.in Ital. vertit. </s>

<s>De Tormentis Bellicis & eorum Inuentoribus lib. </s>

<s>Heronis automata vertit. </s>

<s>De Tormentis Bellicis & eorum Inuentoribus lib. Heronis automata vertit. </s>

<s>Vitas omnium Mathematicorum &longs;crip&longs;it, & trib. </s>

<s>in Tom. <lb/>2.1.P^{s}.à Thalete ad Chri&longs;tum.2.àChri&longs;toad &longs;ua tem<lb/>pora. </s>

<s>2.1.P^{s}.à Thalete ad Chri&longs;tum.2.àChri&longs;toad &longs;ua tem<lb/>pora. </s>

<s>Earumdem vitarum Epitomen Chronologicum confecit. </s>

<s>In Ari&longs;tot. </s>

<s>In Ari&longs;tot. Mechan. Commentar. </s>

<s>Mechan. </s>

<s>Commentar. </s>

<s>De Renautica Poëmation. </s>

<s>De Renautica Poëmation. </s>

<s>Paradoxorum Mathematicorum liber. </s>

<s>Paradoxorum Mathematicorum liber. </s>

<s>De&longs;criptio Palatij Ducum Vrbinarum quod e&longs;t Vrbini. </s>

<s>Poema cui titulus, Lamus. </s><pb/>

<s>Poema cui titulus, Lamus. </s><pb/>

<s>Carmina pia, quæ in&longs;cribuntur, Anni Corona. </s>

<s>Carmina pia, quæ in&longs;cribuntur, Anni Corona. </s>

<s>De Verborum Vitruuianorum &longs;ignificatione. </s>

<s>Carmina varia & eclogæ mixtæ. </s>

<s>Apologi centum, quos &longs;crip&longs;it æmulatus Leonem Bapt. <lb/></s>

<s>Apologi centum, quos &longs;crip&longs;it æmulatus Leonem Bapt. <lb/>Albertum. </s>

<s>Albertum. </s>

<s>De Humanitate Dialogus qui in&longs;cribitur Go&longs;elinus. </s>

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<s>De Aula libri &longs;ex. </s>

<s>De felicitate Principis Dialogus. </s>

<s>De felicitate Principis Dialogus. </s>

<s>De Dignitate Dial. </s>

<s>De Dignitate Dial. </s>

<s>Carmina Romana. </s>

<s>Mo&longs;æi fabulam vertit. </s>

<s>De Italici carminis natura Dial. </s>

<s>De Italici carminis natura Dial. qui in&longs;cribitur Ta&longs;&longs;us. </s>

<s>qui in&longs;cribitur Ta&longs;&longs;us. </s>

<s>De vniuer&longs;ali Diluuio poemation. </s>

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quin que. </s>

<s>Hieremiæ Threnos vertit, & ex Heb. </s>

<s>Hieremiæ Threnos vertit, & ex Heb. fonte annotat. </s>

<s>fonte annotat. </s>

<s>ad<lb/>iecit. </s>

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<s>Onkeli paraphra&longs;in Chaldæam in Pentateuchum ver<lb/>tit & vberes commentarios adiecit. </s>

<s>In Iob Paraphra&longs;is latina ex fonte Heb. </s>

<s>In Iob Paraphra&longs;is latina ex fonte Heb. additis Scholijs. </s>

<s>additis Scholijs. </s>

<s>De &longs;camillis imparibus Vitruuij. </s>

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<s>Quincti Calabri Paralipomena vertit. </s>

<s>Tabulæ Etru&longs;cæ Eugubinæ Interpretatio. </s>

<s>Tabulæ Etru&longs;cæ Eugubinæ Interpretatio. </s>

<s>Oeconomía Tropologicain S.Matthæum. </s>

<s>Oeconomía Tropologicain S.Matthæum. </s>

<s>Vrbini encomium. </s>

<s>Horti geographici ex Arab. </s>

<s>Horti geographici ex Arab. ver&longs;io. </s>

<s>ver&longs;io. </s>

<s>Aduer&longs;us Aulam Carmina. </s>

<s>Aduer&longs;us Aulam Carmina. </s>

<s>Luciani de mi&longs;erijs.Aulicorum ver&longs;io. </s>

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<s>Vniuer&longs;i orbis geographica & Hi&longs;torica de&longs;criptio con<lb/>texta ex &longs;eptingentis & eo amplius &longs;criptoribus. </s>

<s>Fede ici Vrbini Ducis Vita. </s>

<s>Fede ici Vrbini Ducis Vita. </s>

<s>Guidi Vbaldi Vibini Ducis Vita. </s>

<s>Guidi Vbaldi Vibini Ducis Vita. </s>

<s>Epigrammaton & Odarum libritres. </s>

<s>Aliorum Carminum liber. </s>

<s>Aliorum Carminum liber. </s>

<s>Sententiarum moralium liber. </s>

<s>Sententiarum moralium liber. </s>

<s>Dictionarium Arabicum. </s>

<s>Dictionarium Arabicum. </s>

<s>Pro Procopio contra Flauium Blondum. </s>

<s>Pro Procopio contra Flauium Blondum. </s>

<s>Horographium vniucr&longs;ale. </s>

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de Balli&longs;tis conuer&longs;io. </s>

<s>Exercitationes in Ari&longs;totelis Mechan. </s>

<s>Exercitationes in Ari&longs;totelis Mechan. </s>

<s>Templi Ezechielis noua de&longs;criptio. </s>

<s>Antiquitatum Gua&longs;tallen&longs;ium liber. </s>

<s>Antiquitatum Gua&longs;tallen&longs;ium liber. </s>

<s>Hi&longs;toriæ &longs;cribendæ leges. </s>

<s>Etalia quædam. </s><pb pagenum="1"/><figure></figure>

<s>Etalia quædam. </s><pb pagenum="1"/><figure/>

<s>IN MECHANICA ARISTOTE<lb/>LIS PROBLEMATA</s>

<s>EXER CITATIONES.</s>

<s>IN MECHANICA ARISTOTE<lb/>LIS PROBLEMATAEXER CITATIONES.</s>

<s><emph type="italics"/>Mechanices de&longs;criptio, natura, finis.<emph.end type="italics"/></s>

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<s><emph type="italics"/>Mechanices Obiectum.<emph.end type="italics"/></s>

<s>Con&longs;ideratautem Mechanicus Graue & Leue. </s>

<s>Con&longs;ideratautem Mechanicus Graue & Leue. </s>

<s>Graue duplex, Naturâ, Violentiâ. </s>

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<s>Leue contrà, quòd Naturâ à centro fertur. </s>

<s>Gæterùm quicquid graue e&longs;t, &longs;ecundum punctum <lb/>e&longs;t, quod Grauitatis centrum dicitur, & hoc duplex, vt <lb/>duplex e&longs;t grauitas, Naturæ, Violentiæ. </s><pb pagenum="2"/>

<s>Grauitatis centrum in triplici magnitudine con&longs;i<lb/>deraripote&longs;t, lineari, planà, &longs;olidâ. </s>

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<s>Huius autem non memi<lb/>nêre Mechanici, propterea quod aut nihil, aut parum ad <lb/>eorum rem faciat. </s>

<s>Porro Grauitatis centrum ita definit Heron, & qui <lb/>ab Herone Pappus 1.8. Collectionum Mathematicarum. </s>

<s>Porro Grauitatis centrum ita definit Heron, & qui <lb/>ab Herone Pappus 1.8. Collectionum Mathematicarum. </s>

<s>Centrum grauitatis <expan abbr="vniu&longs;cuiu&longs;q;">vniu&longs;cuiu&longs;que</expan> corporis e&longs;t pun<lb/>ctum quod dam intra po&longs;itum, à quo &longs;i graue, mente ap<lb/>pen&longs;um concipiatur, dum fertur, quie&longs;cit, & &longs;eruat eam <lb/>quam in prin cipio habuit po&longs;itionem; neque in ip&longs;a latio<lb/>ne circumuertitur. </s>

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<s>Sienim per tale centrum ducatur planum, fi<lb/>guram quomodolibet &longs;ecans, in partes æ què ponderantes <lb/>eam diuidit. </s>

<s>Nos verò quàm breui&longs;&longs;imè dicimus: <expan abbr="Centr&umacr;">Centrum</expan> <lb/>grauitatis, <expan abbr="vniu&longs;cuiu&longs;q;">vniu&longs;cuiu&longs;que</expan> magnitudinis punctum e&longs;&longs;e intra <lb/>extraue magnitudinem po&longs;itum, per quod &longs;i plano linea <lb/>punctoue diuidatur, in partes &longs;ecatur æqueponderantes. </s><pb pagenum="3"/><figure></figure>

<s>Diximus, Magnitudinis vtlineæ, plani &longs;olidique; cen<lb/>trum complecteremur. </s>

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<s>Diximus in&longs;uper, intra extraue. </s>

<s>Aliquando enim <lb/>grauitatis centrum extra molem corporis cuius corporis <lb/>centrum e&longs;t, cadit, vtin &longs;equenti figura. </s><figure></figure>

<s>Aliquando enim <lb/>grauitatis centrum extra molem corporis cuius corporis <lb/>centrum e&longs;t, cadit, vtin &longs;equenti figura. </s><figure/>

<s>E&longs;to corpus aliquod <lb/>&longs;uperficiesue ABCDE, <lb/>ducatur linea CF, <expan abbr="diuid&emacr;s">diuidens</expan> <lb/>figuras in partes hinc inde <lb/>æqueponderantes ABC, <lb/>EDC. </s>

<s>Ducatur & GH. <lb/>diuídens item in partes æ<lb/>queponderantes GCH, & GAB, EDH. &longs;ecentautem <lb/>&longs;eip&longs;as in I. eritigitur centrum I extra figuræ terminos & <lb/>molemip&longs;am. </s>

<s>Attamen licet hoc verum &longs;it, intra e&longs;&longs;e dici <lb/>pote&longs;t, quippe quod imaginario quodam, & vtita dicam, <lb/>virtuali ambitu ACDA contineatur. </s>

<s>Dicebamus, duplex e&longs;&longs;e grauitatis centrum, Natu<pb pagenum="4"/>râ, Violentià: a&longs;firmamus modò, hæc re quidem vnum e&longs;<lb/>&longs;e, & ratione &longs;olum, non autem reip&longs;a ac&longs;i duo e&longs;&longs;ent con<lb/>&longs;iderari. </s><figure></figure>

<s>E&longs;to enim grauitatis na<lb/>turalis centrum B, corporis A, <lb/>&longs;ecundum quod dimi&longs;&longs;um, &longs;ua<lb/>pte naturâ cadet in C, &longs;i verò <lb/>corpus violenter impellatur in <lb/>D, aiiud acquiret centrum gra<lb/>uitatis ex violentia &longs;ecundum <lb/>quam fertur, motum, in D, <expan abbr="id&emacr;">idem</expan> <lb/>autem &longs;untre, nempe vnum B, <lb/>duo autem &longs;i violentia & natura &longs;eor&longs;um con&longs;ideren<lb/>tur. </s>

<s>Hæc centra, duo motus &longs;equuntur, rectus vterque, <lb/>Naturalis videlicet, & Violentus. </s>

<s>Tertius ex his mixtus, & <lb/>is quidem non rectus, &longs;ed curuus. </s><figure></figure>

<s>Tertius ex his mixtus, & <lb/>is quidem non rectus, &longs;ed curuus. </s><figure/>

<s>Proijciatur enim violen<lb/>ter corpus graue A &longs;uperante <lb/>igitur violentia, rectà feretur <lb/>in B; ea autem elangue&longs;cente <lb/>paullatim per curuam & mi<lb/>xtam <expan abbr="lineã">lineam</expan> &longs;ecetur in C, qua<lb/>tenus enim ad anteriora fer<lb/>tur, violentia e&longs;t; quatenus ve<lb/>rò ad inferiores partes, naturæ. </s>

<s>Vbi verò peruenit in C, <lb/>violentiâ ce&longs;&longs;ante, naturâ verò manente, rectà deor&longs;um <lb/>fertur DCD. </s>

<s>Vbi verò peruenit in C, <lb/>violentiâ ce&longs;&longs;ante, naturâ verò manente, rectà deor&longs;um <lb/>fertur DCD. </s>

<s>Cæteiùm hæc centra, hiqueue motus, naturalis nem<lb/>pe, & violentus diuer&longs;imode &longs;e habent adinuicem. </s>

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<s><emph type="italics"/>Mechanices præcipua in&longs;trumenta.<emph.end type="italics"/></s>

<s>Hic ira con&longs;titutis dicimus, in&longs;trumenta, quibusad <lb/>varias operationes Mechanici vtuntur, e&longs;&longs;e inter &longs;e qui<lb/>dem diuer&longs;a, multiplicia, & &longs;i varietatem &longs;pectes, penè in<lb/>numerabilia; quod quamuis verum&longs;it, ea omnia Ari&longs;tote<lb/>les ad vectem re ducit, & libram: quod etiam G. </s>

<s>Vbaldus <lb/>in libris Mechanicoiumfecit. </s>

<s>Cæterum qui po&longs;t Ari&longs;to<lb/>telem floruere Mechanici, omnia ad quinque, quas ap<lb/>pellant, Potentias, redegêre. </s>

<s>Sunt autem ex Herone, Pap<lb/>po, Guido Vbaldo, qui eos &longs;ecutus e&longs;t, Vectis, Trochlea, <lb/>Axis in Peritrochio, Cuneus, Cochlèa. </s>

<s>Videtur autemi<lb/>p&longs;e G. </s>

<s>Videtur autemi<lb/>p&longs;e G. Vbaldus &longs;extam addere, nempe Libram, de qua & <lb/>primus ip&longs;e Mechanicorum tractatum in &longs;tituit. </s>

<s>Vbaldus &longs;extam addere, nempe Libram, de qua & <lb/>primus ip&longs;e Mechanicorum tractatum in &longs;tituit. </s>

<s>Verum <lb/>enimuero idem ferè &longs;unt Vectis & Libra, ni&longs;i forte quod <lb/>Libra tunc dicitur, cum brachia &longs;unt æ qualia. </s>

<s>Vectis vero <lb/>quomodocun que ea &longs;e habeant; quinque harum <expan abbr="Poten-tiar&umacr;">Poten<lb/>tiarum</expan> imagines ita ob oculos ponimus. </s>

<s>Vectis A. </s>

<s>Vectis A. </s>

<s>Trochlea <lb/>B, Axisin Peritrochio C. </s>

<s>Trochlea <lb/>B, Axisin Peritrochio C. </s>

<s>Cuneus D. </s>

<s>Cuneus D. </s>

<s>Cochlea vero E. </s><pb pagenum="6"/><figure></figure>

<s>Cochlea vero E. </s><pb pagenum="6"/><figure/>

<s>Porro, Cuneum ad libram reducere conatur Ari<lb/>&longs;toteles, quod facit & G. Vbaldus, qui cò refert & Co<lb/>chleam, quippe quod nihil aliud &longs;it Cochlea, quàm Cu<lb/>neus Cylindro inuolutus. </s>

<s>Nos autem duas tantùm Po<lb/>tentias ad vectem reduci po&longs;&longs;e arbitramur, Trochleam <lb/>nempe, & Axem in Peritrochio. </s>

<s>Nos autem duas tantùm Po<lb/>tentias ad vectem reduci po&longs;&longs;e arbitramur, Trochleam <lb/>nempe, & Axem in Peritrochio. </s>

<s>Nequaquam autem Cu<lb/>neum & Cochleam. </s>

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<s>Quartam, quod vnicâ exi&longs;tente &longs;emidiametro, <lb/>nullum in ca punctum &longs;umi po&longs;&longs;it, æqualis alteri, in latio<lb/>ne, velocitatis. </s>

<s>Sit enim circulus AB, cuius centrum C, <lb/>&longs;emidiameter AC, &longs;umatur autem in ea punctum D, i<lb/>temqueue punctum E. </s>

<s>Sit enim circulus AB, cuius centrum C, <lb/>&longs;emidiameter AC, &longs;umatur autem in ea punctum D, i<lb/>temqueue punctum E. </s>

<s>Erit itaque in ip&longs;a circulatione D <lb/>tardius E, ip&longs;um verò E tardius A, & ita citius id feretur <lb/>&longs;emper, quod remotius à mouente termino accipitur. </s><figure></figure>

<s>Hæc ex illo, quibus ne vltro a&longs;<lb/>&longs;en&longs;um præbeamus non vnica de cau<lb/>&longs;a cohibemur. </s>

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<s>Punctum autem, quod &longs;tat, &longs;emidia<lb/>metri pars nulla e&longs;t. </s>

<s>Et &longs;anè cur moto <lb/><expan abbr="&longs;emidiam&emacr;tro">&longs;emidiamentro</expan> fiat circulus, non ideo accidit, quod <expan abbr="alter&umacr;">alterum</expan> <lb/>extremum &longs;tet, alterum verò moueatur:led ideo quòd &longs;e<lb/>midiameter perpetuò candem &longs;eruct longitudinem. </s>

<s>Elli<lb/>p&longs;is &longs;anè centrum habet, &longs;ed ab eo ad circumferentiam <lb/>quatuor tantùm &longs;emidiametri quomodolibet &longs;umpti du<lb/>cuntur æ quales. </s>

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<s>Ad tertium, quod contrarijs feratur lationibus, an<lb/>tror&longs;um, retror&longs;um, &longs;ur&longs;um & deor&longs;um. </s>

<s>Dicimus, facilè <lb/>&longs;olui, Nullus enim, re bene per&longs;pectâ, affirmauerit circu<lb/>lum contrarijs lationibus moueri. </s><figure></figure>

<s>Dicimus, facilè <lb/>&longs;olui, Nullus enim, re bene per&longs;pectâ, affirmauerit circu<lb/>lum contrarijs lationibus moueri. </s><figure/>

<s>E&longs;to enim circulus ABCD, <lb/>circa centrum E; ponamus ro<lb/>tari, & A ver&longs;us B, exempli gra<lb/>tiâ, antror&longs;um, mouebitur <expan abbr="aut&emacr;">autem</expan> <lb/>& B ver&longs;us C, & C ver&longs;us D, tum <lb/>D ver&longs;us A. </s>

<s>Non puto <expan abbr="quenquã">quenquam</expan> <lb/>dicturum, circulum hunc an<lb/>tror&longs;um codem tempore, & re<lb/>tror&longs;um ferri nec &longs;ur&longs;um aut de<lb/>or&longs;um, &longs;i enim qui&longs;piam per eius circuli circumferentiani <lb/>ambularet, is certè centrum ip&longs;um &longs;emper ad dexteram <lb/>haberet, vel ad &longs;ini&longs;tram, &longs;i ad dexteram, antror&longs;um ibit, &longs;i <lb/>ad &longs;ini&longs;tram, tetror&longs;um. </s>

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<s>Circulum quidem duplici notione produci, Natu<lb/>rali videlicet altera, & altera quæ e&longs;t præter naturam, & <lb/>ideo circularem lineam in ter mixtas computari. </s>

<s>Motus mixtus ait, vel proportione &longs;eruata fit, aut <lb/>non; Si proportione &longs;eruatâ, rectam lineam; ea verò non <lb/>&longs;eruata, circularem lineam produci. </s><figure></figure>

<s>E&longs;to enim rectangu<lb/>lum ABCD, cuius late<lb/>ra in datâ &longs;int proportio<lb/>ne, AD cum AB. </s>

<s>E&longs;to enim rectangu<lb/>lum ABCD, cuius late<lb/>ra in datâ &longs;int proportio<lb/>ne, AD cum AB. </s>

<s>Mo<lb/>ueatur A, duplici motu, <lb/>Altero quidem tendens <lb/>in B, altero vero ad mo<lb/>tum lineæ AB, feratur <lb/>ver&longs;us D, &longs;eruata inte<lb/>rim laterum proportione. </s>

<s>Itaque ponatur ex motu ab A <lb/>ver&longs;us B, perueni&longs;&longs;e in E, ex motu autem quo proportio<lb/>naliter fertur cum linea AB, facta ip&longs;a AB, in FH, perue<lb/>ni&longs;&longs;e in G, & EG connectatur. </s>

<s>Eritigitur Parallelogram<lb/>mum AEGF, Parallelogrammo ABCD proportiona<lb/>le &longs;imile, & circa eandem diametrum AGC. </s>

<s>Eritigitur Parallelogram<lb/>mum AEGF, Parallelogrammo ABCD proportiona<lb/>le &longs;imile, & circa eandem diametrum AGC. </s>

<s>Semperigi<lb/>tur punctum A &longs;i duabus lationibus feratur, laterum pro<lb/>portione &longs;eruata, lineam producet rectam, diametrum <lb/>nempe AGC. </s>

<s>Semperigi<lb/>tur punctum A &longs;i duabus lationibus feratur, laterum pro<lb/>portione &longs;eruata, lineam producet rectam, diametrum <lb/>nempe AGC. </s>

<s>Et hoc &longs;anè nullam habet dubitationem, <lb/>ex ijs quæ docet Euclides 1. 6. prop.

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<s>Cæterùm fal&longs;um <lb/>e&longs;t, a&longs;&longs;erere circulum ex mixto motu nun quam &longs;eruatâ <lb/>proportione produci. </s>

<s>&longs;eruat enim a&longs;&longs;iduè mixtus motus <lb/>quo producitur (&longs;i cum mixto motu producere velimus) <lb/>aliquam proportionem, &longs;ed non eandem. </s><figure></figure>

<s>E&longs;to enim recta AB, cui ad rectos <lb/>angulos AC. </s>

<s>E&longs;to enim recta AB, cui ad rectos <lb/>angulos AC. </s>

<s>Moueatur autem A, ver<lb/>&longs;us C per lineam AC, & eodem tempo<lb/>re linea AC, ver&longs;us B, ita tamen, vt &longs;em<lb/>per ip&longs;i AB, &longs;it perpendicularis. </s>

<s>feratur <lb/>autem eâ lege, vt quam proportionem <lb/>habet motus lineæ AC ver&longs;us B, ad mo<lb/>tum puncti A ve, &longs;us C, eandem habeat <lb/>ip&longs;e motus ab A ver&longs;us C, ad re&longs;iduum <lb/>lineæ AB, demptâ nempe ea parte quam <lb/>peragrauit linea AC mota ver&longs;us B. </s>

<s>Sit <lb/>autem, cum AC &longs;uo motu peruenerit <lb/>in D, punctum A, &longs;imiliter &longs;uo motu per eam latum perue<lb/>nitle in E erit eigo ex mixto motu, non quidem in D, nec <lb/>in E, &longs;ed in F, eritque punctum F in circum ferentia circu<lb/>li, cuius e&longs;t diameter ip&longs;a linea AB, quod quidem demon<lb/>&longs;tratur ex conuer&longs;a propo&longs;. </s>

<s>13. lib.

6. Elem. </s>

6. Elem. </s>

<s>E&longs;t enim AE <lb/>hoce&longs;t DF media proportionalis inter EF, hoc e&longs;t, AD, <lb/>& DB. </s>

<s>E&longs;t enim AE <lb/>hoce&longs;t DF media proportionalis inter EF, hoc e&longs;t, AD, <lb/>& DB. </s>

<s>Iterum &longs;i &longs;iat motus AC in GH, ad motum H per <pb pagenum="12"/>lineam AC, v&longs;que in C, vt &longs;e habet proportio AG ad <lb/>GH & GH ad GB, erit ex motu mixto A in H, nempe in <lb/>eiu&longs;dem circuli circum ferentia AFHB. ex quibus ha<lb/>bemus, circulum ex mixto motu fieri po&longs;&longs;e proportioni<lb/>bus quidem mediarum &longs;eruatis, &longs;ed nun quam ij&longs;dem. </s>

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<s>Ait autem; &longs;i duobus ab eadem potentia latis hoc <lb/>quidem plus repellatur, illud verò minus, æquum e&longs;t tar<lb/>diùs id moueri quod plus repellitur, eo quod minus. </s>

<s>De<lb/>trahi autem plus lineam, cuius extremum prepius e&longs;t cen<lb/>tro illa quæ &longs;uum habet terminum à centro remotiorem. </s><figure></figure>

<s>De<lb/>trahi autem plus lineam, cuius extremum prepius e&longs;t cen<lb/>tro illa quæ &longs;uum habet terminum à centro remotiorem. </s><figure/>

<s>E&longs;to, inquit, circulus <lb/>BCDE & alter in eo minor <lb/>MNOP circa idem centrum <lb/>A. Ducanturque; Diametrima<lb/>ioris quidem CD, EB, mino<lb/>ris verò MO, NP. </s>

<s>Itaque vbi <lb/>AB circulata eò peruenerit <lb/>vnde e&longs;t gre&longs;&longs;a, ip&longs;a quoque <lb/>AM eo vnde moueri c&oelig;pe<lb/>rat, perueniet. </s>

<s>Tardiùs antem <lb/>fertur AM, quam AD, pro<lb/>pterea quòd AM à centro <lb/>magis retrahatur quàm ip&longs;a AB. </s>

<s>Tardiùs antem <lb/>fertur AM, quam AD, pro<lb/>pterea quòd AM à centro <lb/>magis retrahatur quàm ip&longs;a AB. </s>

<s>Ducatur igitur ALF & <lb/>à puncto L, ip&longs;i AB perpendicularis L q, cadens in mino-<pb pagenum="13"/>ri circulo, & rur&longs;us ab codem L ip&longs;i AB, parailela duca<lb/>tur LS, Ab S verò eidem perpendicularis ST, & ab F i<lb/>tem FX. </s>

<s>Sunt ergo q L, ST, quidem æquales, nempeillæ, <lb/>per qua<gap/>, &longs;ecundum naturam, mouentur puncta BM. </s>

<s>Sunt ergo q L, ST, quidem æquales, nempeillæ, <lb/>per qua<gap/>, &longs;ecundum naturam, mouentur puncta BM. </s>

<s>Mo<lb/>tu verò retractionis ad centrum, hoc e&longs;t, præter naturam, <lb/>plus motum e&longs;t M quàm B. </s>

<s>Mo<lb/>tu verò retractionis ad centrum, hoc e&longs;t, præter naturam, <lb/>plus motum e&longs;t M quàm B. </s>

<s>Maior enim e&longs;t M q, ip&longs;a BT, <lb/>quod, ceu notum, &longs;uppo&longs;uit Ari&longs;toteles. </s>

<s>Maior enim e&longs;t M q, ip&longs;a BT, <lb/>quod, ceu notum, &longs;uppo&longs;uit Ari&longs;toteles. </s>

<s>nos autem inf. </s>

<s>à <lb/>demon&longs;trabimus. </s>

<s>Si igitur fiat vt motus præter naturam <lb/>ad motum præter naturam, ita motus <expan abbr="&longs;ec&umacr;dum">&longs;ecundum</expan> naturam, <lb/>ad motum &longs;ecundum naturam, punctum B; cum M fuerit <lb/>in L, non eritin S, &longs;ed in F. tunc enim, vt e&longs;t FX motus &longs;e<lb/>cundùm naturam ad XB, præter naturam, ita e&longs;t q L &longs;e<lb/>cundum naturam ad q M præter naturam; &longs;ed BF maior <lb/>e&longs;t ML, ergo proportione &longs;eruatâ, velociùs mouetur B <lb/>quàm M circa idem centrum A. </s>

<s>Hæc autem &longs;umma e&longs;t <lb/>eorum quæ præfert Ari&longs;toteles. </s>

<s>Hæc autem &longs;umma e&longs;t <lb/>eorum quæ præfert Ari&longs;toteles. </s>

<s>Cæterùm nos parallelo<lb/>grammum, quod in figura eius habetur prætermi&longs;imus, <lb/>quippe quod nihil ad eam quæ affertur, demon&longs;tratio<lb/>nem faciat. </s>

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<s>quare, vt TE, ad <lb/>q O, ita M q ad TB, &longs;ed TE maior e&longs;t ip&longs;a q O, quippe <lb/>quòd pars &longs;it q O ip&longs;ius TE, maior ergo & M q ip&longs;a TB, <lb/>quod o&longs;tendendum fuerat. </s>

<s>Cæterùm &longs;ubtilia & ingenio&longs;a i&longs;thæc e&longs;&longs;e non nega<lb/>mus, & longè faciliori & explicatiori modo veritas hæc <lb/>demon&longs;trari pote&longs;t, reiectis nem peillis, &longs;ecundùm, & prae<pb pagenum="14"/>ter naturam motibus, qui <expan abbr="quid&emacr;">quidem</expan> in &longs;implici circulo nece&longs;<lb/>&longs;ario non cadunt: caderent autem forta&longs;&longs;e, &longs;i de circulo <lb/>res e&longs;&longs;et à <expan abbr="p&omacr;deribus">ponderibus</expan> circumlatis ex &longs;tabili centro de&longs;eri<lb/>pto, qua de re agit G. </s>

<s>Vbaldus in Mechanicis ttactatu de <lb/>libra. </s>

<s>tunc enim dici pote&longs;t, pondus quod aliâs rectà ad <lb/>mundi centrum tenderet, à circuli centro in circulatio<lb/>ne retrahi, &longs;ed hæc ad circuli naturam, quatenus circulus <lb/>e&longs;t, ne quaquam &longs;pectant. </s><figure></figure>

<s>E&longs;to igitur circum ferentia <lb/>AFBH, cuius centrum C, dia<lb/>meter ACB, &longs;emidiameter AC. <lb/>&longs;umatur in AC punctum quod<lb/>libet, D, & centro C, &longs;patio CD, <lb/>circumferentia de&longs;cribatur <lb/>DGEI. </s>

<s>Dico punctum A velo<lb/>cius moueri puncto D eâdem <lb/>circulatione rotato. </s>

<s>etenim vt <lb/>diameter ad diametrum, & &longs;emidiameter ad &longs;emidiame<lb/>trum, ita circumferentia ad circumferentiam: igitur vt <lb/>AC ad CD, ita circumferentia AFHB ad circumferen<lb/>tiam DGEI. </s>

<s>At mota linea CA circa centrum C mo<lb/>uetur &longs;imul & CD, eodem igitur tempore rotationem <lb/>complent puncta AD, maius ergo &longs;patium eodem tem<lb/>pore metitur A, ip&longs;a D, quare velocior. </s>

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<s>QVÆSTIONES <lb/>MECHANICÆ.</s>

<s>QVÆSTIO I.</s>

<s>QVÆSTIO I.</s>

<s><emph type="italics"/>Cur maiores libræ exactiores &longs;int mi<lb/>noribus?<emph.end type="italics"/></s>

<s>Prioríbus, ceu fundamentis quibu&longs;dam iactis, oppor<lb/>tunè ad quæ&longs;tiones proponendas, eas queue diluendas &longs;e <lb/>confert Ari&longs;toteles. </s>

<s>Prioríbus, ceu fundamentis quibu&longs;dam iactis, oppor<lb/>tunè ad quæ&longs;tiones proponendas, eas queue diluendas &longs;e <lb/>confert Ari&longs;toteles. </s>

<s>Porro in propo&longs;ita quæ&longs;tione vide<lb/>tur prima fi onte cau&longs;&longs;am quæri de re quæ non e&longs;t: etenim <lb/>quis affirmauerit vnquam, lances quibus Apothecarij & <lb/>Macellarij vtuntur, magnas eas quidem, illis exactiores <lb/>e&longs;&longs;e quibus Gemmatij, atque Argentarij &longs;iliquis, & &longs;eru<lb/>pulis minuti&longs;&longs;ima appendunt, quæ tamen perexiguæ &longs;unt, <lb/>& &longs;i illis comparentur minimæ? </s>

<s>Veruntamen, ita pror&longs;us <lb/>res habet, vt a&longs;&longs;erit Ari&longs;toteles. </s>

<s>Veruntamen, ita pror&longs;us <lb/>res habet, vt a&longs;&longs;erit Ari&longs;toteles. </s>

<s>Non enim propterea <lb/>quòd illæ magnæ &longs;int, hæ verò exiguæ, hæ &longs;unt illis exa<lb/>ctiores; &longs;ed quoniam magnæ, rudes &longs;unt, minores verò ex<lb/>qui&longs;ita diligentia elaboratæ, & à materiæ pertina cia libe<lb/>riores. </s>

<s>Cæteris ergo paribus, exactiores e&longs;&longs;e maiores, ex <lb/>Philo&longs;ophimente, ita docebimus. </s><figure></figure>

<s>Cæteris ergo paribus, exactiores e&longs;&longs;e maiores, ex <lb/>Philo&longs;ophimente, ita docebimus. </s><figure/>

<s>E&longs;to libra maior AB, <lb/>cuius fulcimentum C. <lb/></s>

<s>E&longs;to libra maior AB, <lb/>cuius fulcimentum C. <lb/></s>

<s>Minor verò libra DE, <lb/>circa idem <expan abbr="fulcim&emacr;tum">fulcimentum</expan> <lb/>C, vnà cum maiori, ima<lb/>ginatione, conuer&longs;a. </s>

<s>Ap<lb/>ponatur queduis pon<lb/>dus maiori libræ in A, <lb/>de clinetque; exempli gratiâ in F, erit queue minor libra in G, <lb/>in eadem enim linea &longs;unt CGF. <expan abbr="Vnaq;">Vnaque</expan> igitur ex eodem <pb pagenum="16"/>centro C portionem circuli de&longs;cribet GD, AF, eritqueue <lb/>ACF &longs;ector circuli, cuius diameter AB, &longs;ed DCG &longs;e<lb/>ctor circuli, cuius diameter DE. </s>

<s>Itaque vt diameter ad <lb/>diametrum, ita portio ad portionem: maior autem dia<lb/>meter AB diametro DE: maior ergo portio AF, portio<lb/>ne DG. quod autem maius e&longs;t, minus obtutum fallit, ex<lb/>qui&longs;itius ita que tractum ex maiori AB quàm ex ip&longs;a mi<lb/>nori DE cogno &longs;cemus, quod fuerat o&longs;tendendum. </s>

<s>Cæterùm hac eadem de cau&longs;&longs;a, A&longs;tronomica in<lb/>&longs;trumenta, puta A&longs;trolabia, Armillæ, & alia eiu&longs;modi, <lb/>quo ampliora eò ex qui&longs;itiora, & certiora probantur. </s><figure></figure>

<s>E&longs;to enim A<lb/>&longs;trolabium magnum, <lb/>cuius diameter AB, <lb/>paruum autem CD, <lb/>circa idem centrum <lb/>E. </s>

<s>E&longs;to enim A<lb/>&longs;trolabium magnum, <lb/>cuius diameter AB, <lb/>paruum autem CD, <lb/>circa idem centrum <lb/>E. </s>

<s>Ducatur à centro <lb/>recta EF tangens ma<lb/>iorem circulum in F, <lb/><expan abbr="minor&emacr;">minorem</expan> verò <expan abbr="&longs;ecãs">&longs;ecans</expan> in <lb/>G, vt igitur GD ad to<lb/>tum circulum GCD, <lb/>ita FB. ad totum cir<lb/>culum FAB, vt ergò <lb/>GD ad FB, ita gradus <lb/>&longs;ignati in GD, ad eos qui &longs;ignantur in BF, maiores ergo <lb/>&longs;unt qui in FB, & minutarum partium capaciores. </s>

<s>Hinc <lb/>itaque apparet, <expan abbr="in&longs;trum&emacr;ta">in&longs;trumenta</expan> quælibet quò maiora fuerint, <lb/>eò e&longs;&longs;e & exqui&longs;itiora, quod propo&longs;uerat Ari&longs;toteles, in <lb/>hac quæ&longs;tione de Libra. </s>

<s>Quod autem addit de fraudibus Purpurariorum, <lb/>inquiens; quamobrem machinánturij qui purpuram ven<lb/>dunt, vt <expan abbr="p&emacr;dendo">pendendo</expan> defraudent, dum ad medium, &longs;partum, <pb pagenum="17"/>non ponentes; tum plumbum in alterutram libræ partem <lb/>infundentes; aut ligni quod ad radicem vergebat, in eam <lb/>quam deferri volunt partem con&longs;tituentes, aut &longs;i nodum <lb/>habucrit, ligni enim grauior ea e&longs;t pars, in qua e&longs;t radix, <lb/>nodus verò radix quæ dam e&longs;t. </s>

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<s><emph type="italics"/>Vtrum libræ quæ ponderibus vacuæ æquilibrant, <lb/>omni pror&longs;us careant fraude?<emph.end type="italics"/></s>

<s>Videri cuipiam po&longs;&longs;et, libras, quæ ponderibus va<lb/>cuæ, æquilibrant, omm pror&longs;us fraude carere, verunta<lb/>men ita non e&longs;t, quod diligentiùs (res enim magni mo<lb/>menti e&longs;t) di&longs;quiremus. </s><figure></figure>

<s>E&longs;to enim libra AB, ita diui&longs;a <lb/>in C, vt AC &longs;it partium IS, CB ve<lb/>rò carundem &longs;it 10. apponatur parti <lb/>A lanx ponderans 10, parti vero B <lb/>lanx ponderans 15. ex permutata i<lb/>gitur proportione libra &longs;u&longs;pen&longs;a in <lb/>C, aequè ponderabit; &longs;i autem appo<lb/>natur lanci B &longs;acoma vnciarum 6, & in lance A con&longs;titua<lb/>tur purpura, quæ ita &longs;e habeat ad vncias 6, vt 10 ad 15, ite<lb/>rum æqueponderabit, &longs;ed vt 10 ad 15, ita 4 ad 6. Purpura<lb/>rius ergo fraudulentus, ponens in lance A vncias purpuræ <lb/>4, facto æquilibrio petet pretium vnciarum 6, & ita em<lb/>ptorem decipiet, quod &longs;anè innuerat, non autem demon<lb/>&longs;trauerat Ari&longs;toteles. </s>

<s>Hæc autem faciliora fient ex ijs, <lb/>quæ in &longs;equentibus quæ &longs;tionibus, vbi de vecte agetur, ex<lb/>plicabuntur. </s>

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<s>Si enim <lb/>in lance A con&longs;tituatur &longs;acoma, in B verò purpura non fit <lb/>æquilibrium. </s><pb pagenum="18"/>

<s>QVÆSTIO II.</s>

<s>QVÆSTIO II.</s>

<s><emph type="italics"/>Cur, &longs;i &longs;ur &longs;um libræ fulcimentum &longs;it, appo&longs;ito ad alteram partem <lb/>pondere, de &longs;cendat libra, & eo amoto, iterum a&longs;cendat, & ad æqui<lb/>librium reuertatur. </s>

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<s>Ari&longs;toteles primam quæ&longs;tionis partem ita &longs;oluit: An <lb/>quia &longs;ur&longs;um parte quidem exi&longs;tente, plus libræ extra per<lb/>pend culum &longs;it? </s>

<s>Spartum enim perpendiculum e&longs;t: quare <lb/>nece&longs;&longs;<gap/> e&longs;t deor&longs;um ferriid quod plus e&longs;t, donec a&longs;cendat <lb/>qua bifariam libram diuidit ad ip&longs;um perpendiculum, <lb/>cum onus in cum bat ad libræ partem &longs;ur&longs;us raptam. </s><figure></figure>

<s>Sit libra recta (hoc e&longs;t, in æquilibrio con&longs;tituta) BC, <lb/>&longs;partum autem AD, <lb/>fulcimentum autem <lb/>D, de&longs;uper: &longs;parto au<lb/>tem deor&longs;um proie<lb/>cto ad M perpendicu<lb/>laris erit vbi ADM. <lb/></s>

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<s>Nos autem cla<lb/>rius rem ob oculos ponimus. </s>

<s>Id ergo &longs;ibi vult Ari&longs;toteles, <lb/>propterea quòd pars iugi HDG maior e&longs;t parte ED q, <lb/>eam eleuatam nece&longs;&longs;e e&longs;t de&longs;cendere, & iterum à perpen<lb/>diculari ADM bifariam diui&longs;am ad æquilibrium reuer<lb/>ti, Po&longs;&longs;umus nos idem &longs;impliciori figura demon&longs;trare. </s><figure></figure>

<s>E&longs;to libra AB, bi<lb/>fariam, diui&longs;a in G, <lb/><expan abbr="fulciment&umacr;">fulcimentum</expan> verò &longs;ur<lb/>&longs;um vbi D, prod<gap/>ca<lb/>tur perpendicularis <lb/>DC in E. </s>

<s>Stante igi<lb/>tur libra AB, in æqui<lb/>librio æqualis e&longs;t pars <lb/>CH, ip&longs;i parti CB <lb/>apponatur pondus in <lb/>B. </s>

<s>Stante igi<lb/>tur libra AB, in æqui<lb/>librio æqualis e&longs;t pars <lb/>CH, ip&longs;i parti CB <lb/>apponatur pondus in <lb/>B. </s>

<s>Declinabit igitur <lb/>libra mota circa centrum D, fiat autem in FG, &longs;ecetqueue <lb/>perpendicularem in I. </s>

<s>Declinabit igitur <lb/>libra mota circa centrum D, fiat autem in FG, &longs;ecetqueue <lb/>perpendicularem in I. </s>

<s>Punctum vero C eodem motu cir<lb/>ca idem centrum D erit in H. amoueatur pondus appo&longs;i<lb/>tum: Dico libram à &longs;itu FG declinaturam & iterum re<lb/>uer&longs;uram in &longs;itum pri&longs;tinum ACB. quoniam enim parti <lb/>GH, quæ æqualis e&longs;t parti HF, additur pars IH, quæ à <lb/>perpendiculari e&longs;t v&longs;que ad H, ip&longs;i verò HF eadem pars <lb/>detrahitur, erit IF minor GI. </s>

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<s>Si pondus circa &longs;tabile centrum conuertatur, dimi&longs;<lb/>&longs;um non &longs;tabit, ni&longs;i &longs;ecundum grauitatis centrum fuerit <lb/>in perpendiculari, quæ per centrum, circa quod conuer<lb/>titur, ad mundi centrum cadit. </s>

<s>Stabit autem in ea per<lb/>pendiculari in duobus punctis, altero à centro mundi <lb/>remoti&longs;&longs;imo; altero verò cidem quantum licuerit pro<lb/>ximo. </s><figure></figure>

<s>Stabit autem in ea per<lb/>pendiculari in duobus punctis, altero à centro mundi <lb/>remoti&longs;&longs;imo; altero verò cidem quantum licuerit pro<lb/>ximo. </s><figure/>

<s>E&longs;to corpus A, cuius graui<lb/>tatis centrum B, nixum lineae in<lb/>flexibili BC, cum qua liberè <lb/>conuertatur circa centrum C. <lb/></s>

<s>E&longs;to corpus A, cuius graui<lb/>tatis centrum B, nixum lineae in<lb/>flexibili BC, cum qua liberè <lb/>conuertatur circa centrum C. <lb/></s>

<s>Ducatur autem per mundi cen<lb/>trum perpendicularis BCD. <lb/></s>

<s>Ducatur autem per mundi cen<lb/>trum perpendicularis BCD. <lb/></s>

<s>Sit igitur primò pondus A <expan abbr="&longs;ec&umacr;-dum">&longs;ecun<lb/>dum</expan> gracilis B centrum, in per<lb/>pendiculari ip&longs;a &longs;upra centrum <lb/>C, puta in B. </s>

<s>Sit igitur primò pondus A <expan abbr="&longs;ec&umacr;-dum">&longs;ecun<lb/>dum</expan> gracilis B centrum, in per<lb/>pendiculari ip&longs;a &longs;upra centrum <lb/>C, puta in B. </s>

<s>Moueatur & <expan abbr="de&longs;c&emacr;-dat">de&longs;cen<lb/>dat</expan> in E. </s>

<s>Moueatur & <expan abbr="de&longs;c&emacr;-dat">de&longs;cen<lb/>dat</expan> in E. </s>

<s>Po&longs;t hæc verò in F, hoc <lb/>e&longs;t iterum in ip&longs;a perpendiculari <lb/>infra centrum C. </s>

<s>Po&longs;t hæc verò in F, hoc <lb/>e&longs;t iterum in ip&longs;a perpendiculari <lb/>infra centrum C. </s>

<s>De&longs;cribet er<lb/>go circulum ex centro C, nem<lb/>pe BEF &longs;ecantem perpendicu<lb/>larem in duobus punctis oppo<lb/>&longs;itis BF, dico, pondus libe è di-<pb pagenum="21"/>mi&longs;&longs;um in duobus tantum punctis &longs;uapte naturâ perman<lb/>&longs;urum, BF, in B, primò, quoniam cum corpus ip&longs;um A à <lb/>perpendiculari, quæ &longs;upei ficiei loco intelligitur ABCD <lb/>per centrum grauitatis diuidatur, in partes diuiditur æ<lb/>queponderantes, quare in neutram partem inclinabit. <lb/></s>

<s>Stabit igitur erectum, lineæ ip&longs;i fultum, inflexibili BC, <lb/>quæ nititur puncto C. </s>

<s>Stabit igitur erectum, lineæ ip&longs;i fultum, inflexibili BC, <lb/>quæ nititur puncto C. </s>

<s>In E verò non &longs;tabit, quippe quod <lb/>eo &longs;itu centrum ip&longs;um grauitatis &longs;it extra perpendicula<lb/>rem, & ideo extra fulcimentum &longs;tabile C. </s>

<s>In E verò non &longs;tabit, quippe quod <lb/>eo &longs;itu centrum ip&longs;um grauitatis &longs;it extra perpendicula<lb/>rem, & ideo extra fulcimentum &longs;tabile C. </s>

<s>In F verò ite<lb/>rum &longs;tabit, pendens à centro C, propterea quòd & ibi ab <lb/>eadem perpendiculari diuidatur per grauitatis centrum <lb/>in partes æqueponderantes. </s>

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<s>8. lib.

