texts/archimedes/xml/gueva_mecha_005_la_1627.xml - Colored diff

Main History Search Repository tree

Return to gueva_mecha_005_la_1627.xml CVS log

Up to [CVSROOT] / texts / archimedes / xml

Colored diff for /texts/archimedes/xml/gueva_mecha_005_la_1627.xml between version 1.8 and 1.9

version 1.8, 2004/08/20 13:57:17

version 1.9, 2004/08/30 12:29:26

Line 1796

<s id="N13B9F">Hæc ex Ari&longs;totele, quæ vt clarius dilucidentur, &longs;it nauis AB, <lb/>cuius puppis A, prora verò B, gubernaculum obliquè con&longs;ti<lb/>tutum AC; temo &longs;imili<lb/><figure id="id.005.01.133.1.jpg" xlink:href="005/01/133/1.jpg"/><lb/>ter AD, malus E, ac ve<lb/>lum &longs;ecundum <expan abbr="infimã">infimam</expan> &longs;ui <lb/>oram, &longs;it curua linea FG, <lb/>lateraliter ventum exci<lb/>piens ex parte dextera <lb/>vbi H. </s>

<s id="N13BBD">Tunc qua&longs;i pugna <lb/><expan abbr="quædã">quædam</expan> <expan abbr="cõ&longs;ideretur">con&longs;ideretur</expan> inter <lb/><expan abbr="vent&utilde;">ventum</expan>, ac temonem. </s>

<s id="N13BCE"><expan abbr="Nã">Nam</expan> <lb/>flante vento ex H, <expan abbr="naui-gi&utilde;">naui<lb/>gium</expan> transferri deberet in <lb/>oppo&longs;itum, hoc e&longs;t &longs;ini<lb/><gap/>tror&longs;um ver&longs;us I per li<lb/>neam HLI. </s>

<s id="N13BCE"><expan abbr="Nã">Nam</expan> <lb/>flante vento ex H, <expan abbr="naui-gi&utilde;">naui<lb/>gium</expan> transferri deberet in <lb/>oppo&longs;itum, hoc e&longs;t &longs;ini<lb/>&longs;tror&longs;um ver&longs;us I per li<lb/>neam HLI. </s>

<s id="N13BE3">Incidentibus <lb/>autem fluctibus maris in <lb/>alam temonis AD, prora <lb/>ex B conuerti deberet in H, circa ip&longs;um <expan abbr="punct&utilde;">punctum</expan> A <expan abbr="tanquã">tanquam</expan> cen<lb/>trum talis motionis obliquæ, vt probatum e&longs;t. </s>

<s id="N13BF6">Quoniam verò <lb/>neutrum præualet, nauis, medium cur&longs;um tenens, transfertur <lb/>antror&longs;um ver&longs;us K quo pergere, ac velificare cupiunt nautæ, <lb/>qui iccirco in tali po&longs;itione nauim cum velo con&longs;tituunt. </s>

Line 1821

<s id="N13D05">Vnde quo magis velum appropinquatur pup<lb/>pi, eo magis temo præualet contra impul&longs;um ventorum ad <lb/>conuertendam nauim obliquè. </s>

<s id="N13D0E">Quod autem ait Piccolomineus, in hac motione nauis cari<lb/>nam vectis vicem obtinere, quæ centro grauitatis ip&longs;ius nauis <lb/>tanquam fulcimento innixa mare mouente, ac impellente te<lb/>monem, ventum in prora &longs;u&longs;tineat tanquam onus, valde ambi<lb/><gap/>uum e&longs;t. </s>

<s id="N13D1A">Tum quia non minus ventus per velum, quàm ma<lb/>re per temonem pote&longs;t habere rationem potentiæ mouentis. <lb/></s>

<s id="N13D20">Tum etiam quia ventus præcipuè non &longs;u&longs;tinetur in prora, &longs;ed <lb/>potius in parte veli, quæ vergit ad puppim, vt dictum e&longs;t. </s>

Line 1845

<s id="N13E05">C<emph type="italics"/>vr ex figurarum genere quæcunque rotun<lb/>dæ &longs;unt, & circinatæ, facilius mouentur? <lb/></s>

<s id="N13E0E">Trifariam autem circulum rotari contingit. <lb/></s>

<s id="N13E12">Aut enim &longs;ecundum ab&longs;idem centro &longs;imul mo<lb/>to, quemadmodum plau&longs;tri vertitur rota: aut <lb/>circa manens centrum, veluti trochleæ &longs;tante <lb/>centro, aut in pauimento manente centro, &longs;icut figuli rota con<lb/>nertitur: an celerrima quidem huiu&longs;modi &longs;unt, quoniam par<lb/>na &longs;ui parte planum contingunt, veluti circulus &longs;ecundum <lb/>punctum, & quoniam non offen&longs;ant. </s>

<s id="N13E12">Aut enim &longs;ecundum ab&longs;idem centro &longs;imul mo<lb/>to, quemadmodum plau&longs;tri vertitur rota: aut <lb/>circa manens centrum, veluti trochleæ &longs;tante <lb/>centro, aut in pauimento manente centro, &longs;icut figuli rota con<lb/>vertitur: an celerrima quidem huiu&longs;modi &longs;unt, quoniam par<lb/>ia &longs;ui parte planum contingunt, veluti circulus &longs;ecundum <lb/>punctum, & quoniam non offen&longs;ant. </s>

<s id="N13E21">A terra enim &longs;emotus e&longs;t <lb/>angulus. </s>

<s id="N13E26">Præterea etiam cui obuiam fiunt corpori, id rur&longs;um <lb/>&longs;ecundum pu&longs;illum tangunt. </s>

<s id="N13E2B">Si autem rectilineum e&longs;&longs;et, re<lb/>ctitudine &longs;ua multum plani contingeret. </s>

Line 1854

<s id="N13E3D">Cùm autem mouetur plus illico, ad quod mouetur, ceri inde nu<lb/>tans, ab impellente facilius in ante mouetur. </s>

<s id="N13E42">Quo enim vnum<lb/>quodque vergit, mouetur ex facili. </s>

<s id="N13E47">Siquidem difficulter ad <lb/>contrarium nutus &longs;ui mouetur motum. </s>

<s id="N13E4C">Praterea nonnulli <lb/>autumant, quod circult linea in perpeti ver&longs;atur motu, quem<lb/>ædmodum manentia propter contrarium nixum manent: &longs;icut <lb/>maioribus contingit circulis ad minores. </s>

<s id="N13E4C">Praeterea nonnulli <lb/>autumant, quod circule linea in perpeti ver&longs;atur motu, quem<lb/>admodum manentia propter contrarium nixum manent: &longs;icut <lb/>maioribus contingit circulis ad minores. </s>

<s id="N13E55">Celeriùs enim ab <lb/>æquali mouentur potentia maiores circuli, <expan abbr="mouentq.">mouentque</expan> onera, <lb/>quoniam circuli maioris angulus ad minoris angulum, circu<lb/>li nutum babet quendam: & &longs;icut diameter ad diametrum, <lb/>ita maior circulus ad minorem. </s>

<s id="N13E55">Celeriùs enim ab <lb/>æquali mouentur potentia maiores circuli, <expan abbr="mouentq.">mouentque</expan> onera, <lb/>quoniam circuli maioris angulus ad minoris angulum, circu<lb/>li nutum habet quendam: & &longs;icut diameter ad diametrum, <lb/>ita maior circulus ad minorem. </s>

<s id="N13E64">Infiniti autem &longs;unt minores. <lb/></s>

<s id="N13E68">Si autem ad alterum nutum babet circulus, &longs;imiliter e&longs;t benè <lb/>mobilis. </s>