3. Elem. </s>

3. Elem. </s>

<s>Pondus igi<lb/>tur A conuer&longs;um &longs;eu liberè motum circa centrum C, in <lb/>duobus tantum locis perpendicularis lineæ &longs;tabit remo<lb/>ti&longs;&longs;imo altero, vt e&longs;t B, altero verò cidem quamproximo, <lb/>vt e&longs;t F. </s>

<s>Hoc idem egregiè demon&longs;trauit G. Vbald. </s>

<s>Hoc idem egregiè demon&longs;trauit G. Vbald. in &longs;uis <lb/>Mechanicis, Tractatu de Libra prop.1.<gap/></s>

<s>in &longs;uis <lb/>Mechanicis, Tractatu de Libra prop.1.<gap/></s>

<s>Ad hæc autem dubitare quis po&longs;&longs;et, cur experientiâ <lb/>docente, pondera quæ infra fulcimentum habent, vt lan<lb/>cea &longs;ari&longs;&longs;aue ad planum horizontis perpendiculariter e<lb/>recta, licet eo ca&longs;u grauitatis centrum in ip&longs;a perpendicu<lb/>lari con&longs;tituatur, non &longs;tet quidem, &longs;ed altrin&longs;ecus ca<lb/>dat? </s><pb pagenum="22"/><figure></figure>

<s>Sit enim horizontis <lb/>planum AB, cui in puncto <lb/>C perpendiculariter ere<lb/>cta &longs;tatuatur &longs;ari&longs;&longs;a DC, <lb/>cuius grauitatis centrum <lb/>E, in ip&longs;a perpendiculari. <lb/></s>

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<s>Id certè agit, qui nutantis &longs;ari&longs;&longs;æ, digito, motum &longs;e<lb/>quitur; vt in ip&longs;o motu digitum a&longs;&longs;iduè centro grauitatis <lb/>&longs;ari&longs;&longs;æ &longs;upponat, vnde &longs;it vt nun quam extra fulcimentum <lb/>permanens, nun quam cadat. </s>

<s>Similis huic alia quo que dubitatio &longs;oluitur: Nempe, <lb/>Cur turbines, quibus pueri ludunt, dum quidem rotan<lb/>tur, &longs;tent erecti, rotationevero ce&longs;&longs;ante, cadant. </s><figure></figure>

<s>E&longs;to enim Turbo AB, cu<lb/>ius grauitatis centrum C, planum <lb/>horizontis DE, linea Horizonti <lb/>perpendicularis ABC, tran&longs;iens <lb/>per centrum grauitatis C, &longs;it au<lb/>tem fulcimentum in B. <expan abbr="Itaq;">Itaque</expan> cum <lb/>centrum grauitatis C &longs;it in ip&longs;a <lb/>perpendiculari, &longs;tabit ex demon-<pb pagenum="23"/>&longs;tratis, at ex vitio materiæ non &longs;tabit. </s>

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<s>ea autem paullatim elangue&longs;cente ín ca<lb/>&longs;um vergere; ce&longs;&longs;ante verò penitus cadere. </s>

<s>fit enim ex in<lb/>æqualitate materiæ, vel operis ruditate, vel aliâ quauis <lb/>ex cau&longs;&longs;a, grauitatis centrum non e&longs;&longs;e in C, &longs;ed exempli <lb/>gratiâ vbi F, notentur autem hinc inde Turbinis latera <lb/>notis GH. </s>

<s>Vtique cum F extra perpendicularem fuerit, <lb/>cadet Turbo ad partem G; at id ne &longs;iat, efficitur velocita<lb/>te motus, quo centrum F transfertur in contrariam par<lb/>tem, vbi I. non autem cadit ver&longs;us H, quoniam eadem ve<lb/>locitate iterum transfertur in F, quamobrem cum huius<lb/>cemodi centri a&longs;&longs;idua circa perpendicularem fiat trans<lb/>latio, ad nullam partem Turbo cadere pote&longs;t; elangue<lb/>&longs;cente verò motu rotans, paullatim in cipit inclinari, do<lb/>nec eo penitus ce&longs;&longs;ante, ad eam partem cadit, ad quam à <lb/>per pendiculari grauitatis centrum vergit. </s>

<s>De&longs;cribit au<lb/>tem in rotatione grauitatis centrum, quod in medio non <lb/>e&longs;t paruum circulum, per cuius centrum ip&longs;a perpendi<lb/>cula<gap/>is pertingit. </s>

<s>Modò redeuntes ad libram, cuius ful cimentum e&longs;t <lb/>&longs;ur&longs;um, alio principio, nempe Mechanico, cur depre&longs;&longs;a <lb/>ad æqualitatem reuertatur, demon&longs;trabimus. </s><pb pagenum="24"/><figure></figure>

<s>Sit igitur, vt &longs;u<lb/>periùs, libra AB, cu<lb/>ius centrum grauita<lb/>tis C, fulcimentum, <lb/>verò &longs;ur&longs;um, in D li<lb/>bræ quidem in C per<lb/>pendiculariter con<lb/>iunctum. </s>

<s>Perpendi<lb/>cularis verò quæ per <lb/>fulcimentum, & gra<lb/>uitatis <expan abbr="c&emacr;trum">centrum</expan> tran&longs;<lb/>iens ad mundi cen<lb/>trum tendit DLE. &longs;tante igitur librâ in &longs;ua æqualitate, e<lb/>rit centrum grauitatis C in ip&longs;a perpendiculari infra qui<lb/>dem fulcimentum D. </s>

<s>Loco verò, mundi centro quàm <lb/>proximo. </s>

<s>Pondus po&longs;t hæc apponatur in B, Declinabit au<lb/>tem pars CB, in HF, eleuatâ interim parte AC, in GH. <lb/></s>

<s>Pondus po&longs;t hæc apponatur in B, Declinabit au<lb/>tem pars CB, in HF, eleuatâ interim parte AC, in GH. <lb/></s>

<s>Mota igitur libra tota, circa fulcimentum D mouebitur <lb/>circa idem centrum, & grauitatis centrum C, de&longs;cribens <lb/>portionem circuli CH, fi etque; C in H, & quoniam H, hoc <lb/>e&longs;t C, extra per pendicularem fit, amoto pondere, ex lan<lb/>ce B, cuius pre&longs;&longs;ione libra declinauerat, centrum grauita<lb/>tis per eandem circulì portionem HC, ad perpendicula<lb/>rem de&longs;cendet, donec iterum in ea quie&longs;cat, quo ca&longs;u li<lb/>bra AB ad æquilibrium reuertetur: quod fuerat demon<lb/>&longs;trandum. </s>

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<s>Hinc colligimus &longs;ieri po&longs;&longs;e, libras illas, quæ non <gap/><lb/>quouis, quantumuis paruo pondere declinant, cas fulci-<gap/><lb/>mentum habere &longs;ur&longs;um. </s>

<s>His ad dimus, cæteris paribus, re&longs;i&longs;tentiam eò e&longs;&longs;e <lb/>maiorem, quo minus grauitatis centrum di&longs;tat à fulci<lb/>mento &longs;ur&longs;um, circa quod ip&longs;a libra aduertitur. </s><figure></figure>

<s>E&longs;to libra AB, cuius gra<lb/>uitatis centrum C, & primò <lb/>quidem eius ful cimentum <lb/>&longs;ur&longs;um &longs;it vbi D, itaque &longs;i ap<lb/>po&longs;ito pondere de clinauerit <lb/>libra ad partes B, punctum <lb/>C, dum a&longs;cendet de&longs;cribet <lb/>portionem circuli CE. fulciatur iterum &longs;ur&longs;um puncto F, <lb/>& iterum declinet ad partes B, & iterum punctum C, dum <lb/>a&longs;cendet, circuli portionem de&longs;cribet CG. </s>

<s>E&longs;t autem <lb/>minor angulus contactus ACE, angulo ACG, magis er<lb/>go &longs;ur&longs;um, hoc e&longs;t, ad naturam &longs;ui feretur C, per CG, ex <lb/>centro F, quàm per CE, ex centro D, quod fuerat de<lb/>mon&longs;trandum. </s>

<s>Hæc autem re&longs;i&longs;tentia ex eodem fulcimento & eo<lb/>dem pondere eo faciliùs &longs;uperabitur, quo longius bra<lb/>chium libræ fuerit. </s>

<s>E&longs;to enim iterum libra AB, cuius fulcimentum D, <lb/>centrum grauitatis C, &longs;it & alia libra, cuius brachia bre<lb/>uiora EF, idem habens centrum C, & eidem puncto &longs;u<lb/>&longs;pen&longs;a D. </s>

<s>Dico igitur, eodem pondere appo&longs;ito, faciliùs <pb pagenum="26"/><figure id="fig1"></figure><lb/>declinaturam libram ad <lb/>partes B, quàm &longs;i idem ap<lb/>poneretur in F. </s>

<s>Dico igitur, eodem pondere appo&longs;ito, faciliùs <pb pagenum="26"/><figure id="fig1"/><lb/>declinaturam libram ad <lb/>partes B, quàm &longs;i idem ap<lb/>poneretur in F. </s>

<s>Demit<lb/>tatur enim, à puncto B <lb/>horizonti perpendicula<lb/>ris BG, & ab F item per<lb/>pendicularis FH, Tum <lb/>iuncta DB, centro D, eo<lb/>dem vero &longs;patio DB, circuli portio de&longs;cribatur BI, item <lb/>iuncta DF eodem centro D, &longs;patio DF, portio circuli de<lb/>&longs;cribatu: FK. e&longs;t autem maior DB ip&longs;a DF ex propo&longs;. <lb/></s>

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1. Elem.

quare maiotis circuli portio e&longs;t BI quàm <lb/>FK. </s>

quare maiotis circuli portio e&longs;t BI quàm <lb/>FK. </s>

<s>Obliquior autem, hoc e&longs;t, à perpendiculariremotior <lb/>e&longs;t motus per FK quàm per BI. maior &longs;i quidem e&longs;t angu<lb/>lus KFH angulo IBG. quod nos ita probamus. </s>

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<s>Po&longs;&longs;<gap/>mus & idem quoque aliter o&longs;tendere. </s>

<s>Sint enim &longs;eor&longs;um duæ libræ, maior AB, mïnor EF, <lb/>quàm commune grauitatis centrum C, fulcimentum ve<lb/>rò &longs;ur&longs;um D. </s>

<s>Sint enim &longs;eor&longs;um duæ libræ, maior AB, mïnor EF, <lb/>quàm commune grauitatis centrum C, fulcimentum ve<lb/>rò &longs;ur&longs;um D. </s>

<s>Producatur perpendicularis DC, in G & fiat <lb/>CG æqualis CB, CH verò æqualis CF. </s>

<s>Producatur perpendicularis DC, in G & fiat <lb/>CG æqualis CB, CH verò æqualis CF. </s>

<s>Sunt igitur duo <pb pagenum="27"/><figure id="fig2"></figure><lb/>vectes DG, DH, quo<lb/>rum quidem commu<lb/>ne fulcimentum D, <lb/>pondus verò C, poten<lb/>tiæ vbi HG. </s>

<s>Sunt igitur duo <pb pagenum="27"/><figure id="fig2"/><lb/>vectes DG, DH, quo<lb/>rum quidem commu<lb/>ne fulcimentum D, <lb/>pondus verò C, poten<lb/>tiæ vbi HG. </s>

<s>Sunt au<lb/>tem hi vectes cius na<lb/>turæ, in quibus <expan abbr="p&omacr;dus">pondus</expan> <lb/>e&longs;t inter fulcimentum <lb/>& potentiam, itaque <lb/>vt &longs;e habet DC, ad <lb/>DG, ita potentia in G <lb/>ad pondus in C, item vt DC ad DH ita potentia in H ad <lb/>idem pondus C, &longs;ed minor e&longs;t propo&longs;itio DC, ad DG <lb/>quàm DC ad DH. minor ergo potentia requiritur in G, <lb/>hoc e&longs;t, in B, quàm in H, hoc e&longs;t in F. </s>

<s>Data igitur ponderis <lb/>æqualitate faciliùs &longs;uperabitur re&longs;i&longs;tentia C in B, quàm <lb/>in F: quod o&longs;tendendum fuerat. </s>

<s>Ad huius libræ naturam illæ quoque rediguntur, <lb/>quarum iugum non rectum quidem, &longs;ed curuum, vel ex <lb/>rectis &longs;ur&longs;um in angulum ad fulcimentum detinentibus, <lb/>nec refert vtrum curuitas &longs;it circuli portio quælibet, aut <lb/>ellip&longs;is &longs;ecundum alterum diametrorum; quod ita de<lb/>mon&longs;tramus. </s><figure></figure>

<s>E&longs;to libra, cuius iugum <lb/>curuum <expan abbr="angulat&umacr;ue">angulatunue</expan> ABC, <lb/>cuius fulcimentum B, æqua<lb/>lia autem brachia AB, BC, <lb/>& pondera item <expan abbr="vtrinq;">vtrinque</expan> ap<lb/>pen&longs;a æqualia. </s>

<s>Demittatur <lb/>ex puncto B ad mundi cen<lb/>trum perpendicularis BD. <lb/></s>

<s>Demittatur <lb/>ex puncto B ad mundi cen<lb/>trum perpendicularis BD. <lb/></s>

<s>Stante igitur libra ABC in <lb/>æquilibrio, erit eius graui<pb pagenum="28"/>tatis centrum in ip&longs;a perpendiculari BD, puta in E. </s>

<s>Stante igitur libra ABC in <lb/>æquilibrio, erit eius graui<pb pagenum="28"/>tatis centrum in ip&longs;a perpendiculari BD, puta in E. </s>

<s>Ap<lb/>ponatur pondus in C, declinabit autem libra, &longs;it autem <lb/>iuxta po&longs;itionem FBG. </s>

<s>Ap<lb/>ponatur pondus in C, declinabit autem libra, &longs;it autem <lb/>iuxta po&longs;itionem FBG. </s>

<s>Centrum igitur grauitatis E per <lb/>portionem EH, erit in H. </s>

<s>Centrum igitur grauitatis E per <lb/>portionem EH, erit in H. </s>

<s>A&longs;cendit ergo centrum graui<lb/>tatis in H, hoc e&longs;t, &longs;ur&longs;um, id e&longs;t, contra cius naturam; a<lb/>moto igitur pondere ex C, grauitatis centrum extra per<lb/>pendicularem con&longs;titutum rur&longs;us de&longs;cendet, & iterum <lb/>libra ABC ad æquilibrium reuertetur. </s>

<s>Hoc idem egre<lb/>giè o&longs;tendit G. Vbald. </s>

<s>Hoc idem egre<lb/>giè o&longs;tendit G. Vbald. in tractatu de libra, propo&longs;. </s>

<s>in tractatu de libra, propo&longs;. </s>

<s>Hinc ratio pendet earum imaguncularum, quas ex <lb/>contu&longs;a papyro ligneaue leui materia compingunt, per<lb/>queue manus earum ambas, ferreum filum trajicientes, v<lb/>trinque plumbea appendunt pondera æqualia, ea <expan abbr="quid&emacr;">quidem</expan> <lb/>lege, vt centrum grauitatis infra pedes imaguncula &longs;ta<lb/>tuatur. </s>

<s>Tunc enim exten &longs;o filo imponentes ceu funam<lb/>bulos per illud, vltrò citroque; decurrere faciunt, imagun<lb/>cula interim erecta & in neutram partem cadente, quod <lb/>vt figurâ clarius fiat; </s><figure></figure>

<s>E&longs;to imaguncu<lb/>la AB, per cuius ma<lb/>nus traij ciatur filum <lb/>ferreum curuum <expan abbr="c&umacr;">cum</expan> <lb/>æ qualibus ponderi<lb/>bus hinc inde <expan abbr="app&emacr;-&longs;is">appen<lb/>&longs;is</expan> CD. </s>

<s>Nitatur au<lb/>tem pedibus filo HI <lb/>in <emph type="italics"/>B<emph.end type="italics"/>, &longs;itque; totìus ma<lb/>chinæ grauitatis <expan abbr="c&emacr;-trum">cen<lb/>trum</expan> E, &longs;itque <expan abbr="per-p&emacr;dicularis">per<lb/>pendicularis</expan> per gra<lb/>uitatis <expan abbr="centr&umacr;">centrum</expan> tran&longs;i<lb/>ens A<emph type="italics"/>B<emph.end type="italics"/> E. </s>

<s>Itaque in<lb/>clinata imaguncula, & conuer&longs;a circa punctum <emph type="italics"/>B<emph.end type="italics"/>, &longs;i de-<pb pagenum="29"/>clinet ad partes I, centrum grauitatis eleuabitur in F. </s>

<s>Si <lb/>verò ad partes H eleuabitur in G. quare cum FG loca <lb/>&longs;intremotiora à mundi centro, quàm &longs;it E, non &longs;tabit gra<lb/>uitatis centrum in punctis FG, &longs;ed ad infimum locum re<lb/>uertecur, hoc e&longs;t, in ip&longs;a perpendiculari in E, & imagun<lb/>cula ad perpendiculum ip&longs;i H<emph type="italics"/>B<emph.end type="italics"/>E filo, hoc e&longs;t, ip&longs;i hori<lb/>zonti reuertetur. </s>

<s>Hinc etiam Arictum, T e&longs;tudinun<gap/> queue demolito<lb/>riatum Machinarum vis pendet, nempe ex ratione libra<lb/>rum, quæ fulcimentum habent &longs;ur&longs;um. </s><figure></figure>

<s>E&longs;to enim Aries A<emph type="italics"/>B<emph.end type="italics"/><lb/>funi appen&longs;us CD, cu<lb/>ius grauitatis centrum, <lb/>D, perpendicularis verò <lb/>quæ ad mundi centrum <lb/>ip&longs;a CDE. </s>

<s>Stante igitur <lb/>in æquilibrio machina, <lb/>centrum grauitatis erit <lb/>in ip&longs;a perpendiculari. <lb/></s>

<s>Applicetur alicubi po<lb/>tentia retropellens, eleuabitur igitur centrum grauitatis <lb/>per circuli portionem DF, cuius &longs;emidiameter e&longs;t CD, <lb/>&longs;i etqueue iuxta po&longs;itionem CF. </s>

<s>Aries verò in GFH. </s>

<s>Di<lb/>mi&longs;&longs;a itaque Machina centrum F vtpote graue, non &longs;tabit, <lb/>&longs;ed &longs;uapte naturâ reuertetur in D. </s>

<s>Di<lb/>mi&longs;&longs;a itaque Machina centrum F vtpote graue, non &longs;tabit, <lb/>&longs;ed &longs;uapte naturâ reuertetur in D. </s>

<s>Quadruplici autem <lb/>de cau&longs;&longs;a motus Arietis violenti&longs;&longs;imus e&longs;t ex vi naturalis <lb/>ponderis, quo deor&longs;um fertur, tum velo citate naturalis <lb/>motus in de&longs;cendendo auctæ, tum ex vi pote<gap/> tiæ impel<lb/>lentis, & naturalem motum adiuuantis, tum ex velocita<lb/>te ex motu violento deor&longs;um & antror&longs;um impellente <lb/>acqui&longs;itâ. </s>

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<s>Hæc ille, qui &longs;chemate quo que rem aperit, at eo a<lb/>pud interpretes, & Picolomineum Paraphra&longs;tem, ita <expan abbr="m&emacr;-dosè">men<lb/>dosè</expan> lineato, vt inde ob&longs;curitas lucis loco, legentibus of<lb/>fundatur. </s>

<s>Nos, quod & &longs;uprà quo que fecimus, no&longs;tra fi<lb/>gurâ, &longs;ole ip&longs;o clariorem, ex Ari&longs;to telis ip&longs;ius mente rem <lb/>totam efficiemus. </s><figure></figure>

<s>Sit libra recta, (hoc <lb/>e&longs;t, in æquilibrio con<lb/>&longs;tituta) vbi NG. </s>

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<s>Amoto <lb/>igitur onere nece&longs;&longs;e e&longs;t manere. </s>

<s>Incumbit enim onus ex<lb/>ce&longs;&longs;us medietatis eius, vbi e&longs;t F. </s>

<s>Incumbit enim onus ex<lb/>ce&longs;&longs;us medietatis eius, vbi e&longs;t F. </s>

<s>Sen&longs;us e&longs;t igitur, idcirco <lb/>partem iugi KLO inclinatam, ad æquilibrium non re<lb/>uerti, propterea quòd maior &longs;it ip&longs;a KLO pars quæ tra<lb/>hit, ip&longs;a<gap/> RKL, quæ trahitur & eleuatur. </s><figure></figure>

<s>Pote&longs;t hoc idem longè <lb/>&longs;impliciori themate demon<lb/>&longs;trari. </s>

<s>E&longs;to enim libra AB, <lb/>cuius centrum C, fulcimen<lb/>tum vero deor&longs;um D, Per<lb/>pendicularis per centrum & <lb/>fulcimentum tran&longs;iens EF. <lb/></s>

<s>E&longs;to enim libra AB, <lb/>cuius centrum C, fulcimen<lb/>tum vero deor&longs;um D, Per<lb/>pendicularis per centrum & <lb/>fulcimentum tran&longs;iens EF. <lb/></s>

<s>Apponatur pondus in B, de<lb/>clinabitque; puta ad GH, cen<lb/>trum verò C, ex &longs;tabili fulci<lb/>mento D, circuli portionem de&longs;cribet CI, libra autem <lb/>&longs;ecabit EF perpendicularem in K. Æquales autem &longs;unt <lb/>IG, IH, at ex parte HI de&longs;umpta e&longs;t KI, addita queue ip&longs;i <lb/>IG, maior e&longs;t ergo tota KG, torâ KH. </s>

<s>Non igitur KH <lb/>habet KG, &longs;ed libra, ni&longs;i impedita fuerit, cum centro C <lb/>de&longs;cendente per <gap/>in M, ad ip&longs;am perpendicularem dela<lb/>ta, ad in feriorem partem, mutatis vicibus quie&longs;cet, facto <lb/>nempe fulcimento &longs;ur&longs;um, fietque; horizonti æque di&longs;tans <lb/>iuxta po&longs;itionem LMN. </s>

<s>Demon&longs;tratio <expan abbr="quid&emacr;">quidem</expan> e&longs;t hæc, &longs;ed non ex proprijs prin<lb/>cipijs Mechanicis, <expan abbr="n&emacr;pe">nempe</expan> ex ratione <expan abbr="c&emacr;t">cent</expan><gap/>i grauitatis petitâ. <lb/></s>

<s>Ii&longs;dem enim &longs;tantibus, <expan abbr="c&umacr;">cum</expan> centrum grauitatis C fiat extra <lb/>perpendicularem, de&longs;cendens ad I, nun quam reuert<gap/> tur <lb/>in C, a&longs;cen deret enim; &longs;ed &longs;i liberè circa centrum D con<lb/>uerteretur, de&longs;cendens vt dictum e&longs;t per circulum CIM <lb/>pondus B, fieret in L, A vero in N adepta po&longs;itione <lb/>LMN. </s><pb pagenum="32"/>

<s>Cur autem huius libræ, quæ aliàs inutilis e&longs;t, memi<lb/>nerit Philo&longs;ophus, ea videtur cau&longs;&longs;a, quòd inde vectis vir<lb/>tutem eliciat, vt &longs;uo loco videbimus. </s>

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<s>Dicimus itaque, libram, cuius fulcimentum nec &longs;ur<lb/>&longs;um e&longs;t, nec deor&longs;um, &longs;ed pror&longs;us in medio, nempe in ip&longs;o <lb/>grauitatis centro, vbi brachia & pondera vtrinque appo<lb/>&longs;ita fuerint æqualia, &longs;i ab æquilibrio mouentur, quomo<lb/>docunque po&longs;ita, &longs;tare nec ab eo, quem adepta e&longs;t, &longs;itu di<lb/>moueri. </s>

<s>Quæ&longs;tionem hanc perperam tractârunt recentio<lb/>res quidam, Hieron. </s>

<s>Quæ&longs;tionem hanc perperam tractârunt recentio<lb/>res quidam, Hieron. Cardanus, Nicolaus Tartalea, & alij <lb/>nonnulli, qui Iordani Nemoracij a&longs;&longs;ertiones &longs;unt &longs;ecuti, <lb/>quorum demon&longs;trationes vel paralogi&longs;mos potiùs egre<lb/>giè confutauit in libr. </s>

<s>Cardanus, Nicolaus Tartalea, & alij <lb/>nonnulli, qui Iordani Nemoracij a&longs;&longs;ertiones &longs;unt &longs;ecuti, <lb/>quorum demon&longs;trationes vel paralogi&longs;mos potiùs egre<lb/>giè confutauit in libr. </s>

<s>Mechanicor. </s>

<s>Mechanicor. Tractatu de libra pro<lb/>po&longs;. </s>

<s>4. Guid. Vbald. ad cuius probati&longs;&longs;ima &longs;cripta Lecto<lb/>rem ablegamus. </s>

<s>Tractatu de libra pro<lb/>po&longs;. </s>

<s>Vbald. </s>

<s>ad cuius probati&longs;&longs;ima &longs;cripta Lecto<lb/>rem ablegamus. </s>

<s>fu&longs;i&longs;&longs;imè enim ibi hac de re & ab&longs;oluti&longs;&longs;i<lb/>mè agit. </s>

<s>Nos autem quidem paucis ea, quæ ad hanc co<lb/>gnitionem pertinent, explicabimus. </s><figure></figure>

<s>Nos autem quidem paucis ea, quæ ad hanc co<lb/>gnitionem pertinent, explicabimus. </s><figure/>

<s>E&longs;to enim libra A<emph type="italics"/>B<emph.end type="italics"/>, <lb/>cuius brachia æqualia, <lb/>& centrum grauitatis <lb/>in C, brachijs verò <lb/>AC, C<emph type="italics"/>B<emph.end type="italics"/> æqualibus, æ<lb/>qualia pondera hinc <lb/>inde <expan abbr="apponãtur">apponantur</expan>. </s>

<s>Tum <pb pagenum="33"/>fulcimento in medio, hoc e&longs;t, vbi grauitatis centrum C <lb/>applicato per centrum ip&longs;um C ducatur perpendicularis, <lb/>quæ ad mundi centrum, DCE, &longs;itque primum libra æ<lb/>quedi&longs;tans horizonti, con&longs;tituta. </s>

<s>Tum ex altera parte <lb/>pre&longs;&longs;a moueatur & fiat iuxta po&longs;itionem FCG. </s>

<s>Tum ex altera parte <lb/>pre&longs;&longs;a moueatur & fiat iuxta po&longs;itionem FCG. </s>

<s>Dico eam <lb/>dimi&longs;&longs;am permanere, etenim cum grauitatis centrum &longs;it <lb/>in ip&longs;a perpendiculari, in neutram partem verget, &longs;ed nec <lb/>vergere pote&longs;t, quippe quod non circa fulcimentum ceu <lb/>centrum motus, moueatur grauitatis centrum, &longs;ed in ip&longs;o <lb/>&longs;it ful cimento; &longs;itum ergo non mutat. </s>

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<s>Circa hæc po&longs;&longs;et cuipiam oriri Dubium, num chor<lb/>dulæ, quibus lances appenduntur, variationem aliquam <lb/>circa ea quæ demon&longs;trata &longs;unt, inducere valeant. </s>

<s>Dicimus nullam inde fieri: E&longs;to enim libra AB, cu<lb/>ius centrum & fulcimentum C, ab cuius extremitate A <lb/>dependeat, funiculus AD, ab alia verò <emph type="italics"/>B<emph.end type="italics"/>, funiculus <emph type="italics"/>B<emph.end type="italics"/>E, <pb pagenum="34"/><figure id="fig3"></figure><lb/>quibus appen&longs;æ &longs;int æ<lb/>qualis ponderis lances <lb/>DE. </s>

<s>Dicimus nullam inde fieri: E&longs;to enim libra AB, cu<lb/>ius centrum & fulcimentum C, ab cuius extremitate A <lb/>dependeat, funiculus AD, ab alia verò <emph type="italics"/>B<emph.end type="italics"/>, funiculus <emph type="italics"/>B<emph.end type="italics"/>E, <pb pagenum="34"/><figure id="fig3"/><lb/>quibus appen&longs;æ &longs;int æ<lb/>qualis ponderis lances <lb/>DE. </s>

<s>Moueatur libra, <lb/>fiatque in ICH, funi<lb/>culi verò in lancibus in <lb/>IK, HL. &longs;ecet autem fu<lb/>niculus IK libram A<emph type="italics"/>B<emph.end type="italics"/>, <lb/>in M, LH verò produ<lb/>catur & eandem &longs;ecer <lb/>in N. quoniam igitur <lb/>IC, æqualis e&longs;t CH, pa<lb/>rallelæ autem KI, LN æquales <expan abbr="er&umacr;t">erunt</expan> alterni anguli MIC, <lb/>NHC, &longs;ed & anguli ad verticem ICH, BCH æquales <lb/>&longs;unt, quare triangulum IMC, æquale triangulo HNC, <lb/>& latera lateribus, quæ æqualibus angulis &longs;ubtenduntur. <lb/></s>

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<s>quod fuerat demon&longs;trandum. </s>

<s>QVÆSTIO III.</s>

<s>QVÆSTIO III.</s>

<s><emph type="italics"/>Cur exiguæ vires (quod etiam à principio dixerat) vecte magna <lb/>mouent pondera, vectes in&longs;uper onus accipientes, cum facilius <lb/>&longs;it, minorem mouere grauitatem, minor est au<lb/>tem &longs;ine vecte?<emph.end type="italics"/></s>

<s>Ari&longs;toteles ita quæ&longs;tionem proponit, vt eam R heto<lb/>rico quodam fuco admirabiliorem f<gap/>ciat. </s>

<s>Soluit au<lb/>tem hoc pacto, <expan abbr="inqui&emacr;s">inquiens</expan>, fieri po&longs;&longs;e eam e&longs;&longs;e cau&longs;&longs;am, quod <lb/>vectis &longs;it libra, eius nempe generis quod fulcimentum ha<lb/>bet deor&longs;um, atque id circo in ip&longs;a pre&longs;&longs;ione in partes in<lb/>æquales vectem diuidi. </s><pb pagenum="35"/><figure></figure>

<s>Figura quam ex<lb/>hibet, vix ferè quid &longs;i<lb/>bi velit explicat. </s>

<s>Nos <lb/>ad eius <expan abbr="m&emacr;tem">mentem</expan> aliam <lb/>proponemus <expan abbr="eamq;">eamque</expan> <lb/>longè clariorem. </s>

<s>E&longs;to vectis A<emph type="italics"/>B<emph.end type="italics"/>, <lb/>cuius fulcimentum, <lb/>deor&longs;um in C, pon<lb/>dus D, potentia ex vecte, pondus &longs;u&longs;tinens E. </s>

<s>E&longs;to vectis A<emph type="italics"/>B<emph.end type="italics"/>, <lb/>cuius fulcimentum, <lb/>deor&longs;um in C, pon<lb/>dus D, potentia ex vecte, pondus &longs;u&longs;tinens E. </s>

<s>Perpendi<lb/>cularis per fulcimentum FCG. </s>

<s>Perpendi<lb/>cularis per fulcimentum FCG. </s>

<s>Itaque quoniam poten<lb/>tia in E non &longs;uperat pondus D, nec ab eo &longs;uperatur, &longs;tat <lb/>vectis cum potentia Horizonti æquidi&longs;tans, hoc e&longs;t, in æ<lb/>quilibrio, vectis autem in puncto C diuiditur in partes æ<lb/>queponderantes. </s>

<s>Modo præualeat potentia ponderi, & <lb/>vectem deprimat, fiat autem in LCH, erit igitur <emph type="italics"/>B<emph.end type="italics"/>, in L, <lb/>A in H, D in K, & CF, quæ vectem in partes æque ponde<lb/>rantes diuidebat, in CI. </s>

<s>Iam igitur non æqueponderant <lb/>partes, &longs;i quidem pars vectis FCI, aufertur parti HCI, & <lb/>adiungitur parti ICL, quæ ideo &longs;it pondero&longs;ior, vnde & <lb/>potentia ad ponderis eleuationem adiuuatur. </s>

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<s>Cæterum videtur A riftoteles id &longs;ub<lb/>odora&longs;&longs;e, quod po&longs;tea Archimedes, Mechanicorum prin<lb/>ceps, in propo&longs;. </s>

<s>6. primi Æqueponderantium explicitè <lb/>protulit & probauit: nempe in æquilibrio ita e&longs;&longs;e pondus <lb/>ad pondus, vt brachium ad brachium, ratione permutata. </s><figure></figure>

<s>E&longs;to enim vectis <lb/>AB, quomodolibet <lb/>fulcimento diui&longs;us in <lb/>C. <expan abbr="app&emacr;datur">appendatur</expan> autem <lb/>in A, pondus D, in B <lb/>verò pondus E, ita &longs;e <lb/>habens ad pondus D, vtip&longs;a AC ad CB. </s>

<s>Stabit igitur ve<lb/>ctis, & neutram in partem verget, erit enim centrum gra<lb/>uitatis in C, diui&longs;o nempe ibi vecte in partes æque ponde<lb/>rantes. </s>

<s>Hoc po&longs;t Archimedem, & in&longs;ignes illos veteres <lb/>Mechanicos præclari&longs;&longs;imè demon&longs;trauit G. </s>

<s>Hoc po&longs;t Archimedem, & in&longs;ignes illos veteres <lb/>Mechanicos præclari&longs;&longs;imè demon&longs;trauit G. Vbaldus in <lb/>Mechanicis, Tractatu de Libra propo&longs;. </s>

<s>Vbaldus in <lb/>Mechanicis, Tractatu de Libra propo&longs;. </s>

<s>6. nec non de Ve<lb/>cte propo&longs;. </s>

<s>Cæterùm vt aliquid interim, quod no&longs;trum &longs;it, affe<lb/>ramus, liceat nobis egregios illos viros interrogare, quæ<lb/>nam mirabilis eius effectionis &longs;it cau&longs;&longs;a? </s>

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<s>Teneo, at nondum acquie&longs;co: pe<lb/>tam enim, Cur ea rationis permutatio mirabilem illum <lb/>effectum pariat. </s>

<s>Hoc quod illi non do cent, puto nos, i<lb/>gnorantiæ &longs;omno &longs;epultos, &longs;omnia&longs;&longs;e. </s><figure></figure>

<s>Hoc quod illi non do cent, puto nos, i<lb/>gnorantiæ &longs;omno &longs;epultos, &longs;omnia&longs;&longs;e. </s><figure/>

<s>Æqualitatem &longs;tatus <lb/>e&longs;&longs;e cau&longs;&longs;am, nemo, vt <lb/>puto, inficiabitur. </s>

<s>res e&longs;t <lb/>enim per &longs;e clara. </s>

<s>E&longs;to &longs;i<lb/>quidem linea quæpiam AB, applicetur extremitati A po<pb pagenum="38"/>tentia quæ dam quæ lineam ad &longs;e trahat ad partes nempe <lb/>A, Tum in B quædam alia potentia ip&longs;i quæ in A potentiae, <lb/>æqualis, quæ lin eam trahat &longs;imili modo ad partes B. </s>

<s>Datâ <lb/>igitur harum potentiarum æqualitate, linea AB, nec ad <lb/>partes A, nec ad partes B transferetur, &longs;ed pror&longs;us immo<lb/>bilis &longs;tabit. </s>

<s>His ita con&longs;titutis, Dico vecte quomodolibet diui&longs;o, <lb/>ponderibu&longs;que vtrinque appo&longs;itis, permutatâ propor<lb/>tione &longs;ibi inuicem re&longs;pondentibus, rem e&longs;&longs;e redactam ad <lb/>æqualitatem, & inde &longs;tatum fieri, hoc e&longs;t, æquilibrium. </s><figure></figure>

<s>E&longs;to enim vectis AB, quo modo libet diui&longs;us in C, & <lb/>ip&longs;i quidem C fulcimentum &longs;upponatur. </s>

<s>Appendantur <lb/>quo que vtrinque pondera ex ratione brachiorum AC, <lb/>CB, &longs;ibi inuicem permutatim re&longs;pondentia, &longs;intque; DE. <lb/></s>

<s>Appendantur <lb/>quo que vtrinque pondera ex ratione brachiorum AC, <lb/>CB, &longs;ibi inuicem permutatim re&longs;pondentia, &longs;intque; DE. <lb/></s>

<s>Dico vectem ex æqualitate, in neutram partem <expan abbr="inclina-tur&umacr;">inclina<lb/>turum</expan>, &longs;ed perman&longs;urum in æquilibrio. </s>

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<s>Igitur cum par<lb/>tes CA, AF totius FC, æquales &longs;int partibus CB, BG, <lb/>totius CG, erit totum FC, toti CG æquale. </s>

<s>Diui&longs;us ita-<pb pagenum="39"/>que erit vectis FG in partes æquales FC, CG in puncto <lb/>fulcimenti C. </s>

<s>Diui&longs;us ita-<pb pagenum="39"/>que erit vectis FG in partes æquales FC, CG in puncto <lb/>fulcimenti C. </s>

<s>Et quoniam æquale in æquale non agit, <lb/>&longs;tabit vectis & in neutram partem inclinabit. </s>

<s>Rur&longs;um <lb/>quoniam ad partem FC, duæ &longs;unt brachiorum potentiæ <lb/>FA, HC, appendantur puncto F, duo pondera H, I, ip&longs;is <lb/>DE æqualia, item puncto G, alia duo pondera ij&longs;dem DE <lb/>æqualia KL, iterum æqueponderabit, quippe quod æ<lb/>quahbus brachijs FCCG æqualia appen&longs;a &longs;int pondera <lb/>HI KL. </s>

<s>Cur igitur &longs;eruata permutatim brachiorum & <lb/>ponderum proportione fiat æquilibrium, ex his quæ de<lb/>mon&longs;trauimus, clarè patet. </s>

<s>Sed forte dicet qui&longs;piam, &longs;i brachia, pondera &longs;unt, <lb/>vel ponderibus æquipollentia, &longs;u&longs;tinenti duplicabitur <lb/>pondus. </s><figure></figure>

<s>Sed forte dicet qui&longs;piam, &longs;i brachia, pondera &longs;unt, <lb/>vel ponderibus æquipollentia, &longs;u&longs;tinenti duplicabitur <lb/>pondus. </s><figure/>

<s>E&longs;to enim vectis AB, <lb/>ita diui&longs;us in C, vt pars <lb/>maior CB minori AC &longs;it <lb/>in proportione quintu<lb/>pla. </s>

<s>Appendatur autem <lb/>in A pondus D, <expan abbr="quintupl&umacr;">quintuplum</expan> <lb/>ponderi E appen&longs;o in B. </s>

<s>Appendatur autem <lb/>in A pondus D, <expan abbr="quintupl&umacr;">quintuplum</expan> <lb/>ponderi E appen&longs;o in B. </s>

<s>Si <lb/>igitur brachio AC, quod <lb/>e&longs;t vnum, ad datur pondus <lb/>D, quod e&longs;t quinque, fi ent &longs;ex, item &longs;i brachio CB, quod <lb/>e&longs;t quinque, addatur pondus E, quod e&longs;t vnum, fient &longs;ex. <lb/></s>

<s>Fulcimentum igitur &longs;u&longs;tinebit duodecim, quod e&longs;t ab<lb/>&longs;urdum ex ijs quæ clarè demon&longs;trauit G. Vbald. </s>

<s>Fulcimentum igitur &longs;u&longs;tinebit duodecim, quod e&longs;t ab<lb/>&longs;urdum ex ijs quæ clarè demon&longs;trauit G. Vbald. in Me<lb/>chan. tractatu de Libra propo&longs;. </s>

<s>tractatu de Libra propo&longs;. </s>

<s>5. His re&longs;pondemus, bra<lb/>chia quidem operari non pondere, &longs;ed potentiâ, quæ vis <lb/>quædam e&longs;t, non autem pondus. </s>

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<s>Iacta huiu&longs;cemodi, quam diximus, æqualitate, &longs;e-<pb pagenum="40"/>quitur nece&longs;&longs;ariò, centrum grauitatis ip&longs;ius vectis cum <lb/>appen&longs;is ponderibus, ac &longs;i vnum idemqueue e&longs;&longs;et corpus <lb/>cadere in perpen diculari quæ per centrum ip&longs;um & ful<lb/>cimentum tran&longs;iens ad mundi centrum pertingit. </s>

<s>QVÆSTIO IV.</s>

<s>QVÆSTIO IV.</s>

<s><emph type="italics"/>Quærit hic Ari&longs;toteles, cur ij qui in nauis medio &longs;unt remiges ma<lb/>ximè nauem moueant?<emph.end type="italics"/></s>

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<s>Plurimum autem diuidi vbi plurima <lb/>pars remi à &longs;calmo e&longs;t. </s>

<s>Rem facilem, eo quod verbis potu<lb/>erit, &longs;chemate non declarauit, nos autem apponemus. </s><figure></figure>

<s>Rem facilem, eo quod verbis potu<lb/>erit, &longs;chemate non declarauit, nos autem apponemus. </s><figure/>

<s>E&longs;to enim nauis AB, mare CD, <lb/>remorum alter, quiad proram EF, cu<lb/>ius &longs;calmus G, alterverò in medio na<lb/>uis, HI, circa &longs;calmum K. </s>

<s>E&longs;to enim nauis AB, mare CD, <lb/>remorum alter, quiad proram EF, cu<lb/>ius &longs;calmus G, alterverò in medio na<lb/>uis, HI, circa &longs;calmum K. </s>

<s>Ait igitur, <lb/>remos e&longs;&longs;e vectes, &longs;calmos verò fulci<lb/>menta, pondus quod remo, ceu vecte, <lb/>mouetur mare ip&longs;um. </s>

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<s>Pondus <lb/>autem cò faciliùs mouctur, quo maior e&longs;t vectis pars, quæ <lb/>à fulcimento e&longs;t ad mouentem potentiam. </s>

<s>Acutè &longs;anè Philo&longs;ophus. </s>

<s>Acutè &longs;anè Philo&longs;ophus. </s>

<s>Ego autem &longs;i per mode&longs;tiam <lb/>liceret, dicerem, non quidem e&longs;&longs;e fulcimentum <expan abbr="&longs;calm&umacr;">&longs;calmum</expan>, <lb/>&longs;ed mare ip&longs;um, pondus vero nauim, ad locum &longs;calmi, <expan abbr="n&emacr;-pe">nen<lb/>pe</expan> inter mouentem potentiam, & fulcimentum po&longs;itum, <lb/>etenim & eo pacto po&longs;&longs;umus vti vecte, quod ob&longs;eruat & <lb/>demon&longs;trat G. Vbaldus tractatu de vecte propo&longs;. </s>

<s>Vbaldus tractatu de vecte propo&longs;. </s>

<s>2. Erunt <lb/>igitur in de&longs;cripta figura puncta FI, quæ in mari&longs;unt, ful<lb/>cimenta, quibus remorum extrema in ip&longs;aim pul&longs;ione ni<lb/>tuntur, pondera verò &longs;eu pondus pluribus vectibus & po<lb/>tentijs impul&longs;um nauis ip&longs;a, quæ &longs;calmis e&longs;t annexa. </s>

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<s>quoniam autem vt <lb/>FG ad FE ita potentia mouens in E ad pondus motum <lb/>in G. item vt IK ad IH ita potentia mouens in H ad pon<lb/>dus motum in K, maior autem e&longs;t proportio FG ad FE <lb/>quàm proportio IK ad IH. </s>

<s>Maiori indiget potentia vt <lb/>pellatur pondus in G quàm pondus in K. </s>

<s>Maiori indiget potentia vt <lb/>pellatur pondus in G quàm pondus in K. </s>

<s>Hæc certè vti diximus ita &longs;e habent. </s>

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<s>Addimus, fal&longs;um videri quod a&longs;&longs;erit Ari&longs;toteles, <lb/>nempeillos qui in media naui &longs;unt, remiges, maximè na<lb/>uim mouere; facilius, melius dixi&longs;&longs;et. </s>

<s>Si enim maximè, <lb/>quod ait, denorat, maximo &longs;patio, & velocius pror&longs;us fal<lb/>&longs;um, etenim tardius mouent & minori &longs;patio, quod nos i<lb/>ta demon&longs;tramus. </s><pb pagenum="42"/><figure></figure>

<s>E&longs;to enim Remus AB <lb/>qui marí fulcitur in B, Scal<lb/>mus remi qui ad <expan abbr="prorã">proram</expan> pup<lb/>pimue C, qui in media naui <lb/>D, maior autem remi pars <lb/>e&longs;t à &longs;calmo Dad A quami<lb/>p&longs;ius C 2d A, Pellantur remi & &longs;tante ceu centro BA, in <lb/>E. eodem igitur tempore C eritin F, & D in G, &longs;ed maiu<gap/><lb/>e&longs;t &longs;patium CF &longs;patio DG, Ergo vnica impul&longs;ione, plus <lb/>mouit &longs;calmum, hoc e&longs;t, nauim, potentia ad puppim pro<lb/>ramue remigans, quàm ea quæ operatur in media naui vt <lb/>&longs;entire vid<gap/>batur (&longs;i modo is e&longs;t eius &longs;en&longs;us) Ari&longs;toteles. <lb/></s>

<s>Nece&longs;&longs;arium igitur e&longs;t, quodait, maximè intelligendum, <lb/>faciliùs, Veritatem hanc cogno&longs;centes Triremium præ<lb/>fecti robu&longs;tiores quidem remiges ad proram & puppim, <lb/>inualidiores vcrò circa mediam triremem collocant. </s>

<s>QVÆSTIO V.</s>

<s>QVÆSTIO V.</s>

<s><emph type="italics"/>Dubitat<gap/>r, Cur paruum exi&longs;tens gubernaculum, & in extremo <lb/>nauigio tantas habeat vires, vt ab exiguo temone, & ab hominis <lb/>vnius viribus alioqui modicè vtentis magnæ nauigiorum <lb/>moueantur moles?<emph.end type="italics"/></s>

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<s>quamobrem omnia <lb/>ferè quæ de Temone dicenda fuerant, de remo loquens <lb/>proponit. </s>

<s>Aitautem. </s><figure></figure>

<s>Aitautem. </s><figure/>

<s>Sit remus AB, <lb/>&longs;calmus vero C, remi <lb/>in nauigio <expan abbr="principi&umacr;">principium</expan> <lb/>A, palmula autem, <lb/>quæ in mari B. </s>

<s>Sit remus AB, <lb/>&longs;calmus vero C, remi <lb/>in nauigio <expan abbr="principi&umacr;">principium</expan> <lb/>A, palmula autem, <lb/>quæ in mari B. </s>

<s>Si igi<lb/>tur A, vbi D transla<lb/>tum e&longs;t, non erit B v<lb/>bi E. æqualis enim, <lb/>BE ip&longs;i AD, æquale <lb/>igitur translatum erit, &longs;ed erat minus. </s>

<s>eritigitur vbi F, mi<lb/>nor enim BF, ip&longs;a AD, quareip&longs;o GF ip&longs;a DG. </s>

<s>eritigitur vbi F, mi<lb/>nor enim BF, ip&longs;a AD, quareip&longs;o GF ip&longs;a DG. </s>

<s>Hæc <pb pagenum="44"/>demon&longs;tratio licet vera videatur, rei ta men, de qua e&longs;t <lb/>&longs;ermo, minimè aptatur. </s>

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<s>Illud quoque <lb/>fal&longs;um e&longs;t, nauim ip&longs;am tantum moueri in aëre, quantum <lb/>e&longs;t &longs;patium AD, hoc e&longs;t, remi extremum quod e&longs;t in naui, <lb/>&longs;iquidem &longs;calmi motu, non autem manubrij remi, nauis <lb/>agatur. </s>

<s>Aliter igitur res &longs;e habet, & forte hoc pacto. </s><figure></figure>

<s>Aliter igitur res &longs;e habet, & forte hoc pacto. </s><figure/>

<s>Sit remus AB, cuíus <lb/>manubrium A, palmula <lb/>B, &longs;calmus C. </s>

<s>Sit remus AB, cuíus <lb/>manubrium A, palmula <lb/>B, &longs;calmus C. </s>

<s>Pellatur an<lb/>tror&longs;us A, fiatque; in D, tunc <lb/>&longs;i æqualiter mouerentur <lb/>manubrium & palmula, i<lb/>p&longs;a palmula ficret in G, at <lb/>minus mouetur: fiet ergo <lb/>in E. ip&longs;e verò &longs;calmus C <lb/>translatus erit in F, motaque; erit nauis à C in F, non autem <lb/>ab A in D. </s>

<s>P o&longs;uitautem Ari&longs;toteles &longs;calmum ad medium <lb/>remi, &longs;ed non ad medium collocari &longs;olet, maior enim pars <lb/>in mare propendet puta HB, quo ca&longs;u translationis &longs;pa<lb/>tium fit maius, nempe ab H in I. fit autem motus &longs;calmi ex <lb/>centris qui &longs;unt in &longs;patio ip&longs;o BE, quatenus autem ad te<lb/>monem pertinet, quem remum ait, obliquè puppim ip&longs;am <lb/>propellentem, ita &longs;e res habet. </s>

<s>E&longs;to nauis carina AB, prora A, puppis B, Temonis <lb/>ala BC, gubernaculum BD, cardo verò fulcimentumue <lb/>B; factaitaque impul&longs;ione obliquâ gubernaculi à D in E, <lb/>minor fiet motus in mari à C in F, eritqueue temo vbi EGF, <pb pagenum="45"/><figure id="fig4"></figure><lb/>cardo verò vbi G, translata igitur e<lb/>rit eo motu, puppis ip&longs;a à B in G. facta <lb/>itaque paruâ motione puppis ex B in <lb/>G, prora ip&longs;a quæ longè di&longs;tat à pup<lb/>pi B maiori &longs;patio &longs;uperato translata <lb/>erit in H facta proræ in contrariam <lb/>partem ab ea quæ facta e&longs;t guberna<lb/>culi motione. </s>

<s>E&longs;to nauis carina AB, prora A, puppis B, Temonis <lb/>ala BC, gubernaculum BD, cardo verò fulcimentumue <lb/>B; factaitaque impul&longs;ione obliquâ gubernaculi à D in E, <lb/>minor fiet motus in mari à C in F, eritqueue temo vbi EGF, <pb pagenum="45"/><figure id="fig4"/><lb/>cardo verò vbi G, translata igitur e<lb/>rit eo motu, puppis ip&longs;a à B in G. facta <lb/>itaque paruâ motione puppis ex B in <lb/>G, prora ip&longs;a quæ longè di&longs;tat à pup<lb/>pi B maiori &longs;patio &longs;uperato translata <lb/>erit in H facta proræ in contrariam <lb/>partem ab ea quæ facta e&longs;t guberna<lb/>culi motione. </s>

<s>Porrò quod & in præ<lb/>cedente quæ&longs;tione a dnotauimus, <expan abbr="l&omacr;-gè">lon<lb/>gè</expan> meliùs procedet demon&longs;tratio &longs;i <lb/><expan abbr="fulciment&umacr;">fulcimentum</expan> mare intelligatur, quàm <lb/>&longs;calmus, neque enim mare ceu pon<lb/>dus, &longs;ed &longs;calmus ip&longs;e Temonisuecardo, ponderum in&longs;tar <lb/>transferuntur. </s>

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<s>Obliqui igitur motus qui validèin puppi &longs;it, cau&longs;&longs;a <lb/>e&longs;t non quidem ex conuer&longs;ione temonis percu&longs;&longs;io maris, <lb/>&longs;ed mare ip&longs;um, cuius fluctus naui currente obliquam te<lb/>monis alam ad eam partem quæ mari obuertitur, impel<lb/>lentes temonem cum puppiad contrariam partem vali<lb/>di&longs;&longs;imè transferunt. </s>

<s>E&longs;to nauis carina AB, prora B, puppis A, Temo AC, <lb/>gubernaculum AD; Itaque currentenaui, Temone in<lb/>terim & guberna culo in eadem carinæ linea exi&longs;tentibus, <pb pagenum="46"/><figure id="fig5"></figure><lb/>Temo quidem mare &longs;ecat, nulla fa<lb/>ctâ in puppi, nauis ad &longs;ini&longs;tram dex<lb/>tramue translatione. </s>

<s>E&longs;to nauis carina AB, prora B, puppis A, Temo AC, <lb/>gubernaculum AD; Itaque currentenaui, Temone in<lb/>terim & guberna culo in eadem carinæ linea exi&longs;tentibus, <pb pagenum="46"/><figure id="fig5"/><lb/>Temo quidem mare &longs;ecat, nulla fa<lb/>ctâ in puppi, nauis ad &longs;ini&longs;tram dex<lb/>tramue translatione. </s>

<s>Si verò mouea<lb/>tur gubernaculum à D in E, co moto <lb/>mouebitur aliquantulum & puppis <lb/>ad partes E, quod voluit Ari&longs;toteles. <lb/></s>

<s>Si verò mouea<lb/>tur gubernaculum à D in E, co moto <lb/>mouebitur aliquantulum & puppis <lb/>ad partes E, quod voluit Ari&longs;toteles. <lb/></s>

<s>Sedminimi, vt diximus, ea res ad tan<lb/>tum effectum e&longs;t momenti. </s>

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<s>Pulcherrima enim res e&longs;t, & <lb/>nobis per&longs;pecti&longs;&longs;ima, qui Gua&longs;tallâ re&longs;identiæ olim no<lb/>&longs;træ oppido ad Padum, Mantuam pergentes &longs;æpi&longs;&longs;imè ad <lb/>Ca&longs;trum B<gap/>rgi Iu&longs;is ea qua diximus machinatione lati&longs;<lb/>&longs;imum eiu&longs;dem Padi aluum tran&longs;ie cimus. </s>

<s>Habet autem <lb/>&longs;e hoc pacto. </s><figure></figure>

<s>Habet autem <lb/>&longs;e hoc pacto. </s><figure/>

<s>E&longs;to fluminis citerior <lb/>ripa AB, vlterior CD. </s>

<s>E&longs;to fluminis citerior <lb/>ripa AB, vlterior CD. </s>

<s>Pon<lb/>tones duo tabulis &longs;trati, & v<lb/>nà firmiter juncti EF, Temo <lb/>inter eorum puppes extans <lb/>GH, locus in ripa &longs;tabilis A, <lb/>funis, quo pontones, & ma<lb/>china tota continetur AI. <lb/>fluuij decur&longs;us ver&longs;us BD, <lb/>&longs;tantibus itaque pontonibus <lb/>ad ripam citeriorem AB, Te<lb/>mone in <expan abbr="neutrã">neutram</expan> partem pul<lb/>&longs;o, cum aqua decurrens eum <lb/>re&longs;i&longs;tentem non inueniat, <lb/>&longs;cinditur quidem ab eo, &longs;ed <lb/>non propellit, eo autem con<lb/>uer&longs;o & in GK con&longs;tituto, a<lb/>la eius GK ab aqua defluente propul&longs;a machinam &longs;ecum <lb/>trahit ver&longs;us ripam CD, factâ motione circa centrum &longs;eu <lb/>&longs;tabilem locum A, otio&longs;is interim portitoribus, donec per <lb/>circuli portionem ML deuenerit ad vlteriorem ripam in <lb/>L. </s>

<s>Vnde iterum temone in contrariam partem conuer&longs;o, <lb/>aquâ &longs;imiliter temonem propellente, per eandem circuli <lb/>portionem ad ripam citeriorem reuertitur, à qua paullo <lb/>antè di&longs;ce&longs;&longs;erat. </s>

<s>Ex quibus apparet, motus cau&longs;&longs;am non <pb pagenum="48"/>e&longs;&longs;e &longs;olam cam, quæ ab ala temonis fit, aquæ <expan abbr="percu&longs;&longs;ion&emacr;">percu&longs;&longs;ionem</expan>, <lb/>vt &longs;en&longs;erat Ari&longs;toteles, &longs;ed currentis a quæ temonis alam <lb/>ferientis impul&longs;ion<gap/>m: nihil autem referre, vtrum &longs;tante <lb/>naui a qua currat, vel câ currente a qua &longs;tet, vt in mari fit, <lb/>idem enim vtroque modo temo patitur. </s>

<s>Vt autem machi<lb/>næ huius & totius negotij &longs;pecies facilius animo concipia<lb/>tur, &longs;chema hoc &longs;tudio &longs;orum oculis &longs;ubijciemus. </s><figure></figure>

<s>Vt autem machi<lb/>næ huius & totius negotij &longs;pecies facilius animo concipia<lb/>tur, &longs;chema hoc &longs;tudio &longs;orum oculis &longs;ubijciemus. </s><figure/>

<s>Lembi nauiculæueideo appo&longs;itæ &longs;unt, vt oblongum <lb/>funem &longs;u&longs;tineant; id etenim nî fieret, aquæ immer&longs;us a<lb/>quam &longs;cindens machinæ motum impediret, ideo etiam <lb/>apponuntur, ne funis madens celeriter maceretur & pu<lb/>tre&longs;cat. </s>

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<s>Diximus enim, Temonem currente naui, lateraliter <lb/>conuer&longs;um obuios fluctus ex cipientem puppim ip&longs;am ob<lb/>liquè in alteram partem transferre. </s>

<s>Porrò ea vela, de qui<lb/>bus loquimur, ventorum flatibus obliquè oppo&longs;ita can<lb/>dem ob cau&longs;&longs;am circulariter agitantur, quodvt figurâ eui<lb/>dentius fiat, </s><figure></figure>

<s>E&longs;to velum AB, brachio <lb/>CE obliquè affixum, ita vt <lb/>angulus ACE maior &longs;it an<lb/>gulo BCE, ventus obliquè <lb/>velum feriens FG. <expan abbr="Itaq;">Itaque</expan> quo<lb/>niam ventus in velum obli. <lb/></s>

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<s>Sed enim de Te<lb/>mone agentes non e&longs;t interim cur de caudis auium pi&longs;ci<lb/>umque taceamus, in&longs;tar enim remonum &longs;unt à Naturai<lb/>p&longs;a opportunis animalium partibus, po&longs;tremis videlicet, <lb/>appo&longs;iti, quanquam nec&longs;olum Temonis v&longs;um præ&longs;tent, <lb/>vt videbimus. </s>

<s>E&longs;to pi&longs;cis AB, cuius caput A, cauda verò CB. </s>

<s>E&longs;to pi&longs;cis AB, cuius caput A, cauda verò CB. </s>

<s>Hac <lb/>igitur neutram in partem reflexâ, pi&longs;cis pinnarum motu <lb/>rectâ in anteriorem partem progreditur. </s>

<s>Si autem nece&longs;<lb/>&longs;e ei fuerit ad dextram &longs;ini&longs;tramqueue conuerti non pote<lb/>rit, ni&longs;i cauda ip&longs;a iuuetur. </s>

<s>Omnis enim motus progre&longs;&longs;i<lb/>uus quiete indiget, nec <expan abbr="ab&longs;q;">ab&longs;que</expan> &longs;tabili fulcimento progredi <pb pagenum="50"/><figure id="fig6"></figure><lb/>pote&longs;t, quod in libris de ani<lb/>malium ince&longs;&longs;u docetip&longs;e<lb/>met Philo&longs;ophus. </s>

<s>Omnis enim motus progre&longs;&longs;i<lb/>uus quiete indiget, nec <expan abbr="ab&longs;q;">ab&longs;que</expan> &longs;tabili fulcimento progredi <pb pagenum="50"/><figure id="fig6"/><lb/>pote&longs;t, quod in libris de ani<lb/>malium ince&longs;&longs;u docetip&longs;e<lb/>met Philo&longs;ophus. </s>

<s>Sit igitur, <lb/>pi&longs;cem conuerti velle, & fie<lb/>ri capite in D, deflectet illi<lb/>co caudam in E, caque; aquam <lb/>ceu &longs;tabile quippiam <expan abbr="feri&emacr;s">feriens</expan> <lb/>eiqueue quod<gap/>mmodo fultus, <lb/>reliquum corpus CA refle<lb/>ctet in D, &longs;i autem conuerti <lb/>velit in F, caudam defle ctet in G, & eadem ratione <gap/> cte<lb/>tur in F. </s>

<s>Sed & Temonis quoque v&longs;um præ&longs;tat natatili<lb/>bus & volatilibus cauda. </s>

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<s>Hæc itaque nos de Temone, quatenus ad hanc <lb/>quæ&longs;tionem pertinet, con&longs;idera&longs;&longs;e &longs;it &longs;atis. </s>

<s>QVÆSTIO VI.</s>

<s>QVÆSTIO VI.</s>

<s><emph type="italics"/>Dubitatur, Cur quanto Antenna &longs;ublimior fuerit, ÿ&longs;dem velis, & <lb/>vento eodem celeriùs ferantur nauigia?<emph.end type="italics"/></s>

<s>Soluit Philo&longs;ophus, inquiens: An quia malus quidem <lb/>&longs;it vectis, fulcimentum verò mali &longs;edes, in qua colloca<lb/>tur, pondus autem quod moueri debet, ip&longs;um nauigium: <lb/>mouens verò is, qui vela tendit &longs;piritus? </s>

<s>Si igitur quanto <lb/>remotior fuerit fulcimentum facilius cadem potentia, & <lb/>citiùs idem mouet pondus, altius certè &longs;ublatâ antennâ, <lb/>velum à mali &longs;ede, quae fulcimentum e&longs;t remotius faciens, <lb/>id efficiet. </s>

<s>Si igitur quanto <lb/>remotior fuerit fulcimentum facilius eadem potentia, & <lb/>citiùs idem mouet pondus, altius certè &longs;ublatâ antennâ, <lb/>velum à mali &longs;ede, quae fulcimentum e&longs;t remotius faciens, <lb/>id efficiet. </s>

<s>Hæcille. </s>

<s>Hæcille. </s>

<s>quæ &longs;ic figurâ explicamus. </s><pb pagenum="51"/><figure></figure>

<s>quæ &longs;ic figurâ explicamus. </s><pb pagenum="51"/><figure/>

<s>E&longs;to nauis AB, malus CD, <lb/>mali &longs;edes D, locus antennæ <lb/>&longs;ublimior C, depre&longs;&longs;ior E: ita<lb/>que quoniam CD vectis e&longs;t, <lb/>quo mouens remotior fuerit à <lb/>fulcimento D, co citiùs & vio<lb/>lentiùs pellet, velocius ergo <lb/>nauis mouebitur antenna in <lb/>C, quàm in E, con&longs;tituta. </s>

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<s>Cætcrùm quod ad puppis faciliorem <lb/>eleuationem ex mali ip&longs;ius altitudine pertinet, ad vectis <pb pagenum="52"/>contemplationem reducimus. </s>

<s>e&longs;t enim quæ dam vectium <lb/>&longs;pecies ab alijs non con&longs;iderata, cuius brachia in angu<lb/>lum de&longs;inunt, vtip&longs;e angulus in operatione &longs;it fulcimen<lb/>tum. </s><figure></figure>

<s>E&longs;to enim vectis, de quo agimus, <lb/>ABC, cuius brachia AB, BC. iuncta <lb/>ad angulum B, &longs;itqueue B in operatione <lb/>fulc mentum. </s>

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<s>&longs;it autem modò rectus. </s>

<s>Ponaturi<lb/>gitur pondus aliquod in C, tum po<lb/>tentia quædam applicetur in A, quae i<lb/>p&longs;am vectis extremitatem A propel<lb/>lat in D. erit igitur AB in DB & an<lb/>gulo &longs;eruato BC in BE. </s>

<s>Pondus igi<lb/>tur cum parte vectis BC eleuabitur in E. </s>

<s>Pondus igi<lb/>tur cum parte vectis BC eleuabitur in E. </s>

<s>In hoc autem <lb/>vectis genere attenditur proportio quam habet AB ad <lb/>BC. </s>

<s>In hoc autem <lb/>vectis genere attenditur proportio quam habet AB ad <lb/>BC. </s>

<s>Si enim potentia quæ applicatur in A ita &longs;e habet ad <lb/>pondus in C vt CB, ip&longs;i BA, fiet æ quilibrium. </s>

<s>Si maior <lb/>autem fuerit proportio potentiæ in A, ad pondus in C, ea <lb/>quam habet AB ad BC, &longs;uperatâ ponderis re&longs;i&longs;tentiâ fiet <lb/>motus. </s>

<s>Res autem haud aliter &longs;e habet, ac &longs;i producta in <lb/>F, fieret BF æqualis BC. </s>

<s>Res autem haud aliter &longs;e habet, ac &longs;i producta in <lb/>F, fieret BF æqualis BC. </s>

<s>Tunc enim vectis ad rectitudi<lb/>nem, &longs;eruatâ proportione, redigeretur, & ita potentia in <lb/>A, fulcimento B operaretur in F, vt operabatur in C. </s>

<s>Tunc enim vectis ad rectitudi<lb/>nem, &longs;eruatâ proportione, redigeretur, & ita potentia in <lb/>A, fulcimento B operaretur in F, vt operabatur in C. </s>

<s>Ad huius vectis naturam referuntur fabrorum mal<lb/>lei, quibus clauos reuellunt, forcipes item quæ tenaci <lb/>mor&longs;u clauorum capita vmbellasue apprendentes, vio<lb/>lenterè tabulis extrahunt. </s>

<s>In malleo itaque &longs;ubtili, vt in <lb/>figura videre e&longs;t, AB vectis e&longs;t pars quæ à fulcimento ad <lb/>potentiam; ac verò quæ à fulcimento ad pondus, ponderi <pb pagenum="53"/><figure id="fig7"></figure><lb/>&longs;iquidem æquiparatur re&longs;i<lb/>&longs;tentia quae fit in C. </s>

<s>In malleo itaque &longs;ubtili, vt in <lb/>figura videre e&longs;t, AB vectis e&longs;t pars quæ à fulcimento ad <lb/>potentiam; ac verò quæ à fulcimento ad pondus, ponderi <pb pagenum="53"/><figure id="fig7"/><lb/>&longs;iquidem æquiparatur re&longs;i<lb/>&longs;tentia quae fit in C. </s>

<s>I dem ob<lb/>&longs;eruamus in forcipe, in quo <lb/>duo quidem brachia AD, <lb/>CB, quatenus ad appren&longs;io<lb/>nem pertinet, fulcimentum, <lb/>habentin ip&longs;o <expan abbr="c&emacr;tro">centro</expan> &longs;eu ver<lb/>rebra, & ideo quo longiores <lb/>fuerint, eo tenaciùs appre<lb/>hendunt & retinent. </s>

<s>quate<lb/>nus autem ad extractionem, <lb/>facit, pro vnico forceps totus habetur vecte, cuius <expan abbr="quid&emacr;">quidem</expan> <lb/>pars à potentia ad fulcimentum AB. quæ verò à <expan abbr="fulcim&emacr;-to">fulcimen<lb/>to</expan> ad hoc e&longs;t clauum ip&longs;um qui reuellitur AC. </s>

<s>Violenti&longs;<lb/>&longs;imè autem extrahunt forcipes, propterea quod maxima <lb/>&longs;it proportio longitudinis brachij BA, ad eam quæ e&longs;t ab <lb/>A ad C. </s>

<s>Violenti&longs;<lb/>&longs;imè autem extrahunt forcipes, propterea quod maxima <lb/>&longs;it proportio longitudinis brachij BA, ad eam quæ e&longs;t ab <lb/>A ad C. </s>

<s>His igitur hoc pacto examinatis, ad nauim & malum <lb/>reuertentes, dicimus, tunc facillimam fieri puppis eleua<lb/>tionem, proræ verò demer&longs;ionem, cum maxima fuerit <lb/>proportio, quam habet altitudo mali, ad eam nauis <expan abbr="part&emacr;">partem</expan> <lb/>quæ à malo ad ip&longs;am puppis extremitatem, pertingit. <lb/></s>

<s>Quamobrem prudentes nauium fabri, vt huic difficultati <lb/>occurrant, malum non in medio quidem nauis, &longs;ed in ter<lb/>tia ferè parte longitudinis quæ à prora e&longs;t, puppim ver&longs;us <lb/>con&longs;tituunt. </s><figure></figure>

<s>E&longs;to enim nauis AB; cuius <lb/>malus CD: prora A: puppis B; <expan abbr="v&emacr;-to">ven<lb/>to</expan> igitur velum impellente, <expan abbr="mal&umacr;">malum</expan> <lb/>ad partem contrariam vergit, pu<lb/>ta in FD. </s>

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<s>non pote&longs;t autem; quoniam &longs;uburræ grauitas & <lb/>onera, quæ naui impo&longs;ita inter D. & <emph type="italics"/>B.<emph.end type="italics"/> grauitatis centrum <lb/>circa punctum E con&longs;tituunt, quod quidem vi ventorum <lb/>inclinante malo ab E, in G eleuaretur, quo igitur minor <lb/>fuerit proportio CD ad DE & maius pondus ip&longs;um cu<lb/>ius grauitatis centrum in E minus præualebit potentia <lb/>pellens in C ad eleu<gap/>tionem partis nauigij, quæ à mali &longs;e<lb/>de ad puppim intercedit, An igitur malus &longs;it vectis, pesve<lb/>rò fulcimentum, pondus autem quodvecte mouetur, <expan abbr="ips&umacr;">ipsum</expan> <lb/>nauigium, vt placuit Ari&longs;toteli, & qua item ratione malus <lb/>in nauim vt vectis operetur, exijs quae dicta &longs;unt, facilè pa<lb/>tet. </s>

<s>QVÆSTIO VII.</s>

<s>QVÆSTIO VII.</s>

<s><emph type="italics"/>Quaritur, Cur quando ex puppi nauigare voluerint, non flante ex <lb/>puppi vento, veli quidem partem, quæ ad gubernatorem vergit, <lb/>con&longs;tringunt; illam verò quæ proram ver&longs;us e&longs;t, pedem <lb/>facientes, relaxant?<emph.end type="italics"/></s>

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<s>propellit igitur quidem ip&longs;e <lb/>ventus, in puppim verò illum con&longs;tituit gubernaculum, <lb/>retrahens, & mare compellens: &longs;imul & nautæ ip&longs;i cum <lb/>vento contendunt; in contrariam enim &longs;e reclinant par<lb/>tem. </s>

<s>Hæcille. </s>

<s>Hæcille. </s>

<s>Cuius &longs;en&longs;um breuitate &longs;ubob&longs;curum, mirâ facilita<lb/>te explicat Picolomineus. </s>

<s>Cuius &longs;en&longs;um breuitate &longs;ubob&longs;curum, mirâ facilita<lb/>te explicat Picolomineus. </s>

<s>Nos autem vt rem lucidiorem <lb/>faciamus, &longs;chema, quod necip&longs;e fecit, nec Philo&longs;ophus, <lb/>proponemus. </s>

<s>E&longs;to nauis A <emph type="italics"/>B<emph.end type="italics"/>, cuius prora A, puppis verò D, guber<lb/>naculum C<emph type="italics"/>B<emph.end type="italics"/>, temonis ala <emph type="italics"/>B<emph.end type="italics"/>D, veli &longs;inus EF, velum vero <lb/>ita con&longs;titutum, vt directè ex puppi flantem ventum exci-<pb pagenum="55"/><figure id="fig8"></figure><lb/>piat. </s>

<s>Hoc vbi euenerit, naui<lb/>gium, rectâ è puppi mouetur <lb/>in proram; Si autem ventus la<lb/>teraliter &longs;pirat, puta à parte <lb/>G ver&longs;us H & nihilo &longs;ecius na<lb/>uigium, ac &longs;i ventus ex pup<lb/>pi e&longs;&longs;et antror&longs;um propelle<lb/>re volunt, velum quidem obli<lb/>quant partem cius infimam, <lb/>pedem nempe, quæ e&longs;t in F <lb/>contrahentes, Cornu verò <lb/>antennæ vbi E, proram ver&longs;us <lb/>laxantes ventumque; ip&longs;um obliquè ex cipientesid <expan abbr="effici&umacr;t">efficiunt</expan>, <lb/>vt ventus minus violenter feriat, & minori &longs;ui parte <expan abbr="vel&umacr;">velum</expan> <lb/>impleat, & quoniam ventus velum pellit in partem con<lb/>trariam, nempe in H, ip&longs;ivt vento re&longs;i&longs;tant conuer&longs;o gu<lb/>bernaculo ex C in L, & temone <emph type="italics"/>B<emph.end type="italics"/>D, in <emph type="italics"/>B<emph.end type="italics"/>M compellunt <lb/>proram ad partem à qua ventu<gap/> ip&longs;e &longs;pirat. </s>

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<s>Tunc enim in rectum mouebitur nauis, cum &longs;ibi inui<lb/>cem æ quatæ vires, qua&longs;i libramentum con&longs;tituerint. </s>

<s>Hæc <lb/>ille, cuius &longs;en&longs;um figurâ propo&longs;itâ facilè aperiemus. </s><figure></figure>

<s>Hæc <lb/>ille, cuius &longs;en&longs;um figurâ propo&longs;itâ facilè aperiemus. </s><figure/>

<s>E&longs;to carina AB, cuius prora <lb/>A, puppis, B temo BC, ventus verò <lb/>obliquè feriens H. </s>

<s>E&longs;to carina AB, cuius prora <lb/>A, puppis, B temo BC, ventus verò <lb/>obliquè feriens H. </s>

<s>Conuer&longs;us ita<lb/>que temo vt in BC vndarum vi cur<lb/>rente naui repul&longs;us &longs;it in EF ten<lb/>dens ver&longs;us I, quo ca&longs;u prora con<lb/>uertitur in D, nempe contra <expan abbr="vent&umacr;">ventum</expan> <lb/>qui &longs;pirat ex H. fit autem conuer<lb/>&longs;io circa punctum G, quod fulcimenti locum obtinet. </s>

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<s>Hæc Picolominei ratio, quam <lb/>explicauimus, &longs;anè ingenio&longs;a e&longs;t, verum enimuero, quo<lb/>niam fulcimentum &longs;ui naturâ &longs;tare debet, hic verò <expan abbr="nullã">nullam</expan> <lb/>habeat &longs;ta bilitatem, difficultatem patitur. </s>

<s>QVÆSTIO VIII.</s>

<s>QVÆSTIO VIII.</s>

<s><emph type="italics"/>Quæritur, Cur ex figuris omnibus rotundæ faciliùs <lb/>moueantur?<emph.end type="italics"/></s>

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<s>Hæc ferè Philo&longs;ophus, cuius rationes ad eum &longs;olum<lb/>modo circularem motum faciunt, qui fit &longs;e cundum ab&longs;i<lb/>dem, vt in carrorum rotis v&longs;u venit, nec aptantur rotis fi<lb/>gulorum trochlei&longs;queue, cuiu&longs;modi &longs;unt illæ, quæ &longs;upra <lb/>puteos appenduntur. </s>

<s>Nos igitur, ad Ari&longs;totelis mentem, <lb/>primam rotationis &longs;peciem, quæ e&longs;t &longs;ecundum ab&longs;idem, <lb/>examinabimus. </s><figure></figure>

<s>Nos igitur, ad Ari&longs;totelis mentem, <lb/>primam rotationis &longs;peciem, quæ e&longs;t &longs;ecundum ab&longs;idem, <lb/>examinabimus. </s><figure/>

<s>E&longs;to rota &longs;phæ<lb/>raue AB, cuius cen<lb/>trum C; Horizontis <lb/>planum DE; conta<lb/>ctus circuli in plano <lb/>B. <expan abbr="perp&emacr;">perpem</expan> dicularis ho<lb/>rizonti à puncto <expan abbr="c&omacr;-tactus">con<lb/>tactus</expan> B ip&longs;a <emph type="italics"/>B<emph.end type="italics"/>CA, <lb/>tran&longs;iens per <expan abbr="centr&umacr;">centrum</expan> <lb/>C, partes rotæ circa <lb/>perpendicularem AF<emph type="italics"/>B<emph.end type="italics"/>, AG<emph type="italics"/>B<emph.end type="italics"/>, angulus contactus G<emph type="italics"/>B<emph.end type="italics"/>E. <lb/></s>

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<s>Angulum porro, quem à <lb/>terra &longs;emotum dicit, ip&longs;e angulus e&longs;t contingentiae. </s>

<s>cleua<pb pagenum="58"/>tur enim ex <emph type="italics"/>B<emph.end type="italics"/> in G. </s>

<s>cleua<pb pagenum="58"/>tur enim ex <emph type="italics"/>B<emph.end type="italics"/> in G. </s>

<s>Si autem corpus quodpiam in plano <lb/>fuerit, puta HI in puncto illud tanget ci culus ei occur<lb/>rens, exempli gratiâ in K. </s>

<s>Si autem corpus quodpiam in plano <lb/>fuerit, puta HI in puncto illud tanget ci culus ei occur<lb/>rens, exempli gratiâ in K. </s>

<s>Hæc igitur accidunt circulari <lb/>figuræ. </s>

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<s>Primò igitu circu<lb/>laris &longs;phæricaue figura in æquilibrio &longs;tat; æquales enim <lb/>&longs;unt partes quæ circa perpendicularem: ceu &longs;unt AF<emph type="italics"/>B<emph.end type="italics"/>, <lb/>AG<emph type="italics"/>B.<emph.end type="italics"/> &longs;i enim impul&longs;us fiat ex parte F, pars oppo&longs;ita nuta<lb/>bit, & propendet in pa<gap/>tem G, & &longs;uo nutu motuque; &longs;ecum <lb/>trahet partem AF<emph type="italics"/>B<emph.end type="italics"/>, fietqueue progre&longs;&longs;us. </s>

<s>Si enim ducatur <lb/>FCG diameter, ip&longs;i horizonti æ que di&longs;tans, erit veluti li<lb/>bra, cuius pondera vtrinque AF<emph type="italics"/>B<emph.end type="italics"/>, AG<emph type="italics"/>B<emph.end type="italics"/>, brachia verò <lb/>æqualia CF, CG. </s>

<s>Potentia autem quâ trahitur pellitur<lb/>ue ad in&longs;tar ponderis &longs;e habet, quo addito partium alteri, <lb/>facto queue rece&longs;&longs;u ab æquilibrio, &longs;equetur motus. </s>

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<s>Angulos autem hî c&longs;ectores ip&longs;os vocat; oportet <lb/>enim circulos tum maiores tum minores circa idein cen<lb/>trum e&longs;&longs;e con&longs;titutos. </s>

<s>Hæc autem non ab&longs;imili ab eo <lb/>quod &longs;uprà po&longs;uimus &longs;chemate explicantur. </s><pb pagenum="59"/><figure></figure>

<s>Hæc autem non ab&longs;imili ab eo <lb/>quod &longs;uprà po&longs;uimus &longs;chemate explicantur. </s><pb pagenum="59"/><figure/>

<s>E&longs;to enim circulus <lb/>AB circa centrum, C, <lb/>Horizontis planum DE, <lb/>tangens circulum in B, <lb/>linea verò perpendicu<lb/>laris per centrum BCA. <lb/></s>