<s id="N13E68">Si autem ad alterum nutum habet circulus, &longs;imiliter e&longs;t benè <lb/>mobilis. </s>

<s id="N13E6D">Et aliam &longs;anè babet inclinationem circulus, & <gap/>a<emph.end type="italics"/><pb pagenum="130" xlink:href="005/01/138.jpg"/><emph type="italics"/>quæ à circulo mouentur, licet planitiem ab&longs;ide non contingat, <lb/>&longs;ed aut iuxta planitiem, aut oeluti trochleæ. </s>

<s id="N13E6D">Et aliam &longs;anè habet inclinationem circulus, & <gap/>a<emph.end type="italics"/><pb pagenum="130" xlink:href="005/01/138.jpg"/><emph type="italics"/>quæ à circulo mouentur, licet planitiem ab&longs;ide non contingat, <lb/>&longs;ed aut iuxta planitiem, aut ueluti trochleæ. </s>

<s id="N13E7D">Etenim hoc &longs;e <lb/>habentes modo facillimè mouentur, & onera commouent. </s>

<s id="N13E82">An <lb/>quia parua &longs;ui portione cùm tangit, tum offen&longs;at circulus, &longs;ed <lb/>aliam ob cau&longs;am? </s>

<s id="N13E89">ea autem e&longs;t, quæ dicta est prius, quod circu<lb/>lus &longs;cilicet ex duabus effectus e&longs;t lationibus: quamobrem il<lb/>larum alteram pro nutu &longs;emper habet, & veluti continuò mo<lb/>tum illum moueat quicumque mouent, quando &longs;ecundum cir<lb/>tumferentiam illum mouerint: latam enim ip&longs;am mouent. <lb/></s>

<s id="N13E89">ea autem e&longs;t, quæ dicta est prius, quod circu<lb/>lus &longs;cilicet ex duabus effectus e&longs;t lationibus: quamobrem il<lb/>larum alteram pro nutu &longs;emper habet, & veluti continuò mo<lb/>tum illum moueat quicumque mouent, quando &longs;ecundum cir<lb/>cumferentiam illum mouerint: latam enim ip&longs;am mouent. <lb/></s>

<s id="N13E95">Eam quidem igilur, quæ in obliquum e&longs;t, motionem, ip&longs;um <lb/>impellit mouens: &longs;ecundum verò illam, quæ &longs;uper diametrum <lb/>est, &longs;eip&longs;um mouet circulus.<emph.end type="italics"/></s>

<s id="N13E95">Eam quidem igitur, quæ in obliquum e&longs;t, motionem, ip&longs;um <lb/>impellit mouens: &longs;ecundum verò illam, quæ &longs;uper diametrum <lb/>est, &longs;e ip&longs;um mouet circulus.<emph.end type="italics"/></s>

<s id="N13EA0">COMMENTARIVS.</s>

<s id="N13EA6">Vt quæ&longs;tioni re&longs;pondeat Ari&longs;toteles cur corpora, <lb/>quæ rotundam, aut orbiculatam figuram obtinent, <lb/>&longs;ecundum illam facilius moueantur, triplicem mo<lb/>dum di&longs;tinguit, quo ip&longs;a moueri rotando contingit. </s>

<s id="N13EAF"><expan abbr="Pri-mumq.">Pri<lb/>mumque</expan> e&longs;&longs;e docet, quo &longs;ecundum ab&longs;idem, &longs;eu extimam ip<lb/>forum curuaturam cientur, moto &longs;imul etiam centro, vt <lb/>plau&longs;trorum rotæ, quæ &longs;imul cum axe feruntur. </s>

<s id="N13EAF"><expan abbr="Pri-mumq.">Pri<lb/>mumque</expan> e&longs;&longs;e docet, quo &longs;ecundum ab&longs;idem, &longs;eu extimam ip<lb/>sorum curuaturam cientur, moto &longs;imul etiam centro, vt <lb/>plau&longs;trorum rotæ, quæ &longs;imul cum axe feruntur. </s>

<s id="N13EBB">Secundum <lb/>verò modum, ait e&longs;&longs;e illum, quo circularia ip&longs;a corpora re<lb/>cta quidem &longs;tantia, &longs;eu rectè ad horizontem con&longs;tituta mo<lb/>uentur circa centrum immotum; veluti &longs;tantes trochlea<lb/>rum rotulæ, quæ circa manentem axem, &longs;eu centrum ad di<lb/>uer&longs;os v&longs;us conuertuntur. </s>

<s id="N13EC8">Tertium denique modum e&longs;&longs;e <lb/>inquit, quo circa immotum pariter centrum mouentur, non <lb/>tamen &longs;tando, &longs;ed qua&longs;i pro&longs;trata iuxta planitiem &longs;oli, aut <lb/>pauimenti horizonti paralellam; &longs;icut rota figuli, quæ ad <lb/>impul&longs;um pedis illius conuertitur, ac circumagitur &longs;upra <lb/>axim pauimento perpendiculariter affixum, &longs;eruando &longs;em<lb/>per eandem di&longs;tantiam ab horizonte. </s>

<s id="N13ED9">Loquendo itaque de primo modo, pluribus ex cau&longs;is, ait <lb/>Ari&longs;toteles præfata corpora celerius, ac facilius moueri <lb/>quàm illa, quæ rectilineas adepta &longs;unt figuras, &longs;eu rectilineis <lb/>figuris terminantur, vt triangulari, vel quadrangulari, pirami-<pb pagenum="131" xlink:href="005/01/139.jpg"/>des, & cubi. </s>

<s id="N13EE7">Prima e&longs;t, quia minima &longs;ui parte planum con<lb/>tingunt hoc e&longs;t minori, quam cuiu&longs;libet alterius figuræ cor<lb/>pora, re&longs;pectu, verbi gratia &longs;phæræ, quæ planum tangit in <lb/>puncto. </s>

<s id="N13EF0">Secunda verò e&longs;t, quia hoc pacto non offendunt, aut <lb/>impingunt ni&longs;i &longs;cilicet rarius, ac difficilius; A terra enim &longs;e<lb/>motus e&longs;t angulus, inquit Ari&longs;toteles, nimnum angulum <lb/>contingentiæ, &longs;eu contactus, quia po&longs;t punctum contingen<lb/>tiæ, totum latus curuilineum ip&longs;orum corporum orbicula<lb/>rium, quod cum plano con&longs;tituit huiu&longs;modi angulum, è ter<lb/>ra eleuatur; ac propterea minus impingunt in offendicula, <lb/>quàm alia corpora, quorum latera <expan abbr="nõ">non</expan> &longs;tatim po&longs;t minimum <lb/>contactum eleuantur, &longs;ed ip&longs;i plano, &longs;eu terræ adhærent. <lb/></s>

<s id="N13EF0">Secunda verò e&longs;t, quia hoc pacto non offendunt, aut <lb/>impingunt ni&longs;i &longs;cilicet rarius, ac difficilius; A terra enim &longs;e<lb/>motus e&longs;t angulus, inquit Ari&longs;toteles, nimirum angulum <lb/>contingentiæ, &longs;eu contactus, quia po&longs;t punctum contingen<lb/>tiæ, totum latus curuilineum ip&longs;orum corporum orbicula<lb/>rium, quod cum plano con&longs;tituit huiu&longs;modi angulum, è ter<lb/>ra eleuatur; ac propterea minus impingunt in offendicula, <lb/>quàm alia corpora, quorum latera <expan abbr="nõ">non</expan> &longs;tatim po&longs;t minimum <lb/>contactum eleuantur, &longs;ed ip&longs;i plano, &longs;eu terræ adhærent. <lb/></s>