<s>E&longs;to enim circulus <lb/>AB circa centrum, C, <lb/>Horizontis planum DE, <lb/>tangens circulum in B, <lb/>linea verò perpendicu<lb/>laris per centrum BCA. <lb/></s>

<s>Sit autem circa idem <expan abbr="c&emacr;-trum">cen<lb/>trum</expan> C, minor circulus <lb/>FG, ducatur queue CH &longs;e<lb/>cu<gap/> minorem circulum in I, tangens verò maiorem in H, <lb/>con&longs;tituen&longs;queue cum AC linea angulum ACH, duos an<lb/>gulos, ex Ari&longs;totelis mente comprehendentem, hoc e&longs;t, <lb/>duos &longs;ectores ACH, FCI. quoniam igitur &longs;ector &longs;eu an<lb/>gulus ACH, &longs;uo &longs;patio &longs;uperat angulum &longs;eu &longs;ectorem <lb/>FGI, facilè ex nutu quem maior &longs;upra minorem habet, <lb/>maior ip&longs;e mìnorem mouet. </s>

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<s>Si enim in figura producatur ad oppo&longs;i<lb/>tam partem &longs;emidiameter HC in K &longs;ecans minorem cir<lb/>culum in L, duos alios &longs;ectores angulosue habebimus, <expan abbr="n&emacr;-pe">nen<lb/>pe</expan> KCB, LCG, ip&longs;is ACHFCI æ quales. </s>

<s><expan abbr="Itaq;">Itaque</expan> quan<lb/>tum adiuu at motum anguli ACH maioris nutus, in de<lb/>&longs;cendendo ad partes B, tantundem retardat anguli item <lb/>maioris KCB, contra nutus (vtita appellem) in <expan abbr="a&longs;cend&emacr;-do">a&longs;cenden<lb/>do</expan> ad partes A. & &longs;anè quatenus ad reinaturam pertinet <lb/>& ad ip&longs;um æquilibrium, non differunt maiores circuli à <lb/>minoribus, nec &longs;unt maiores minoribus mobiliores, imo <lb/>ex ali quaratione minores videntur fore ad motum faci<pb pagenum="60"/>liores, tum quia data materiæ æqualitate &longs;unt leuiores, <lb/>tum etiam quod maior e&longs;t angulus contactus ad planuin <lb/>circum ferentiae minoris quàm maioris circuli, vt in &longs;ubie<lb/><figure id="fig9"></figure><lb/>cta figura angulus ABC maior <lb/>e&longs;t angulo DBC, in materiali i<lb/>gitur circulo rotaue maiore &longs;ui <lb/>parte tanget planum DB circu<lb/>lus, ip&longs;o AB. quicquid tamen fit, <lb/>mobiliores &longs;unt maiores circuli <lb/>non quidem ex natura circuli, <lb/>quæ tam in maioribus quàm in <lb/>ip&longs;is minoribus e&longs;t par, &longs;ed alijs de cau&longs;&longs;is, quas &longs;uo loco <lb/>examin abimus. </s>

<s><expan abbr="Itaq;">Itaque</expan> quan<lb/>tum adiuu at motum anguli ACH maioris nutus, in de<lb/>&longs;cendendo ad partes B, tantundem retardat anguli item <lb/>maioris KCB, contra nutus (vtita appellem) in <expan abbr="a&longs;cend&emacr;-do">a&longs;cenden<lb/>do</expan> ad partes A. & &longs;anè quatenus ad reinaturam pertinet <lb/>& ad ip&longs;um æquilibrium, non differunt maiores circuli à <lb/>minoribus, nec &longs;unt maiores minoribus mobiliores, imo <lb/>ex ali quaratione minores videntur fore ad motum faci<pb pagenum="60"/>liores, tum quia data materiæ æqualitate &longs;unt leuiores, <lb/>tum etiam quod maior e&longs;t angulus contactus ad planuin <lb/>circum ferentiae minoris quàm maioris circuli, vt in &longs;ubie<lb/><figure id="fig9"/><lb/>cta figura angulus ABC maior <lb/>e&longs;t angulo DBC, in materiali i<lb/>gitur circulo rotaue maiore &longs;ui <lb/>parte tanget planum DB circu<lb/>lus, ip&longs;o AB. quicquid tamen fit, <lb/>mobiliores &longs;unt maiores circuli <lb/>non quidem ex natura circuli, <lb/>quæ tam in maioribus quàm in <lb/>ip&longs;is minoribus e&longs;t par, &longs;ed alijs de cau&longs;&longs;is, quas &longs;uo loco <lb/>examin abimus. </s>

<s>Cæterùm vt aliquid de motu qui &longs;e cundum ab&longs;idem <lb/>fit, ex no&longs;tro penu promamus, Dicimus, Circulos, rota&longs;ue, <lb/>quæ hoc pacto mouentur, vel per horizontis planum mo<lb/>ueri, vel per accliue, aut decliue. </s>

<s>Siautem perhorizontis <lb/>planum, ideo facilem e&longs;&longs;e motum, quòd nunquam, cæte<lb/>ris paribus, centrum grauitatis ip&longs;ius corporis à centro <lb/>mundi, in ip&longs;a rotatione, fiat remotius. </s><figure></figure>

<s>E&longs;to enim planum, <lb/>horizontis AB, cui circu<lb/>lus in&longs;i&longs;tat AD, circa cen<lb/>trum C, diui&longs;us per <expan abbr="centr&umacr;">centrum</expan> <lb/>ip&longs;um à perpendiculari <lb/>ACD; Ducatur autem per <lb/>centrum C recta linea ho<lb/>rizonti æquidi&longs;tans, ECFG: dum diuidatur circulus vt<lb/><gap/>unque in partes AH, HF, FI, ID, & CI, CH iungan<lb/>tur. </s>

<s>Po&longs;th æcintelligatur circulum &longs;ecundum ab&longs;idem <lb/>moueri ad partes G, erit igitur aliquando punctum H, <lb/>rangens horizontis planum, tangat autem in K, tum F in <pb pagenum="61"/>L, I in N. </s>

<s>Ducanturqueue KP, LQ, NR, OS <lb/>ip&longs;i AC parallelæ horizonti autem perpen diculares. <lb/></s>

<s>Centrum ergo circuli, quod idem & grauitatis e&longs;t <expan abbr="centr&umacr;">centrum</expan>, <lb/>feretur per rectam CPQRS, &longs;unt enim KP, LQ, NR, <lb/>OS ip&longs;i AC &longs;emidiam etro æquales, <expan abbr="n&umacr;quam">nunquam</expan> igitur cen<lb/>trum ip&longs;um C in circuli rotatione ab horizontis plano e<lb/>leuabitur, nec à mundi centro fietremotius. </s>

<s>Hoc autem longè aliter cæteris figuris contingit, <lb/>quarum motus ideo in æ qualis, quòd non &longs;em per in rota<lb/>tione centium grauitatis eandem &longs;eruet à mundi centro <lb/>di&longs;tantiam. </s><figure></figure>

<s>E&longs;to enim Ellip&longs;is <lb/>ABCD, cuius <expan abbr="c&emacr;trum">centrum</expan> <lb/>E, diameter longior <lb/>BED, breuior AEC, <lb/>Horizontis planum, <lb/>FCG. locus contactus <lb/>C perpendicularis à <lb/>contactu per centrum i<lb/>p&longs;a CEA diuidens El<lb/>lip&longs;im in partes æquales, & æqueponderantes ABC, <lb/>ADC. </s>

<s>Sumantur in quadrante CD, <expan abbr="p&umacr;cta">puncta</expan> HI, tum EH, <lb/>HI iungantur, eritautem EH longior ip&longs;a EC, tum EI, <lb/>ip&longs;a EH & ED, p&longs;a EI. </s>

<s>Sumantur in quadrante CD, <expan abbr="p&umacr;cta">puncta</expan> HI, tum EH, <lb/>HI iungantur, eritautem EH longior ip&longs;a EC, tum EI, <lb/>ip&longs;a EH & ED, p&longs;a EI. </s>

<s>Rotetur ellip&longs;is &longs;ecun dum ab&longs;i<lb/>dem, fiet igitur punctum H in K, & à puncto K horizonti <lb/>perpendicularis erigatur KL, quæ fiat æ qualis EH. </s>

<s>Rotetur ellip&longs;is &longs;ecun dum ab&longs;i<lb/>dem, fiet igitur punctum H in K, & à puncto K horizonti <lb/>perpendicularis erigatur KL, quæ fiat æ qualis EH. </s>

<s>P o&longs;t <lb/>hæc punctum I eritin M, & ab M perpen dicularis, æqua<lb/>lis EI. rui&longs;us D fiat in O, & ip&longs;i ED, æqualis perpendicu<lb/>laris OP. </s>

<s>P o&longs;t <lb/>hæc punctum I eritin M, & ab M perpen dicularis, æqua<lb/>lis EI. rui&longs;us D fiat in O, & ip&longs;i ED, æqualis perpendicu<lb/>laris OP. </s>

<s>Mota igitur ellip&longs;ià C in K, haud ita difficilis e<lb/>rit motus, quippe quod haud multum EH &longs;uperet EC, at <lb/>difficilior erit translatio in M, difficillima verò in O. Val<gap/><lb/>de enim à &longs;itu E, ibi attollitur grauitatis centrum, a&longs;cen<lb/>dens nempe vbi P. </s>

<s>Videmus igitur ex his eandem poten<pb pagenum="62"/>tiam in mouendo ellip&longs;im, haud pariter &longs;e habere, vt in <lb/>mouendo circulum. </s>

<s>ibi enim centrum grauitatis fertur <lb/>per æquidi&longs;tantem horizonti, hic verò modò attollitur, <lb/>modò deprimitur, quod &longs;anè mole&longs;tiam & difficultatem <lb/>facit. </s>

<s>Sed idem alijs figuris contingere, & maximè latera<lb/>tis, ita docebimus. </s><figure></figure>

<s>Sed idem alijs figuris contingere, & maximè latera<lb/>tis, ita docebimus. </s><figure/>

<s>E&longs;to enim triangulum <lb/>æquilaterum ABC, cuius <lb/>grauitatis centrum E hori<lb/>zontis planum BD. </s>

<s>E&longs;to enim triangulum <lb/>æquilaterum ABC, cuius <lb/>grauitatis centrum E hori<lb/>zontis planum BD. </s>

<s>Demit<lb/>tatur à vertice A perpendi<lb/>cularis horizonti AF tran&longs;<lb/>ibit autem per centrum E, <lb/>& bifariam diuidet ba&longs;im <lb/>BC in F. </s>

<s>Demit<lb/>tatur à vertice A perpendi<lb/>cularis horizonti AF tran&longs;<lb/>ibit autem per centrum E, <lb/>& bifariam diuidet ba&longs;im <lb/>BC in F. </s>

<s>Sunt autem trianguli ABF, ACF, æquales & <lb/>æqueponderantes. </s>

<s>angulus verò AFC rectus. </s>

<s>lungatur <lb/>EC, erit igitur maior EC, ip&longs;a EF. </s>

<s>lungatur <lb/>EC, erit igitur maior EC, ip&longs;a EF. </s>

<s>Rotetur iraque trian<lb/>gulum circa punctum C, fiatque; EC horizonti perpendi<lb/>cularis, &longs;itqueue GH, & per E horizonti parallela ducatur <lb/>EK, moto igitur triangulo, centrum grauitatis E transla<lb/>tum erit in H, &longs;ed KC æqualis e&longs;t EF, minor autem ip&longs;a <lb/>CH, eleuatur ergo centrum grauitatis ab Ein H, nempe <lb/>&longs;upra K, totum &longs;patium KH. ex qua eleuatione fit in mo<lb/>tu difficultas. </s>

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<s>Ad hanc quæ&longs;tionem illud quoque facit, cur per de<lb/>cliue planum grauiora corpora, & rotunda maximè; ma<lb/>gno impetu dimi&longs;&longs;a, delabantur. </s>

<s>E&longs;to enim rota &longs;phæraue aut Cylindrus CD, cuius <lb/>centrum E, tangens decliue planum AB in D, quæritur <pb pagenum="63"/>cur dimi&longs;&longs;a hæc magno impetu deferantur ad partes B, <lb/>Ducatur per grauitatis centrum E ad horizontem, BK <lb/>perpendicularis FEL &longs;ecans decliue planum in G, cir<lb/>cum ferentiam verò in H. opponitur autem EG angulo <lb/>recto EDG, maior ergo EG ip&longs;a ED, hoc e&longs;t, EH, inter <lb/><figure id="fig10"></figure><lb/>circumferentiam igitur & pla<lb/>num decliue, &longs;patium interce<lb/>dit HG. </s>

<s>E&longs;to enim rota &longs;phæraue aut Cylindrus CD, cuius <lb/>centrum E, tangens decliue planum AB in D, quæritur <pb pagenum="63"/>cur dimi&longs;&longs;a hæc magno impetu deferantur ad partes B, <lb/>Ducatur per grauitatis centrum E ad horizontem, BK <lb/>perpendicularis FEL &longs;ecans decliue planum in G, cir<lb/>cum ferentiam verò in H. opponitur autem EG angulo <lb/>recto EDG, maior ergo EG ip&longs;a ED, hoc e&longs;t, EH, inter <lb/><figure id="fig10"/><lb/>circumferentiam igitur & pla<lb/>num decliue, &longs;patium interce<lb/>dit HG. </s>

<s>Ducatur item DI ip&longs;i <lb/>FG æquidi&longs;tans. </s>

<s>non tran&longs;ibit <lb/>igitur per centrum E. minor e<lb/>rit igitur diametro CD, quare <lb/>circulum in partes inæquales <lb/>&longs;ecabit, & non per grauitatis <lb/>centrum, quod idem cum ma<lb/>gnitudinis &longs;eu figuræ centro &longs;upponitur. </s>

<s>Dimi&longs;&longs;a igitur <lb/>rota, contingit quidem planum decliue in puncto D. </s>

<s>Dimi&longs;&longs;a igitur <lb/>rota, contingit quidem planum decliue in puncto D. </s>

<s>At <lb/>centrum grauitatis premit &longs;e cun dam per lineam perpen<lb/>dicularem FG, non &longs;u&longs;tentatur autem in H, quippe quod <lb/>inter planum & circum <expan abbr="ferentiã">ferentiam</expan> intercedat &longs;patium HG, <lb/>nec H locum habeat cui innitatur, corpus autem ita per <lb/>lineam DI e&longs;t diui&longs;um, vt longè maior &longs;it pars IFCHD <lb/>ip&longs;a DI, & centrum in ea parte eadat quæ non fulcitur. </s>

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<s>ci&longs;catur. </s>

<s>Po&longs;&longs;umus etiam Rota &longs;phæraue in plano decliui <lb/>collocata, datam potentiam inuenire, quæ extremitati <lb/>diametri ad eam partem quavergit applicata ip&longs;am rotam <lb/>&longs;phæramue impediatne delabatur. </s><pb pagenum="64"/><figure></figure>

<s>E&longs;to planum in clinatum <lb/>AB, cui Rota &longs;phæraue in&longs;i<lb/>&longs;tat tangatque; illud in C. </s>

<s>E&longs;to planum in clinatum <lb/>AB, cui Rota &longs;phæraue in&longs;i<lb/>&longs;tat tangatque; illud in C. </s>

<s>Rota <lb/>verò ip&longs;a &longs;phæraue DC, cu<lb/>ius centrum E, diameter ve<lb/>rò DEC ip&longs;i BA ad <expan abbr="punct&umacr;">punctum</expan> <lb/>contactus C, perpendicula<lb/>ris. </s>

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<s>Similes autem <lb/>&longs;unt ECI, ECK, trianguli, e&longs;tqueue ECI angulus æqualis <lb/>angulo EKC, hoc e&longs;t, ip&longs;i CBF. vnde &longs;equitur, quo mi<lb/>nor fuerit inclinationis angulus, eo facilius rotam &longs;phæ<lb/>ramue in piano inclinato &longs;u&longs;tineri. </s>

<s>quo enim minor fuerit <lb/>angulus ECI, eo minus latus EI & minor proportio EI <lb/>ad IH, & ideo minor potentia &longs;u&longs;tinens requiratur in H. <lb/></s>

<s>quo enim minor fuerit <lb/>angulus ECI, eo minus latus EI & minor proportio EI <lb/>ad IH, & ideo minor potentia &longs;u&longs;tinens requiratur in H. <lb/></s>

<s>Cæterùm accliue & decliue planum nihil differunt ni&longs;i <lb/>re&longs;pectu. </s>

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<s>Quæritur, Cur maiores <pb pagenum="65"/>rotae impingentes, facilius offendicula &longs;uperent quàm mi<lb/>nores. </s>

<s>Neque enim &longs;atisfacere videtur quod ait Ari&longs;tote<lb/>les, ex contactu in puncto eo anguli à plano eleuationeid <lb/>fieri, alijs ergo principijs dubitatio &longs;oluitur. </s><figure></figure>

<s>E&longs;to rota quidem maior <lb/>AB, circa centrum C minor <lb/>vero DB circa centrum, E, <lb/><expan abbr="tãgentes">tangentes</expan> horizontis planum <lb/>in B. </s>

<s>E&longs;to rota quidem maior <lb/>AB, circa centrum C minor <lb/>vero DB circa centrum, E, <lb/><expan abbr="tãgentes">tangentes</expan> horizontis planum <lb/>in B. </s>

<s>Diameter maioris AB, <lb/>minoris DB, offen diculum, <lb/>horizonti perpendiculare <lb/>FG. </s>

<s>Diameter maioris AB, <lb/>minoris DB, offen diculum, <lb/>horizonti perpendiculare <lb/>FG. </s>

<s>Ducatur per F horizonti <lb/>parallela FK &longs;ecans minoris <lb/>rotæ peripheriam in H, dia<lb/>metrum verò AB in K, & à <lb/>puncto H ad <expan abbr="plan&umacr;">planum</expan> horizon<lb/>tis perpendicularis demittatur HI: erit autem HI æqua<lb/>lis ip&longs;i offendiculo FG, & iungantur BH, BF. <expan abbr="Itaq;">Itaque</expan> quo<lb/>niam BH ab extremo B cadit in triangulum KFB, erit <lb/>KHB angulus maior angulo KFB. </s>

<s>Parallelæ autem &longs;unt <lb/><emph type="italics"/>K<emph.end type="italics"/>F, BG, pares ergo anguli <emph type="italics"/>K<emph.end type="italics"/>HB, HBG, pares item <emph type="italics"/>K<emph.end type="italics"/>FB, <lb/>FBG, Maior ergo HBI, ip&longs;o FBC. </s>

<s>At minoris rotæ gra<lb/>uitatis centrum mouetur &longs;ecundum lineam BH, maius <lb/>verò &longs;ecun dum literam BF, difficilius ergo mouebitur, & <lb/>&longs;uperabit offen diculum minorrota, quàm maior: quod <lb/>fuerat demon&longs;trandum. </s>

<s>Po&longs;&longs;umus idem o&longs;tendere magis mechanicè, hoc <lb/>e&longs;t, tem ad vectem reducendo. </s>

<s>E&longs;to horizontis planum <lb/>AB, rota maior CD planum tangens in D. rotæ verò ma<lb/>ioris centrum E. </s>

<s>E&longs;to horizontis planum <lb/>AB, rota maior CD planum tangens in D. rotæ verò ma<lb/>ioris centrum E. </s>

<s>Rota verò minor FD, tangens itidem <lb/>planum in D. rotæ autem centrum G, offendiculi verò re<lb/>ctitudo DH. </s>

<s>Rota verò minor FD, tangens itidem <lb/>planum in D. rotæ autem centrum G, offendiculi verò re<lb/>ctitudo DH. </s>

<s>Ducatur per Hip&longs;i AB horizonti æquidi<lb/>&longs;tans HI &longs;ecans minorem circulum in K, maiorem verò <pb pagenum="66"/><figure id="fig11"></figure><lb/>in I. </s>

<s>Ducatur per Hip&longs;i AB horizonti æquidi<lb/>&longs;tans HI &longs;ecans minorem circulum in K, maiorem verò <pb pagenum="66"/><figure id="fig11"/><lb/>in I. </s>

<s>Ducantur etiam dia<lb/>metri maioris quidem <lb/>LEM, minoris NGO, <lb/>Tum à puncto K perpen<lb/>dicularis ducatur ad <lb/>GO, ip&longs;a KP, item à pun<lb/>cto I ad EM perpendi<lb/>cularis <expan abbr="Iq.">Ique</expan> Dico EQ ad <lb/>QL, minorem habere <lb/>proportionem quam GP, <lb/>ad PN. </s>

<s>Connectatur <lb/>GK, & ei per E parallela <lb/>ducatur ER, &longs;ecans maiorem circulum in R, & ab Rip&longs;i <lb/>EM perpen dicularis ducatur RS. quoniam igitur ER <lb/>parallela e&longs;t ip&longs;i GK, erit GER angulus HGK angulo <lb/>æqualis. </s>

<s>Recti autem &longs;unt HGP, GES reliqui ergo KGP, <lb/>RES ad inuicem &longs;unt æquales. </s>

<s>Sed & ESR, GPK recti <lb/>&longs;unt, quare ERSGKP anguli æquales &longs;unt, & trianguli <lb/>GPKESR, per pr. </s>

<s>Sed & ESR, GPK recti <lb/>&longs;unt, quare ERSGKP anguli æquales &longs;unt, & trianguli <lb/>GPKESR, per pr. diff. </s>

<s>1.6. &longs;imiles. </s>

<s>Vtergo GK hoc e&longs;t <lb/>GN ad GP, ita ER hoc e&longs;t EL ad ES. </s>

<s>Vtergo GK hoc e&longs;t <lb/>GN ad GP, ita ER hoc e&longs;t EL ad ES. </s>

<s>Componendo igi<lb/>tur vt NP ad PG, ita LS ad SE. quamobrem &longs;i fulcimen<lb/>tum e&longs;&longs;etin S, pondus in E, <expan abbr="pot&emacr;tia">potentia</expan> in L, idem &longs;ieret ac fiat <lb/>fulcimento in P, pondere in G, potentia verò in N con&longs;ti<lb/>tuta. </s>

<s>& id quidem &longs;i eiu&longs;dem ponderis vtraque rota &longs;up<lb/>ponatur. </s>

<s>Rur&longs;us quoniam vt DK ad totum circulum DF, <lb/>ita DR ad totum DC. </s>

<s>Rur&longs;us quoniam vt DK ad totum circulum DF, <lb/>ita DR ad totum DC. </s>

<s>Minor e&longs;t autem proportio DI ad <lb/>totum circulum DC, ergo minor e&longs;t DI ip&longs;a DR. </s>

<s>Minor e&longs;t autem proportio DI ad <lb/>totum circulum DC, ergo minor e&longs;t DI ip&longs;a DR. </s>

<s>Maior <lb/>ergo MI ip&longs;a MR, maior ergo QI ip&longs;a SR, propius ergo <lb/>centro E e&longs;t Q ip&longs;o puncto S, minor e&longs;t igitur proportio <lb/>EG ad LQ quàm ES ad SL. </s>

<s>Maior <lb/>ergo MI ip&longs;a MR, maior ergo QI ip&longs;a SR, propius ergo <lb/>centro E e&longs;t Q ip&longs;o puncto S, minor e&longs;t igitur proportio <lb/>EG ad LQ quàm ES ad SL. </s>

<s>Minor ergo potentia requi<lb/>ritur in L ad &longs;u&longs;tinendum pondus E ex fulcimento Q hoc <lb/>e&longs;t I, quàm requiratur in N ad &longs;u&longs;tinendum pondus G ex <lb/>fulcimento P, hoc e&longs;t K. </s>

<s>Minor ergo potentia requiritur <pb pagenum="67"/>ad transferendam maiorem retam CD vltra offendicu<lb/>lum IV, hoc e&longs;t, DH, quàm requiratur ad trans ferendam <lb/>minorem vltra offendiculum KT, hoc e&longs;t HD, quod fue<lb/>rat o&longs;ten dendum. </s>

<s>Ad hæc, quæri pote&longs;t, quo pacto plau&longs;trorum rotæ <lb/>in ip&longs;a plau&longs;tri conuer&longs;ione &longs;e habeant, nempe quæ &longs;it li<lb/>neailla curua, quam in conuer&longs;ione de&longs;cribunt. </s><figure></figure>

<s>E&longs;to rotarum in <lb/>plano orbita, <expan abbr="d&umacr;">dum</expan> plau<lb/>&longs;trum rectâ procedit <lb/>AB, CD, Sunt autemi<lb/>p&longs;æ lineæ, quod o&longs;ten<lb/>demus po&longs;tea, æquedi<lb/>&longs;tantes. </s>

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<s>Hoc etiam <lb/>theorema probamus. </s>

<s>Cylindros, quorum ba&longs;es axi &longs;unt perpendiculares, <lb/>dum in æquato plano conuoluuntur, rectâ incedere & <lb/>per parallelas, quarum di&longs;tantia axis &longs;eu latoris longitudi<lb/>ne præfinitur. </s><figure></figure>

<s>E&longs;to enim Cylin<lb/>drus ABCD, cuius a<lb/>xis GH, <expan abbr="horiz&omacr;tis">horizontis</expan> pla<lb/>no in&longs;i&longs;tens &longs;ecundum <lb/>latus AB, cui latus op<lb/>po&longs;itum & aequale CD. <lb/></s>

<s>Moueatur Cylindrus <lb/>rotans, donec latus <lb/>CD, in plano &longs;it vbi EF. </s>

<s>Moueatur Cylindrus <lb/>rotans, donec latus <lb/>CD, in plano &longs;it vbi EF. </s>

<s>De&longs;cribat autem circuli CB <expan abbr="lineã">lineam</expan> <lb/>BF. </s>

<s>De&longs;cribat autem circuli CB <expan abbr="lineã">lineam</expan> <lb/>BF. </s>

<s>Circulo verò AD lineam AE. </s>

<s>Circulo verò AD lineam AE. </s>

<s>Dico eas rectas e&longs;&longs;e, & <lb/>parallelas. </s>

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<s>Sed & parallelas e&longs;&longs;e <lb/>ad inuicem ita o&longs;tendimus. </s>

<s>quoniam &longs;emicirculus AD, <lb/>æqualis e&longs;t &longs;emicirculo BC, erit linea AE, æqualis lineæ <lb/>BF, &longs;ed & AB, æqualis e&longs;t ip&longs;i DC, quare & ip&longs;i EF. </s>

<s>quoniam &longs;emicirculus AD, <lb/>æqualis e&longs;t &longs;emicirculo BC, erit linea AE, æqualis lineæ <lb/>BF, &longs;ed & AB, æqualis e&longs;t ip&longs;i DC, quare & ip&longs;i EF. </s>

<s>Oppo<lb/>&longs;ita igitur quadrilateri figura ABFE latera æqualia &longs;unt, <lb/>quare EF æquedi&longs;tat ip&longs;i AB, tum AE ip&longs;i BF, quod fue<lb/>rat demon&longs;trandum. </s>

<s>Probabimus etiam &longs;i cylindri ba&longs;es axi perpendicu<lb/>lares non fuerint, & ideo ellip&longs;es in ip&longs;a rotatione perpla<lb/>num, parallelas quidem de&longs;cribere, &longs;ed non rectas. </s>

<s>E&longs;to enim Cylindrus ABCD, cuius ba&longs;es ellip&longs;es <expan abbr="inuic&emacr;">inuicem</expan> <lb/><expan abbr="æquedi&longs;tãtes">æquedi&longs;tantes</expan>, quarum axes longiores AB, CD, Commu<lb/>nis autem &longs;ectio cylindri & plani ad axem & horizontem <lb/>planum perpendicularis EHF. </s>

<s>Diuidatur autem &longs;emicir-<pb pagenum="69"/>culus EHF in partes æquales quatuor FI, IH, HG, GE. <lb/><figure id="fig12"></figure><lb/>Tum per diui&longs;ionum puncta lateri parallelae, rectæ ducan<lb/>tur KGL, M<emph type="italics"/>H<emph.end type="italics"/>N, OIP, quæ quidem <expan abbr="c&umacr;">cum</expan> ba&longs;es AMB, DNC <lb/>parallelæ &longs;int, eruntinuicem æ quales, cumqueue circum<lb/>ferentia E<emph type="italics"/>H<emph.end type="italics"/>F æquales, eosqueue rectos angulos <expan abbr="c&omacr;&longs;tituent">con&longs;tituent</expan>. <lb/></s>

<s>Diuidatur autem &longs;emicir-<pb pagenum="69"/>culus EHF in partes æquales quatuor FI, IH, HG, GE. <lb/><figure id="fig12"/><lb/>Tum per diui&longs;ionum puncta lateri parallelae, rectæ ducan<lb/>tur KGL, M<emph type="italics"/>H<emph.end type="italics"/>N, OIP, quæ quidem <expan abbr="c&umacr;">cum</expan> ba&longs;es AMB, DNC <lb/>parallelæ &longs;int, eruntinuicem æ quales, cumqueue circum<lb/>ferentia E<emph type="italics"/>H<emph.end type="italics"/>F æquales, eosqueue rectos angulos <expan abbr="c&omacr;&longs;tituent">con&longs;tituent</expan>. <lb/></s>

<s>Ducatur po&longs;t hæc &longs;eor&longs;um recta QR, & eidem perpendi<lb/>cularis ST eam &longs;ecans in V. applicetur autem rectæ ST <lb/>æqualis Cylindri lateri BC, ip&longs;a <foreign lang="greek">hz. </foreign></s>

<s>ita tamen vt punctum <lb/>E congruat puncto V, &longs;itqueue V<foreign lang="greek">h</foreign> æqualis EB, V<foreign lang="greek">z</foreign>verò æ<lb/>qualis EC. </s>

<s>ita tamen vt punctum <lb/>E congruat puncto V, &longs;itqueue V<foreign lang="greek">h</foreign> æqualis EB, V<foreign lang="greek">z</foreign>verò æ<lb/>qualis EC. </s>

<s>Tum fiant VX, XY, YZ, Z<foreign lang="greek">a</foreign> æ quales ip&longs;is EG, <lb/>G<emph type="italics"/>H<emph.end type="italics"/>, <emph type="italics"/>H<emph.end type="italics"/>I, IF, & per puncta X, Y, Z, <foreign lang="greek">a</foreign> & paralleli ip&longs;i ST du<lb/>cantur <foreign lang="greek">o a p, n *z c, l g m, k x q</foreign>, tum & his ex altera parte re<lb/>&longs;pondentes parallelæ per puncta <foreign lang="greek">b, g, d, e. </foreign></s>

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<s>Moto igitur Cylindro circulus EHF rectam <lb/>de&longs;cribet<foreign lang="greek">ae</foreign>, ellip&longs;is verò AMB, curuam <foreign lang="greek">ohr</foreign>, ellip&longs;is au<lb/>rem DNC, ip&longs;am curuam <foreign lang="greek">pzs. </foreign></s>

<s>In hoc <expan abbr="aut&emacr;">autem</expan> Cylindri mo<lb/>tuillud mirabile, velociores nempe, in ip&longs;a rotatione e&longs;&longs;e <lb/>ellip&longs;es ip&longs;o circulo EHF. </s>

<s>In hoc <expan abbr="aut&emacr;">autem</expan> Cylindri mo<lb/>tuillud mirabile, velociores nempe, in ip&longs;a rotatione e&longs;&longs;e <lb/>ellip&longs;es ip&longs;o circulo EHF. </s>

<s>Ducatur enim recta<foreign lang="greek">o<10></foreign> quæ oc<lb/>currat ip&longs;i VS in S, & <foreign lang="greek">oh</foreign> iungatur, fietqueue triangulum <lb/><foreign lang="greek">oh</foreign>S. c&longs;t autem, angulus <foreign lang="greek">o</foreign> S <foreign lang="greek">h</foreign> rectus, maior erg. <foreign lang="greek">oh</foreign> i<lb/>p&longs;a <foreign lang="greek">o</foreign> S, &longs;ed recta <foreign lang="greek">o</foreign> S æqualis e&longs;t ip&longs;i<foreign lang="greek">an</foreign>, hoce&longs;t, &longs;emicircu<lb/>lo FHE. multo maior e&longs;t autem curua, <foreign lang="greek">o, n, l, k, h</foreign>, ip&longs;a recta <lb/><foreign lang="greek">oh</foreign>, &longs;ed eodem tempore quo &longs;emicirculus EHF conficit <lb/>in rotatione <expan abbr="&longs;pati&umacr;">&longs;patium</expan> <foreign lang="greek">a</foreign> V, eodem dimidia ellip&longs;is BMA me<lb/>titur curuam <foreign lang="greek">onlkh. </foreign></s>

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<s>Hæc quo que &longs;peculatio ad motum qui &longs;ecundum <lb/>ab&longs;idem fit, manife&longs;tè pertinet. </s>

<s>Coni, quorum ba&longs;es cir<lb/>culi &longs;unt, &longs;i in plano &longs;ecundum latus rotentur, ba&longs;i circu<lb/>lum de&longs;cribunt, cuius centrum immobile coni ip&longs;ius e&longs;t <lb/>vertex, &longs;emidiameter verò ip&longs;um latus. </s><figure></figure>

<s>E&longs;to conus ABC cu<lb/>ius vertex C ba&longs;is AB, axis <lb/>DC, ba&longs;is verò centrum, <lb/>D, latus quo planum tan<lb/>git BC, &longs;ecatur itaque Co<lb/>nus per latus BC & axem <lb/>DE à plano horizonti per<lb/>pendiculari, cuius & coni <lb/>communis &longs;ectio e&longs;t ABC <lb/>triangulum, & quoniam coni grauitatis centrum e&longs;t in <pb pagenum="71"/>axe ip&longs;o, conus in partes æque <expan abbr="p&omacr;derantes">ponderantes</expan> &longs;ecatur AEBC, <lb/>AFBC, &longs;tat ergo conus &longs;ibimet æquili bris. </s>

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<s>His ita que de moturotundorum, qui circa ab&longs;idem <lb/>fit, con&longs;ideratis, reliquum e&longs;&longs;et de motu trochlearum, qui <lb/>circa centrum &longs;it, opportunè agere, &longs;ed cùm in &longs;equenti <lb/>quæ&longs;tione de hoc &longs;ermonem faciat Philo&longs;ophus, ad ea <lb/>quæ ibi di&longs;puta buntur, lectorem ablegamus. </s>

<s>Modò de tertia motus &longs;pecie nobis erit &longs;ermo; in <lb/>qua quidem &longs;pecienonnulla perpendemus, quæ omi&longs;it A<lb/>ri&longs;toteles. </s>

<s>Modò de tertia motus &longs;pecie nobis erit &longs;ermo; in <lb/>qua quidem &longs;pecienonnulla perpendemus, quæ omi&longs;it A<lb/>ri&longs;toteles. </s>

<s>Agitur autem hîc de rotundorum corporum <pb pagenum="72"/>motu, qui fit çirca axem horizonti perpendicularem, axis <lb/>altera extremitate in codem horizontis plano manente, <lb/>vti videre e&longs;t in ip&longs;is figulorum rotis. </s>

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<s>Ad hæc circa axem ita libratur rota, vt <lb/>quantumuis exigua potentia alteri parti applicetur, alte<lb/>raillico &longs;uperata moueatur. </s>

<s>Licet enim propliè ea <expan abbr="tant&umacr;">tantum</expan> <lb/>corpora æquilibrare dicantur, quæ ob ponderis hinc in de <pb pagenum="73"/>æqualitatem horizonti fiunt æquidi&longs;tantes, nihilominus <lb/>& hic aliquam e&longs;&longs;e æquilibrij &longs;imilitudinem patebit. </s><figure></figure>

<s>E&longs;to enim rota ABCD, <lb/>cuius axis horizonti perpendi<lb/>cularis FEG tran&longs;iens per cen<lb/>trum E, tangens autem planum <lb/>in puncto G. </s>

<s>E&longs;to enim rota ABCD, <lb/>cuius axis horizonti perpendi<lb/>cularis FEG tran&longs;iens per cen<lb/>trum E, tangens autem planum <lb/>in puncto G. </s>

<s>Ducatur diame<lb/>ter BED, Itaque &longs;i per diame<lb/>trum BED, & axem FEG cor<lb/>pus diuidatur, eo quòd <expan abbr="centr&umacr;">centrum</expan> <lb/>grauitatis in axe inueniatur, <lb/>corpus ip&longs;um in duas partes <expan abbr="t&umacr;">tum</expan> <lb/>mole tum <expan abbr="p&omacr;dere">pondere</expan> æquales &longs;ecabitur, nempe BAD, BCD. <lb/></s>

<s>Nullaigitur adhibita vi extranea &longs;tabit corpus in <expan abbr="quodã">quodam</expan>, <lb/>vt diximus, æquilibrio. </s>

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<s>Quærimus igitur primò; Cur ea quæ hoc pacto <expan abbr="ro-tãtur">ro<lb/>tantur</expan>, in ip&longs;a rotatione locum non mutent, ni&longs;i extrin&longs;eca <lb/>aliqua id fiat ex cau&longs;&longs;a. </s>

<s>E&longs;to enim rota aut aliud quippiam rotundum ccu <lb/>Turbines &longs;unt, quibus pueri ludunt, quod circa axem ho<pb pagenum="74"/><figure id="fig13"></figure><lb/>rizonti perpendicularem mo<lb/>ueatur, ABCD, cuius centrum <lb/>E, Diameter AEC. </s>

<s>E&longs;to enim rota aut aliud quippiam rotundum ccu <lb/>Turbines &longs;unt, quibus pueri ludunt, quod circa axem ho<pb pagenum="74"/><figure id="fig13"/><lb/>rizonti perpendicularem mo<lb/>ueatur, ABCD, cuius centrum <lb/>E, Diameter AEC. </s>

<s>Modò circa <lb/>centrum E in finiti imagin entur <lb/>circuli, alij alijs minores v&longs;que <lb/>ad <expan abbr="centr&umacr;">centrum</expan> ip&longs;um, vti &longs;unt FGH; <lb/>ibi enim circuli e&longs;&longs;e de&longs;inunt, <lb/>vbi nullum amplius e&longs;t &longs;patium. <lb/></s>

<s>Applicetur itaque potentia in <lb/>B, quæ rotam v. </s>

<s>Applicetur itaque potentia in <lb/>B, quæ rotam v. geat ver&longs;us A. <lb/>codem igitur tempore & in&longs;imul A ver&longs;us D, D ver&longs;us C, <lb/>& Cver&longs;us B mouebitur. </s>

<s>geat ver&longs;us A. <lb/>codem igitur tempore & in&longs;imul A ver&longs;us D, D ver&longs;us C, <lb/>& Cver&longs;us B mouebitur. </s>

<s>quantum enim &longs;emicirculorum <lb/>à parte CBA tran&longs;it vltra diametrum AEC, tantundem <lb/>&longs;emicir culorum, qui &longs;unt ad partem ADC, tran&longs;ibit ad <lb/>partes CBA. </s>

<s>quantum enim &longs;emicirculorum <lb/>à parte CBA tran&longs;it vltra diametrum AEC, tantundem <lb/>&longs;emicir culorum, qui &longs;unt ad partem ADC, tran&longs;ibit ad <lb/>partes CBA. </s>

<s>At vbi de&longs;ierit motus, ibi de&longs;init rotatio; vbi <lb/>autem de&longs;init &longs;patium, de&longs;init motus, &longs;ed vbi de&longs;inunt cir<lb/>culi, de&longs;init &longs;patium, quare in centro cum non &longs;int circuli, <lb/>nec &longs;patium ibi de&longs;init motus. </s>

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<s>quo igitur figura ijs partibus, <lb/>quæ longius à centro ab&longs;unt, abundauerit magis, eo faci<lb/>lius, & velocius in circulum rotata mouebitur. </s>

<s>Modò o<lb/>&longs;tendemus, circularem cæteras omnes ea qua diximus <lb/>partium à centro remoti&longs;&longs;imarum copiâ abundare. </s><figure></figure>

<s>Modò o<lb/>&longs;tendemus, circularem cæteras omnes ea qua diximus <lb/>partium à centro remoti&longs;&longs;imarum copiâ abundare. </s><figure/>

<s>E&longs;to triangulum puta æqui<lb/>iaterum, ABC circa centrum D. <lb/></s>

<s>E&longs;to triangulum puta æqui<lb/>iaterum, ABC circa centrum D. <lb/></s>

<s>Ducantur Catheti per centrum ab <lb/>oppo&longs;itis angulis ad oppo&longs;ita late<lb/>ra ADG, BDF, CDE, erunt autem <lb/>lateribus perpendiculares. </s>

<s><expan abbr="quoniã">quoniam</expan> <lb/>igitur latera AD, DB, DC, rectis <lb/>angulis &longs;ubtenduntur, maiora <expan abbr="er&umacr;t">erunt</expan> <lb/>lateribus DE, DF, DG. tres igitur <lb/>lineæ in hoc triangulo &longs;unt longi&longs;&longs;imæ DA; DB, DC. tres <lb/>verò breui&longs;&longs;imæ DE, DG, DF, quamobrem rotato &longs;uper <lb/>centrum D triangulo, tres tantum partes eius ABC velo<lb/>ci&longs;&longs;imæ erunt, tres verò tardi&longs;&longs;imæ E, G, F. </s>

<s>Minus igitur a<lb/>pta e&longs;t motui huic triangularis figura, quam quadrata, in <lb/>qua partes à centroremoti&longs;&longs;imè, & ideo veloci&longs;&longs;imè &longs;unt <lb/>quatuor. </s>

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<s>Quæri etiam pote&longs;t, Num axe in clinato, rotæ motus ali<lb/>qualiter impediatur? </s>

<s>Nos negatiuam partem amplecti<lb/>mur. </s><pb pagenum="76"/><figure></figure>

<s>Nos negatiuam partem amplecti<lb/>mur. </s><pb pagenum="76"/><figure/>

<s>E&longs;to enim tota ABCD, cuius cen<lb/>trum E axis inclin itus, circa quem <lb/>conuertitur EGF. </s>

<s>E&longs;to enim tota ABCD, cuius cen<lb/>trum E axis inclin itus, circa quem <lb/>conuertitur EGF. </s>

<s>Duobus aute pun<lb/>ctis fulcitur GF. </s>

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<s>E&longs;t autem axis FEG, ceu vectis in <lb/>quo pondus in E, potentiæ &longs;u&longs;tinentes GF; non enim hic <lb/>vt in axe perpendiculari pondus totum ab inferiori fulci<lb/>mento &longs;u&longs;tinetur. </s>

<s>quo igitur minor erit proportio FE ad <lb/>FG, eo minori in digebit potentiâ is qui pondus &longs;u&longs;tinet in <lb/>G. </s>

<s>quo igitur minor erit proportio FE ad <lb/>FG, eo minori in digebit potentiâ is qui pondus &longs;u&longs;tinet in <lb/>G. </s>

<s>Et hæc &longs;anè ita &longs;e habent, grauitatis çentro in axe ip&longs;o <lb/>con&longs;tituto, &longs;i enim extra fuerit motus impeditur & moto<lb/>re ce&longs;&longs;ante citò quie&longs;cit. </s>

<s>E&longs;to enim grauitatis centrum in <lb/>K. </s>

<s>E&longs;to enim grauitatis centrum in <lb/>K. </s>

<s>Dum igitur circa axem fit motus, centrum circulatum <lb/>aliquando erit in L; Secetautem rotæ diameter AC per<lb/>pendicularem Hl in M. </s>

<s>Dum igitur circa axem fit motus, centrum circulatum <lb/>aliquando erit in L; Secetautem rotæ diameter AC per<lb/>pendicularem Hl in M. </s>

<s>Porrò à punctis LK ad ip&longs;am <expan abbr="per-p&emacr;dicularem">per<lb/>pendicularem</expan> ducantur ad rectos angulos lineæ LN, KO. <lb/></s>

<s>Maior e&longs;t autem MK ip&longs;a ML, maior ergo MO, ip&longs;a MN. <lb/>magisigitur à mundi centro di&longs;tat punctum N puncto O. <lb/></s>

<s>Maior e&longs;t autem MK ip&longs;a ML, maior ergo MO, ip&longs;a MN. <lb/>magisigitur à mundi centro di&longs;tat punctum N puncto O. <lb/></s>

<s>Centrum ergo grauitatis K &longs;i liberè dimittatur, requie&longs;cet <lb/>in K & contranaturam transferetur in L. </s>

<s>Centrum ergo grauitatis K &longs;i liberè dimittatur, requie&longs;cet <lb/>in K & contranaturam transferetur in L. </s>

<s>Ce&longs;&longs;ante igitur <lb/>violentiâ & præualentenaturâ citò rota &longs;uâ &longs;ponte quie<lb/>&longs;cet, quod fuerat o&longs;tendendum. </s>

<s>QVÆSTIO IX.</s>

<s>QVÆSTIO IX.</s>

<s><emph type="italics"/>Quæritur, Cur ea quæ per maiores cir culos tolluntur, & trahuntur <lb/>faciliùs, & celeriùs moueri contingat, veluti maioribus tro<lb/>chleis, & &longs;cytalis &longs;imiliter?<emph.end type="italics"/></s>

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<s>Quod vltimo loco affirmauit, trochleas e&longs;&longs;e in&longs;tar <lb/>librarum, verum e&longs;t. </s>

<s>Quo d autem dixit, faciliùs & cele<lb/>rius mouere maiores libras ijs quæ minores &longs;unt, &longs;i &longs;inipli<lb/>citer intelligatur, fal&longs;um, quippe quod facilitas motus, in <lb/>tractorijs machinis velo citati &longs;it contraria, quod demon<lb/>&longs;trauit Guid. </s>

<s>Quo d autem dixit, faciliùs & cele<lb/>rius mouere maiores libras ijs quæ minores &longs;unt, &longs;i &longs;inipli<lb/>citer intelligatur, fal&longs;um, quippe quod facilitas motus, in <lb/>tractorijs machinis velocitati &longs;it contraria, quod demon<lb/>&longs;trauit Guid. Vbald. in tractatu de Trochlea in 2. Corol<lb/>lario propo&longs;itione vltima. </s>

<s>Vbald. </s>

<s>in tractatu de Trochlea in 2. Corol<lb/>lario propo&longs;itione vltima. </s>

<s>Ad id autem quod dixit, quo <expan abbr="maior&emacr;s">maiorens</expan> fuerint tro<lb/>chleæ, eo faciliùs mouere, non e&longs;t, vt dicebamus, &longs;impli<lb/>citer verum, quod facilè o&longs;tendemus. </s><figure></figure>

<s>Efto enim trochlea AB circa centrum C, appen&longs;a in <lb/>puncto D, perpendicularis quæ ad mundi centrum DCE, <lb/>pondera æqualia vtrinque appen&longs;a FG. </s>

<s>Efto enim trochlea AB circa centrum C, appen&longs;a in <lb/>puncto D, perpendicularis quæ ad mundi centrum DCE, <lb/>pondera æqualia vtrinque appen&longs;a FG. </s>

<s>E&longs;to item alia <lb/>Trochlea, eaque; maior HI, circa centrum K appen&longs;a in L, <lb/>perpen dicularis, quæ ad mundi centrum LKM, æqualia <pb pagenum="78"/>pondera vtrinque appen&longs;a N, O. </s>

<s>Dico maiorem Hl ip&longs;a <lb/>minori DE facilius pondera non mouere, eo quòd &longs;it ma<lb/>ior, illa verò difficiliùs, propterea quòd &longs;it minor. </s>

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<s>Dico igitur, Axium, circa quos tro<lb/>chleæ rotæue conuertuntur ad rotas ip&longs;as, varias habere <lb/>proportiones. </s>

<s>O&longs;tendemus autem <expan abbr="rotã">rotam</expan> illam, trochleam<lb/>ue faciliùs moueri, & mouere pondera, quo rotæ diame<lb/>ter ad axis diametrum maiorem habuerit proportionem, <lb/>& ideo fieri po&longs;&longs;e rotam maiorem ad &longs;uum axem <expan abbr="minor&emacr;">minorem</expan> <lb/>habere proportionem quam rotam minorem ad &longs;uum. </s><figure></figure>

<s>E&longs;to enim <lb/>trochlea AB cir<lb/>ca centrum C, <lb/>cuius diameter <lb/>DCE &longs;it in ip&longs;a <lb/>quæ ad mundi <lb/>centrum <expan abbr="perp&emacr;-diculari">perpen<lb/>diculari</expan>: &longs;it au<lb/>tem appen&longs;a in D. </s>

<s>Alia &longs;imiliter ei æqualis &longs;it trochlea F <lb/>G circa centrum H, cuius diameter IHK, conueniens <pb pagenum="79"/>cum perpen diculari quæ ad mundi centrum. </s>

<s>appendatur <lb/>autem in I. </s>

<s>appendatur <lb/>autem in I. </s>

<s>Habeant autem & axes, circa quos conuertan<lb/>tur. </s>

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<s>Succedit igitur im<lb/>pedimentum loco ponderis. </s>

<s>Duos igitur habemus vectes <lb/>DC, IH, quorum fulcimenta contra ip&longs;a C, H. </s>

<s>Duos igitur habemus vectes <lb/>DC, IH, quorum fulcimenta contra ip&longs;a C, H. </s>

<s>Pondera <lb/>verò inter fulcimenta & potentiasin L, M. </s>

<s>Pondera <lb/>verò inter fulcimenta & potentiasin L, M. </s>

<s>Intelligantur <lb/>autem potentiæ applicatæ punctis DI. </s>

<s>Intelligantur <lb/>autem potentiæ applicatæ punctis DI. </s>

<s>Igitur ex natura e<lb/>iu&longs;modi vectis, in quo pondus inter fulcimentum e&longs;t & <lb/>potentiam erit vt CL, ad CD, ita potentia in D ad <expan abbr="p&omacr;dus">pondus</expan>, <lb/>hoc e&longs;t, re&longs;i&longs;tentiam fricationis, quæ fit in L. </s>

<s>Sed maior <lb/>e&longs;t proportio CL ad CD quàm HM ad HI. </s>

<s>Sed maior <lb/>e&longs;t proportio CL ad CD quàm HM ad HI. </s>

<s>Maior igitur <lb/>ad &longs;uperandum idem &longs;eu æquale impedimentum poten<lb/>tia requiritur in D, qu<gap/>m in I. </s>

<s>Maior igitur <lb/>ad &longs;uperandum idem &longs;eu æquale impedimentum poten<lb/>tia requiritur in D, qu<gap/>m in I. </s>

<s>Itaque cum vis tota in rota<lb/>rum & axium, diametrorum proportione con&longs;i&longs;tat, fieri <lb/>pote&longs;t, quod dicebamus, minorem trochleam dari, quæ <lb/>maiorem habeat proportionem ad &longs;uum axem, quàm, <lb/>maior ad &longs;uum, quo ca&longs;u minor rota facilius imp edimen<lb/>tum, quod diximus, ip&longs;a maiori rota &longs;eu trochlea &longs;upera<lb/>bit. </s>

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<s>Duabus autem partibus con&longs;tant, alterâ, quæ ab <lb/>axe ad angulum; quæ verè vectis e&longs;t; alterâ, cui manusi<lb/>p&longs;a admouetur, ex qua res tota manubrium dicitur. </s>

<s>Fiunt <lb/>autem manubria hæc vt plurimum amouibilia, &longs;unt <expan abbr="tam&emacr;">tamen</expan> <lb/>ceu rotarum ip&longs;arum partes, & rotis ip&longs;is commodè affi<lb/>gerentur, ni&longs;i in rotatione à tran&longs;uer&longs;arijs, quibus rotæ &longs;u<lb/>&longs;tinentur, impedimentum fieret. </s><figure></figure>

<s>E&longs;to enim rota AB, cu<lb/>ius axis E, terebretur autem <lb/>in F, ibiqueue paxillus affigatur <lb/>FK. </s>

<s>E&longs;to enim rota AB, cu<lb/>ius axis E, terebretur autem <lb/>in F, ibiqueue paxillus affigatur <lb/>FK. </s>

<s>Sit & alia rota CD, cu<lb/>ius axis G, manubrium axi <lb/>appo&longs;itum GHI. </s>

<s>Sit & alia rota CD, cu<lb/>ius axis G, manubrium axi <lb/>appo&longs;itum GHI. </s>

<s>Sint autem <lb/>rotæ æquales & axes æqua<lb/>les. </s>

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<s>Sunt autem eorum circulorum &longs;emidiametri, qui <lb/>à punctis FL, in ip&longs;a rotatione de&longs;cribuntur. </s>

<s>Ita igitur &longs;e <lb/>habebit potentia applicata in L ad diametrum &longs;emidia<lb/>metrumue axis rotæ CD, vt &longs;e habet potentia applicata <lb/>in F, ad diametrum &longs;emidiame trumue axis E rotæ AB, &longs;ed <lb/>&longs;patia &longs;unt æqualia & potentiæ æquales, quare nihil re<lb/>fert, vtrum manubrium lateria ffigatur, vel axi à latere ro<lb/>tæ &longs;eparatum applicetur. </s><figure></figure>

<s>Duplex autem e&longs;t ma<lb/>nubriorum forma; altera e<lb/>nim rectis partibus con&longs;tat, <lb/>altera verò curua e&longs;t tota, <lb/>&longs;ed rectis vtimur vt mani<lb/>bus apprendamus, curuis <lb/>verò vt locum illis appona<lb/>mus, & pedis pre&longs;&longs;ione ceu <lb/>in molis lapideis, quibus <lb/>gladij acuuntur, fieri a&longs;&longs;olet, conuertantnr. </s>

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<s>quæ cum ce&longs;&longs;ent in manubrijs quæ manu <lb/>aguntur, ideo alia forma, nempe ex rectis partibus pa&longs;&longs;im <lb/>fiunt. </s>

<s>E&longs;to igiturillud quod ex rectis partibus AB, curuum <lb/>verò CD, linea verò, &longs;ecundum quam pede fit pre&longs;&longs;io <pb pagenum="82"/>CDE. </s>

<s>E&longs;to igiturillud quod ex rectis partibus AB, curuum <lb/>verò CD, linea verò, &longs;ecundum quam pede fit pre&longs;&longs;io <pb pagenum="82"/>CDE. </s>

<s>Hæc itaque de manubrijs &longs;eu vectibus nos con&longs;i<lb/>dera&longs;&longs;e &longs;it &longs;atis. </s>

<s>Quæriinterim po&longs;&longs;et, Cur duabus datis rotis æqua<lb/>lis magnitudinis in æqualis ponderis, circa æquales axes <lb/>con&longs;titutis leuior faciliùs moueatur & citiùs quie&longs;cat; <lb/>grauior verò di&longs;ficilius moucatur & tardiùs ce&longs;&longs;et à mo<lb/>tu, ea videtur ratio, quod grauior re&longs;i&longs;tens magis cum &longs;u<lb/>peratur impre&longs;&longs;am vim &longs;u&longs;cipit, & diutiùs retinet, quod <lb/>ce&longs;&longs;at in leuiore. </s>

<s>QVÆSTIO X.</s>

<s>QVÆSTIO X.</s>

<s><emph type="italics"/>Dubitat Ari&longs;toteles, Cur faciliùs, quando &longs;ine pondere est, mouca<lb/>tur libra, quàm cum pondus habet. </s>

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<s>In <lb/>obliquum autem haudqua quam vergit. </s>

<s>Nos quod ip&longs;e <lb/>non fecit figurâ ip&longs;a appo&longs;itâ rem clariorem faciemus. </s><figure></figure>

<s>Nos quod ip&longs;e <lb/>non fecit figurâ ip&longs;a appo&longs;itâ rem clariorem faciemus. </s><figure/>

<s>Efto libra AB, cuius ful<lb/>cimentum C, pondera vtrin<lb/>que appen&longs;a AB, quorum v<lb/>trumque ponderet 10. Item <lb/>libra DE, cuius fulcimentum <lb/>F pondere vero appen&longs;a D, E, <lb/>ip&longs;is A, B, dimidio leuiora, <expan abbr="n&emacr;-pe">nen<lb/>pe</expan> S. </s>

<s>Addatur ponderi B pon<lb/>dus G, & ponderi E pondus <lb/>H, quorum &longs;imiliter <expan abbr="vtrumq;">vtrumque</expan> <lb/>ponderet S, nutabunt igitur <lb/>libræ ponderibus appo&longs;itis, & <pb pagenum="83"/>BG &longs;ecetur in K, EH verò in N, grauius e&longs;t autem GB, e&longs;t <lb/>enim IS, ip&longs;o EH, quod e&longs;t 10. Difficiliùs autem de&longs;cen<lb/>det BG, quàm EH. hoc autem ex doctrina Ari&longs;totelis, <lb/>quia non &longs;olum in contrarium quod graue e&longs;t, &longs;ed in obli<lb/>quum etiam difficulter mouetur, in contrarium enim ei <lb/>ad quod vergit onus mouere difficile e&longs;t, quò autem ver<lb/>git facilè in obliquum autem puta per lineas BK, EN non <lb/>vergit onus. </s>

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<s>quo enim maius e&longs;t pondus cæteris <lb/>paribus, quod nos in præ cedente quæ&longs;tione demon&longs;tra<lb/>uimus, eò maiìor fit ip&longs;a collifio. </s>

<s>Porrò huius <expan abbr="quoq;">quoque</expan> &longs;peculationis e&longs;t, Cur æqualia & <lb/>&longs;imilia corpora in æqualibus &longs;imilibu&longs;queue bafibus con&longs;ti<lb/>tuta eodem &longs;imiliqueue plano fulta, ponderibus tamen in<lb/>æqualia, non eâdem facilitate euertantur, &longs;ed horum gra<lb/>uiora difficilius. </s><pb pagenum="84"/><figure></figure>

<s>Sit enim Pri&longs;ma &longs;eu <lb/>Cylindrus ABCD, cuius <lb/>grauitatis centrum E in <lb/>plano Cl, ba&longs;i fultus CD. <lb/></s>

<s>Sit enim Pri&longs;ma &longs;eu <lb/>Cylindrus ABCD, cuius <lb/>grauitatis centrum E in <lb/>plano Cl, ba&longs;i fultus CD. <lb/></s>

<s>Sit & alter Cylindrus <lb/>FGHI, cuius grauitatis <lb/>centrum K fultus ba&longs;i HI <lb/>æqualis quidem & &longs;imilis <lb/>ip&longs;i AD. </s>

<s>Sit & alter Cylindrus <lb/>FGHI, cuius grauitatis <lb/>centrum K fultus ba&longs;i HI <lb/>æqualis quidem & &longs;imilis <lb/>ip&longs;i AD. </s>

<s>Sit autem grauior FGHI, ip&longs;o ABCD. Dico, pari <lb/>potentiâ vtrumque impellente, facilius euer&longs;um iri Cy<lb/>lindrum AD, ip&longs;o Fl. </s>

<s>Ducantur EC, KH, & æquales po<lb/>tentiæ applicentur punctis BG, pellentes Cylindros ad <lb/>partes AF. </s>

<s>Ducantur EC, KH, & æquales po<lb/>tentiæ applicentur punctis BG, pellentes Cylindros ad <lb/>partes AF. </s>

<s>Euer&longs;io autem non fiet donec facta corporis <lb/>conuer&longs;ione circa puncta CH, grauitatis centra E, K <expan abbr="trãs-ferunturin">trans<lb/>ferunturin</expan> L, M, in ip&longs;is &longs;cilicet <expan abbr="perp&emacr;dicularibus">perpendicularibus</expan> ACFH. <lb/></s>

<s>Demit tantur EN, KO, perpendiculares ip&longs;is CD, HF. </s>

<s>Et <lb/>quoniam CNE, HOK anguli recti &longs;unt, erunt EC KH i<lb/>p&longs;is EN, KO, maiores, quare & LC, MH ip&longs;is EN KO, ma<lb/>iores atto lluntur ergo in ip&longs;a cuer&longs;ione, grauitatum cen<lb/>tra E in L, K in M. </s>

<s>At quod grauius e&longs;t, difficilius contra <lb/>&longs;ui naturam mouetur, ideo difficilius euertetur corpus <lb/>FI, ip&longs;o AD, quod fuerat demon&longs;trandum. </s>

<s>QVÆSTIO XI.</s>

<s>QVÆSTIO XI.</s>

<s><emph type="italics"/>Dubitat Philo&longs;ophus, Cur &longs;uper &longs;cytalas facilius portentur onera <lb/>quàm &longs;uper currus, cum tamen ij magnas habeant rotas, <lb/>illæ verò pu&longs;illas?<emph.end type="italics"/></s>

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<s>quicquid tamen &longs;it, ad maiorem claritatem <lb/>aliquantulum in hac ip&longs;a quæ&longs;tione immorabimur. </s>

<s>Rotatas &longs;cytalas proponit hîc Ari&longs;toteles. </s>

<s>Rotatas &longs;cytalas proponit hîc Ari&longs;toteles. </s>

<s>Coniun<lb/>ctasautem e&longs;&longs;e rotas ip&longs;is &longs;cytalis e&longs;t intelligen dum, nem<lb/>pe, vt &longs;imul rotæ cum &longs;cytalis conuertantur. </s>

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8. & à no&longs;tris Me<lb/>chanicis pa&longs;&longs;im ab&longs;que rotis Cylindrica &longs;implici videli<lb/>cet, & tereti formâ ad v&longs;um adhiberi. </s>

<s>E&longs;to igitur Ari<lb/><figure id="fig14"></figure><lb/>&longs;totelis quidem &longs;cytala <lb/>AB, Pappi verò &longs;eu vul<lb/>garis, & communis CD. <lb/></s>

<s>E&longs;to igitur Ari<lb/><figure id="fig14"/><lb/>&longs;totelis quidem &longs;cytala <lb/>AB, Pappi verò &longs;eu vul<lb/>garis, & communis CD. <lb/></s>

<s>His non modò lapicidæ <lb/>pa&longs;&longs;im, &longs;ed & nautæ na<lb/>uiumqueue fabri &longs;ubdu<lb/>cendis & mari inducen<lb/>dis nauibus vtuntur, quod varare dicunt vernaculè, Hi<lb/>&longs;panico, vt arbitror, vocabulo. </s>

<s>ca enim natio teres lignum <lb/>baculumue appellat Varam. </s>

<s>ca enim natio teres lignum <lb/>baculumue appellat Varam. </s>

<s>Quæriautem po&longs;&longs;et, vtra harum formatum &longs;it vti<lb/>lior atque commodior? </s>

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<s>Quatenus autem ad v&longs;um pertinet. </s>

<s>E&longs;to horizontis <pb pagenum="86"/><figure id="fig15"></figure><lb/>planum AB, &longs;cytalae duae<lb/>CD, EF, Pondus verò <lb/>eis impo&longs;itum G, tan<lb/>gens ip&longs;as in <expan abbr="p&umacr;ctis">punctis</expan> CE, <lb/>&longs;cytalæ autem planum <lb/>in punctis D, F, Pellatur <lb/>à potentia quapiam <expan abbr="p&omacr;-dus">pon<lb/>dus</expan> Gad anteriora, <expan abbr="n&emacr;-pe">nen<lb/>pe</expan> ad partes E. rotabuntur igitur &longs;cytalæ & pars quædam <lb/>&longs;cytalæ D, in qua &longs;it contactus a&longs;cendet in I, C verò de<lb/>&longs;cendetin H, nulla re motum impediente, quippe quòd <lb/>nulla ponderis &longs;cytalarum, & plani ad inuicem fiat offen<lb/>&longs;atio. </s>

<s>E&longs;to horizontis <pb pagenum="86"/><figure id="fig15"/><lb/>planum AB, &longs;cytalae duae<lb/>CD, EF, Pondus verò <lb/>eis impo&longs;itum G, tan<lb/>gens ip&longs;as in <expan abbr="p&umacr;ctis">punctis</expan> CE, <lb/>&longs;cytalæ autem planum <lb/>in punctis D, F, Pellatur <lb/>à potentia quapiam <expan abbr="p&omacr;-dus">pon<lb/>dus</expan> Gad anteriora, <expan abbr="n&emacr;-pe">nen<lb/>pe</expan> ad partes E. rotabuntur igitur &longs;cytalæ & pars quædam <lb/>&longs;cytalæ D, in qua &longs;it contactus a&longs;cendet in I, C verò de<lb/>&longs;cendetin H, nulla re motum impediente, quippe quòd <lb/>nulla ponderis &longs;cytalarum, & plani ad inuicem fiat offen<lb/>&longs;atio. </s>

<s>Præterea cum &longs;cytalarum centra ab horizontis pla<lb/>no æqualiter di&longs;tent, pondus quidem horizonti æquidi<lb/>&longs;tanter mouetur, & ideo cius centrum grauitatis nequa<lb/>quam, in motu qui &longs;it, eleuatur. </s>

<s>Cæterùm materiæ imperfectione remota nihil re<lb/>fert ad facilitatem, vtrum maioris minorisue diametri <lb/>&longs;int&longs;cytalæ, vt ea po&longs;ita eo quod maiores circuli faciliùs <lb/>offendicula &longs;uperent, quod demon&longs;tratum e&longs;t in quæ&longs;tio<lb/>ne 8. eo vtiliores &longs;unt &longs;cytalæ, quo cra&longs;&longs;iores. </s>

<s>Quatenus <lb/>autem ad plau&longs;tri naturam &longs;pectat, cuius ad &longs;cytalas Phi<lb/>lo&longs;ophus fecit comparationem, vt o&longs;ten da mus difficilius <lb/>ex eo moueri pondera. </s><figure></figure>

<s>E&longs;to plau&longs;tri rota <lb/>KL, cuius centrum M, a<lb/>xis verò NO circa quem <lb/>rotaip&longs;a conuertiturKL. <lb/></s>

<s>E&longs;to plau&longs;tri rota <lb/>KL, cuius centrum M, a<lb/>xis verò NO circa quem <lb/>rotaip&longs;a conuertiturKL. <lb/></s>

<s>Funis quo rota ex axis <lb/>centro M trahitur MP, <lb/>pondus vero QR. </s>

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<s>Cætetùm quod ip&longs;e reticuit, n<gap/>s dicemus, nempe <lb/>validi&longs;&longs;imè enormia pondera per &longs;cytalas moueri, &longs;i &longs;cy<lb/>talis ip&longs;is vectes adiungantur. </s>

<s>Et &longs;anè motus erit tar di&longs;&longs;i<lb/>mus, veruntamen tar ditas ip&longs;a facilitate, quæ in de fit, v<lb/>berrimè compen&longs;atur. </s><figure></figure>

<s>Et &longs;anè motus erit tar di&longs;&longs;i<lb/>mus, veruntamen tar ditas ip&longs;a facilitate, quæ in de fit, v<lb/>berrimè compen&longs;atur. </s><figure/>

<s>E&longs;to igitur horizontis planum AB, &longs;cytalæ CD, fo<lb/>ramina in &longs;cytalis EFGH, vectes foraminibus in&longs;erti IE, <lb/>KF, LG, MH. </s>

<s>Pondus vero &longs;cytalis impo&longs;itum N. </s>

<s>Pondus vero &longs;cytalis impo&longs;itum N. </s>

<s>Appli<lb/>catis igìtur quatuor potentijs extremitatibus vectium I, <lb/><emph type="italics"/>K<emph.end type="italics"/>, L, M, ij&longs;que in anteriora propul&longs;is, fiet &longs;cytalarum rota-<pb pagenum="88"/>tio, & ponderis N translatio ad anteriores partes B. </s>

<s>E&longs;to <lb/>item &longs;eor&longs;um &longs;cytala PR, cuius centrum Q, vectis eidem <lb/>per centrum in&longs;ertus O, P, Q, R. facto igitur vectis motu <lb/>O P Q R fiet ex O; centro <expan abbr="aut&emacr;">autem</expan> Q circuli quadrans O T. <lb/>exi&longs;tente igitur O in T erit P in S. facta quartæ partisip&longs;ius <lb/>&longs;cytalæ rotatione. </s>

<s>Et quoniam ex eodem centro &longs;unt qua<lb/>drantes PSOT. erit vt OQ ad QP. ita quadrans OT, ad <lb/>quadrantem PS. </s>

<s>Et quoniam ex eodem centro &longs;unt qua<lb/>drantes PSOT. erit vt OQ ad QP. ita quadrans OT, ad <lb/>quadrantem PS. </s>

<s>Maxima autem e&longs;t proportio OQ, ad <lb/>QP. </s>

<s>Maxima igitur proportio OT ad PS. </s>

<s>Maxima igitur proportio OT ad PS. </s>

<s>Ex magno igitur <lb/>motu O ad T, paruus &longs;it &longs;cytalæ motus à P in S. tardius i<lb/>gitur progreditur &longs;cytala, quæ longioribus vectibus rota<lb/>tur, vis tamen maxima, quippe quod vt &longs;o habet QP, hoc <lb/>e&longs;t, QR ad QO, ita potentia in O ad pondus quod premit <lb/>in P vel in V. </s>

<s>Facillimè ita que pondera vectibus & &longs;cyta<lb/>lis per horizontis planum transferri, exi&longs;tis patet. </s>

<s>QVAESTIO XII.</s>

<s>QVAESTIO XII.</s>

<s><emph type="italics"/>Quæritur, Cur Mi&longs;&longs;ilia longius funda mittantur quam manu, <lb/>præ&longs;ertim cum proijcienti fundæ pondus addatur lapidis &longs;eu mi&longs;&longs;i<lb/>lis ponderi: & minus mi&longs;&longs;ili, manu proiecto, com<lb/>prehendatur?<emph.end type="italics"/></s>

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<s>quantò igitur productius fuerit quod à cen<lb/>tro e&longs;t, tanto citiùs mouetur; iactus autem, qui manu fit, <lb/>fundæ re&longs;pectu breuior e&longs;t. </s>

<s>Hæc Philo&longs;ophus. </s>

<s>Hæc Philo&longs;ophus. </s>

<s>Et &longs;anè perquàm appo&longs;itè, <expan abbr="itaq;">itaque</expan> <pb pagenum="89"/>illi pror&longs;us a&longs;&longs;entirer, ni&longs;i pro comperto habercm, in la ctu <lb/>qui fundâ fit, non e&longs;&longs;e manum ip&longs;am motus centium, &longs;ed <lb/>potius partem illam brachij, quæ humero iungitur, & id<lb/>co motum eo fieri velociotem, quo longior e&longs;t linea quæ <lb/>ab humero ad &longs;ummitatem fundæ e&longs;t, ea quæ ab humero <lb/>ad manum ip&longs;am. </s>

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<s>Quamobrem con&longs;iderandum e&longs;t, quo pacto fiat à tardi<lb/>tate velocitas. </s>

<s>Re&longs;pondemus, velocitatem acquirinon ex <lb/>&longs;implici, quæ circa funditoris caput &longs;it, rotatione, &longs;ed ex <lb/>co impetu qui fit in ip&longs;a lapidis emi&longs;&longs;ione, qui quidem im<lb/>petus &longs;i ante vel po&longs;t illud tempus fiat, quod à funditore <lb/>captatur, ca&longs;&longs;a pror&longs;us & inualida fit ip&longs;a iaculatio. </s><figure></figure>

<s>E&longs;to funda AB, manus <lb/>B, brachium BC. </s>

<s>E&longs;to funda AB, manus <lb/>B, brachium BC. </s>

<s>Vt igitur&longs;e <lb/>habet CH, ad CB, ita veloci<lb/>tas AD ad velocitatem, BE; <lb/>Vidimus nos pueros, arundi<lb/>ni ad caput &longs;ci&longs;&longs;æ, paruos la<lb/>pides in&longs;erentes, arundinem<lb/>queue manu rotantes longi&longs;&longs;i<lb/>mè lapides ip&longs;os proijcere; A<lb/>rundo FG, lapis F, manus G, <lb/>brachium GH. </s>

<s>QVÆSTIO XIII.</s>

<s>QVÆSTIO XIII.</s>

<s><emph type="italics"/>Quæritur, Cur circa idemiugum, maiores collopes (vectes &longs;unt, <lb/>quos alij &longs;cytalas appellant, vt Pappus & Heron) faciliùs quàm mi<lb/>nores mouentur: & item &longs;uculæ, quæ graciliores &longs;unt eadem <lb/>vi quam cra&longs;&longs;iores?<emph.end type="italics"/></s>

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<s>quippe quod ab ea dem vi plus <expan abbr="trã&longs;-feratur">tran&longs;<lb/>feratur</expan> illud extremum quod longius à centro di&longs;tat. </s>

<s>In <lb/>gracilioribus verò &longs;uculis datâ collopum paritate plus e&longs;<lb/>&longs;e id quod à ligno di&longs;tat. </s><figure></figure>

<s>In <lb/>gracilioribus verò &longs;uculis datâ collopum paritate plus e&longs;<lb/>&longs;e id quod à ligno di&longs;tat. </s><figure/>

<s>E&longs;to iugum &longs;ucu<lb/>laue maior, AB circa <lb/>centrum C, minor verò <lb/>circa idem <expan abbr="centr&umacr;">centrum</expan> DE. <lb/></s>

<s>E&longs;to iugum &longs;ucu<lb/>laue maior, AB circa <lb/>centrum C, minor verò <lb/>circa idem <expan abbr="centr&umacr;">centrum</expan> DE. <lb/></s>

<s>Collops <expan abbr="aut&emacr;">autem</expan> AF, pon<lb/>dus quod per iugum at<lb/>tollitur G. </s>

<s>Collops <expan abbr="aut&emacr;">autem</expan> AF, pon<lb/>dus quod per iugum at<lb/>tollitur G. </s>

<s>A it igitur A<lb/>ri&longs;toteles, &longs;uculas, iu<lb/>gaue AB, DE ceu cen<lb/>tra e&longs;&longs;e, à quibus extat colops AB, ex maiori quidem, totâ <lb/>&longs;ui parte BF, ex minori autem EF. quo igitur, ait, longior <lb/>fuerit collops extans, eo maior, & deo velocior ad <expan abbr="part&emacr;">partem</expan> <lb/>F per maiorem circulum FH, fiet collopis motus & pon<lb/>deris eleuatio, at maior e&longs;t collops EF ip&longs;o BF, facil. </s>

<s>us er<lb/>go mouebitur pondus per &longs;uculam DE, ex collope EF, ab <lb/>cadem vi, quam per &longs;uculam AB, & collopem BF. </s>

<s>us er<lb/>go mouebitur pondus per &longs;uculam DE, ex collope EF, ab <lb/>cadem vi, quam per &longs;uculam AB, & collopem BF. </s>

<s>Hæc &longs;en&longs;i&longs;&longs;e videtur Ari&longs;to teles, qui cra&longs;&longs;a, vt aiunt, <lb/>Minerua rem pulchram & &longs;ubtilem e&longs;t pro&longs;equutus. </s>

<s>Di<lb/>cimus igitur primò, in&longs;trumentum illud quod Latini &longs;u<lb/>culam, id e&longs;t, &longs;ero&longs;ulam, à &longs;tridore arbitror qui in conuer<lb/>&longs;ione fit, appellauere, Græci verò <foreign lang="greek">o)/non</foreign>, id e&longs;t, A &longs;inum, quip<lb/>pe quod ceu A &longs;inus pondera &longs;u&longs;tineat portetque. </s>

<s>Hanc <lb/>eandem Machinam veteres Mechanici vocauere Axem <lb/>in Peritrochio, cuius nos imaginem, è Pàppo in 8. Col<lb/>lect. </s>

<s>Hanc <lb/>eandem Machinam veteres Mechanici vocauere Axem <lb/>in Peritrochio, cuius nos imaginem, è Pàppo in 8. Col<lb/>lect. Mathematicarum de&longs;umptam in ip&longs;o huius no&longs;trio<lb/>peris initio, inter quinque Potentias propo&longs;uimus. </s>

<s>Mathematicarum de&longs;umptam in ip&longs;o huius no&longs;trio<lb/>peris initio, inter quinque Potentias propo&longs;uimus. </s>

<s>Huius <lb/>vim inter antiquos diligenti&longs;&longs;ime examinauêre Heron, & <pb pagenum="91"/>ip&longs;emet Pappus, inter iuniores verò Guilibaldus co Tra<lb/>ctatu quem hac de Potentia Mechanicis &longs;uis in&longs;eruit. <lb/></s>

<s>Summa e&longs;t, hanc Machinam ad vectem reduci. </s>

<s>Nec ve<lb/>rum e&longs;t quod &longs;cribit Ari&longs;to teles, iugum &longs;uculamue cen<lb/>tra e&longs;&longs;e, hæc enim centrum habent, quod in figura &longs;upe<lb/>rius po&longs;ita notatur &longs;igno C. igitur vt &longs;e habet FC, ad CA, <lb/>ita pondus G ad potentiam in F; e&longs;t autem maior propor<lb/>tio FC ad CD, quàm FC, ad CA. faciliùs ergo mouebit <lb/>potentia quæ in F, pondus in D, quàm eadem potentia F, <lb/>pondus in A, hoc e&longs;t, G. </s>

<s>Huius naturæ &longs;unt quo que Erga<lb/>tæ, quas machinas no&longs;tr<gap/>, Græco luxato vocabulo Arga<lb/>nos appellant. </s>

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<s>Cæterùm facilitatem à velocitate <lb/>non oriri &longs;uperius demon&longs;trauimus. </s>

<s>QVAESTIO XIV.</s>

<s>QVAESTIO XIV.</s>

<s><emph type="italics"/>Proponitur dubitatio, Cur eiu&longs;dem magnitudinis lignum facilius <lb/>genu frangatur &longs;i qui&longs;piam æque diductis manibus extrema com<lb/>prehendens fregerit, quàm &longs;i iuxta genu. </s>

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<s>quanto autem remotius <lb/>à centro fuerit, facilius mouetur quodcunque: Moueri <lb/>autem quod frangitur nece&longs;&longs;e e&longs;t. </s>

<s>E&longs;to lignum quod frangi debet AB, genu vel pedis <lb/>locus C, manuum latè diductarum &longs;itus DE, minus didu<lb/>ctarum FG; ltaque quoniam DE magis à centro C di&longs;tant <lb/>quàm FG, velo cius mouebuntur puncta DE ip&longs;is FG, er<lb/>go inde facilius fiet fractio quam ex FG. </s>

<s>E&longs;to lignum quod frangi debet AB, genu vel pedis <lb/>locus C, manuum latè diductarum &longs;itus DE, minus didu<lb/>ctarum FG; ltaque quoniam DE magis à centro C di&longs;tant <lb/>quàm FG, velocius mouebuntur puncta DE ip&longs;is FG, er<lb/>go inde facilius fiet fractio quam ex FG. </s>

<s>Hæcille ex &longs;uis <pb pagenum="92"/><figure id="fig16"></figure><lb/>principijs. </s>

<s>Hæcille ex &longs;uis <pb pagenum="92"/><figure id="fig16"/><lb/>principijs. </s>

<s>Nos dili<lb/>gentius, &longs;i fieri poterit, <lb/>effectus huius cau&longs;&longs;am <lb/>per&longs;crutemur. </s>

<s>E&longs;to igi<lb/>tur in &longs;ecunda figura <lb/>lignum oblongum AB, <lb/>cuius medium C, linea <lb/>ducatur CD perpen<lb/>dicularis ip&longs;i AB. </s>

<s>E&longs;to igi<lb/>tur in &longs;ecunda figura <lb/>lignum oblongum AB, <lb/>cuius medium C, linea <lb/>ducatur CD perpen<lb/>dicularis ip&longs;i AB. </s>

<s>Ad<lb/>moucatur genu <expan abbr="p&umacr;cto">puncto</expan> <lb/>C, manus verò diuari<lb/>centur in AB, facta i<lb/>gitur vtrinque impre&longs;<lb/>&longs;ione, lignum non <expan abbr="frã-getur">fran<lb/>getur</expan>, ni&longs;i partium in CD coniunctarum &longs;eparatio fiat, <lb/>&longs;itqueue altera in E, altera verò in F, fractum ergo erit <expan abbr="lign&umacr;">lignum</expan>, <lb/>& centro C immobili permanente, partes facto angulo <lb/>GCH erunt in GC, HC: Modò lignum &longs;uæ integritati re<lb/>&longs;tituetur, & denuò admoto genu puncto C, manus didu<lb/>cantur in I, K, quæ lo ca viciniora &longs;intip&longs;i C, quam AB, Di<lb/>co hinc difficilius fractionem fieri quam ex AB. </s>

<s>Con&longs;ide<lb/>ramus enim in integro ligno AB, duos vectes ACD, BCD, <lb/>quorum anguli concurrunt in commune fulcimentum C, <lb/>Sunt autem vectes angulati, & eius naturæ, quam exami<lb/>nauimus in quæ&longs;tiones. </s>

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<s>Sed nos hac eadem de <lb/>re nonnulla in declaranda quæ&longs;tione 16. perpendemus. </s>

<s>QVAESTIO XV.</s>

<s>QVAESTIO XV.</s>

<s><emph type="italics"/>Proponitur inueftigandum, Cur litterales crocæ (glareas dicunt <lb/>Latini, velcalculos, quos vmbilicos appellat Cicero lib.

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<s>Id &longs;anè explorati&longs;&longs;imum e&longs;t, <pb pagenum="94"/>angulos omnes, & emin entias quaslibet in corporibus e&longs;<lb/>&longs;e infirmiores, offen&longs;ionibus enim expo&longs;itæ &longs;unt, necre&longs;i<lb/>&longs;ten di habent facultatem. </s>

<s>Itaque in attritione quæ fit in <lb/>eorum agitatione perpetua, eminentiæ contunduntur, & <lb/>&longs;uperficies ip&longs;a paullatim leuigatur. </s><figure></figure>

<s>Itaque in attritione quæ fit in <lb/>eorum agitatione perpetua, eminentiæ contunduntur, & <lb/>&longs;uperficies ip&longs;a paullatim leuigatur. </s><figure/>

<s>E&longs;to angulatus lapis ABCD. <lb/></s>

<s>E&longs;to angulatus lapis ABCD. <lb/></s>

<s>Dum igitur perpeti motione <expan abbr="atq;">atque</expan> <lb/>a&longs;&longs;iduâ ver&longs;atione agitatur, fer<lb/>turqueue, eminentiæ anguliqueue, vt<lb/>pote debiles & imbecilli, conte<lb/>runtur, & inde figura fit quædam <lb/>irregularis, ad primam quidem la<lb/>pidis <expan abbr="formã">formam</expan> accedens, leuistamen <lb/>& quouis angulo carens, qualis e&longs;t E remotis ABCD, an<lb/>gularibus eminentijs. </s>

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1. cap.