<s id="N13F08">Tertia cau&longs;a e&longs;t, nam huiu&longs;modi corpora cuicunque ob<lb/>uient offendiculo, illud pariter nonni&longs;i &longs;ecundum pu&longs;illam <lb/>&longs;ui partem attingunt, eadem ratione, qua planum, &longs;eu &longs;olum <lb/>&longs;uper quod ip&longs;a mouentur, &longs;ecus, ac rectilineam figuram ha<lb/>bentia, quæ &longs;emper &longs;ua rectitudine &longs;ecundum magnam, vel <lb/>&longs;altem maiorem partem contingunt. </s>

Line 1886

<s id="N13F29">Etenim &longs;i con&longs;tituatur &longs;u<lb/>per planum AB horizonti <lb/><figure id="id.005.01.139.1.jpg" xlink:href="005/01/139/1.jpg"/><lb/>paralellum erecta aliqua <lb/>rota, vt CDEF tanquam <lb/>circulus, eius diameter à <lb/>contactu plani vbi C per<lb/>pendiculariter ad angulos <lb/>rectos per centrum &longs;upra <lb/>tra&longs;cendens ad D, totam <lb/>rotam eiu&longs;que pondus in <lb/>duas partes æquales di&longs;tri<lb/>buet, nempe in DFC, & <lb/>DEC. <expan abbr="Eritq.">Eritque</expan> ip&longs;a rota in <pb pagenum="132" xlink:href="005/01/140.jpg"/>æquilibrio, quia non magis vna quam altera pars vtrinque <lb/>à perpendiculo DC grauitare pote&longs;t. </s>

<s id="N13F55">Quod &longs;i impul&longs;us <lb/>quamuis perexiguus in ip&longs;am rotam à motore incutiatur, <lb/>vt ex parte E ver&longs;us F, &longs;tatim pars vbi F nutabit ac pro<lb/>pendet ver&longs;us B; <expan abbr="&longs;uoq.">&longs;uoque</expan> nutu, totam rotam &longs;ecum trahet il<lb/>luc. </s>

<s id="N13F64">Nam quælibet vis pote&longs;t æquiponderantia ab æquili<lb/>brio dimouere. </s>

<s id="N13F69">Semel autem mota ip&longs;a rota, ni&longs;i impe<lb/>diatur deinceps nutabit ad partem ver&longs;us quàm primò fuit <lb/>incitata; ideoq facilè vlterius atque vlterius mouebitur. <lb/></s>

<s id="N13F69">Semel autem mota ip&longs;a rota, ni&longs;i impe<lb/>diatur deinceps nutabit ad partem ver&longs;us quàm primò fuit <lb/>incitata; ideoque facilè vlterius atque vlterius mouebitur. <lb/></s>

<s id="N13F71">Quo enim vnumquodque vergit, mouetur ex facili, &longs;ubdit <lb/>ip&longs;e Philo&longs;ophus, &longs;icut vice ver&longs;a difficulter in contrarium; <lb/>vt fu&longs;ius con&longs;tabit quæ&longs;t. </s>

Line 1899

<s id="N13FA6">Circulus enim vel glo<lb/>bus non tangit planum, ni&longs;i in puncto in quod eius diame<lb/>ter incidit ad angulos rectos; quo &longs;anè pacto cadere non <lb/>pote&longs;t perpendicularis tendens ad mundi centrum in pla<lb/>num, quod non e&longs;t horizonti paralellum. </s>

<s id="N13FB1">Cumque præ<lb/>dictum punctum, cui poti&longs;&longs;imum onus incumbit, &longs;u&longs;tineri <lb/>non po&longs;&longs;it ab eo, quod non contingit; hinc fit, vt &longs;emper <lb/>ver&longs;us inferiores partes decliues propendat, ac nutet, de<lb/>feratque propterea ip&longs;a orbiculata corpora quou&longs;que ab <lb/>alio fulciatur. </s>

<s id="N13FBE">Vt per&longs;picuè apparebit in propo&longs;ita &longs;phæra <pb pagenum="133" xlink:href="005/01/141.jpg"/>vel rota ABC, &longs;i decliue <lb/><figure id="id.005.01.141.1.jpg" xlink:href="005/01/141/1.jpg"/><lb/>planum DE contingat in <lb/>C ad angulos rectos ip&longs;ius <lb/>diametri BC: linea verò <lb/>cadens per centrum ip&longs;ius <lb/>&longs;phæræ ad centrum mundi, <lb/>&longs;it AF. </s>

<s id="N13FD9">Nam &longs;ic totum fe<lb/>rè onus incumberet in pun<lb/>cto G, quod cum fulciri <lb/><expan abbr="nõ">non</expan> po&longs;&longs;it in ip&longs;a DE, quam <lb/>nullo modo tangit, nece&longs;&longs;a<lb/>riò <expan abbr="prop&etilde;det">propendet</expan> in F, <expan abbr="rapietq.">rapietque</expan> <lb/>&longs;ecum ad partes E totum <lb/>globum, qui deinceps rur<lb/>&longs;us eadem ratione nutabit per aliud &longs;imile punctum, <expan abbr="infe-tiusq.">infe<lb/>tiusque</expan> citi&longs;&longs;imo cur&longs;u de&longs;cendet &longs;uccedentibus &longs;ibi ad inui<lb/>cem punctis, ac partibus. </s>

<s id="N13FD9">Nam &longs;ic totum fe<lb/>rè onus incumberet in pun<lb/>cto G, quod cum fulciri <lb/><expan abbr="nõ">non</expan> po&longs;&longs;it in ip&longs;a DE, quam <lb/>nullo modo tangit, nece&longs;&longs;a<lb/>riò <expan abbr="prop&etilde;det">propendet</expan> in F, <expan abbr="rapietq.">rapietque</expan> <lb/>&longs;ecum ad partes E totum <lb/>globum, qui deinceps rur<lb/>&longs;us eadem ratione nutabit per aliud &longs;imile punctum, <expan abbr="infe-tiusq.">infe<lb/>riusque</expan> citi&longs;&longs;imo cur&longs;u de&longs;cendet &longs;uccedentibus &longs;ibi ad inui<lb/>cem punctis, ac partibus. </s>

<s id="N14001">Ex hac autem maxima aptitudine, quam rotæ, vel &longs;imili<gap/><lb/>orbiculata corpora habent ad motum, occa&longs;ionem &longs;ump&longs;i&longs;<lb/>&longs;e videntur nonnulli arbitrandi, circuli periferiam nunquam <lb/>quie&longs;cere, &longs;ed perpetuo motu cieri, vt hic &longs;ubiungit Ari&longs;to<lb/>teles. </s>

<s id="N14001">Ex hac autem maxima aptitudine, quam rotæ, vel &longs;imilia <lb/>orbiculata corpora habent ad motum, occa&longs;ionem &longs;ump&longs;i&longs;<lb/>&longs;e videntur nonnulli arbitrandi, circuli periferiam nunquam <lb/>quie&longs;cere, &longs;ed perpetuo motu cieri, vt hic &longs;ubiungit Ari&longs;to<lb/>teles. </s>

<s id="N1400E">Quia &longs;cilicet circulus contrarium nixum non habet, <lb/>quo re&longs;i&longs;tat motui, aut motori &longs;icut corpora manentia, quæ <lb/>ex eo quie&longs;cunt, velmanent, quia habent, in quo contra ni<lb/>tantur, & quo ob&longs;i&longs;tant motui, ac mouenti. </s>

<s id="N14017">Vbiaddendum <lb/>quippe fui&longs;&longs;et ab Ari&longs;totele, falsò eos ita putare; nam licet <lb/>circuli periferia nixum non habeat, quo retardetur, aut im<lb/>pediatur à proprio motu; non tamen &longs;emper habet in &longs;e <lb/>principium proximum, ac formale &longs;ui motus, quod certè <lb/>cum &longs;it qualitas impetus impre&longs;&longs;i, hæc paulatim ex &longs;e re<lb/>mittitur, ac tandem deficit, vt patet in proiectis, quæ iccirco <lb/>de&longs;i&longs;tunt à motu. </s>