5. ita &longs;cribit: <emph type="italics"/>Turresitaque<lb/>rotundæ aut polygoniæ &longs;unt faciendæ, quadrat as enim machinæ <lb/>celerius di&longs;&longs;ipant; & angulos, Arietes tundendo frangunt, inro<lb/>tundationibus autem, vti cuneos adcentrum adigendo lædere non <lb/>po&longs;&longs;unt.<emph.end type="italics"/> Hæcille. </s>

<s>Cur autem no&longs;tri rotundas figuras alias <lb/>vtiles reijciant, ab ijs petendum qui in ea facultate ver<lb/>&longs;antur. </s>

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<s>Quæo-<pb pagenum="95"/>m<gap/>a cùm vera &longs;int, nemo, vt arbitror, dixerit, ab&longs;olutè, <lb/>quod voluit Ari&longs;toteles, id ex rotatione velociori & par<lb/>tium à centro remotione, fieri. </s>

<s>QVAESTIO XVI.</s>

<s>QVAESTIO XVI.</s>

<s><emph type="italics"/>Dubitatur, quare, quò longiora &longs;unt ligna, <gap/><expan abbr="ãto">anto</expan> imbecilliora fiant, <lb/>& &longs;itolluntur, inflectuntur magis: tamet&longs;i quod breue est ceu bi<lb/>cubit umfuerit, tenue, quod verò cubitorum cen<lb/>tum cra&longs;&longs;um?<emph.end type="italics"/></s>

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<s>Si igitur flexilis <lb/>fuerit vectis, ip&longs;um inflectimagis cum extollitur nece&longs;&longs;e <lb/>e&longs;t, quod longis accidit lignis, in breuibus autem quod vl<lb/>timum e&longs;t, quie&longs;centi hypomochlio depropè fit. </s>

<s>Hæc <lb/>&longs;ubiectâ figurâ ob oculos ponimus. </s><figure></figure>

<s>Hæc <lb/>&longs;ubiectâ figurâ ob oculos ponimus. </s><figure/>

<s>E&longs;to longum ac fle<lb/>xile lignum AB, manu ele<lb/>uetur in A, fle ctetur <expan abbr="itaq;">itaque</expan> <lb/>in B, & declinabit in C. et<lb/>enim manus quæ &longs;u&longs;tin et <lb/>in A, fulcimenti loco &longs;uccedit: longitudo vero AB ponde<lb/>ris vices refert, at que vectis, quare quo longius abfuerit à <lb/>fulcimento, id e&longs;t, manu extremum B, eo magis flectetur; <lb/>&longs;i autem lignum breuius fuerit, nempe terminatum in D, <lb/>nequaquam fle ctetur, eò quòd eius extremum D minus à <lb/>fulcimento quod e&longs;t in A &longs;it remotum. </s>

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<s>Dicimus autem materiam, <lb/>quatenus ad hanc contemplationem &longs;pectat, in duplici <lb/>e&longs;&longs;e differentia. </s>

<s>aut enim rarefactionis & con&longs;tipationis <lb/>e&longs;t incapax, vt in chalybe videmus, nitro, metallo, mar<lb/>more, aut capax quidem, & hæc duplex: Vel enim natura <lb/>nata e&longs;t ad rectitudinem quandam, vt ar borum flagella <lb/>virgæque, autnon item, ceu &longs;tannum, plumbum, & cæte<lb/>ra eiu&longs;modi. </s><figure></figure>

<s>E&longs;to primò vitreum <lb/>corpus gracile, procerum, <lb/>teres AB, manu capiaturin <lb/>A, <expan abbr="itaq.">itaque</expan> pondere ip&longs;ius cor<lb/>poris præualente ad partes <lb/>B, quia in C puncto, quod <lb/>circa medium e&longs;t, ex parte <lb/>&longs;uperiori non fit rarefactio, <lb/>nec in in feriori con&longs;tipatio, <lb/>nec interim datur penetra<lb/>tio corporum, fit fractio à <lb/>&longs;uperiori parte, & pars CB à <lb/>reliqua parte AC, auul&longs;a & <lb/>&longs;eparata cadit in D, &longs;uccedit autem ip&longs;a &longs;eparatio rarefa<lb/>ctioni. </s>

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<s>De priori modo iam egimus. </s>

<s>Modò &longs;u&longs;pendatur in <lb/>medio vt AB, in C. eo igitur ca&longs;u cum fulcimentum &longs;it in <lb/>C, <expan abbr="vtrinq;">vtrinque</expan> fit flexio in D, & E, & id quidem &longs;i materia fle<lb/>xionem patitur: &longs;in minus, fractio fit in C. </s>

<s>Si autem ab ex<lb/><figure id="fig17"></figure><lb/>tremis fiat &longs;u&longs;pen&longs;io, vt in <lb/>AB, tunc ceu duo vectes <lb/>fient, quorum fulcimenta in <lb/>extremis AB. </s>

<s>Si autem ab ex<lb/><figure id="fig17"/><lb/>tremis fiat &longs;u&longs;pen&longs;io, vt in <lb/>AB, tunc ceu duo vectes <lb/>fient, quorum fulcimenta in <lb/>extremis AB. </s>

<s>Pondera au<lb/>tem communia in medio vbi <lb/>Cremoti&longs;&longs;ima enim ea pars e&longs;t ab extremis AB. </s>

<s>Pondera au<lb/>tem communia in medio vbi <lb/>Cremoti&longs;&longs;ima enim ea pars e&longs;t ab extremis AB. </s>

<s>Cedente <lb/><figure id="fig18"></figure><lb/>igitur materia &longs;uomet pon<lb/>deri, &longs;iquidein in flexibilis fu<lb/>erit, frangetur, & fiet <expan abbr="parti&umacr;">partium</expan> <lb/>&longs;eparatio in C, duoque in de <lb/>corpora AD, BE. </s>

<s>Cedente <lb/><figure id="fig18"/><lb/>igitur materia &longs;uomet pon<lb/>deri, &longs;iquidein in flexibilis fu<lb/>erit, frangetur, & fiet <expan abbr="parti&umacr;">partium</expan> <lb/>&longs;eparatio in C, duoque in de <lb/>corpora AD, BE. </s>

<s>Si autem fle<lb/>xionis capax, vt AB in po&longs;tre<pb pagenum="98"/>ma figura, facta ex contrario, nempe in in feriori parte cir<lb/>ca C rarefactione, in &longs;uperiori verò conden&longs;atione, pon<lb/>dere præualente curuabitur, fietque; lignum quidue aliud <lb/>huiu&longs;modi, vt ADB, nec amplius pondere &longs;uapte naturâ <lb/>inferiùs vergente ad rectitudinem reuertetur. </s>

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<s>E&longs;to horizontis planum, illudqueue &longs;olidi&longs;&longs;imum, & <lb/>impenetrabile AB, trabs eidem adperpendiculum erecta <lb/>CD fulta ba&longs;i vbi C grauitatis centrum F. pondus &longs;uper<lb/>impo&longs;itum FG, cuius grauitatis centrum H: Sint autem <lb/>H & E in eadem perpendiculari, quæ ad mun di centrum <lb/>HEC. </s>

<s>Itaque eo quod tum penderis tum trabis centra <lb/>grauitent in perpendiculari, illa verò fulciatur in C, to-<pb pagenum="99"/><figure id="fig19"></figure><lb/>tius ponderis moles recumbet <lb/>in C: non de&longs;cendet autem in I, <lb/>propterea quod &longs;upponatur i<lb/>p&longs;um planum AB, impenetrabi<lb/>le. </s>

<s>Itaque eo quod tum penderis tum trabis centra <lb/>grauitent in perpendiculari, illa verò fulciatur in C, to-<pb pagenum="99"/><figure id="fig19"/><lb/>tius ponderis moles recumbet <lb/>in C: non de&longs;cendet autem in I, <lb/>propterea quod &longs;upponatur i<lb/>p&longs;um planum AB, impenetrabi<lb/>le. </s>

<s>Igitur vt pondus H de&longs;cen<lb/>dat in C, alterum duorum e&longs;t <lb/>nece&longs;&longs;arium, nempe vel trabem <lb/>&longs;ubiectam comminui, aut eius <lb/>partes &longs;e&longs;e penetrare, & plura <lb/>corpora e&longs;&longs;e in eodem loco, pu<lb/>ta KC, quorum hoc &longs;ecun dum <lb/>naturæ penitus repugnat, illud <lb/>vero primum, penè impo&longs;&longs;ibile. </s>

<s>Diuidatur enim trabs in <lb/>partes æquales tres, lineis KL, ip&longs;a igitur KC infima &longs;u&longs;ti<lb/>net mediam KL, hæc verò &longs;upremam LD, hæc autem <expan abbr="p&omacr;-dus">pon<lb/>dus</expan>, ip&longs;um &longs;uperpo&longs;itum in H. </s>

<s>Seigitur &longs;u&longs;tinent partes. <lb/></s>

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<s>Præterea in præcedenti quæ&longs;tione mon&longs;trauimus <lb/>tunc facilem e&longs;&longs;e gracilis & oblongi ligni fractionem, <expan abbr="c&umacr;">cum</expan> <lb/>maxima e&longs;t longitudinis ad cra&longs;&longs;itudinem proportio. </s>

<s>Hîc <lb/>verò contrà accidit, etenim MD pars vectis quæ à fulci<lb/>mento e&longs;t ad potentiam minimam habet proportionem <lb/>ad rectam DC, quæ à fulcimento ad locum fractionis ex<lb/>tenditur, vbi C, quod vt euidentius pateat, </s><figure></figure>

<s>E&longs;to &longs;eor&longs;umtrabs AB, <lb/>cuius medium C. </s>

<s>E&longs;to &longs;eor&longs;umtrabs AB, <lb/>cuius medium C. </s>

<s>Sit autem <lb/>pondus D impo&longs;itum pun<lb/>cto C. facilè igitur frange<lb/>tur lignum AB, propterea <lb/>quòd maxima &longs;it proportio <lb/>AC ad CE; re&longs;i&longs;tentia verò <lb/>fiat in E, addatur vniatu que; <pb pagenum="100"/>ligno AB lignum FH. </s>

<s>Cra&longs;&longs;ius igitur e&longs;t totum AL, ip&longs;o <lb/>A<gap/>, & ideo minor proportio AC ad CG quàm AC, ad <lb/>CE. </s>

<s>Cra&longs;&longs;ius igitur e&longs;t totum AL, ip&longs;o <lb/>A<gap/>, & ideo minor proportio AC ad CG quàm AC, ad <lb/>CE. </s>

<s>Addavur adhuc & IM. </s>

<s>Longè itaque difficilius fran<lb/>getur in K propterea quòd longè minor &longs;it proportio AC <lb/>ad CK quàm ciuidem ad CE & CG. </s>

<s>Longè itaque difficilius fran<lb/>getur in K propterea quòd longè minor &longs;it proportio AC <lb/>ad CK quàm ciuidem ad CE & CG. </s>

<s>His igitur con&longs;ide<lb/>ratis, & demon&longs;tratis concludimus, impo&longs;libile e&longs;&longs;e ere<lb/>ctam trabem ponderi cedere, & frangi. </s>

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<s>Præterea, quoniam pondus, cuifulcrum re&longs;i<lb/>&longs;tit, vel ex natura premit, vel ex violentia, illud quidem <lb/>per lincam perpen dicularem, quæ ad mundi <expan abbr="c&emacr;trum">centrum</expan>, hoc <lb/>autem lateraliter & diuer&longs;imodè, varia fit fulcrorum di&longs;<lb/>po&longs;itio. </s>

<s>Cuius rei &longs;umma hæce&longs;t, vt &longs;emper contra impe<lb/>tum &longs;upponantur. </s><figure></figure>

<s>Cuius rei &longs;umma hæce&longs;t, vt &longs;emper contra impe<lb/>tum &longs;upponantur. </s><figure/>

<s>E&longs;to enim horizontis planum <lb/>AB, <expan abbr="eid&emacr;">eidem</expan> perpendiculares CADB, <lb/>ítaque &longs;i naturaliter pondus pre<lb/>matex C, fulcrum &longs;upponetur AE. <lb/></s>

<s>Siautem ex F ip&longs;um GE, &longs;i verò ex <lb/>H, &longs;upponaturiuxta BE. </s>

<s>Siautem ex F ip&longs;um GE, &longs;i verò ex <lb/>H, &longs;upponaturiuxta BE. </s>

<s>Si verò &longs;e<lb/>cundum I ponderi opponatur KE. <lb/></s>

<s>Hæc nos de arrectarijs fulcrisue; <lb/>nunc de tran&longs;uer&longs;arijs, & inclinatis agemus, & primum <lb/>de tran&longs;uer&longs;arijs, quatenus ad tectorum trabeationes &longs;pe<lb/>ctat. </s>

<s>E&longs;to tran&longs;uer&longs;aria trabs AB, muris <expan abbr="vtrinq;">vtrinque</expan> fulta CD, <pb pagenum="101"/><figure id="fig20"></figure><lb/>cuius grauitatis centrum <lb/>E, in <expan abbr="perp&emacr;diculari">perpendiculari</expan> FEG, <lb/>quæ quidem ad mundi <lb/>centrum vergit. </s>

<s>E&longs;to tran&longs;uer&longs;aria trabs AB, muris <expan abbr="vtrinq;">vtrinque</expan> fulta CD, <pb pagenum="101"/><figure id="fig20"/><lb/>cuius grauitatis centrum <lb/>E, in <expan abbr="perp&emacr;diculari">perpendiculari</expan> FEG, <lb/>quæ quidem ad mundi <lb/>centrum vergit. </s>

<s><expan abbr="Itaq;">Itaque</expan> eo<lb/>dem tendente grauitatis <lb/>contro, &longs;i pondus quod <lb/>premit in E, non præua<lb/>leat vnioni <expan abbr="parti&umacr;">partium</expan> ip&longs;ius <lb/>materiæ quæ e&longs;t in E, re&longs;i&longs;tet trabs &longs;uomet ponderi, nec <lb/>frangetur. </s>

<s>Si autem vel in firmitate materiæ, aut vitio, vel <lb/>maxima exiftente proportione AF ad FE, fractio fiet in E, <lb/>& &longs;ecutâ partium &longs;epaiatione duæ fient vtrin que trabes <lb/>AH, Bl, quorum grauitatis centra KL. </s>

<s>Erunt igitur duo <lb/>vectes AE, BE, quorum fulcimenta MN, quamobrem &longs;i <lb/>proportio EM ad MH ita præualeat, vt pondus quod e &longs;t <lb/>in E, &longs;uperet pondus muri O &longs;uperimpo&longs;iti, & item muri <lb/>P, corruent quidem trabes, & murorum fiet hinc inde di&longs;<lb/>&longs;ipatio. </s>

<s>Si autem non præualuerit ea, quam diximus, pro<lb/>portio, &longs;u&longs;pen&longs;æ remanebunt vtrin que trabes vt AHBI. </s>

<s>Si autem non præualuerit ea, quam diximus, pro<lb/>portio, &longs;u&longs;pen&longs;æ remanebunt vtrin que trabes vt AHBI. </s>

<s>Huic difficultati egregiè occurrunt Architecti, ali<lb/>quando autem hoc modo: </s><figure></figure>

<s>Huic difficultati egregiè occurrunt Architecti, ali<lb/>quando autem hoc modo: </s><figure/>

<s>E&longs;to tran&longs;uer&longs;aria <lb/>trabs &longs;uâ gracilitate, alia<lb/>ue de cau&longs;&longs;a imbecilla <lb/>AB, muri quibus <expan abbr="vtrinq;">vtrinque</expan> <lb/>&longs;u&longs;tinetur CD, Trabis i<lb/>p&longs;ius grauitatis centrum <lb/>G. </s>

<s>Itaque adpactis trabi <lb/>lignis EF, caprcolos ad<lb/>dunt muro vtrinque ful<lb/>tos CE, DF, corum capita adpactis lignis admouentes EF, <lb/>&longs;ed & tunc validi&longs;&longs;ima fit colligatio, &longs;i inter E & F capreo<lb/>lorum capita inte grum lignum trabi &longs;upponatur EF. </s>

<s>Ra<pb pagenum="102"/>tio autem validitatis patet; premente enim grauitatis <expan abbr="c&emacr;-tro">cen<lb/>tro</expan> in G, fulcra hincinde &longs;uccurrunt CE, DF, quæ cum &longs;e<lb/>ip&longs;is fieri non valeant breuiora, ne corpori detur penetra<lb/>tio, re&longs;i&longs;tunt & robu&longs;ti&longs;&longs;imè ip&longs;i ponderi &longs;uperimpo&longs;ito <lb/>contranituntur. </s>

<s>Videntur autem in hoc opere duo con<lb/>&longs;iderari vectes, GH, GB, quorum fulcimenta EF, potentia <lb/>premens vtrinque G. </s>

<s>Videntur autem in hoc opere duo con<lb/>&longs;iderari vectes, GH, GB, quorum fulcimenta EF, potentia <lb/>premens vtrinque G. </s>

<s>Pondera autem parietum partes ca<lb/>pitibus trabis impo&longs;itæ in A & B. </s>

<s>Pondera autem parietum partes ca<lb/>pitibus trabis impo&longs;itæ in A & B. </s>

<s>Quoniam igitur parua <lb/>e&longs;t proportio GE ad EH, parua potentia premens in G, <lb/>maximè autem pondus in A, fieri non pote&longs;t trabem fran<lb/>gi aut muros vtrin que di&longs;&longs;ipare in AB. </s>

<s>Po&longs;&longs;unt etiam to<lb/>tius trabis tres partes con&longs;iderari AE, EF, FB, quarum ful<lb/>cimenta quatuor A, E, F, B, Diui&longs;o igitur pondere & mul<lb/>tiplicatis fulcimentis impo&longs;&longs;ibile e&longs;t trabem conuelli & <lb/>vitium facere. </s>

<s>Sed & tectorum contignationes imbecillaque; tran&longs;<lb/>uer&longs;aria Mechanici corroborare &longs;olent, additis nempe <lb/>arrectaria trabe atque cauterijs. </s><figure></figure>

<s>Sed & tectorum contignationes imbecillaque; tran&longs;<lb/>uer&longs;aria Mechanici corroborare &longs;olent, additis nempe <lb/>arrectaria trabe atque cauterijs. </s><figure/>

<s>E&longs;to enim tran&longs;<lb/>uer&longs;aria trabs AB <lb/>parietibus vtrinque <lb/>fulta I, K, <expan abbr="arrectari&umacr;">arrectarium</expan> <lb/>CD. </s>

<s>E&longs;to enim tran&longs;<lb/>uer&longs;aria trabs AB <lb/>parietibus vtrinque <lb/>fulta I, K, <expan abbr="arrectari&umacr;">arrectarium</expan> <lb/>CD. </s>

<s>Cauterij vtrin<lb/>que AD, BD, ita <lb/>tran&longs;uer&longs;ariæ trabi <lb/>in AB, & arrectario <lb/>in D in&longs;erti, vt ne<lb/>quaquam inde ela<lb/>bi valeant. </s>

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<s>Stabit ergo compa<lb/>ges tota & &longs;uapte vi robu&longs;ti&longs;&longs;imè connexa totius tecti <lb/>pondus &longs;u&longs;tinebit. </s>

<s>Quoniam autem v&longs;u venire &longs;olet, cauterios nimia <lb/>longitudine debiles, aliquando tum proprio tum extra<lb/>neo cedentes ponderi deor&longs;um vergentes pandare, Ar<lb/>chitecti capreolis hinc inde &longs;uppo&longs;itis, ceu fulcris, huic <lb/>medentur infirmitati. </s><figure></figure>

<s>Sint enim cauterij <lb/>debiles hinc inde AB, <lb/>AC, media trabs arre<lb/>ctaria, quam <expan abbr="Monach&umacr;">Monachum</expan> <lb/>dicimus AD. </s>

<s>Sint enim cauterij <lb/>debiles hinc inde AB, <lb/>AC, media trabs arre<lb/>ctaria, quam <expan abbr="Monach&umacr;">Monachum</expan> <lb/>dicimus AD. </s>

<s>Cauterio<lb/>rum mediæ partes E, F, <lb/>in punctis igitur EF, vtpote maximè ab extremis di&longs;tanti<lb/>bus debiles cauterij val de laborant. </s>

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<s>Hîc autem damnandi veniunt ij, quitran&longs;uer&longs;ariæ <lb/>quidem trabis capitibus cauteriorum pedes non <expan abbr="in&longs;er&umacr;t">in&longs;erunt</expan>, <lb/>&longs;ed ea vice tran&longs;uer&longs;ariolo quodam medios cauterios v<lb/>trin que connectunt ad in&longs;tar elementi A, quam compa<lb/>gem, capram, appellant. </s>

<s>Sint enim cauterij hinc inde AB, <lb/>AC, quorum medias partes connectit tran&longs;uer&longs;ariolum, <lb/>DE. </s>

<s>Sint enim cauterij hinc inde AB, <lb/>AC, quorum medias partes connectit tran&longs;uer&longs;ariolum, <lb/>DE. </s>

<s>Dico igitur colligationem i&longs;tam magnopere impro<lb/>bandam. </s>

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<s>tos, non &longs;tare. </s>

<s>Sint enim muri vtrinque AC, BD. </s>

<s>Sint enim muri vtrinque AC, BD. </s>

<s>Ducatur hori<lb/>zonti æquidi&longs;tans CD, iuxta quam lateres lapide&longs;ue non <lb/>cuneati, &longs;eriatim collocentur EF. </s>

<s>Ducatur hori<lb/>zonti æquidi&longs;tans CD, iuxta quam lateres lapide&longs;ue non <lb/>cuneati, &longs;eriatim collocentur EF. </s>

<s>Dicimus amoto arma-<pb pagenum="105"/><figure id="fig21"></figure><lb/>mento, hoc e&longs;t, pro<lb/>hibente ip&longs;o lateres <lb/>ruere. </s>

<s>Dicimus amoto arma-<pb pagenum="105"/><figure id="fig21"/><lb/>mento, hoc e&longs;t, pro<lb/>hibente ip&longs;o lateres <lb/>ruere. </s>

<s>Producantur <lb/>enim AC in G, BD <lb/>verò in H, cum ip&longs;is <lb/>CG, DH, æquales <lb/>fiant CI, DK, & recta <lb/>IK iungatur, crit igi<lb/>tur GD &longs;patium ip&longs;i <lb/>CK &longs;patio &longs;imile qui<lb/>dem & æquale, quod <lb/>cùm ita &longs;it, nihil prohibet quin tota laterum GD moles in <lb/>&longs;patium CK transferatur, & corruat. </s>

<s>Si autem cunei ip&longs;i latere&longs;ue, cuneatim di&longs;po&longs;iti, ita <lb/>&longs;int vt ad vnum centrum tendant, licet ad rectam lineam <lb/>collocentur, non delabentur, &longs;ed &longs;tabunt; quod ita o&longs;ten<lb/>demus. </s><figure></figure>

<s>Sint cunci latere&longs;ue <lb/>cuneatim di&longs;po&longs;iti ABCD, <lb/>tendentes ad centrum, &longs;eu <lb/>commune punctum E, Du<lb/>cantur CAE, DBE, &longs;intqueue <lb/>muri vtrinque ponderire&longs;i<lb/>&longs;tentes CL, DM, Demitta<lb/>tur perpendicularis, quæ ad <lb/>mundi centrum FGE &longs;ecans AB, in G. </s>

<s>Tum fiat GK aequa<lb/>lis GF & per K ip &longs;i AGB parallela ducatur, HKI claudens <lb/>&longs;patium AHIB. </s>

<s>Tum fiat GK aequa<lb/>lis GF & per K ip &longs;i AGB parallela ducatur, HKI claudens <lb/>&longs;patium AHIB. </s>

<s>Quoniam igitur vt EC, ad EA, ita CD ad <lb/>AB per 4. propo&longs;. </s>

<s>lib.

6. maior erit CD ip&longs;a AB, & eâdem <lb/>de cau&longs;&longs;a maior AB, ip&longs;a HI, & idcirco maius ABDC &longs;pa<lb/>tium, &longs;patio AHIB. </s>

6. maior erit CD ip&longs;a AB, & eâdem <lb/>de cau&longs;&longs;a maior AB, ip&longs;a HI, & idcirco maius ABDC &longs;pa<lb/>tium, &longs;patio AHIB. </s>

<s>Non igitur pote&longs;t linea CD, fieri in <lb/>AB, neque AB, in HI, neque &longs;patium totum CABD, tran&longs;<lb/>ferri in &longs;patium AHIB non data (quod naturæ ip&longs;i repu<pb pagenum="106"/>gnat) corporum penetratione. </s>

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<s>Idem enim patitur quod epi&longs;tylia in &longs;pecie <lb/>Aræos&longs;tyla, quæ, vt&longs;cribit Vitruuius lib.

3. c. </s>

3. c. 2. propter in<lb/>teruallorum magnitudinem franguntur. </s>

<s>2. propter in<lb/>teruallorum magnitudinem franguntur. </s>

<s>Id quoque ha<lb/>bet vitij, quod cunei ita di&longs;po&longs;iti &longs;uo pondere in cumbas <lb/>vtrinque violenti&longs;&longs;imè pellant. </s>

<s>Vtilis tamen e&longs;&longs;c pote&longs;t <lb/>ad portarum & fene&longs;trarum, quæ in medijs muris &longs;unt, & <lb/>mediocri vano aperiuntur, &longs;uperliminaria. </s>

<s>Si verò ad minorem circuli portionem curuetur Ca<lb/>mera, vtilior quidem erit &longs;tructura ea ip&longs;a, de qua locuti <lb/>&longs;umus; non tamen omninò &longs;ine vitio. </s><figure></figure>

<s>E&longs;to fornix ex minori <lb/>circuli portione AB, cuius in<lb/>cumbæ AF, BH muris fultæ <lb/>AC, BD. </s>

<s>E&longs;to fornix ex minori <lb/>circuli portione AB, cuius in<lb/>cumbæ AF, BH muris fultæ <lb/>AC, BD. </s>

<s>Con&longs;tet autem vel <lb/>ex lapidibus cuneatis, vel ex <lb/>coctilibus lateribus ad E <expan abbr="c&emacr;-trum">cen<lb/>trum</expan> tendentibus. </s>

<s>Sitque; for<lb/>nicis linea exterior FGH, in<lb/>terior AIB. </s>

<s>Sitque; for<lb/>nicis linea exterior FGH, in<lb/>terior AIB. </s>

<s>Ducantur EA, <lb/>ED, & producantur in M, N. <lb/></s>

<s>Ducantur EA, <lb/>ED, & producantur in M, N. <lb/></s>

<s>Quoniam igitur vt EM ad EA, ita MGN ad AIB, maior e<lb/>rit MGN lineaip&longs;a AIB, quamobrem fieri non pote&longs;t vt <lb/>aptetur lineæ AIB, & in eius locum de&longs;cendat. </s>

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<s>Validè autem <lb/>&longs;peciem hanc, loca quibus incumbit, propellere, ita o<lb/>&longs;tendemus. </s>

<s>Producatur in eadem figura CA in K, & DB in L. <lb/></s>

<s>Producatur in eadem figura CA in K, & DB in L. <lb/></s>

<s>Partes igitur quæ muris ad perpendiculum fulciuntur, <lb/>&longs;unt AKF, BLH, minimæ illæ quidem, maxima verò pars <pb pagenum="107"/>e&longs;t extra fulcimenta, nempetota AKLB quæ idcircó &longs;uo<lb/>pte pondere deor&longs;um vergens & in incumbas <expan abbr="vtrinq;">vtrinque</expan> pel<lb/>lens aperitur, & facillimè vitium facit. </s>

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<s>Circinantur autem hoc pacto, diui&longs;a nempe <lb/>&longs;ubten&longs;a, in partes tres, ea&longs;que æquales, ponitur circini <lb/>pes in altero diui&longs;ionum puncto & pars circuli de&longs;cribi<lb/>tur, mox in altero puncto circini pede collocato alia cir<lb/>culi portio lineatur, quibus arcus ip&longs;e integratur. </s>

<s>Appel<lb/>lant autem tertium acutum, eo quod ex &longs;ubten&longs;a in tres <lb/>partes diui&longs;a, arcus non fiatrotundus, &longs;ed in acutum an<lb/>gulum ex duabus circuli portionibus de&longs;inens. </s><figure></figure>

<s>Sint igitur muri <lb/>AC, BD, in quibus v<lb/>trinque incumbæ KA, <lb/>BI. </s>

<s>Sint igitur muri <lb/>AC, BD, in quibus v<lb/>trinque incumbæ KA, <lb/>BI. </s>

<s>Ducatur itaque &longs;ub<lb/>ten&longs;a horizonti æquidi<lb/>&longs;tans AP, quæ in tres æ<lb/>quales partes diuidatur <lb/>punctis E, F, tum centris <lb/>EF, circulorum portio<lb/>nes de&longs;cribantur hinc <lb/>AG, HK, inde verò BG, <pb pagenum="108"/>IH, ex quibus arcus totus integratur. </s>

<s>Vtilis hæc quidem <lb/>&longs;pecies e&longs;t, licet inuenu&longs;ta, propterea quod haud violen<lb/>ter incumbas vtrinque repellat, & in &longs;ummo magnis &longs;u&longs;ti<lb/>nendis oneribus &longs;it apta. </s>

<s>Producantur CH in N, DB verò <lb/>in O, &longs;itqueue centrum grauitatis AG in L, partis vero BG <lb/>in M. </s>

<s>Producantur CH in N, DB verò <lb/>in O, &longs;itqueue centrum grauitatis AG in L, partis vero BG <lb/>in M. </s>

<s>Quoniam igitur centra hæc ob elatam portionum <lb/>con&longs;titutionem quam proxima lineis AN, BO, fulcimen<lb/>torum fiunt, maximè <expan abbr="&longs;u&longs;tin&emacr;tur">&longs;u&longs;tinentur</expan>, & deor&longs;um potius quam <lb/>lateraliter in cumbas ip&longs;as premunt. </s>

<s>Si quid tamen <expan abbr="hab&emacr;t">habent</expan> <lb/>vitij, illud e&longs;t quod grauitatis centra momentum haben<lb/>tia ad interiorem partem ver&longs;us PQ vim faciant, & nifi <lb/>partes magno &longs;uperimpo&longs;ito pondere comprimantur, <lb/>partes quæ &longs;unt circa HG, &longs;ur&longs;um pellentes aliquali &longs;ibi <lb/>rectitudine comparata corruunt, facta nempe circa L, M, <lb/>coniunctarum partium &longs;eparatione. </s>

<s>His hoc pacto explicatis de &longs;emicirculari fornice a<lb/>gemus, quæ cæteris omnibus vtilior e&longs;t, & longè pulcher<lb/>rima, quamobrem Antiquis Architectis omnibus inpri<lb/>mis admodum familiaris: </s><figure></figure>

<s>E&longs;to vanum <lb/>ABCD, muris v<lb/>trinque clau&longs;um. <lb/></s>

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<s>Tertio denique modo huic infirmitati me dentur, <lb/>vt videre e&longs;t in &longs;equenti figura, in qua vanum ADBC, mu<lb/>ri vtrinque AF, BH, fornix verò FGH. </s>

<s>Itaque dum muros <lb/><figure id="fig22"></figure><lb/>ex&longs;truunt, arre<lb/>ctarias trabes, ro<lb/>bore aliaue mate<lb/>ria firmi&longs;&longs;ima, illis <lb/>in&longs;erunt, quales <lb/>&longs;unt IF<emph type="italics"/>K<emph.end type="italics"/> LHM, <lb/>ea proceritate vt <lb/>futuri fornicis &longs;u<lb/>perent &longs;ummita<lb/>tem. </s>

<s>Itaque dum muros <lb/><figure id="fig22"/><lb/>ex&longs;truunt, arre<lb/>ctarias trabes, ro<lb/>bore aliaue mate<lb/>ria firmi&longs;&longs;ima, illis <lb/>in&longs;erunt, quales <lb/>&longs;unt IF<emph type="italics"/>K<emph.end type="italics"/> LHM, <lb/>ea proceritate vt <lb/>futuri fornicis &longs;u<lb/>perent &longs;ummita<lb/>tem. </s>

<s>Con&longs;umma<lb/>to enim fornice, <lb/>nondum tamen, <lb/>exarmato, tran&longs;<lb/>uer&longs;ariam <expan abbr="trab&emacr;">trabem</expan> à <lb/>&longs;ummo fornicis <lb/>dor&longs;o parumper <lb/>eminentem in punctis I, L, arrectarijs trabibus validi&longs;&longs;i<lb/>mis clauibus connectunt, tum punctis NP, Oq, capreolos <pb pagenum="111"/>tran&longs;uer&longs;ario, & arrectarijs ferreis, clauis affigunt. </s>

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<s>Cum <lb/>enim PQ proxima &longs;int punctis FH, quæ cum arrectarijs à <lb/>muro di&longs;tinentur, magna in ijs fit vtrobique re&longs;i&longs;tentia. </s>

<s>Rebus igitur ita &longs;e habentibus cum ob&longs;erua&longs;&longs;ent Ar<lb/>chitecti, ob enormitatem ponderis fornices in tertia illa <lb/><figure id="fig23"></figure><lb/>parte quæ &longs;umma e&longs;t <lb/>laborare, <expan abbr="quãtum">quantum</expan> ter<lb/>tijs vtrinque partibus <lb/>&longs;oliditatis addunt, tan<lb/>tundem ex illa parte <lb/>&longs;uprema demere <expan abbr="&longs;ol&emacr;t">&longs;olent</expan>, <lb/>vt videre e&longs;t in &longs;ubie<lb/>cta figura, in qua par<lb/>tes A, B, &longs;olidæ & cra&longs;<lb/>&longs;iores, quibus hærent <lb/>partes, quæ CE, DG <lb/>cra&longs;&longs;æ quidem & illæ, <lb/>tum vero &longs;umma EFG, <lb/>alijs &longs;ubtilior. </s>

<s>Rebus igitur ita &longs;e habentibus cum ob&longs;erua&longs;&longs;ent Ar<lb/>chitecti, ob enormitatem ponderis fornices in tertia illa <lb/><figure id="fig23"/><lb/>parte quæ &longs;umma e&longs;t <lb/>laborare, <expan abbr="quãtum">quantum</expan> ter<lb/>tijs vtrinque partibus <lb/>&longs;oliditatis addunt, tan<lb/>tundem ex illa parte <lb/>&longs;uprema demere <expan abbr="&longs;ol&emacr;t">&longs;olent</expan>, <lb/>vt videre e&longs;t in &longs;ubie<lb/>cta figura, in qua par<lb/>tes A, B, &longs;olidæ & cra&longs;<lb/>&longs;iores, quibus hærent <lb/>partes, quæ CE, DG <lb/>cra&longs;&longs;æ quidem & illæ, <lb/>tum vero &longs;umma EFG, <lb/>alijs &longs;ubtilior. </s>

<s>Minus <lb/>igitur grauante ponde<lb/>re in F, minor fit ad in cumbas pre&longs;&longs;io, aut &longs;i qua fit, à <expan abbr="parti&umacr;">partium</expan> <lb/>ACE, BDG &longs;oliditate haud inualidè &longs;u&longs;tinetur. </s><pb pagenum="112"/>

<s>Cæterùm admonet nos locus, vt aliquid de forni<lb/>cum di&longs;&longs;olutionibus in medium afferamus: cau&longs;&longs;is enim <lb/>morborum cognitis, facilius periti medici adhibere &longs;o<lb/>lent remedia. </s><figure></figure>

<s>E&longs;to enim &longs;emicircula<lb/>ris fornix ABC, cuius cen<lb/>trum E, perpendicularis ve<lb/>rò quæ per centrum DBE, &longs;e<lb/>micirculi ABC, diameter <lb/>AEC, incumbæ <expan abbr="vtrinq;">vtrinque</expan> A, C. <lb/></s>

<s>Itaque &longs;i nulla fiat incumba<lb/>rum repul&longs;io, &longs;tabit fornix; &longs;i verò fiat, ruinam facict. </s>

<s>Pellanturitaque ad exteriores partes, vt in &longs;ecunda <lb/><figure id="fig24"></figure><lb/>figura, H in F, & C in G, <lb/>ex qua pul&longs;ione cum ma<lb/>ius fiat &longs;patium quod in<lb/>tegro fornice impleba<lb/>tur, iam di&longs;tractis <expan abbr="vtrinq;">vtrinque</expan> <lb/>fornicis partibus <expan abbr="n&omacr;">non</expan> im<lb/>pletur, Diuiditur igitur <lb/>locus maior factus in tres partes, quarum hincinde duas <lb/>replent fornicis partes, tertiam verò quæ media e&longs;t, re<lb/>plet in&longs;ertus, ne vacuum detur, aër, vt in figura videre e&longs;t, <lb/>in qua &longs;olutæ vtrinque fornicis partes HIKF, PMNG, aër <lb/>autem medius &longs;patium replens IKMN. </s>

<s>Pellanturitaque ad exteriores partes, vt in &longs;ecunda <lb/><figure id="fig24"/><lb/>figura, H in F, & C in G, <lb/>ex qua pul&longs;ione cum ma<lb/>ius fiat &longs;patium quod in<lb/>tegro fornice impleba<lb/>tur, iam di&longs;tractis <expan abbr="vtrinq;">vtrinque</expan> <lb/>fornicis partibus <expan abbr="n&omacr;">non</expan> im<lb/>pletur, Diuiditur igitur <lb/>locus maior factus in tres partes, quarum hincinde duas <lb/>replent fornicis partes, tertiam verò quæ media e&longs;t, re<lb/>plet in&longs;ertus, ne vacuum detur, aër, vt in figura videre e&longs;t, <lb/>in qua &longs;olutæ vtrinque fornicis partes HIKF, PMNG, aër <lb/>autem medius &longs;patium replens IKMN. </s>

<s>Diuidantur &longs;in<lb/>guli qua drantes FK, GN, in partes tres, quarum duæ &longs;int <lb/>hincinde FQ, GR, & à centris, quæ &longs;eparatis quadranti<lb/>bus facta &longs;untin ST, rectæ ducantur SQV. TRX. </s>

<s>Quo<lb/>niam igitur tertiæ partes vtrinque VIKQ MNRX pro<lb/>pria grauitate depre&longs;&longs;æ, nullum quo &longs;u&longs;tineantur fulci<lb/>mentum habent, corruent quidem. </s>

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<s>tangant tautem &longs;e in <expan abbr="p&umacr;-cto">pun<lb/>cto</expan> Z. quo pacto igitur fornices incumbis cedentibus in <lb/>medio aperti, <expan abbr="di&longs;&longs;oluãtur">di&longs;&longs;oluantur</expan> & ruinam faciant, ex i&longs;tis patet. </s>

<s>Ex demon&longs;tratis qua&longs;i ex con&longs;ectario habemus for<lb/>nices quo fuerint cra&longs;&longs;iores dato pari in cum barum &longs;ece&longs;<lb/>&longs;u, ruinæ minus e&longs;&longs;e obnoxios quàm tenuiores, hoc e&longs;t, <lb/>maiori aperitione indigere ad ruinam cra&longs;&longs;iores quam te<lb/>nuiores, quod licet ex iam dictis re&longs;ultet, nos tamen cla<lb/>rius ex &longs;ubiecto &longs;chemate demon&longs;trabimus. </s><figure></figure>

<s>E&longs;to enim cra&longs;&longs;ioris <lb/>fornicis pars <expan abbr="quid&emacr;">quidem</expan> ABCD, <lb/>tenuioris EFCD circa <expan abbr="id&emacr;">idem</expan> <lb/>centrum R. </s>

<s>E&longs;to enim cra&longs;&longs;ioris <lb/>fornicis pars <expan abbr="quid&emacr;">quidem</expan> ABCD, <lb/>tenuioris EFCD circa <expan abbr="id&emacr;">idem</expan> <lb/>centrum R. </s>

<s>Ducatur au<lb/>tem RM, &longs;ecans CD in G. <lb/>EF in H AB, in M. </s>

<s>Ducatur au<lb/>tem RM, &longs;ecans CD in G. <lb/>EF in H AB, in M. </s>

<s>Centro <lb/>igitur G fiet euer&longs;io portio<lb/>num fornicum, MD, HD, <lb/>Ducantur GA, GE & producta AD in N ip&longs;i AN perpen<lb/>dicularis ducatur GN. quoniam igitur GE cadit in trian<lb/>gulo AGN erit ex 21. propo&longs;. </s>

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<s>GA, maior GE. <lb/></s>

<s>Corruente igitur maioris fornicis portione MD, recta <lb/>GA centro G punctum A de&longs;cribet portionem AI, mino<lb/>ris interim ex GE, de&longs;cribente EL, at cadenti angulo A <lb/>occurrit in perpendiculari IK in puncto I angulus oppo<lb/>&longs;itæ portionis, O, ip&longs;i autem E cadenti per EL non occur<lb/>ret punctum P, cadens per Pq eo quod neutrum eorum <lb/>pertingat ad perpendicularem IK. Tenuioris ergo forni<pb pagenum="114"/>cis partes è &longs;uis locis auul&longs;æ ex eadem aperitione ruinam <lb/>facient, quod non contingit partibus cra&longs;&longs;ioris. </s>

<s>Tenuioris ergo forni<pb pagenum="114"/>cis partes è &longs;uis locis auul&longs;æ ex eadem aperitione ruinam <lb/>facient, quod non contingit partibus cra&longs;&longs;ioris. </s>

<s>quod &longs;a<lb/>nè fuerat de clarandum. </s>

<s>Quæritur adhuc, quare grauiores fornices in &longs;um<lb/>mis ædificijs non &longs;ine vitio fiant? </s>