Line 1938

<s id="N14111">Ex parte verò portionis circunferentiæ, &longs;eu la<lb/>teris curui; quia CD magis etiam di&longs;tat ab eodem centro, <lb/>ac minus curuatur, quàm GH; <expan abbr="minusq.">minusque</expan> proinde retrahitur <lb/>nè moueatur motu naturali, ad rectum &longs;cilicet magis ap<lb/>propinquanti ideoque velocius ac facilius. </s>

<s id="N14120">Sed angulus C <lb/>inclinari non pote&longs;t ver&longs;us L quin &longs;ecum rapiat angulum <lb/>G, quem intra &longs;e continet. </s>

<s id="N14127">Igitur angulus ip&longs;e C, nutum, <lb/>& propen&longs;ionem habet ad angulum G, vt &longs;imul ac facilius <lb/>moueantur modo quo diximus ad quemlibet impul&longs;um <lb/>motoris. </s>

<s id="N14130">Cumque in&longs;initi &longs;int huiu&longs;modi anguli in explica<lb/>tis circulis, hinc &longs;it, vt rectè ex illis concludat Ari&longs;toteles, <lb/>mobiliores e&longs;&longs;e circulos maiores, ac celerius moueri ab ea<pb pagenum="136" xlink:href="005/01/144.jpg"/>dem, vel æquali potentia; &longs;icut celerius mouentur maiores <lb/>libræ, quàm minores ab eodem, vel æquali pondere. </s>

<s id="N14130">Cumque infiniti &longs;int huiu&longs;modi anguli in explica<lb/>tis circulis, hinc &longs;it, vt rectè ex illis concludat Ari&longs;toteles, <lb/>mobiliores e&longs;&longs;e circulos maiores, ac celerius moueri ab ea<pb pagenum="136" xlink:href="005/01/144.jpg"/>dem, vel æquali potentia; &longs;icut celerius mouentur maiores <lb/>libræ, quàm minores ab eodem, vel æquali pondere. </s>

<s id="N1413E">Non <lb/>enim aliter &longs;e habet circulus &longs;tans &longs;uper planum, quàm libra <lb/>&longs;upra fulcimentum in æquilibrio con&longs;tituta. </s>

<s id="N14147">At Ari&longs;totelem per angulos circuli intelligere angulo<gap/><lb/>à nobis explicatos, illud confirmat, quod cum dixi&longs;&longs;et an<lb/>gulum circuli maioris habere nutum ad angulum circuli <lb/>minoris, qua&longs;i id probans ait: Et &longs;icut diameter ad diame<lb/>trum, ita circumferentia ad circumferentiam. </s>

<s id="N14147">At Ari&longs;totelem per angulos circuli intelligere angulos <lb/>à nobis explicatos, illud confirmat, quod cum dixi&longs;&longs;et an<lb/>gulum circuli maioris habere nutum ad angulum circuli <lb/>minoris, qua&longs;i id probans ait: Et &longs;icut diameter ad diame<lb/>trum, ita circumferentia ad circumferentiam. </s>

<s id="N14153">In quibus <lb/>verbis vtrumque ip&longs;orum angulorum latus comprehendit <lb/>nempe rectum, & <expan abbr="curu&utilde;">curuum</expan>. </s>

<s id="N1415E"><expan abbr="Idemq.">Idemque</expan> e&longs;t, ac dicere, quia <expan abbr="c&utilde;">cum</expan> præ<lb/>dicti anguli con&longs;tent ex huiu&longs;modi lateribus, &longs;icut latera ma<lb/>iora, eo quod magis di&longs;tent à centro, velocius mouentur; ita <lb/>pariter angulus ex illis con&longs;titutus, velocius mouebitur; ma<lb/>gis enim di&longs;tat à centro extremum diametri maioris, quàm <lb/>minoris, &longs;imiliter que portio maioris circumferentiæ ab illo <lb/>de&longs;criptæ, quàm minoris, vt per &longs;e patet. </s>

<s id="N14176">Quod autem Baldus obijcit Ari&longs;toteli, prædictum nu<lb/>tum, quem ip&longs;e gratis explicat per angulos fectores, nul<lb/>lam arguere maiorem mobilitatem circuli maioris, eo quod <lb/>quantum vnus &longs;ector adiuuat de&longs;cen&longs;um ex vna parte, tan<lb/>tum alter oppo&longs;itus retardet a&longs;cen&longs;um ex alia, nihil con<lb/>uincit. </s>

<s id="N14176">Quod autem Baldus obijcit Ari&longs;toteli, prædictum nu<lb/>tum, quem ip&longs;e gratis explicat per angulos sectores, nul<lb/>lam arguere maiorem mobilitatem circuli maioris, eo quod <lb/>quantum vnus &longs;ector adiuuat de&longs;cen&longs;um ex vna parte, tan<lb/>tum alter oppo&longs;itus retardet a&longs;cen&longs;um ex alia, nihil con<lb/>uincit. </s>

<s id="N14183">Nam idem dici po&longs;&longs;et de extremitate diametri lon<lb/>gius à centro di&longs;tante, vt nihil conferat ad maiorem veloci<lb/>tatem, eo quod altera extremitas tantundem debeat retar<lb/>dare; Quod &longs;anè fal&longs;um e&longs;t, quoniam tam in illo, quàm in <lb/>i&longs;to motu &longs;upponitur impetus aliquis impre&longs;&longs;us, virtute cu<lb/>ius motus ip&longs;e exerceatur, ac vna pars circuli, vel diametri <lb/>&longs;uperet aliam æqualem. </s>

<s id="N14192">Alioquin &longs;icut &longs;ola maior di&longs;tan<lb/>tia extremitatis diametri non &longs;ufficit ad motum illius; ita <lb/>nec maior nutus circuli maioris. </s>

<s id="N14199">Vtrumque tamen confert <lb/>ad velocitatem &longs;uppo&longs;ito motu. </s>

<s id="N1419E">Nam virtus illa impre&longs;&longs;a <lb/>nutu proprio ip&longs;ius circuli adiuta, efficacius operatur in e<gap/><lb/>parte vbi imprimitur, vel in quam prius impre&longs;&longs;a fuerir à <lb/>motore. </s>

<s id="N1419E">Nam virtus illa impre&longs;&longs;a <lb/>nutu proprio ip&longs;ius circuli adiuta, efficacius operatur in ea <lb/>parte vbi imprimitur, vel in quam prius impre&longs;&longs;a fuerit à <lb/>motore. </s>

<s id="N141AA">Quod verò adducit ad probandum potius minores circu-<pb pagenum="137" xlink:href="005/01/145.jpg"/>los videri ad motum faciliores, eo quod maior e&longs;t angulus <lb/>contingentiæ ad planum, circumferentiæ minotis, quàm <lb/>maioris circuli, vt in &longs;ubiecta figura maior e&longs;t angulus ABC, <lb/>quàm DBC: probat quidem mi<lb/><figure id="id.005.01.145.1.jpg" xlink:href="005/01/145/1.jpg"/><lb/>nores circulos minus offen&longs;are <lb/>propter maiorem eleuationem <lb/>ip&longs;ius anguli à terra, vt &longs;upra ex <lb/>plicuimus; &longs;ed non probat per &longs;e <lb/>facilius moueri; imò oppo&longs;itum. <lb/></s>