<s>E&longs;to ædificium ABGH, cuius <expan abbr="vtrinq;">vtrinque</expan> muri ABCD, <lb/>EFGH, maiorum &longs;ummitates AD, EH, mediæ murorum <lb/>partes KL, fornicum &longs;ummus quidem DIE, medius verò <lb/><figure id="fig25"></figure><lb/>KML. Dico, magis cedere pul<lb/>&longs;os muros &longs;ummos circa DE, <lb/>quam in medio circa KL. </s>

<s>E&longs;to ædificium ABGH, cuius <expan abbr="vtrinq;">vtrinque</expan> muri ABCD, <lb/>EFGH, maiorum &longs;ummitates AD, EH, mediæ murorum <lb/>partes KL, fornicum &longs;ummus quidem DIE, medius verò <lb/><figure id="fig25"/><lb/>KML. Dico, magis cedere pul<lb/>&longs;os muros &longs;ummos circa DE, <lb/>quam in medio circa KL. </s>

<s>Sunt <lb/>enim muri BA, GH ceu vectes <lb/>quidam, <expan abbr="quor&umacr;">quorum</expan> extremis par<lb/>tibus à fulcimentis BG remo<lb/>ti&longs;&longs;imis potentia admouetur, <lb/>hoc e&longs;t, ip&longs;ius fornicis DIE ad <lb/>DE in cumbans repul&longs;io; lon<lb/>gior e&longs;t autem pars à <expan abbr="fulcim&emacr;-to">fulcimen<lb/>to</expan> ad potentiam AB, ip&longs;a BK. <lb/></s>

<s>Data igitur paritate potentia<lb/>rum plus operabitur ea quæ in <lb/>D, illa quæ K. facilius crgo re<lb/>pellentur muri in DE quàm in <lb/>KL. </s>

<s>Data igitur paritate potentia<lb/>rum plus operabitur ea quæ in <lb/>D, illa quæ K. facilius crgo re<lb/>pellentur muri in DE quàm in <lb/>KL. </s>

<s>Alia quo que ratio intercedit, &longs;iquidem pondus muri <lb/>&longs;uperioris ADK, premens inferiorem murum KBC, cum <lb/>&longs;ua grauitate firmiorem, & pul&longs;ionibus minus obnoxium <lb/>reddit. </s>

<s>Difficilius enim propellitur id quod graue e&longs;t <expan abbr="quã">quam</expan> <lb/>quod leue, vt nos quæ&longs;tione 10. demon&longs;trauimus. </s>

<s>QVÆSTIO XVII.</s>

<s>QVÆSTIO XVII.</s>

<s><emph type="italics"/>Quærit Ari&longs;toteles, Cur paruo exi&longs;tente cuneo magna &longs;cindantur <lb/>pondera & corporum moles, validaque, fiat impre&longs;&longs;io?<emph.end type="italics"/></s>

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<s>Etenim quæ&longs;tio hæc <pb pagenum="115"/>clari&longs;&longs;imorum virorum ingenia magnopere fatigauit. </s>

<s>Ex <lb/>quibus Ari&longs;toteles inter veteres, Guid. </s>

<s>Ex <lb/>quibus Ari&longs;toteles inter veteres, Guid. Vbald. inter re<lb/>centiores ad vectis naturam (ne quid in Mechanicis ad <lb/>vectem non reduci putaretur) cuneum ip&longs;um trahere co<lb/><figure id="fig26"/><lb/>nati &longs;unt. </s>

<s>Vbald. </s>

<s>inter re<lb/>centiores ad vectis naturam (ne quid in Mechanicis ad <lb/>vectem non reduci putaretur) cuneum ip&longs;um trahere co<lb/><figure id="fig26"></figure><lb/>nati &longs;unt. </s>

<s>Nos autem pro <lb/>veritate certantes, &longs;i in <lb/>horum &longs;ententiam vltrò <lb/>non tran&longs;ierimus, multa <lb/>venia digni à non iniquo <lb/>iudice exi&longs;timabimur. </s>

<s>A<lb/>ri&longs;totelis mentem clarè <lb/>& fusè explicat G. V<lb/>bald. </s>

<s>in Mechan. </s>

<s>Nos autem pro <lb/>veritate certantes, &longs;i in <lb/>horum &longs;ententiam vltrò <lb/>non tran&longs;ierimus, multa <lb/>venia digni à non iniquo <lb/>iudice exi&longs;timabimur. </s>

<s>A<lb/>ri&longs;totelis mentem clarè <lb/>& fusè explicat G. V<lb/>bald. in Mechan. vbi de <lb/>Cuneo peculiariter a<lb/>git. </s>

<s>vbi de <lb/>Cuneo peculiariter a<lb/>git. </s>

<s>E&longs;to igitur &longs;cindendum quippiam ABCD, Cuneus <lb/>EFG, cuius pars HFI &longs;ci&longs;&longs;uræ in&longs;erta HI, facta igitur vali<lb/>da percu&longs;&longs;ione in EG, fiet vt cum EG fuerit in NO, H &longs;it v<lb/>bi N, A vbi P, itemque I vbi O, D verò vbi Q & facta erit <lb/>&longs;ci&longs;&longs;io NSO, toti nempe cuneo EFG, æqualis. </s>

<s>Vultigitur <lb/>Ari&longs;toteles, duos in cunco vectes con&longs;iderari EF, GF, quo<lb/>rum alterius, nempe EF, fulcimentum &longs;it in H, pondus ve<lb/>ro in F; alterius autem, hoc e&longs;t, GF fulcimentum quidem <lb/>&longs;it in I, pondus verò itidem &longs;it in F. </s>

<s>His nequaquam con<lb/>&longs;entiens G. Vbald. aliam viam ingreditur. </s>

<s>His nequaquam con<lb/>&longs;entiens G. Vbald. </s>

<s>aliam viam ingreditur. </s>

<s>Ait enim EHF <lb/>vectes quidem e&longs;&longs;e, quorum commune fulcimentum F, <lb/>potentias verò mouentes in EG. </s>

<s>Ait enim EHF <lb/>vectes quidem e&longs;&longs;e, quorum commune fulcimentum F, <lb/>potentias verò mouentes in EG. </s>

<s>Pondera vtrinque inter <lb/>fulcimenta & potentias, vbi HI, idemque; e&longs;&longs;e ac &longs;i EF, GF, <lb/><gap/>eor&longs;um à cuneo con&longs;iderati in puncto F, adinuicem fulti <lb/>atque di&longs;tracti pondera pellerent H in NP, I verò in O, <lb/><expan abbr="q.">que</expan> Verumenimuerò quoniam cunei angulus non muta<lb/>tur, nec vertex ip&longs;e centri vllum pror&longs;us præbet v&longs;um, nec <lb/>eius latera vtrinque di&longs;tracta ad contrarias partes didu<pb pagenum="116"/>cuntur, vectes in cuneo hoc pacto con&longs;iderare videtur à <lb/>veritate alienum. </s>

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<s>Solutio igitur i&longs;ta mco iudicio, tanto Philo&longs;o<lb/>pho pror&longs;us videtur indigna. </s>

<s>Porrò G. Vbald. </s>

<s>Porrò G. Vbald. ijs quæ de diuaricatis vectibus in <lb/>medium adduxerat non acquie&longs;cens alias quærit cau&longs;&longs;as, <lb/>cur cuneus minoris anguli validiùs &longs;cindat. </s>

<s>ijs quæ de diuaricatis vectibus in <lb/>medium adduxerat non acquie&longs;cens alias quærit cau&longs;&longs;as, <lb/>cur cuneus minoris anguli validiùs &longs;cindat. </s>

<s>Idque; ex quo<lb/>dam lemmate demon&longs;trare conatur, figura autem eius ita <lb/>ferè &longs;e habet. </s><figure></figure>

<s>Idque; ex quo<lb/>dam lemmate demon&longs;trare conatur, figura autem eius ita <lb/>ferè &longs;e habet. </s><figure/>

<s>E&longs;to cuneus ABC, <lb/>item alius DEF. <expan abbr="Dem&omacr;-&longs;trauit">Demon<lb/>&longs;trauit</expan> igitur ex a&longs;&longs;um<lb/>pto, quo acutior fuerit <lb/>angulus BIM, eo facilius <lb/>pondera moueri, & ideo <lb/>facilius ceu vecte AB <lb/>moueri pondus I quàm <lb/>vecte DE pondus <expan abbr="q.">que</expan> In<lb/>geniosè quidem. </s>

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<s>Ex quibus o<lb/>mnibus, nî fallimur, clarè patet, curacutiores angulo cu<lb/>nei obtu&longs;ioribus facilius &longs;cindant, quæ quidem ratio lon<lb/>gè ab ea di&longs;tat, ex qua cæteri ferè omnes Cuneum ad ve<lb/>ctis naturam referre hactenus contenderunt. </s>

<s>Cæterùm vtramque eorum quos diximus, <expan abbr="cuneor&umacr;">cuneorum</expan> <lb/>&longs;peciem &longs;olerti&longs;&longs;ima cognouit Natura, & ideo quoniam <lb/>res vel contu&longs;ione vel perforatione, vel &longs;ecatione con&longs;i<lb/>ciuntur, triplicem dentium qualitatem dentatis animali-<pb pagenum="119"/><figure id="fig27"></figure><lb/>bus dedit, Molares, <lb/>qui & Maxillares ap<lb/>pellantur, quibus <lb/>cibus contunditur, <lb/>Canini, quibus fit <lb/>perforatio, Anterio<lb/>res, quibus cibus <lb/>&longs;cinditur, quos ideo <lb/><foreign lang="greek">temnikou\s</foreign>, id e&longs;t, &longs;ecan<lb/>tes appellant Graeci. </s>

<s>Cæterùm vtramque eorum quos diximus, <expan abbr="cuneor&umacr;">cuneorum</expan> <lb/>&longs;peciem &longs;olerti&longs;&longs;ima cognouit Natura, & ideo quoniam <lb/>res vel contu&longs;ione vel perforatione, vel &longs;ecatione con&longs;i<lb/>ciuntur, triplicem dentium qualitatem dentatis animali-<pb pagenum="119"/><figure id="fig27"/><lb/>bus dedit, Molares, <lb/>qui & Maxillares ap<lb/>pellantur, quibus <lb/>cibus contunditur, <lb/>Canini, quibus fit <lb/>perforatio, Anterio<lb/>res, quibus cibus <lb/>&longs;cinditur, quos ideo <lb/><foreign lang="greek">temnikou\s</foreign>, id e&longs;t, &longs;ecan<lb/>tes appellant Graeci. </s>

<s>Molares KK, <lb/>CaniniL, L, Temni<lb/>ci &longs;eu &longs;ecantes M. </s>

<s>Molares KK, <lb/>CaniniL, L, Temni<lb/>ci &longs;eu &longs;ecantes M. </s>

<s>Cuneus orbicularis lineari&longs;queue AB, in <lb/>quo axis linea e&longs;t, ad cuius naturam accedit AB cuneus <lb/>&longs;uperficialis CD, accedens ad &longs;uperficiei naturam, quam <lb/>vitro imaginamur EFGD, in aciem cunei de&longs;inentem, <lb/>GD, Lateratus lineari&longs;que cuneus, clauus HI. </s>

<s>Cunei autem omnes dupliciter &longs;unt efficaces, vel e<lb/>nim malleo, vt in ijs fit, quibus lìgna &longs;cin duntur & &longs;calpris <lb/>fieri &longs;olet, adiguntur, vel impul&longs;u & pre&longs;&longs;ione, vt in gla<lb/>dijs fit, pugionibus, cælatorum &longs;calpris, &longs;ubulis, & cæteris <lb/>eiu&longs;modi. </s>

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<s>Multa hîc addere potui&longs;&longs;emus ad Cochleam &longs;pe<lb/>ctantia, quippe quòd Cochlea cuneus &longs;it Cylindro inuo<lb/>lutus, qui quidem ad mallei, &longs;ed vectis virtute &longs;ibi adiun<lb/>ctâ, validi&longs;&longs;imè operatur, & &longs;excentis in&longs;eruit v&longs;ibus. </s>

<s>Ve<lb/>runtamen cùm de hac &longs;pecie egregiè di&longs;&longs;erat G. Vbaldus, <pb pagenum="120"/>con&longs;ultò hanc di&longs;putationem omittimus; idque hac quo<lb/>que de cau&longs;&longs;a, quod nihil de cochlea, ac &longs;i eam non noui&longs;<lb/>&longs;et, locutus &longs;it Ari&longs;toteles. </s>

<s>Po&longs;&longs;umus autem in actu &longs;ci&longs;&longs;ionis, quæ cuneo fit, a<lb/>liâ tamen ratione vectem con&longs;iderare, nempe non in cu<lb/>neo quidem, &longs;ed in ip&longs;a re quæ &longs;cinditur. </s><figure></figure>

<s>E&longs;to enim quip<lb/>piam &longs;ci&longs;&longs;ile ABCD, <lb/>cui alteri extremita<lb/>tum, puta BD, cuneus <lb/>adigatur EFG, <expan abbr="fiatq;">fiatque</expan> <lb/>&longs;ci&longs;&longs;io per longitudi<lb/>nem &longs;ecundum <expan abbr="lineã">lineam</expan> <lb/>EH. facta igitur ex <lb/>cunei ingre&longs;&longs;u <expan abbr="parti&umacr;">partium</expan> &longs;eparatione B, expelletur in I, D ve<lb/>rò in K. fient igitur materiæ &longs;ci&longs;&longs;æ partes AIBH, CKDH, <lb/>ceu duo vectes, quorum hinc inde in corpore ip&longs;o fulci<lb/>menta L, M potentiæ vtrinque dilatantes BD, pondus ve<lb/>rò materiæ re&longs;i&longs;tentia, in &longs;eparationis loco vbi N. </s>

<s>Duca<lb/>tur NL, quanto itaque BN maiorem habebit proportio<lb/>nem ad LN, eo faciliùs re&longs;i&longs;tentia quæ in N, &longs;uperabitur. <lb/></s>

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<s>à <lb/>principio enim difficultatem &longs;entimus, deinde ex ea <expan abbr="quã">quam</expan> <lb/>diximus proportionc &longs;ci&longs;&longs;io ip&longs;a fit apprime facilis. </s>

<s>Vti-<pb pagenum="121"/>mur etiam vecte cuneato ad &longs;cindendum & aperiendum: <lb/>adacto enim &longs;ci&longs;&longs;uræ cuneo, idqueue manu malleoue, tum <lb/>ab altera extremitate pre&longs;&longs;o, valida fit ex vectis vi <expan abbr="c&omacr;tinui">continui</expan> <lb/><figure id="fig28"></figure><lb/>corporis &longs;eparatio. </s>

<s>Ma<lb/>teria &longs;ci&longs;&longs;ilis AB <expan abbr="&longs;calpr&umacr;">&longs;calprum</expan> <lb/>ceu vectis cuneatus CD, <lb/>cuius fulcimentum, E, <lb/>pondus verò vbi C, po<lb/>tentia vbi D, quo ca&longs;u <lb/>quo maior e&longs;t proportio <lb/>DE ad EC, eo e&longs;t ip&longs;a &longs;ci&longs;&longs;io leuior & facilior. </s>

<s>QV AESTIO XVIII.</s>

<s>QV AESTIO XVIII.</s>

<s><emph type="italics"/>Quærit hic Ari&longs;toteles, Cur per Trochleas ab exiguapotentia in<lb/>gentia moueantur pondera?<emph.end type="italics"/></s>

<s>De Trochlea Pappus, & veteres: inter recentiores e<lb/>gregiè admodum, vt omnia examinauit in Mechani<lb/>cis G. Vbaldus. </s>

<s>De Trochlea Pappus, & veteres: inter recentiores e<lb/>gregiè admodum, vt omnia examinauit in Mechani<lb/>cis G. Vbaldus. </s>

<s>Nos tamen interim po&longs;t clari&longs;&longs;imos illos <lb/>viros aliquid quod nouitatem & &longs;ubtilitatem &longs;apiat, de <lb/>no&longs;tro penu promemus. </s>

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<s>Tigna &longs;anè voca&longs;&longs;e videtur ea ligna, quæ à Vitruuio <lb/>Rechami dicuntur, in quibus nempe ip&longs;i in&longs;eruntur orbi<lb/>culi. </s>

<s>Et&longs;i de tignis eiu&longs;mo di aliud quippiam &longs;entire videa<lb/>tur Picolomineus. </s>

<s>Et&longs;i de tignis eiu&longs;mo di aliud quippiam &longs;entire videa<lb/>tur Picolomineus. </s>

<s>Græea lectio pro tignis habet <foreign lang="greek">cu/la</foreign>, id <lb/>e&longs;t, ligna; item vbi Leoniceni ver&longs;io legit, ad &longs;e inuicem <lb/>iunctis, textus habet <foreign lang="greek">snm<gap/>ai/nousin e(autoi_s e)ranti/ws</foreign>, hoc e&longs;t, in<lb/>uicem ex oppo&longs;ito concurrunt. </s>

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<s>Si quis alterum funis principium trahat, ma<lb/>gna trahat pondera, et&longs;i trahens potentia &longs;it exigua? </s>

<s>Nos <lb/>verbis figuram, & figurâ verba ip&longs;a elucidabimus. </s><figure></figure>

<s>Nos <lb/>verbis figuram, & figurâ verba ip&longs;a elucidabimus. </s><figure/>

<s>Sint duo ligna ex oppo&longs;ito concurrentia, <lb/>in quibus Trochleæ, hoc e&longs;t, orbiculi AB, fu<lb/>nis ductarius DABC, cuius alterum caput re<lb/>ligatum e&longs;t ligno trochleæ A, vbi e&longs;t C. </s>

<s>Tro<lb/>chlea A loco &longs;tabili commendata, vbi E. </s>

<s>Tro<lb/>chlea A loco &longs;tabili commendata, vbi E. </s>

<s>Pon<lb/>dus alteri ligno Trochleæ appen&longs;um F. </s>

<s>Pon<lb/>dus alteri ligno Trochleæ appen&longs;um F. </s>

<s>Tra<lb/>cto itaque fune DABC, eleuatur & trahitur <lb/>pondus F. </s>

<s>Tra<lb/>cto itaque fune DABC, eleuatur & trahitur <lb/>pondus F. </s>

<s>Ex quibus clarè patet, <expan abbr="Philo&longs;oph&umacr;">Philo&longs;ophum</expan> <lb/>propo&longs;ui&longs;&longs;e Trochleam duobus tantum orbi<lb/>culis munitam, quod vtique &longs;atis erat ad ex<lb/>plicationem. </s>

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<s>Si enim vectis pars <lb/>quæ à fulcimento ad manum breuior fuerit illâ, quæ à <lb/>fulcimento ad pondus difficilius vecte pondus mouebi<lb/>tur quam manu. </s>

<s>Idem quoque accidet, &longs;i eo modo vecte <lb/>vtamur, quem ob&longs;eruat Guidus Vbald. </s>

<s>Idem quoque accidet, &longs;i eo modo vecte <lb/>vtamur, quem ob&longs;eruat Guidus Vbald. Tract. </s>

<s>Tract. </s>

<s>de Vecte <lb/>prop.

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<s>Si enim, ait, <lb/>vnicâ Trochleâ pondus facile trahitur, id multo validius <lb/>pluribus fiet. </s>

<s>Veruntamen non ab&longs;olutè ex orbiculorum <lb/>multiplicationeid fieriita o&longs;tendemus. </s><figure></figure>

<s>Veruntamen non ab&longs;olutè ex orbiculorum <lb/>multiplicationeid fieriita o&longs;tendemus. </s><figure/>

<s>Sint duæ op<lb/>po&longs;itæ lineae rectae, <lb/>vtpote trabes AB, <lb/>CD, <expan abbr="inuic&emacr;">inuicem</expan> æqui<lb/>di&longs;tantes & ip&longs;æ <lb/>&longs;tabiles: &longs;uperiori <lb/>tres appendantur <lb/>orbiculi ex <expan abbr="p&umacr;ctis">punctis</expan> <lb/>E, F, G, <expan abbr="n&emacr;pe">nempe</expan> ML, <lb/>PQ, TV. inferiori <lb/><expan abbr="aut&emacr;">autem</expan> duobus pun<lb/>ctis IH, nempe <lb/>NO, RS. </s>

<s>Erunti<lb/>gitur invniuer&longs;um <lb/>quinque, indatur pereos funis ductarius KLMNOP <lb/>QRSTVX, ex cuius extremitate pendeat pondus X, <pb pagenum="124"/>Trahatur funis in K. </s>

<s>Erunti<lb/>gitur invniuer&longs;um <lb/>quinque, indatur pereos funis ductarius KLMNOP <lb/>QRSTVX, ex cuius extremitate pendeat pondus X, <pb pagenum="124"/>Trahatur funis in K. </s>

<s>Dico ex multiplicatione <expan abbr="orbiculor&umacr;">orbiculorum</expan>, <lb/>trahentipondus nequaquam minui. </s>

<s>Sint autem orbicu<lb/>lorum diametri, LM, NO, PQ, RS, TV, applicetur poten<lb/>tîa in S. </s>

<s>Sint autem orbicu<lb/>lorum diametri, LM, NO, PQ, RS, TV, applicetur poten<lb/>tîa in S. </s>

<s>Erit igitur ad hoc vt &longs;u&longs;tineat æqualis ponderi X, <lb/>orbiculi enim TV &longs;emidiametri &longs;unt æquales. </s>

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<s>Nihil igitur rebus ita <lb/>di&longs;po&longs;itis, orbiculorum multiplicatio ad facilitatem ope<lb/>ratur. </s>

<s>Alia itaque ratio quærenda e&longs;t, quam non &longs;atis ex<lb/>plica&longs;&longs;e videtur Ari&longs;toteles. </s>

<s>Alia itaque ratio quærenda e&longs;t, quam non &longs;atis ex<lb/>plica&longs;&longs;e videtur Ari&longs;toteles. </s>

<s>Probabimus autem, nullam <lb/>ex &longs;uperioribus orbiculis fieri ponderum imminutionem, <lb/>&longs;ed totam vim in inferioribus con&longs;i&longs;tere. </s>

<s>At nos interim <lb/>quippiam quod ad rem faciat, proponamus. </s><figure></figure>

<s>At nos interim <lb/>quippiam quod ad rem faciat, proponamus. </s><figure/>

<s>E&longs;to punctum A, cuirectæ ap<lb/>pendantur lineæ BAC, diui&longs;æ qui<lb/>dem in A, &longs;it autem lineæ BA caput <lb/>B, ip&longs;ius verò CA caput C. </s>

<s>E&longs;to punctum A, cuirectæ ap<lb/>pendantur lineæ BAC, diui&longs;æ qui<lb/>dem in A, &longs;it autem lineæ BA caput <lb/>B, ip&longs;ius verò CA caput C. </s>

<s>Modò <lb/>intelligantur vnitæ in A, &longs;itqueue vni<lb/>ca linea à puncto A ceu funiculus <lb/>dependens BAC; Appendatur capi<lb/>ti B pondus B. </s>

<s>Modò <lb/>intelligantur vnitæ in A, &longs;itqueue vni<lb/>ca linea à puncto A ceu funiculus <lb/>dependens BAC; Appendatur capi<lb/>ti B pondus B. </s>

<s>Capiti vero C, <expan abbr="p&omacr;dus">pondus</expan> <lb/>C, inter &longs;e æqualia. </s>

<s>Potentia igitur <lb/>in A, duo &longs;u&longs;tinebit pondera BC. <lb/></s>

<s>Potentia igitur <lb/>in A, duo &longs;u&longs;tinebit pondera BC. <lb/></s>

<s>Pondera verò ex æqualitate æque<lb/>ponderabunt. </s>

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<s>Habemus <lb/>igitur ex i&longs;tis ad &longs;u&longs;tinendum pondus ex &longs;uperiori parte <pb pagenum="125"/>appen&longs;um potentiam requiri ip&longs;i ponderi æqualem. </s>

<s>Ani<lb/>mo po&longs;thæc concipiatur alia recta linea DEF, cuius inte<lb/>gra longitudo &longs;i exten deretur, e&longs;&longs;et DE, EF. </s>

<s>Ani<lb/>mo po&longs;thæc concipiatur alia recta linea DEF, cuius inte<lb/>gra longitudo &longs;i exten deretur, e&longs;&longs;et DE, EF. </s>

<s>Appendatur <lb/>in E pondus E æ quale alteri ponderum B vel, C, &longs;int autem <lb/>duæ potentiæ pondus E &longs;u&longs;tinentes D, F. </s>

<s>Appendatur <lb/>in E pondus E æ quale alteri ponderum B vel, C, &longs;int autem <lb/>duæ potentiæ pondus E &longs;u&longs;tinentes D, F. </s>

<s>Vtraque igitur <lb/>dimidium &longs;u&longs;tinebit ponderis E, &longs;ed potentia quæ &longs;u&longs;ti<lb/>nebat pondus B, in C erat ip&longs;i B æqualis, vbi appen&longs;io pon<lb/>deris erat in &longs;uperiori parte in A, hîc autem, vbi appen&longs;io <lb/>e&longs;t in parte in feriori, vtraque potentia dimidium &longs;u&longs;tinet <lb/>appen&longs;i ponderis. </s>

<s>Videmus igitur illam appen&longs;ionem <lb/>quidem pondus nullatenus imminuere, hanc verò pon<lb/>dus ip&longs;um, bifariam diui&longs;um, &longs;u&longs;tinentibus potentijs im<lb/>partiri. </s>

<s>Hæ cin lineis, Mathematicâ v&longs;i ab&longs;tractione, con<lb/>&longs;iderauimus, nunc verò eadem mechanicè perpenda<lb/>mus. </s><figure></figure>

<s>Hæ cin lineis, Mathematicâ v&longs;i ab&longs;tractione, con<lb/>&longs;iderauimus, nunc verò eadem mechanicè perpenda<lb/>mus. </s><figure/>

<s>Sit igitur <lb/>punctum A, vt <lb/>in &longs;e quenti figu<lb/>ra clauus paxil<lb/>lu&longs;ue, cui appen<lb/>&longs;us funiculus <lb/>BAC, & funicu<lb/>li capitibus pon<lb/>dera BC, &longs;it quo<lb/>que anulus D, <lb/>per quem traìe<lb/>ctus funiculus <lb/>EDF. </s>

<s>Anulo au<lb/>tem <expan abbr="c&omacr;iunctum">coniunctum</expan> <lb/>pondus G. </s>

<s>Anulo au<lb/>tem <expan abbr="c&omacr;iunctum">coniunctum</expan> <lb/>pondus G. </s>

<s>His igiturita con&longs;titutis, eadem demon&longs;tra<lb/>buntur quæ &longs;uperius, nempe oportere vt fiat æquilibrium <lb/>B, C, e&longs;&longs;e æqualia, tum potentias, quæ &longs;unt in EF pondus <lb/>G inter eas diui&longs;um &longs;u&longs;tinere. </s>

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<s>Hæc autem agentes reii<lb/>p&longs;ius naturam non mutauerunt, &longs;ed &longs;ibi, vt diximus, ex or<lb/>biculis maximam commoditatem <expan abbr="atq;">atque</expan> facilitatem com<lb/>parârunt. </s>

<s>Ex his principîjs tota Trochlearum ratio pendet, <lb/>quæ tamen alia quoque con&longs;ideratione in idem tenden<lb/>te examinari pote&longs;t, quod quidem fecere veteres, & ip&longs;e, <lb/>qui veteres optim è imitatus e&longs;t, Guid. </s>

<s>Vbaldus. </s>

<s>Vbaldus. </s>

<s>Vidimus vtique nos, à potentia quæ e&longs;t in B, pondus <lb/>par &longs;u&longs;tineri in C, Potentiam autem quæ e&longs;t in E <expan abbr="dimidi&umacr;">dimidium</expan> <lb/>&longs;u&longs;tinere ponderis quod e&longs;t in G. </s>

<s>Nos igiturij&longs;dem in&longs;i<lb/>&longs;tentes adiecta libra, vecteue, bifariam diui&longs;o rem ip&longs;am <lb/>ex &longs;ubiecto diagrammate lucidiorem faciemus. </s>

<s>E&longs;to linea quædam &longs;tabilis ceu trabs horizontiæ<lb/>quedi&longs;tans AB, cui in A funiculus annectatur AC, cuius <lb/>extremum C vecti cuidam alligetur CD, in medio diui&longs;o <lb/>vbi E, tum alteri vectis eiu&longs;dem extremitati D, funiculus <lb/>nectatur DG, & à puncto E pondus appendatur F. puta li<lb/>brarum mille, Tum puncto G in medio vectis HI, funis re<lb/>ligetur DG, & ex altero vectis extremo alligato fune HK <lb/>commendetur lo co &longs;tabili in K, & ab alio capite vectis vbi <lb/>Iad medium vectis MN, vbi L, funis annectatur lL, tum <lb/>ex vectis capite M, funis commendetur MO, loco &longs;tabili <lb/>in O, & alteri capiti N, funis, NP, qui alligetur medio ve<lb/>cti QR in P, & ex Q, funis QS. </s>

<s>Commendetur loco &longs;tabili <lb/>in S, & alteri vectis extremo R funis alligetur RT, cui <lb/>quidem potentia &longs;u&longs;tinens applicetur in T. </s>

<s>Commendetur loco &longs;tabili <lb/>in S, & alteri vectis extremo R funis alligetur RT, cui <lb/>quidem potentia &longs;u&longs;tinens applicetur in T. </s>

<s>Dico igitur, <pb pagenum="127"/><figure id="fig29"></figure><lb/>rebus ita di&longs;po&longs;itis, <lb/>potentiam in T ita <lb/>&longs;e habere ad pondus <lb/>F, vt vnum ad &longs;ex de<lb/>cim, hoc e&longs;t, in pro<lb/>portione e&longs;&longs;e &longs;ub<lb/>&longs;exdecupla. </s>

<s>Dico igitur, <pb pagenum="127"/><figure id="fig29"/><lb/>rebus ita di&longs;po&longs;itis, <lb/>potentiam in T ita <lb/>&longs;e habere ad pondus <lb/>F, vt vnum ad &longs;ex de<lb/>cim, hoc e&longs;t, in pro<lb/>portione e&longs;&longs;e &longs;ub<lb/>&longs;exdecupla. </s>

<s>Sunt <lb/>autem, hic vectes <lb/>quatuor in feriorum <lb/>cubiculorum, loco, <lb/>CD, HI, MN, QR, <lb/>qucrum, centra E, <lb/>G, L, P. quoniam e<lb/>nim A hoc e&longs;t, C, v<lb/>nà cum potentia G, <lb/>hoc e&longs;t, D, &longs;u&longs;tinet <lb/>pondus F alterum, <lb/>ponderis dimidium <lb/>&longs;u&longs;tinebit C, <expan abbr="alter&umacr;">alterum</expan> <lb/>vero D. erunt igitur <lb/>vtrinque librae quin<lb/>gentæ. </s>

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<s>Hactenus igitur nobis i&longs;thæc <lb/>de Trochleæ natura & vi po&longs;t alios, con&longs;idera&longs;&longs;e &longs;it &longs;atis. </s>

<s>QVÆSTIO XIX.</s>

<s>QVÆSTIO XIX.</s>

<s><emph type="italics"/>Dubitat Philo&longs;ophus, Cur &longs;i quis &longs;uper lignum magnam imponat <lb/>&longs;ecurim, de&longs;uperque magnum adijciat pondus, ligni quippiam quod <lb/>cur andum &longs;it, non diuidit; &longs;i verò &longs;ecurim extollens percutiat, illud <lb/>&longs;cindit, cum alioquin multo minus habeat ponder is id quod <lb/>percutit, quam illud quod&longs;uperiacet <lb/>& premit?<emph.end type="italics"/></s>

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<s>Porrò effe<lb/>ctus huius, de quo agitur, di&longs;putatio illuc &longs;pectat, videli<lb/>cet ad cadentium atque proiectorum naturam. </s>

<s>Ad maio<lb/>rem autem rei euidentiam hæc addimus. </s><figure></figure>

<s>Ad maio<lb/>rem autem rei euidentiam hæc addimus. </s><figure/>

<s>E&longs;to libra AB, cu<lb/>ius centrum C, libra<lb/>ta æqualibus ponde<lb/>ribus DE, apponatur <lb/>ponderi E pondus F, <lb/>item ponderi D pon<lb/>dus G ip&longs;i ponderi F <lb/>æquale, æquilibrabit <lb/>itidem, Modò non apponatur &longs;impliciter pondus G &longs;ex <lb/>ex H in lancem A dimittatur, tunc &longs;anè non æquilibrabit, <lb/>&longs;ed libram deprimet. </s>

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<s>Cæterùm cur mallei & &longs;ecuris ictus &longs;it violenti&longs;&longs;i<lb/>mus, ideo fit quod non ex vnico neque duplici, &longs;ed ex tri<lb/>plici grauitate operetur. </s>

<s>E&longs;to enim &longs;ecuris A, cuius manu<lb/>brium AB, brachium vero &longs;ecuri vtentis BC, erit igitur C <pb pagenum="130"/><figure id="fig30"></figure><lb/>locus vbi humero <lb/>brachium iungi<lb/>tur, motus ip&longs;ius <lb/>centrum, attollit <lb/>autem &longs;ecurim is <lb/>qui percutit, & re<lb/>tro ad &longs;capulas re<lb/>ducens totis viri<lb/>bus ex centro C <lb/>&longs;ecurim vibrat, <lb/>portionem circuli <lb/>de&longs;cribens ADE <lb/>ictumqueue faciens <lb/>in E. </s>

<s>E&longs;to enim &longs;ecuris A, cuius manu<lb/>brium AB, brachium vero &longs;ecuri vtentis BC, erit igitur C <pb pagenum="130"/><figure id="fig30"/><lb/>locus vbi humero <lb/>brachium iungi<lb/>tur, motus ip&longs;ius <lb/>centrum, attollit <lb/>autem &longs;ecurim is <lb/>qui percutit, & re<lb/>tro ad &longs;capulas re<lb/>ducens totis viri<lb/>bus ex centro C <lb/>&longs;ecurim vibrat, <lb/>portionem circuli <lb/>de&longs;cribens ADE <lb/>ictumqueue faciens <lb/>in E. </s>

<s>Vires igitur acquirit &longs;ecuris, tum ex naturali grauita<lb/>te, cadens ex D, in E, tum ex proprio pondere, tum etiam <lb/>ex violentia eidem à percutiente impre&longs;&longs;a. </s>

<s>Fiunt autem <lb/>motus tam naturalis quàm violentus eo validiores, quo <lb/>maius e&longs;t &longs;patium, quo res mota mouetur, idqueue praecipuè <lb/>cum violentia ip&longs;am &longs;ecundat naturam. </s>

<s>Itaque maior fit <lb/>ictus in E quàm in F, & in F maior quàm in D. </s>

<s>Itaque maior fit <lb/>ictus in E quàm in F, & in F maior quàm in D. </s>

<s>Item violen<lb/>tius feriret percutiens, &longs;imanubrium e&longs;&longs;et longius, puta <lb/>BG. </s>

<s>Item violen<lb/>tius feriret percutiens, &longs;imanubrium e&longs;&longs;et longius, puta <lb/>BG. </s>

<s>Tunc enim maior e&longs;&longs;et circulus GH, & motus tum <lb/>prolixior, tum velocior. </s>

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<s>Certè va<lb/>lidius, & certius fieri &longs;ci&longs;&longs;ionem ex cuneo & malleo, ea ra<lb/>tio e&longs;t, quod cuneus adactus, nec inde remotus eam inte <lb/>rim &longs;eruat, quam antea fecerat partium &longs;eparationem, <pb pagenum="131"/>quod quidem &longs;ecuri non accidit, quæ adacta ad nouam <lb/>percu&longs;&longs;ionem faciendam extrahitur. </s>

<s>Hoc etiam con&longs;ideramus, &longs;ecuris in circulo motum, <lb/>ex A in D, e&longs;&longs;e videndum, id e&longs;t, non &longs;ecundum naturam, <lb/>&longs;ur&longs;um enim fertur quod e&longs;t graue, ex D verq in F <expan abbr="mixt&umacr;">mixtum</expan>: <lb/>magis autem ad naturalem accedere qui fit ex F in E. </s>

<s>Tar<lb/>dior ergo ex A in D, velocior ex D, in F, veloci&longs;&longs;imus ex F <lb/>in E; quæ dam quæ ad hanc rem faciunt, egregiè con&longs;ide<lb/>rat Guid, Vbald. </s>

<s>Tar<lb/>dior ergo ex A in D, velocior ex D, in F, veloci&longs;&longs;imus ex F <lb/>in E; quæ dam quæ ad hanc rem faciunt, egregiè con&longs;ide<lb/>rat Guid, Vbald. in calce Tractatus, De Cuneo; ip&longs;um <lb/>con&longs;ule. </s>

<s>in calce Tractatus, De Cuneo; ip&longs;um <lb/>con&longs;ule. </s>

<s>Ad hæc &longs;uccurrit nobis pulcherrima quæ&longs;tio. </s>

<s>Du<lb/>bitari enim pote&longs;t, vtrumictus ex en&longs;e e&longs;ficacior &longs;it à par<lb/>te quæ e&longs;t circa aciem, aut circa medium en&longs;em, vel pro<lb/>pe manubrium capulumue; etenim hinc inde &longs;unt ra<lb/>tiones. </s>

<s>E&longs;to quidem en&longs;is AB, cuius capulus A, &longs;piculum ve <lb/>rò B, centrum grauitatis C, pars capulo proxima D. </s>

<s>E&longs;to quidem en&longs;is AB, cuius capulus A, &longs;piculum ve <lb/>rò B, centrum grauitatis C, pars capulo proxima D. </s>

<s>Libra<lb/>to itaque gladio tres fiunt circulorum portiones BE, CF, <lb/>DG, quæritur quo loco ictus &longs;it validior, nempe in E, in F, <lb/>velin G. </s>

<s>Libra<lb/>to itaque gladio tres fiunt circulorum portiones BE, CF, <lb/>DG, quæritur quo loco ictus &longs;it validior, nempe in E, in F, <lb/>velin G. </s>

<s>Videtur validiorem futurum in E, quippe quod <lb/>ex maiori &longs;emidiametro AB, maioris &longs;it circuli portio BE, <lb/>& ideo velociormotus ex B in E. </s>

<s>Videtur validiorem futurum in E, quippe quod <lb/>ex maiori &longs;emidiametro AB, maioris &longs;it circuli portio BE, <lb/>& ideo velociormotus ex B in E. </s>

<s>Contra efficaciorem <lb/>futurum apparet in F, propterea quod ibi ex centro C to<lb/>tius fiat grauitatis impre&longs;&longs;io, fieri autem validi&longs;&longs;imum in <lb/>G, licetibi motus &longs;it tardior inde videtur, quod &longs;icon&longs;ide<lb/>retur en&longs;is vt vectis, cuius fulcim entum e&longs;t A, potentia <lb/>premens in B, ponderis vero loco re&longs;i&longs;tentia rei quæ per<lb/>cutitur in D. </s>

<s>Maior e&longs;t autem proportio BA, ad AD, quam <lb/>BA ad AC, & ideo violentior fiet pre&longs;&longs;io ex ictu in D, <expan abbr="quã">quam</expan> <lb/>in C. </s>

<s>Maior e&longs;t autem proportio BA, ad AD, quam <lb/>BA ad AC, & ideo violentior fiet pre&longs;&longs;io ex ictu in D, <expan abbr="quã">quam</expan> <lb/>in C. </s>

<s>Hi&longs;ce hoc pacto con&longs;ideratis, putarem ictum effica<lb/>ciorem fieri in F ex medio C, quam ex extremis & oppo<lb/>&longs;itis partibus EG. </s>

<s>Hi&longs;ce hoc pacto con&longs;ideratis, putarem ictum effica<lb/>ciorem fieri in F ex medio C, quam ex extremis & oppo<lb/>&longs;itis partibus EG. </s>

<s>Licet enim in B velocitas &longs;it maior, dee&longs;t <lb/>ibi pondus. </s>

<s>Si enim en&longs;is iterum vt vectis con&longs;ideretur, e<pb pagenum="132"/>runt AB. duo fulcimenta &longs;u&longs;tinentía pondus in C, vbi gra<lb/>uitatis e&longs;t centrum. </s>

<s>Si igitur paria fuerint &longs;patia BC, CA, <lb/><figure id="fig31"></figure><lb/>in B erit dìmidium <lb/>ponderis C, quantum <lb/>ergo velocitate præ<lb/>ualetictus in B, <expan abbr="tant&umacr;">tantum</expan> <lb/>ponderis amittit. </s>

<s>Si igitur paria fuerint &longs;patia BC, CA, <lb/><figure id="fig31"/><lb/>in B erit dìmidium <lb/>ponderis C, quantum <lb/>ergo velocitate præ<lb/>ualetictus in B, <expan abbr="tant&umacr;">tantum</expan> <lb/>ponderis amittit. </s>

<s>D <lb/>verò plus quidem de <lb/>pondere participat, <lb/>&longs;ed velocitatis habet <lb/>minimum, in C verò <lb/>velocitas e&longs;t medio<lb/>cris, tota tamen ip&longs;ius <lb/>ex grauitatis centro <lb/>ponderis fit impre&longs;<lb/>&longs;io. </s>

<s>Quidam, quod huc pertinet, vt ex acieip&longs;a quæ lon<lb/>gius à capulo abe&longs;t, violenti&longs;&longs;imum facerent ictum, Ar<lb/>gentum viuum, quod &longs;ui naturâ graui&longs;&longs;imum quidem e&longs;t <lb/>& mobili&longs;&longs;imum in canali à manubrio ad verticem exca<lb/>uato infundunt, quo in gladij de&longs;cen&longs;u ad verticem velo<lb/>ci&longs;&longs;imè delato illuc transfert grauitatem totam, quare <lb/>tum velocitate tum grauitate concurrentibus ictus fit <lb/>violenti&longs;&longs;imus & longè validi&longs;&longs;imus. </s>