<s id="N141AA">Quod verò adducit ad probandum potius minores circu-<pb pagenum="137" xlink:href="005/01/145.jpg"/>los videri ad motum faciliores, eo quod maior e&longs;t angulus <lb/>contingentiæ ad planum, circumferentiæ minoris, quàm <lb/>maioris circuli, vt in &longs;ubiecta figura maior e&longs;t angulus ABC, <lb/>quàm DBC: probat quidem mi<lb/><figure id="id.005.01.145.1.jpg" xlink:href="005/01/145/1.jpg"/><lb/>nores circulos minus offen&longs;are <lb/>propter maiorem eleuationem <lb/>ip&longs;ius anguli à terra, vt &longs;upra ex<lb/>plicuimus; &longs;ed non probat per &longs;e <lb/>facilius moueri; imò oppo&longs;itum. <lb/></s>

<s id="N141C9">Nam quo curuior e&longs;t linea, eo re<lb/>motior à moturecto, ac naturali, <lb/><expan abbr="ideoq.">ideoque</expan> tardius mouetur, vt cum <lb/>Ari&longs;totele pariter probauimus in <lb/>principio. </s>

<s id="N141D7">Nec recurrere fas e&longs;tad rotam materialem, quæ <lb/>&longs;i maior fit, maiore &longs;ui parte tangit planum, cum idip&longs;um <lb/>de&longs;truat eius a&longs;&longs;umptum, quod fundatur in eleuatione an<lb/>guli contactus &longs;upra punctum B &longs;upponendo contactum <lb/>fieri in puncto ip&longs;o B, & non in parte diui&longs;ibili. </s>

<s id="N141E2">Quod &longs;i di<lb/>catur reuera fieri in parte diui&longs;ibili tanto maiore, quanto <lb/>maior fuerit circumferentia, tunc variatur &longs;uppo&longs;itio ante<lb/>cedentis in con&longs;equenti, <expan abbr="nihilq.">nihilque</expan> propterea verè concluditur. </s>

Line 1972

<s id="N14247">Vtitur autem Ari&longs;toteles illis verbis: &longs;ecundum verò il<lb/>lam (&longs;cilicet motionem) quæ &longs;upra diametrum e&longs;t, &longs;eip&longs;um <lb/>mouet circulus: ad connotandam ip&longs;am motionem mi&longs;tam, <lb/>ac circularem re&longs;ultantem ex duabus lationibus explicatis. <lb/></s>

<s id="N14251">Quam quidem &longs;uper diametrum quadrilateri exempli&longs;ica<lb/>uerat in principio, non &longs;eruata tamen eadem proportione <lb/>Quod non abs re fuerit in hac figura palam exprimere. </s>

<s id="N14251">Quam quidem &longs;uper diametrum quadrilateri exemplifica<lb/>uerat in principio, non &longs;eruata tamen eadem proportione <lb/>Quod non abs re fuerit in hac figura palam exprimere. </s>

<s id="N1425A">Sit enim circulus ABCD <lb/><figure id="id.005.01.146.1.jpg" xlink:href="005/01/146/1.jpg"/><lb/>circa centrum E, cuius &longs;emi<lb/>diameter EC. </s>

<s id="N14267">A qua excite<lb/>tur quadratum ECFD. <expan abbr="Sitq.">Sitque</expan> <lb/>diameter quadrati recta CD. <lb/></s>

<s id="N14274">Dico igitur quod &longs;i punctum <lb/>C, quod e&longs;t extremum &longs;emi<lb/>diametri, moueri debeat <expan abbr="v&longs;q;">v&longs;que</expan> <lb/>ad D, circa immotum <expan abbr="centr&utilde;">centrum</expan> <lb/>E, nullo ferè conatu mouen<lb/>tis mouebitur per arcum, cui <lb/>&longs;ubtenditur recta CD. <expan abbr="Eo-demq.">Eo<lb/>demque</expan> tempore ip&longs;um D transferetur in A; &longs;icut etiam <lb/>A in B, & B vbinunc e&longs;t punctum C: quod e&longs;t, totum <lb/>circulum nullo, aut paruo negotio, à mouente circulariter <lb/>moueri. </s>

<s id="N14297">Cum enim punctum C per lationem &longs;ecundum <lb/>naturam, ad quam ex &longs;e habet nutum, & propen&longs;io<lb/>nem, qualibet exigua vi moueatur yer&longs;us F; per latio-<pb pagenum="139" xlink:href="005/01/147.jpg"/>nem verò præter naturam retrahatur ver&longs;us centrum E; im<lb/>pellente &longs;cilicet ip&longs;o mouente; vtique &longs;i pari proportione <lb/>ip&longs;orum laterum CF, & CE deduceretur, ip&longs;is duabus <lb/>lationibu proculdubio moueretur per diametrum CD, vt <lb/>cum Ari&longs;totele demon&longs;trauimus in principio. </s>

<s id="N14297">Cum enim punctum C per lationem &longs;ecundum <lb/>naturam, ad quam ex &longs;e habet nutum, & propen&longs;io<lb/>nem, qualibet exigua vi moueatur ver&longs;us F; per latio-<pb pagenum="139" xlink:href="005/01/147.jpg"/>nem verò præter naturam retrahatur ver&longs;us centrum E; im<lb/>pellente &longs;cilicet ip&longs;o mouente; vtique &longs;i pari proportione <lb/>ip&longs;orum laterum CF, & CE deduceretur, ip&longs;is duabus <lb/>lationibus proculdubio moueretur per diametrum CD, vt <lb/>cum Ari&longs;totele demon&longs;trauimus in principio. </s>

<s id="N142AB">At cum non <lb/>&longs;eruetur eadem proportio inter lationem &longs;ecundum natu<lb/>ram, ac præter naturam, vt ibi etiam explicuimus; hinc fit, vt <lb/>punctum C moueatur per arcum CD, cui diameter qua<lb/>drati &longs;ubtenditur, & in quo nulla e&longs;t pars, &longs;uper quam di&longs;ce<lb/>dendo à puncto C, non moueatur vtraque latione, nunc <lb/>magis; nune minus &longs;e appropinquando puncto F, ac &longs;etuan<lb/>do &longs;emper eandem di&longs;tantiam à centro E. </s>

<s id="N142AB">At cum non <lb/>&longs;eruetur eadem proportio inter lationem &longs;ecundum natu<lb/>ram, ac præter naturam, vt ibi etiam explicuimus; hinc fit, vt <lb/>punctum C moueatur per arcum CD, cui diameter qua<lb/>drati &longs;ubtenditur, & in quo nulla e&longs;t pars, &longs;uper quam di&longs;ce<lb/>dendo à puncto C, non moueatur vtraque latione, nunc <lb/>magis; nunc minus &longs;e appropinquando puncto F, ac &longs;eruan<lb/>do &longs;emper eandem di&longs;tantiam à centro E. </s>

<s id="N142BD">Mouetur it a que <lb/>punctum C v&longs;que ad D, motione re&longs;ultante ex duabus <lb/>lationibus explicatis: at que adeo nulla alia adhibita vi, aut <lb/>impul&longs;u, qui corre&longs;pondeat ei &longs;icut illis, vt dictum e&longs;t. </s>

<s id="N142C6">Et <lb/>&longs;ic verificatur, quod ait Ari&longs;toteles: &longs;ecundum hanc motio<lb/>nem, quæ fit &longs;uper diametrum; (nempe per arcum, cui illa <lb/>&longs;ubtenditur) &longs;eip&longs;um mouere circulum. </s>

Line 1987

<s id="N142D1">Quæ&longs;tio Nona.</s>

<s id="N142D6">C<emph type="italics"/>vr ea, quæ per maiores circulos tolluntur, & <lb/>trabuntur, facilius & citius moueri contin<lb/>git, veluti maioribus trocbleis, quàm mino<lb/>ribus, & &longs;cytalis &longs;imiliter? </s>

<s id="N142D6">C<emph type="italics"/>vr ea, quæ per maiores circulos tolluntur, & <lb/>trahuntur, facilius & citius moueri contin<lb/>git, veluti maioribus trochleis, quàm mino<lb/>ribus, & &longs;cytalis &longs;imiliter? </s>

<s id="N142E2">An quoniam <lb/>quantò maior fuerit illa, quæ à centro e&longs;t, in <lb/>æquali tempore maius mouetur &longs;patium? <lb/></s>

<s id="N142EA">Quamobrem æquali inexi&longs;tente onere, idem faciet: quemad<lb/>modum diximas, maiores libras minoribus exactiores e&longs;&longs;e. <lb/></s>

<s id="N142EA">Quamobrem æquali inexi&longs;tente onere, idem faciet: quemad<lb/>modum diximus, maiores libras minoribus exactiores e&longs;&longs;e. <lb/></s>

<s id="N142F0">Spartum enim in illis centrum e&longs;t: libræ autem vtrin que par<lb/>tes, quæ ex centro &longs;unt, exi&longs;tunt.<emph.end type="italics"/></s>

<s id="N142F9">COMMENTARIVS.</s>

<s id="N142FF">Maior e&longs;t difficultas, & controuer&longs;ia circa experien<lb/>tiamhic <expan abbr="&longs;uppo&longs;itã">&longs;uppo&longs;itam</expan> ab Ari&longs;totele, dum quæ&longs;tionem <lb/>proponit, quam circa cau&longs;am ip&longs;ius addnctam in <pb pagenum="140" xlink:href="005/01/148.jpg"/>&longs;olutione. </s>

<s id="N142FF">Maior e&longs;t difficultas, & controuer&longs;ia circa experien<lb/>tiam hic <expan abbr="&longs;uppo&longs;itã">&longs;uppo&longs;itam</expan> ab Ari&longs;totele, dum quæ&longs;tionem <lb/>proponit, quam circa cau&longs;am ip&longs;ius adductam in <pb pagenum="140" xlink:href="005/01/148.jpg"/>&longs;olutione. </s>

<s id="N1430F">Scribit enim facilius ac celerius tolli, ac trahi <lb/>pondera per maiores circulos, quàm per minores. </s>

<s id="N14314">Con&longs;ti<lb/>tuitque exemplum de trochleis, ac &longs;cytalis, quæ &longs;i maiores <lb/>&longs;int, aptius onera mouent. </s>

<s id="N1431B">Quod fal&longs;um omnino e&longs;&longs;e cona<lb/>tur o&longs;tendere Blancanus ex Guido Vbaldo. </s>

<s id="N14320">Nam &longs;implex <lb/>trochlea per rotulam cui funis &longs;upernè inditur nullas addit <lb/>vires potentiæ mouenti, eo quod reducatur ad vectem, cu<lb/>ius fultura e&longs;t in medio ip&longs;ius. </s>

<s id="N14329">Vnde &longs;iue rotula illa magna <lb/>fuerit &longs;iue paiua, &longs;emper eadem ratione nullam augere po<lb/>te&longs;t facilitatem, aut velocitatem in hac motione. </s>

<s id="N14329">Vnde &longs;iue rotula illa magna <lb/>fuerit &longs;iue parua, &longs;emper eadem ratione nullam augere po<lb/>te&longs;t facilitatem, aut velocitatem in hac motione. </s>

<s id="N14330">Subdit que <lb/>Blancanus, experientia quoque con&longs;tare eodem labore <lb/>aquam hauriri, &longs;iue rotula illa magna fuerit &longs;iue parua. </s>

<s id="N14339">Verum &longs;i hoc vniuer&longs;aliter demon&longs;traret experientia, &longs;ru<lb/>&longs;tra pa&longs;&longs;im adhiberentur trochleæ ad leuanda, ac trahenda <lb/>pondera; nec e&longs;&longs;et cur iuxta maiorem ponderum grauita<lb/>tem, maioribus rotis, ac trochleis <expan abbr="vter&etilde;tur">vterentur</expan> Architecti quan<lb/>do minoribus vti po&longs;&longs;ent. </s>

<s id="N14339">Verum &longs;i hoc vniuer&longs;aliter demon&longs;traret experientia, fru<lb/>&longs;tra pa&longs;&longs;im adhiberentur trochleæ ad leuanda, ac trahenda <lb/>pondera; nec e&longs;&longs;et cur iuxta maiorem ponderum grauita<lb/>tem, maioribus rotis, ac trochleis <expan abbr="vter&etilde;tur">vterentur</expan> Architecti quan<lb/>do minoribus vti po&longs;&longs;ent. </s>

<s id="N14348">Quamuis igitur &longs;implex trochlea <lb/>&longs;upernè appen&longs;a nullam addat vim potentiæ motrici, &longs;icut <lb/>nec vectis, cuius fulcimentum non &longs;it propinquius oneri; <lb/>multam tamen affert commoditatem. </s>

<s id="N14351">Vnde eadem quip<lb/>pè vi, &longs;ed; non eodem labore eleuatur onus beneficio tro<lb/>chleæ, aut vectis prædicti, quàm &longs;ine illis. </s>

<s id="N14358">Commoditas enim <lb/>minuit laborem, ac &longs;i non auget potentiam, confert tamen <lb/>ad applicationem, & exercitium illius: id quod e&longs;t augere <lb/>facilitatem. </s>

<s id="N14361">Rur&longs;us quæcumque &longs;it facilitas, qua rotis, vel <lb/>trochleis pondera leuantur, certum e&longs;t velocius ea leuari <lb/>maioribus, quàm minoribus rotis; &longs;ed hoc ip&longs;um e&longs;t faci<lb/>lius mouere, quia licet non omnis facilitas includat veloci<lb/>tatem, vt pater in pluribus machinis tractorijs, quæ facilius, <lb/>&longs;ed tardius mouent; nihilominus velocitas &longs;emper inuoluit <lb/>facilitatem; Ergo nihil contra experientiam a&longs;&longs;ump&longs;it Ari<lb/>&longs;toteles, vt Blancanus contendit. </s>

<s id="N14374">Baldus item ait non e&longs;&longs;e &longs;impliciter verum idip&longs;um, quod <lb/>Philo&longs;ophus a&longs;&longs;erit, vt &longs;cilicet quo maiores fuerint trochleæ, <lb/>cò facilius moueant. </s>

<s id="N1437B">Quia tam maior, quàm minor trochlea <lb/>per eius centrum grauitatis diuiditur à perpendiculari ea-<pb pagenum="141" xlink:href="005/01/149.jpg"/>dente ad centrum mundi in duas partes æquales, & æquè <lb/>ponderantes, ac proinde &longs;emper e&longs;t eadem illarum pro<lb/>portio inter &longs;e, & eadem ponderum ratio, ex qua prouenit <lb/>motus. </s>

<s id="N1438B">Fatetur tamen hoc tantum procedere ab&longs;tractè lo<lb/>quendo cum alioquin in trochleis, ac rotis materialibus ne<lb/>gare non po&longs;&longs;it experientiam quam &longs;upponit Ari&longs;toteles. <lb/></s>

<s id="N14394">Quare totam maiorem facilitatem, quam experimur in ip&longs;is <lb/>trochleis, ac rotis maioribus, ip&longs;e ad maiorem proportio<lb/>nem, quam vt plurimum rota maior habet cum proprio axe <lb/>reducit. </s>