<s>QVAESTIO XX.</s>

<s>QVAESTIO XX.</s>

<s><emph type="italics"/>Dubitatur, Cur &longs;tatera qua carnes ponderantur, paruo appendicu<lb/>lo, magnatrutinet onera, cum alioqui tota, dimidiata exi&longs;tat <lb/>libra, altera vero parte &longs;ola&longs;it <lb/>&longs;tatera?<emph.end type="italics"/></s>

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<s>Ait igitur, appendiculum licet parui <expan abbr="p&omacr;-deris">pon<lb/>deris</expan> &longs;it, ideo maiori ponderi virtute æquari, quod lon<lb/>gius à centro, hoc e&longs;t, ab ip&longs;o fulcimento &longs;i&longs;tatur. </s>

<s>quic<lb/>quid tamen &longs;it, &longs;tateram e&longs;&longs;e vectem, res e&longs;t explorati&longs;<lb/>&longs;ima. </s><figure></figure>

<s>quic<lb/>quid tamen &longs;it, &longs;tateram e&longs;&longs;e vectem, res e&longs;t explorati&longs;<lb/>&longs;ima. </s><figure/>

<s>E&longs;to igitur &longs;tatera AB, <lb/>cuius appendiculum cur<lb/>rens F, fulcimentum cen<lb/>trumue C, lanx quæ cate<lb/>na &longs;u&longs;penditur E &longs;patium <lb/>à loco fulcimenti ad ap<lb/>pendiculum CF. quod ve<lb/>rò à fulcimento ad cate<lb/>nam, ex qua lanx appen<lb/>ditur AC. </s>

<s>Intelligatur autem & aliud fulcimentum D, &longs;it<lb/>queue maius &longs;pacium AD, quam AC. </s>

<s>Intelligatur autem & aliud fulcimentum D, &longs;it<lb/>queue maius &longs;pacium AD, quam AC. </s>

<s>Porrò ita &longs;e habeat <lb/>pondus in E ad appendiculi F pondus, vt CF &longs;patium, ad <lb/>&longs;patium AC, quo ca&longs;u &longs;eruata, permutatim, ponderum & <lb/>brachiorum proportione, fiet ae quilibrium. </s>

<s>Si autem pon<lb/>deribus ita con&longs;titutis iterum &longs;u&longs;pendatur in D, non fiet <lb/>æquilibrium, propterea quod minor &longs;it proportio DF ad <lb/>DA, ea quæ e&longs;t FC ad CA. </s>

<s>Minor ergo e&longs;t proportio FD <lb/>ad DA, quam ponderis E ad pondus F, & idcirco facta <lb/>&longs;u&longs;pen&longs;ione præualebit pondus E ponderi F. </s>

<s>Minor ergo e&longs;t proportio FD <lb/>ad DA, quam ponderis E ad pondus F, & idcirco facta <lb/>&longs;u&longs;pen&longs;ione præualebit pondus E ponderi F. </s>

<s>Ita que vt it e<lb/>rum fiat æquilibrium, nece&longs;&longs;e e&longs;t <expan abbr="iter&umacr;">iterum</expan> proportiones bra<lb/>chiorum &longs;eu &longs;patiorum proportionibus ponderum æqua<lb/>re. </s>

<s>Transferatur igitur (lancis interim immoto pondeie) <lb/>ip&longs;um appendiculum in B, fiatque vt FC ad CA, ita BD ad <lb/>DA. </s>

<s>Transferatur igitur (lancis interim immoto pondeie) <lb/>ip&longs;um appendiculum in B, fiatque vt FC ad CA, ita BD ad <lb/>DA. </s>

<s>Stabitautem iterum &longs;tatera ad eam redacta quam <pb pagenum="134"/>diximus brachiorum & ponderum permutatam propor<lb/>tionem. </s>

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<s>Rectè <lb/>igitur dicebat Philo&longs;ophus, in &longs;tatera plures e&longs;&longs;e libras, <lb/>quanquam & ea quoque de cau&longs;&longs;a dici po&longs;&longs;it, quod, quot <lb/>&longs;unt appen diculi, è locoin locum translationes, totidem <lb/>ex proportionum variatione fiant libræ. </s>

<s>Et hoc quidem <lb/>&longs;en&longs;i&longs;&longs;e videtur Ari&longs;toteles. </s><figure></figure>

<s>Et hoc quidem <lb/>&longs;en&longs;i&longs;&longs;e videtur Ari&longs;toteles. </s><figure/>

<s>Po&longs;&longs;emus & alio <lb/>modo &longs;tatera vti, nempe <lb/>&longs;tabili appendiculo, mo<lb/>bili autem fulcimento. <lb/></s>

<s>E&longs;to enim &longs;tatera AB, <lb/>cuius lanx C appen&longs;a in <lb/>A, appendiculum verò <lb/>&longs;tabile D, appen&longs;um in <lb/>B, Apponatur ip&longs;i l&acedil;nci <lb/>C, pondus E. </s>

<s>Vnicum ergo fiet corpus CEABD con&longs;tans <lb/>ex lance, libra & ponderibus. </s>

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<s>Ex <lb/>illo autem inuento &longs;i corpus totum appendatur, partes æ<lb/>queponderabunt. </s>

<s>Appendatur autem, puta in G, &longs;it <expan abbr="aut&emacr;">autem</expan> <lb/>grauitatis centrum in H. </s>

<s>Appendatur autem, puta in G, &longs;it <expan abbr="aut&emacr;">autem</expan> <lb/>grauitatis centrum in H. </s>

<s>Quoniam igitur He&longs;t extra ful<lb/>cimentum G, declinabit &longs;tateræ pars GA, centro G per <pb pagenum="135"/>circuli portionem Hl, à centro grauitatis in ip&longs;a de&longs;cen<lb/>&longs;ione de&longs;criptam. </s>

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<s>Hicautem <lb/>modusideo non e&longs;t in v&longs;u, quod mole&longs;tum &longs;it libram &longs;eu <lb/>&longs;tateram cum ponderibus vltro citroqueue transferre, quæ <lb/>difficultas commodè appendiculi mobilitate vitatur. </s>

<s>QVAESTIO XXI.</s>

<s>QVAESTIO XXI.</s>

<s><emph type="italics"/>Quæritur, Cur facilius dentes extrahunt Chirurgi, denti forcipis <lb/>onere adiecto, quam &longs;i&longs;ola manu vtantur?<emph.end type="italics"/></s>

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<s>Hoc igitur ad ex<lb/>tractionem vtuntur^{**}, vt facilius moueant. </s>

<s>Figuram hoc <lb/>pactto proponit Philo&longs;ophus. </s><figure></figure>

<s>Figuram hoc <lb/>pactto proponit Philo&longs;ophus. </s><figure/>

<s>E&longs;to dentiforcipis alterum <lb/>quidem extremum vbi A, alte<lb/>rum autem quod extrahit B, ve<lb/>ctis vbi ADF, alter vectis, vbi <lb/>BCE, fulcimentum verò CGD <lb/>connexio vbi G. </s>

<s>E&longs;to dentiforcipis alterum <lb/>quidem extremum vbi A, alte<lb/>rum autem quod extrahit B, ve<lb/>ctis vbi ADF, alter vectis, vbi <lb/>BCE, fulcimentum verò CGD <lb/>connexio vbi G. </s>

<s>Densautem pondus: vtroque igitur ve<lb/>cte B, & F &longs;imul comprehendentes mouent, Hæcille. </s>

<s>Densautem pondus: vtroque igitur ve<lb/>cte B, & F &longs;imul comprehendentes mouent, Hæcille. </s>

<s>At<lb/>tamen rem ip&longs;am &longs;ubtilius con&longs;iderantibus aliter videtur <lb/>habere, acip&longs;e a&longs;&longs;erat. </s>

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<s>Dicimus igitur, tum dentem ip&longs;um, tum dentifor<lb/>cipem vectes e&longs;&longs;e, varia tamen ratione & &longs;atis &longs;ane diuer<lb/>&longs;a. </s>

<s>Dens enim fit vectis eius nempe naturæ quæ fulcimen<lb/>tum habet in angulo, quo ca&longs;u ip&longs;ius Dentiforcipis <expan abbr="parti&umacr;">partium</expan>, <lb/>quibus Dens apprehenditur, ea quæ longior e&longs;t poten<lb/>tiæ mouentis loco &longs;uccedit, breuior vero fulcimentum <lb/>facit, Dentis vero re&longs;i&longs;tentia ponderis vices refert. </s><figure></figure>

<s>E&longs;to enim dens qui<lb/>dem A, cuius diameter <lb/>BC, longitudo v&longs;que ad <lb/>extremas radices CD, <lb/>pars dentiforcipis breui<lb/>or CG, longior BG. </s>

<s>E&longs;to enim dens qui<lb/>dem A, cuius diameter <lb/>BC, longitudo v&longs;que ad <lb/>extremas radices CD, <lb/>pars dentiforcipis breui<lb/>or CG, longior BG. </s>

<s>Fit <lb/>ergo vectis BCD, habens <lb/>&longs;ulcimentum in C. </s>

<s>Fit <lb/>ergo vectis BCD, habens <lb/>&longs;ulcimentum in C. </s>

<s>Den<lb/>teigitur apprehen&longs;o in BC, & manu dentiforcipe ceu ve<lb/>cte ad inferiora compre&longs;&longs;o C, fit fulcimentum centrum<lb/>ue. </s>

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<s>An autem ita &longs;it, alij videant, nobis enim <lb/>digito rem o&longs;tendi&longs;&longs;e fuerit &longs;atis. </s>

<s>QVÆSTIO XXII.</s>

<s>QVÆSTIO XXII.</s>

<s><emph type="italics"/>Hîc quærit Ari&longs;toteles, Cur nuces ab&longs;que ictu facile confringuntur <lb/>in&longs;trumentis quæ ad eum faciunt v&longs;um, & hoc licet multum aufe<lb/>ratur virium, ce&longs;&longs;ante motu & violentia, quod accidit dum mal<lb/>leo confringuntur. </s>

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<s>ma<lb/>ius verò quod à vertebra ad extremitates, quæ confrin<lb/>gentis manu comprimuntur. </s>

<s>Ait igitur, & id quam oppo<lb/>fite, vim ex vectibus ictus loco &longs;uccedere & idem operari. </s><figure></figure>

<s>Ait igitur, & id quam oppo<lb/>fite, vim ex vectibus ictus loco &longs;uccedere & idem operari. </s><figure/>

<s>E&longs;to igitur in &longs;trumentum, <lb/>de quo agimus CDBF, ex duo<lb/>bus vectibus con&longs;tans, quorum <lb/>alter CAF, alter vero DAB ver<lb/>tebra &longs;eu connexio A locus v<lb/>bi nux frangitur K, manubria <lb/>vero BF. quo igitur prolixiores <lb/>erunt AB, AF, breuiores vero ACAD, violentius fiet <expan abbr="c&omacr;-fractio">con<lb/>fractio</expan>. </s>

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<s>At talis e&longs;t <lb/>angulus qui fit in in &longs;trumento, cum partes vectis à verte<lb/>bra adnucem fuerint breuiores. </s>

<s>magìs ergo dilatantur <lb/>vectes, & magis dilatati magis comprimuntur, magis au<lb/>tem compre&longs;li validius frangunt, quod dixerat Ari&longs;to<lb/>teles. </s>

<s>magìs ergo dilatantur <lb/>vectes, & magis dilatati magis comprimuntur, magis au<lb/>tem compre&longs;li validius frangunt, quod dixerat Ari&longs;to<lb/>teles. </s>

<s>Cæterum & illud quod &longs;cribit, ex grauiori & durio<lb/>ri materia in&longs;trumentum citius fractionem facere, quam <lb/>ex leuiori & minus dura, ex parte quidem materiæ verum <lb/>e&longs;t, nec pertinet ad proportionem, quæ &longs;ane in <expan abbr="huiu&longs;mod&imacr;">huiu&longs;modim</expan> <lb/>in&longs;trumentis formæ ferè habent rationem. </s>

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<s>Sunt autem &longs;imilia in&longs;trumentis <lb/>illis, quibus figuli cretaceas pilas ad chirobali&longs;tarum v&longs;um <lb/>facere & efformare con&longs;ueuerunt. </s>

<s>QVÆSTIO XXIII.</s>

<s>QVÆSTIO XXIII.</s>

<s>Pvlcherrimam proponit hoc loco Philo&longs;ophus con<lb/>templationem, eamque ad mixtos motus <expan abbr="pertin&emacr;tem">pertinentem</expan>. <lb/></s>

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<s>Difficile hoc intellectu prima fronte, & &longs;ane admi<lb/>rabile, itaque in tentam con templationem requirit. </s>

<s>Nos <lb/>primo cum Ari&longs;totele, rem totam explicabimus, tum ali<lb/>quid forta&longs;&longs;e non p&oelig;nitendum no&longs;tro de promptuario <lb/>proferemus. </s><figure></figure>

<s>E&longs;to itaque Rhombus ABCD, <lb/>cuius latera AB, BD, DC, CA, diame<lb/>trorum maior AD, minor BC, &longs;ecan<lb/>tes &longs;e inuicem in puncto &longs;eu figuræ <lb/>centro K. </s>

<s>E&longs;to itaque Rhombus ABCD, <lb/>cuius latera AB, BD, DC, CA, diame<lb/>trorum maior AD, minor BC, &longs;ecan<lb/>tes &longs;e inuicem in puncto &longs;eu figuræ <lb/>centro K. </s>

<s>Sunt <expan abbr="aut&emacr;">autem</expan> ex ip&longs;ius Rhom<lb/>binatura latera æqualia & parallela, <lb/>Angulorum vero qui maiori diame<lb/>tro opponuntur, recto maiores, qui <lb/>vero minori minores. </s>

<s>His igitur con<lb/>&longs;ideratis, intelligatur punctum A mo<lb/>ueri peculiari & &longs;im plici motu, per li<lb/>neam AB, ab A ver&longs;us B, & eodem <expan abbr="t&emacr;-pore">ten<lb/>pore</expan> moueri totam lineam AB, ver&longs;us lineam DC, hac ta<lb/>men lege, vt &longs;emper eidem DC feratur parallela, & eius <lb/>alterum extremorum feratur per AC, alterum vero per <lb/>BD, Intelligatur etiam punctum B moueri eodem tem<lb/>pore proprio motu, eoque &longs;implici, per eandem rectam <lb/>BA, ver&longs;us A, & cum eadem, vt dictum e&longs;t, mota; ferri ver-<pb pagenum="141"/>&longs;us CD. </s>

<s>Erunt autem &longs;emper AB puncta in eadem linea <lb/>quæ mouetur, &longs;ibi inuicem ex contrarijs partibus occur<lb/>rentia. </s>

<s>Itaque cum ex duobus motibus &longs;emper propor<lb/>tionalibus, hoc e&longs;t, laterum proportione &longs;eruata, recta <lb/>producatur, vt demon&longs;tratum e&longs;t à principio, vbi produ<lb/>ctio circuli ex Philo&longs;ophi mente e&longs;t declarata, <expan abbr="vtraq;">vtraque</expan> pun<lb/>cta quæ ean dem laterum proportionem &longs;eruantia <expan abbr="mou&emacr;-tur">mouen<lb/>tur</expan>, rectas lineas <expan abbr="produc&emacr;t">producent</expan> A quidem AD, B autem ip&longs;am <lb/>BC. </s>

<s>Feraturigitur A, tum mixto tum &longs;implici motu per <lb/>diametrum AD. </s>

<s>Feraturigitur A, tum mixto tum &longs;implici motu per <lb/>diametrum AD. </s>

<s>B vero quoque tum mixto, tum proprio <lb/>per diametrum BC, &longs;upponitur autem motus omnes &longs;im<lb/>plices, tum punctorum, tum etiam line ae, à qua puncta ip&longs;a <lb/>feruntur, æquali velocitate fieri. </s>

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<s>Erit igitur in E, item li<lb/>neam totam AB eodem tempore pertran&longs;i&longs;&longs;e dimidia op<lb/>po&longs;itarum linearum, ACBD, & e&longs;&longs;e translatam, vbi FKG. <lb/></s>

<s>Quoniam igitur æquali celeritate lineæ AB extremitas <lb/>A, translata e&longs;t in F & A, punctum per eam motum in E, e<lb/>rit &longs;patium AE, æquale &longs;patio AF. </s>

<s>Quoniam igitur æquali celeritate lineæ AB extremitas <lb/>A, translata e&longs;t in F & A, punctum per eam motum in E, e<lb/>rit &longs;patium AE, æquale &longs;patio AF. </s>

<s>Ductis igitur lineis <lb/>FKG, EKH lateribus AB, AC æquidi&longs;tantibus, erit figura <lb/>AEKF. </s>

<s>Rhombus &longs;imilis quidem Rhombo ABCD, recta <lb/>igitur FK æqualis erit oppo&longs;itæ AE. quare A punctum <lb/>translatum erit ex mixto motu in K. </s>

<s>Rhombus &longs;imilis quidem Rhombo ABCD, recta <lb/>igitur FK æqualis erit oppo&longs;itæ AE. quare A punctum <lb/>translatum erit ex mixto motu in K. </s>

<s>Eodem pacto <expan abbr="quoniã">quoniam</expan> <lb/>punctum B. eadem velocitate mouetur ver&longs;us A, & linea <lb/>AB ver&longs;us CD, cum B fuerit in E extremum line æ motæ <lb/>BA, <expan abbr="n&emacr;pe">nempe</expan> B eritin G. æquales ergo &longs;unt BE, BG & Rhom<pb pagenum="142"/>bus EBGK, circa diametrum BKC ip&longs;i Rhombo ABCD <lb/>&longs;imilis, & ideo GK æqualis oppo&longs;itæ BE & BG æqualis <lb/>EK. </s>

<s>Cum ergo B confecerit &longs;patium BE, erit ex mixto <lb/>motu in K, &longs;uperato nempe &longs;patio BK, idque eodem tem<lb/>pore quo A percurrerat totum &longs;patium AK. </s>

<s>Cum ergo B confecerit &longs;patium BE, erit ex mixto <lb/>motu in K, &longs;uperato nempe &longs;patio BK, idque eodem tem<lb/>pore quo A percurrerat totum &longs;patium AK. </s>

<s>Ex æquali i<lb/>gitur &longs;implicium motuum velocitate, in æqualia &longs;patia <lb/>AB puncta pertran&longs;ierunt, quæ res miraculo, cuius dilu<lb/>tio quæritur, præbet occa&longs;ionem. </s>

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<s>Primam dubitatio<lb/>nem hoc pacto &longs;oluit Philo&longs;ophus; A fertur tum proprio, <lb/>tum alieno motu, hoc e&longs;t, line æ AB ver&longs;us oppo&longs;itam par<lb/>tem CD, Itaque cum vterque motus deor&longs;um vergat, mo<lb/>tus fit velocior. </s>

<s>Contra vero B proprio quidem motu fer<lb/>tur ver&longs;us A, hoc e&longs;t, &longs;ur&longs;um, alieno vero, hoc e&longs;t, line æ BA <lb/>ver&longs;us D, hoc e&longs;t, deor&longs;um, qui motus cum inuicem aduer<lb/>&longs;entur, motus ip&longs;e fit tardior, non igitur e&longs;t mirum, A eo<lb/>dem tempore maius &longs;patium pertran&longs;ire quam B. </s>

<s>Hæc &longs;olutio non modo vera videtur, &longs;ed mirabilis <lb/>& ip&longs;omet Philo&longs;opho digni&longs;&longs;ima, cui quidem <expan abbr="temerari&umacr;">temerarium</expan> <lb/>iudicaremus contradicere, nîin genere ver&longs;aremur, in <lb/>quo non probabilia quæruntur, &longs;ed demon&longs;trata, &longs;ed ve<lb/>ra. </s>

<s>Futilem igitur e&longs;&longs;e rationem hanc ip&longs;ius Ari&longs;totelis <lb/>pace, hoc pacto o&longs;tendemus. </s>

<s>E&longs;to quadratum ABCD, cuius diametri ACBD &longs;e<lb/>cantes &longs;e&longs;e in E, moueatur eodem pacto BA, ver&longs;us CD, <pb pagenum="143"/><figure id="fig32"></figure><lb/>item A, ver&longs;us B, & B ver&longs;us A, ita<lb/>que punctum A tum proprio tum <lb/>alieno, hoc e&longs;t lineæ illud <expan abbr="defer&emacr;-tis">deferen<lb/>tis</expan> motu deor&longs;um trudet, hoc e&longs;t, <lb/>ver&longs;us CD. </s>

<s>E&longs;to quadratum ABCD, cuius diametri ACBD &longs;e<lb/>cantes &longs;e&longs;e in E, moueatur eodem pacto BA, ver&longs;us CD, <pb pagenum="143"/><figure id="fig32"/><lb/>item A, ver&longs;us B, & B ver&longs;us A, ita<lb/>que punctum A tum proprio tum <lb/>alieno, hoc e&longs;t lineæ illud <expan abbr="defer&emacr;-tis">deferen<lb/>tis</expan> motu deor&longs;um trudet, hoc e&longs;t, <lb/>ver&longs;us CD. </s>

<s>Motus ergo velocior <lb/>erit motu puncti B, quod lationi<lb/>bus fertur ferè contrarijs, hoc e&longs;t, <lb/>ex B ver&longs;us A &longs;ur&longs;um, cum linea <lb/>autem BA ver&longs;us C deor&longs;um. </s>

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<s>Stante igitur cau&longs;<lb/>&longs;a &longs;equi debui&longs;&longs;et effectus; non &longs;equitur autem, Ari&longs;tote<lb/>lis igitur cau&longs;&longs;a non e&longs;t cau&longs;&longs;a. </s>

<s>Rhombo quoque inuer&longs;o <lb/>idem clarius o&longs;tendemus hoc pacto: Sit Rhombus ABCD, <lb/><figure id="fig33"></figure><lb/>cuius diametri AC, BD &longs;ecan<lb/>tes &longs;e&longs;e in E. </s>

<s>Rhombo quoque inuer&longs;o <lb/>idem clarius o&longs;tendemus hoc pacto: Sit Rhombus ABCD, <lb/><figure id="fig33"/><lb/>cuius diametri AC, BD &longs;ecan<lb/>tes &longs;e&longs;e in E. </s>

<s>Mota igitur linea <lb/>AB ver&longs;us CD, nempe deor&longs;um <lb/>& A quoque deor&longs;um ver&longs;us B, <lb/>contra vero B quidem &longs;ur<lb/>&longs;um ver&longs;us A, deor&longs;um vero <lb/>ver&longs;us C, erit B tardior A, &longs;ed <lb/>contrarium fit, quippe quod <lb/>longior &longs;it BD, per quam mouetur B ip&longs;a AC, per quam <lb/>mouetur A. </s>

<s>His igitur non &longs;atisfacientibus veriorem &longs;i perim<lb/>becillitatem no&longs;tram licuerit, huius effectus cau&longs;&longs;am in<lb/>ue&longs;tigabimus. </s>

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<s>Si autem Rhombus in <lb/>duos &longs;oluatur triangulos, alter diametrorum datur æqua<lb/>lis æqualibus lateribus æquicrurium triangulorum; <expan abbr="itaq;">itaque</expan> <lb/>in i&longs;tis mixti motus per diametros aequeveloces erunt &longs;im<lb/>plicibus, qui per latera longiora, velociores autem illis <lb/>qui per latera breuiora. </s>

<s>His igitur hoc pacto non perfun<lb/>ctoriè con&longs;ideratis, facile ex proprijs cau&longs;&longs;is, nî fallimu<gap/>, <lb/>hocce Ari&longs;totelicum & mirabile Problema &longs;oluitur. </s><pb pagenum="145"/><figure></figure>

<s>E&longs;to enim Rhombus ABDC, <lb/>cuius diameter longior AD maior &longs;it <lb/>tum lateribus, tum etiam altera dia<lb/>metro BC. &longs;ecent autem &longs;e inuicem <lb/>diametri in E. </s>

<s>E&longs;to enim Rhombus ABDC, <lb/>cuius diameter longior AD maior &longs;it <lb/>tum lateribus, tum etiam altera dia<lb/>metro BC. &longs;ecent autem &longs;e inuicem <lb/>diametri in E. </s>

<s>Ducatur queue ip&longs;is AB, <lb/>CD, parallela FG &longs;ecans longiorem <lb/>diametrum AD, in H, breuiorem ve<lb/>ro BC in I. & per I ip&longs;is BD AC paral<lb/>lela ducatur KIL, Cum ergo B mixto <lb/>motu per diametrum BC erit in I & <lb/>A per diametrum AD, mixto &longs;imili<lb/>ter motu erit in H, & quia motus mi<lb/>xti fiunt per diametros, vt dictum e&longs;t, <lb/>vt &longs;e habet AD ad BC, ita AE ad EB, per 15. propol. </s>

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<s>6. AH ad BI. e&longs;t enim <lb/>IH ip&longs;i AB parallela. </s>

<s>Longior e&longs;t autem AH ip&longs;a BI, quip<lb/>pe quod AE longior &longs;it ip&longs;a EB. motus igitur mixtus pun<lb/>cti A per diametrum AD v&longs;que ad H velocior e&longs;t motu B, <lb/>per diametrum BC v&longs;quead I. </s>

<s>Mota igitur linea AB mo<lb/>uebuntur communia eius & diametrorum BC, AD pun<lb/>cta, quibus &longs;ecantur &longs;emper diametrorum proportione <lb/>&longs;eruata. </s>

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<s>Hæc igitur nos circa hoc mirabile Ari&longs;totelicum proble<lb/>ma con&longs;iderare &longs;it &longs;atis. </s>

<s>QVÆSTIO XXIV.</s>

<s>QVÆSTIO XXIV.</s>

<s>Mirabilem aliam quæ&longs;tionem proponit Ari&longs;toteles, <lb/>quæ itidem ad mixtos motus pertinet. </s>

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<s>Satautem erat &longs;i dixi&longs;&longs;et, ita &longs;e habere <lb/>circum ferentias vt &longs;e habent diametri &longs;eu &longs;emidiametri, <lb/>& ideo lineas in rotatione de&longs;criptas inuicem &longs;e habere vt <lb/>diametros. </s>

<s>Ob&longs;curiu&longs;culè, hæc &longs;ua figura o&longs;tendit Ari&longs;to<lb/>teles. </s>

<s>Ob&longs;curiu&longs;culè, hæc &longs;ua figura o&longs;tendit Ari&longs;to<lb/>teles. </s>

<s>Nos igitur claritatem amantibus, no&longs;tram aliquan<lb/>to, nî fallimur, clariorem, proponemus. </s><figure></figure>

<s>Nos igitur claritatem amantibus, no&longs;tram aliquan<lb/>to, nî fallimur, clariorem, proponemus. </s><figure/>

<s>E&longs;to circulus <lb/>maior ABCD, mi<lb/>nor FGHI, circa i<lb/>dem, & commune <lb/><expan abbr="c&emacr;trum">centrum</expan> E. </s>

<s>E&longs;to circulus <lb/>maior ABCD, mi<lb/>nor FGHI, circa i<lb/>dem, & commune <lb/><expan abbr="c&emacr;trum">centrum</expan> E. </s>

<s>Circum<lb/>uoluatur maior ad <lb/>partes D. </s>

<s>Circum<lb/>uoluatur maior ad <lb/>partes D. </s>

<s>Sint <expan abbr="aut&emacr;">autem</expan> <lb/>diametri, maioris <lb/><expan abbr="quid&emacr;">quidem</expan> AEC, BED, <lb/>minoris verò FEH, <lb/>GEI, fitque CD, <lb/>quadrans maioris, <lb/>HI vero minoris circuli. </s>

<s>Moto igitur maiori circulo <expan abbr="&longs;ec&umacr;-dum">&longs;ecun<lb/>dum</expan> ab&longs;idem, cum D fuerit in K erit CK ip&longs;i CD æqualis, <lb/>fietque; DE ex puncto K perpendicularis ip&longs;i CK, eritque vbi <lb/>KO, & quia punctum I e&longs;t in linea DE, erit I facta <expan abbr="quadrã-tis">quadran<lb/>tis</expan> rotatione in linea KO vbi L, centrum vero E in ip&longs;a <lb/>KO, vbi O. </s>

<s>Reuoluto igitur qua drante maioris, & confe<lb/>cto &longs;patio CK minoris circuli quadrans HI conficiet &longs;pa<lb/>tium HL, quod ip&longs;i CK &longs;patio e&longs;t æquale. </s>

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<s>Nec &longs;ecius admirationem facitro<pb pagenum="148"/>tato minori circulo, maiorem vna <expan abbr="circumuolut&umacr;">circumuolutum</expan> lineam <lb/>metiri circumferentiæ minoris circuli æqualem. </s>

<s>Rotetur <lb/>enim minoris circuli quadrans HI per rectam HL. erit i<lb/>gitur punctum I vbi M, æquali exi&longs;tente recta HM, ip&longs;i <lb/>curuæ HI. </s>

<s>Rotetur <lb/>enim minoris circuli quadrans HI per rectam HL. erit i<lb/>gitur punctum I vbi M, æquali exi&longs;tente recta HM, ip&longs;i <lb/>curuæ HI. </s>

<s>Tuncautem facto motu centrum E erit vbi P, <lb/>exi&longs;tente EP, ip&longs;i HM æquali, demittatur autem ex P per <lb/>M, ip&longs;is HL CK perpendicularis PMN. </s>

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<s>Eandemaequalemue potentiam, <expan abbr="aliquã">aliquam</expan> <lb/>magnitudinem tardius quidem mouere, aliquam vero <lb/>celerius. </s>

<s>quod autem natum e&longs;t aptum moueri, tardius <lb/>moueri, &longs;i &longs;imul cum non apto nato moueri, moueatur, <lb/>quam &longs;i &longs;eparatim moueretur, celerius autem &longs;i non &longs;imul <lb/><figure id="fig34"></figure><lb/>cum eo moueatur. </s>

<s>E&longs;to enim corpus A leue <lb/>quidem & aptum natum moueri&longs;ur&longs;um, cui <lb/>connectatur B, aptum natum moueri deor<lb/>&longs;um, Si quis igitur mouere conetur corpus A <lb/>&longs;ur&longs;um difficilius mouebit, & tardius <expan abbr="iunct&umacr;">iunctum</expan> <lb/>nempeip&longs;i B, quam &longs;i ab ip&longs;o e&longs;&longs;et <expan abbr="&longs;ei&umacr;ctum">&longs;eiunctum</expan>. <lb/></s>

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<s>Dicimus enim, nullam materialem <expan abbr="rotã">rotam</expan> circa axem <lb/>eidem affixum, dum rotatur, po&longs;&longs;e eundem locum &longs;eruare, <lb/>ni&longs;i cauum fiat, quod axem ip&longs;um recipiat, in tran&longs;uer&longs;a<lb/>rijs quibus rota &longs;u&longs;tinetur & progre&longs;&longs;iuum axis motum <lb/>impediat. </s>

<s>E&longs;to enim rota ABCD, cuius centrum E, diametri <lb/>AEC, BED, e&longs;to alia minor rota GH, item minor KL, tum <lb/>minor NO, & adhuc minor QR, circaidem centrum E. <lb/></s>

<s>E&longs;to enim rota ABCD, cuius centrum E, diametri <lb/>AEC, BED, e&longs;to alia minor rota GH, item minor KL, tum <lb/>minor NO, & adhuc minor QR, circaidem centrum E. <lb/></s>

<s>Rotetur itaque &longs;ecundum ab&longs;idem integri quadrantis <pb pagenum="150"/><figure id="fig35"></figure><lb/>&longs;patium CD, eritque <lb/>D, in F, item &longs;i ex rota <lb/>GH, ex quadrante <lb/>HT, erit T in I. </s>

<s>Rotetur itaque &longs;ecundum ab&longs;idem integri quadrantis <pb pagenum="150"/><figure id="fig35"/><lb/>&longs;patium CD, eritque <lb/>D, in F, item &longs;i ex rota <lb/>GH, ex quadrante <lb/>HT, erit T in I. </s>

<s>Ex a<lb/>lijs item minoribus in <lb/>M, P, S. erit <expan abbr="itaq;">itaque</expan> <expan abbr="lon-gi&longs;&longs;im&umacr;">lon<lb/>gi&longs;&longs;imum</expan> &longs;patium CF, <lb/><expan abbr="breui&longs;&longs;im&umacr;">breui&longs;&longs;imum</expan> vero RS, <lb/>Mota igitur rota cir<lb/>ca <expan abbr="circul&umacr;">circulum</expan> &longs;eu axem, <lb/>QR, maior rota &longs;pa. <lb/></s>

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<s>At cum nulla materialis rota circa lineam punctumue <lb/>imaginarium conuerti po&longs;&longs;it, ideo axi ferreo alteriu&longs;ue <lb/>materiæ circa quem & cum quo circumuoluatur rota, ca<lb/>uum &longs;emirotundum incidere oportet, in quo in&longs;ertus axis <lb/>dum conuertitur à loco in quo conuertitur, non recedat. </s>

<s>QVÆSTIO XXV.</s>

<s>QVÆSTIO XXV.</s>

<s><emph type="italics"/>Quæritur, Cur lectulorum &longs;pondas &longs;ecundum duplam faciant pro<lb/>portionem, hanc quidem &longs;ex pedum, vel paulo ampliorem, illam <lb/>verotrium. </s>

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<s>Ego autem demon&longs;trarem hoc pacto. </s>

<s>E&longs;to &longs;ponda ABCD, cuius longitudo AB, cra&longs;&longs;itudo <lb/>AC, in ea foramen vtrin que pertinens EF, re&longs;tis per fora-<pb pagenum="152"/><figure id="fig36"></figure><lb/>men inditus GFE, &longs;itque Epars &longs;eu ca<lb/>put exterius, quodnodo in E di&longs;tine<lb/>tur. </s>

<s>E&longs;to &longs;ponda ABCD, cuius longitudo AB, cra&longs;&longs;itudo <lb/>AC, in ea foramen vtrin que pertinens EF, re&longs;tis per fora-<pb pagenum="152"/><figure id="fig36"/><lb/>men inditus GFE, &longs;itque Epars &longs;eu ca<lb/>put exterius, quodnodo in E di&longs;tine<lb/>tur. </s>

<s>Sit autem &longs;pondæ lignum iuxta <lb/>longitudinem vt natura a&longs;&longs;olet &longs;ci&longs;&longs;ile. <lb/></s>

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<s>quo enim fu<lb/>nis <expan abbr="l&omacr;gior">longior</expan>, eodebilior, & pre&longs;&longs;io quæ in medio fit, ea vide<lb/>licet parte quæ ab extremis e&longs;t remoti&longs;&longs;ima, magis funem <lb/>fatigat. </s>

<s>Longiores autem funes &longs;unt quæ diametraliter <lb/>extenduntur. </s><figure></figure>

<s>Longiores autem funes &longs;unt quæ diametraliter <lb/>extenduntur. </s><figure/>

<s>Quatenus ad <expan abbr="tertiã">tertiam</expan> <lb/>rationem pertinet, hoc <lb/>pacto funes intexit <lb/>Philo&longs;oph^{9}. E&longs;to lectu<lb/>lus cum &longs;uis <expan abbr="&longs;p&omacr;dis">&longs;pondis</expan> AB <lb/>CD, cuius &longs;ponda AD, <lb/>&longs;it pedum &longs;ex, AB vero <lb/><expan abbr="tri&umacr;">trium</expan>, Diuidatur AD bi<lb/>faríam in E & BC in F. item AE in tres AG, GH, HE & in <lb/>totidem ED, nempe EL, LM, MD. </s>

<s>Similiter medietas al<lb/>terius <expan abbr="&longs;p&omacr;dæ">&longs;pondæ</expan> BF in tres partes di&longs;tinguatur BN, NO, OF, <pb pagenum="153"/>& FC &longs;imiliterin tres FI, IK, KC, tum alterofunis capite <lb/>in ducto per foramen A, ibique probe firmato, indatur per <lb/>F, inde per I, po&longs;tca per GHK CE, & in E probe alligetur: <lb/>Erunt igitur funis quatuor partes æquales AF, IG, HK, <lb/>EC, quibus adijciuntur particulæ cadentes extra, quæ <lb/>&longs;unt FI, GH, KC. </s>

<s>Po&longs;t hæc alterius funis principium per <lb/>foramen traij citur, quod e&longs;t in angulo B. </s>

<s>Po&longs;t hæc alterius funis principium per <lb/>foramen traij citur, quod e&longs;t in angulo B. </s>

<s>Deinde per E, in<lb/>de per L, N, O, M, D, F & in F probe vincitur, & nodo fa<lb/>cto ob&longs;irmatur. </s>

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<s>Sed interim &longs;ubit <lb/>mirari, cur veteres vtiliori modo prætermi&longs;&longs;o, <expan abbr="inutilioi&emacr;">inutilioiem</expan> <lb/>fuerint amplexati. </s>

<s>Poterant enim reticulatim hoc per li<lb/>neas lateribus æ quidi&longs;tantes intexere. </s><figure></figure>

<s>Poterant enim reticulatim hoc per li<lb/>neas lateribus æ quidi&longs;tantes intexere. </s><figure/>

<s>E&longs;to enim lectulus <lb/>eiu&longs;dem dimen&longs;ionis <lb/>ABCD, in cuius latere <lb/>AD &longs;int foramina quin<lb/>que E, F, G, H, I, totidem <lb/>in latere oppo&longs;ito QP, <lb/>ONM. </s>

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<s>quibus adiectis <lb/>particulis extra cadentibus QP, FG, ON, HI, & RS, erit <lb/>integra &longs;umma pedum xxxii. </s>

<s>Vide igitur quantum hinc <lb/>minus in&longs;umatur re&longs;tium quam eo modo, quem proba<lb/>uit, & ceu vtiliorem propo&longs;uit Ari&longs;toteles. </s>

<s>Vide igitur quantum hinc <lb/>minus in&longs;umatur re&longs;tium quam eo modo, quem proba<lb/>uit, & ceu vtiliorem propo&longs;uit Ari&longs;toteles. </s>

<s>Præterea vali<lb/>di&longs;&longs;imum e&longs;t hoc texturæ opus nec ex eo fit vera &longs;ponda<lb/>rum di&longs;tractio &longs;ci&longs;&longs;ioue, quibus haud parum obnoxia e&longs;t <lb/>ea ratio, quam præfertip&longs;e Philo&longs;ophus. </s>

<s>Concludimusi<lb/>gitur, autnos eius verba & &longs;en&longs;um non intellexi&longs;&longs;e, aut <lb/>veteresip&longs;os, quorum v&longs;um ip&longs;e explicat, rei, quam nos <lb/>proponimus, naturam & commoditatem (quod ta<lb/>men vix credibile e&longs;t) igno<lb/>rare. </s><pb pagenum="155"/>

<s>QVÆSTIO XXVI.</s>

<s>QVÆSTIO XXVI.</s>

<s><emph type="italics"/>Proponitur à Philo &longs;opho examinandum, Cur difficilius&longs;it, langa <lb/>ligna ab extremo &longs;uper humeros ferre, quam &longs;ecundum me<lb/>dium, æquali exi&longs;tente pondere?<emph.end type="italics"/></s>

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<s>Quærerer autem qui&longs;piam, (ip&longs;e enim <lb/>id reticet) curvibratio hæc ferenti &longs;it nocua. </s>

<s>Nos itaque <lb/>id expliçare conabimur. </s><figure></figure>

<s>Nos itaque <lb/>id expliçare conabimur. </s><figure/>

<s>E&longs;to igitur lignum <lb/>oblongum, flexile, & vt <lb/>ita dicam, vibrabile <lb/>AB, imponatur hume<lb/>ro<gap/> eique hæreat in C, <lb/>manu vero &longs;u&longs;tineatur facta compre&longs;&longs;ione in B. </s>

<s>Nuteti<lb/>gitur & vibretur, in ip&longs;a vibratione, ad partem A. </s>

<s>Nuteti<lb/>gitur & vibretur, in ip&longs;a vibratione, ad partem A. </s>

<s>Sit au<lb/>tem centrum grauitatis eius D, Lignum igitur in ip&longs;a vi<lb/>bratione de&longs;cendet &longs;ua pre&longs;&longs;us grauitate in E, tum facta <lb/>ligni con&longs;tipatione in ea parte quæ e&longs;t inferius inter C & <lb/>D, & inde re&longs;i&longs;tentia, codem fere impetu quo de&longs;cende<lb/>rat, repul&longs;um per D, nec enim in &longs;ua rectitudine &longs;tabit, a<lb/>&longs;cendet in F, facta iterum materiæ con&longs;ti patione inter C <lb/>& F. </s>

<s>Mouebitur igitur lignum &longs;ua grauitate, motu fre<lb/>quenti&longs;&longs;imo, &longs;ur&longs;um deor&longs;um, & is interim qui lignum hu<lb/>mero fert, procedit antror&longs;um, impedit igitur motus i&longs;te, <lb/>qui fit &longs;ur&longs;um deor&longs;um lationem, quæ fit ad anteriora; La<lb/>torem ip&longs;um quodammodo retrahens. </s>

<s>Mouebitur igitur lignum &longs;ua grauitate, motu fre<lb/>quenti&longs;&longs;imo, &longs;ur&longs;um deor&longs;um, & is interim qui