<s id="N1439F">Sed quidquid &longs;it de facilitate, aut difficultate &longs;imul <expan abbr="pro-ueni&etilde;te">pro<lb/>ueniente</expan> ex hoc capite, quam certè admittimus, ac infra <expan abbr="etiã">etiam</expan> <lb/>explicabimus: &longs;i&longs;tendo in &longs;ola ratione maioris, aut minoris <lb/>ambitus rotæ prout hic &longs;upponit Ari&longs;toteles, cæteris &longs;cilicet <lb/>paribus; explorati&longs;&longs;imum e&longs;t, ac negari minimè pote&longs;t, quam <lb/>facilius adhuc &longs;eruata eadem proportione axis, &longs;eu cra&longs;&longs;itiei <lb/>illius ad ambitum rotæ, ferantur <expan abbr="põdera">pondera</expan>, &longs;i maioribus a&longs;por<lb/>tentur, eleuentur; aut trahantur rotis; &longs;icut etiam &longs;cytalis, de <lb/>quibus hic eadem e&longs;t ratio. </s>

<s id="N143BE">Loquitur autem Ari&longs;toteles <lb/>de illo genere <expan abbr="&longs;eytalar&utilde;">&longs;eytalarum</expan>, quæ &longs;imiliter circa axim <expan abbr="coniunct&utilde;">coniunctum</expan> <lb/>ad eleuanda pondera conuertuntur, appo&longs;ito in altera ex<lb/>tremitate <expan abbr="illar&utilde;">illarum</expan> ferreo quoddam manubrio, vt in &longs;pecie e&longs;t <lb/>in &longs;ubiecta figura. </s>

<s id="N143BE">Loquitur autem Ari&longs;toteles <lb/>de illo genere <expan abbr="&longs;eytalar&utilde;">&longs;cytalarum</expan>, quæ &longs;imiliter circa axim <expan abbr="coniunct&utilde;">coniunctum</expan> <lb/>ad eleuanda pondera conuertuntur, appo&longs;ito in altera ex<lb/>tremitate <expan abbr="illar&utilde;">illarum</expan> ferreo quoddam manubrio, vt in &longs;pecie e&longs;t <lb/>in &longs;ubiecta figura. </s>

<s id="N143D5">Scytala enim de &longs;e <expan abbr="tant&utilde;">tantum</expan> &longs;ignificat lignum <lb/>quoddam <expan abbr="oblong&utilde;">oblongum</expan>, ac teres <expan abbr="tanquã">tanquam</expan> <expan abbr="cylindr&utilde;">cylindrum</expan>, cui <expan abbr="quandoq.">quandoque</expan> <lb/>alijs adiunctis diuer&longs;æ machinæ, ac in&longs;trumenta vectoria, &longs;i<lb/>ue tractoria efficiuntur, quorum nonnulla adhuc &longs;oytalæ <lb/>vocantur, vt hæc de qua loquimur, & alia de qua infra quæ<lb/>&longs;tione 11. </s>

<s id="N143D5">Scytala enim de &longs;e <expan abbr="tant&utilde;">tantum</expan> &longs;ignificat lignum <lb/>quoddam <expan abbr="oblong&utilde;">oblongum</expan>, ac teres <expan abbr="tanquã">tanquam</expan> <expan abbr="cylindr&utilde;">cylindrum</expan>, cui <expan abbr="quandoq.">quandoque</expan> <lb/>alijs adiunctis diuer&longs;æ machinæ, ac in&longs;trumenta vectoria, &longs;i<lb/>ue tractoria efficiuntur, quorum nonnulla adhuc &longs;cytalæ <lb/>vocantur, vt hæc de qua loquimur, & alia de qua infra quæ<lb/>&longs;tione 11. </s>

Line 2033

<s id="N14433">Magis <lb/>enim retardat, ac impedit axis cra&longs;&longs;ior, quam &longs;ubtilior. </s>

<s id="N14438">Quod <lb/>adhuc (aliter tamen quàm ille) po&longs;&longs;umus probare; Nimirum <lb/>quia ambitus &longs;ubtilioris axis per minorem &longs;ui partem attin<lb/>git rotam, quàm ambitus cra&longs;&longs;ioris: & &longs;ic minus impedit <lb/>circumuolutionem. </s>

<s id="N14443">Itemque po&longs;t punctum, quod e&longs;t in <lb/>&longs;ummitate circumferentiæ, & cui poti&longs;&longs;imum onus rotæ in<lb/>cumbit, partes vtrinque circulariter declinantes, decliuio<lb/>res &longs;unt in axe &longs;ubtiliori; eo quod minor circumferentia <lb/>magis curuetur; &longs;icut è contra quæ amplior e&longs;t, rectius pro<lb/>cedat, &longs;iue magis rectæ appropinquetur. </s>

<s id="N14450">Cumque partes <lb/>decliuiores, minus valeant onus &longs;u&longs;tinere nè dilabatur, <lb/>quàm partes, quæ minus declinant; hinc fit, vt &longs;ubtilior <lb/>axis ex decliuiotibus con&longs;titutus, minus retardet, aut impe<lb/>diat rotæ circumuolutionem. </s>

<s id="N14450">Cumque partes <lb/>decliuiores, minus valeant onus &longs;u&longs;tinere nè dilabatur, <lb/>quàm partes, quæ minus declinant; hinc fit, vt &longs;ubtilior <lb/>axis ex decliuioribus con&longs;titutus, minus retardet, aut impe<lb/>diat rotæ circumuolutionem. </s>

<s id="N1445D">Cæterum data axium paritate, præter cau&longs;am ab Ari&longs;to<lb/>tele a&longs;&longs;ignatam adhuc duplici ex capite reperiemus, maio<lb/>res rotas citiùs, ac faciliùs quàm minores conuolui. </s>

Line 2048

<s id="N144B8">Quæ&longs;tio Decima.</s>

<s id="N144BD">C<emph type="italics"/>vr facilius quando &longs;ine pondere e&longs;t, moue<lb/>tur libra, quàm cùm pondus babet? </s>

<s id="N144BD">C<emph type="italics"/>vr facilius quando &longs;ine pondere e&longs;t, moue<lb/>tur libra, quàm cùm pondus habet? </s>

<s id="N144C5"><expan abbr="&longs;imiliq.">&longs;imilique</expan> <lb/>modo rota, & buiu&longs;modi quippiam, quod gra<lb/>uius quidem e&longs;t, maius autem minore, & le<lb/>uiore? </s>

<s id="N144C5"><expan abbr="&longs;imiliq.">&longs;imilique</expan> <lb/>modo rota, & huiu&longs;modi quippiam, quod gra<lb/>uius quidem e&longs;t, maius autem minore, & le<lb/>uiore? </s>

<s id="N144D1">An quia non &longs;olum in contrarium, <lb/>quod graue e&longs;t, &longs;ed in obliquum etiam diffi<lb/>culter mouetur? </s>

<s id="N144D8">In contrarium enim ei, ad quod vergit onus, <lb/>mouere difficile e&longs;t: quo autem vergit, e&longs;t facilè: in obliquum <lb/>autem baud quaquam vergit.<emph.end type="italics"/></s>

<s id="N144D8">In contrarium enim ei, ad quod vergit onus, <lb/>mouere difficile e&longs;t: quo autem vergit, e&longs;t facilè: in obliquum <lb/>autem haud quaquam vergit.<emph.end type="italics"/></s>

<s id="N144E3">COMMENTARIVS.</s>

<s id="N144E9">Dvo in vnum collecta quærit hic Ari&longs;toteles, nempe <lb/>cur facilius moueatur ràm libra ponderibus vacua <lb/>re&longs;pectu &longs;ui ip&longs;ius cum pondera &longs;u&longs;tinet; quàm ro-<pb pagenum="144" xlink:href="005/01/152.jpg"/>ta leuior re&longs;pectu grauioris, non &longs;olum æqualis magnitudi<lb/>nis, &longs;ed etiam maioris, quam aliàs quæ&longs;tione præcedenti di<lb/>xerat mouerifacilius, ac velocius minore cæteris paribus. <lb/></s>

<s id="N144E9">Dvo in vnum collecta quærit hic Ari&longs;toteles, nempe <lb/>cur facilius moueatur tàm libra ponderibus vacua <lb/>re&longs;pectu &longs;ui ip&longs;ius cum pondera &longs;u&longs;tinet; quàm ro-<pb pagenum="144" xlink:href="005/01/152.jpg"/>ta leuior re&longs;pectu grauioris, non &longs;olum æqualis magnitudi<lb/>nis, &longs;ed etiam maioris, quam aliàs quæ&longs;tione præcedenti di<lb/>xerat moueri facilius, ac velocius minore cæteris paribus. <lb/></s>

<s id="N144FA"><expan abbr="Cau&longs;amq.">Cau&longs;amque</expan> &longs;ci&longs;citandi eam e&longs;&longs;e videtur, quoniam libra in <lb/>æquilibrio con&longs;tituta, &longs;icut etiam rota &longs;tans perpendicula<lb/>riter &longs;uper planum, aut in axe &longs;uffulta, quæ &longs;imilem habet <lb/>rationem, cuiu&longs;cunque grauitatis fuerit, &longs;tatim atque ex ali<lb/>qua parte impingatur, vel onus aliquod alteri eius extremo <lb/>&longs;uperaddatur; amplius manere non pote&longs;t in illo &longs;itu, aut <lb/>po&longs;itione, eo quod nece&longs;&longs;ariò æquilibrium aufe atur per <lb/>additionem ponderis, vel impetum incu&longs;&longs;um in alteram eius <lb/>extremitatem; <expan abbr="proindeq.">proindeque</expan> &longs;iue ip&longs;a libra &longs;itferrea, &longs;iue li<lb/>gnea grauior, aut leuior, æquè facilè deberet moueri: idem<lb/>que verificari de rota. </s>

<s id="N144FA"><expan abbr="Cau&longs;amq.">Cau&longs;amque</expan> &longs;ci&longs;citandi eam e&longs;&longs;e videtur, quoniam libra in <lb/>æquilibrio con&longs;tituta, &longs;icut etiam rota &longs;tans perpendicula<lb/>riter &longs;uper planum, aut in axe &longs;uffulta, quæ &longs;imilem habet <lb/>rationem, cuiu&longs;cunque grauitatis fuerit, &longs;tatim atque ex ali<lb/>qua parte impingatur, vel onus aliquod alteri eius extremo <lb/>&longs;uperaddatur; amplius manere non pote&longs;t in illo &longs;itu, aut <lb/>po&longs;itione, eo quod nece&longs;&longs;ariò æquilibrium auferatur per <lb/>additionem ponderis, vel impetum incu&longs;&longs;um in alteram eius <lb/>extremitatem; <expan abbr="proindeq.">proindeque</expan> &longs;iue ip&longs;a libra &longs;it ferrea, &longs;iue li<lb/>gnea grauior, aut leuior, æquè facilè deberet moueri: idem<lb/>que verificari de rota. </s>

<s id="N1451A">Quæ&longs;tioni tamen re&longs;pondet Ari&longs;toteles, grauiora corpo<lb/>ra difficilius moueri non modo directè contra proprium <lb/>nutum, quo tendunt deor&longs;um, vt cum fur&longs;um eleuantur; &longs;ed <lb/>etiam obliquè cum feruntur ad latera in tran&longs;uer&longs;um, quo <lb/>certè natura &longs;ua pondus non vergit. </s>

<s id="N1451A">Quæ&longs;tioni tamen re&longs;pondet Ari&longs;toteles, grauiora corpo<lb/>ra difficilius moueri non modo directè contra proprium <lb/>nutum, quo tendunt deor&longs;um, vt cum rur&longs;um eleuantur; &longs;ed <lb/>etiam obliquè cum feruntur ad latera in tran&longs;uer&longs;um, quo <lb/>certè natura &longs;ua pondus non vergit. </s>

<s id="N14525">Quamobrem hoc ip<lb/>&longs;o, quod libra, vel rota dimoueri non po&longs;&longs;it ah æqui<lb/>librio, quin obliquè cireumferatur per motum mi&longs;tum, ac <lb/>præter naturalem circa proprium fulcimentum, vel axim; <lb/>quo grauior fuerit, eo difficilius mouebitur, <expan abbr="magisq.">magisque</expan> huic <lb/>motui repugnabit, grauior autem e&longs;t libra ponderibus onu<lb/>&longs;ta, quàm vacua. </s>

<s id="N14525">Quamobrem hoc ip<lb/>&longs;o, quod libra, vel rota dimoueri non po&longs;&longs;it ab æqui<lb/>librio, quin obliquè circumferatur per motum mi&longs;tum, ac <lb/>præter naturalem circa proprium fulcimentum, vel axim; <lb/>quo grauior fuerit, eo difficilius mouebitur, <expan abbr="magisq.">magisque</expan> huic <lb/>motui repugnabit, grauior autem e&longs;t libra ponderibus onu<lb/>&longs;ta, quàm vacua. </s>

<s id="N14538"><expan abbr="Similiterq.">Similiterque</expan> rota ferrea, quàm lignea, vel <lb/>ferrea, aut lignea quadripalmaris diametri, quàm alia eiu&longs;<lb/>dem materiæ, &longs;ed bipalmaris. </s>

Line 2099

<s id="N1463F">C<emph type="italics"/>vr &longs;uper &longs;cytalas facilius portantur one<lb/>ra, quàm &longs;uper currus, cùm tamen ÿ ma<lb/>gnas habeant rotas, illæ verò pu&longs;illas? </s>

<s id="N14649">An <lb/>quoniam in &longs;cytalis nulla e&longs;t offen&longs;atio, in <lb/>curribus autem axis est, ad quem offen&longs;ant. <lb/></s>

<s id="N14651">De&longs;uper enim illum præmunt, & à lateri<lb/>bus. </s>

<s id="N14651">De&longs;uper enim illum premunt, & à lateri<lb/>bus. </s>

<s id="N14656">Quod autem e&longs;t in &longs;cytalis, ad i&longs;thæc duo mouetur, & <lb/>infernè &longs;ub&longs;trato &longs;patio, & onere &longs;uperimpo&longs;ito. </s>

<s id="N1465B">In viri&longs;<lb/>que enim ÿs reuoluitur locis circulus, & motus impellitur.<emph.end type="italics"/></s>

<s id="N1465B">In viri&longs;<lb/>que enim ijs reuoluitur locis circulus, & motus impellitur.<emph.end type="italics"/></s>

<s id="N14664">COMMENTARIVS.</s>

Line 2132

<s id="N14712">C<emph type="italics"/>vr longiùs feruntur mi&longs;&longs;ilia funda, quàm <lb/>manu mi&longs;&longs;a, cùm alioqui proiector manu <lb/>magis pondus comprehendat, quàm cùm il<lb/>lud &longs;u&longs;pendit? </s>

<s id="N1471E">Præterea &longs;ic quidem duo mo<lb/>uet pondera, fundæ videlicet, & mi&longs;silis: illo <lb/>autem modo &longs;olum mi&longs;sile. </s>

<s id="N14725">An quia in funda <lb/>quidem commotum mi&longs;sile funditor proÿcit? </s>

<s id="N14725">An quia in funda <lb/>quidem commotum mi&longs;sile funditor proijcit? </s>

<s id="N1472A">Fundam enim <lb/>circulo, &longs;ubinde rotans, id iaculatur: ex manu autem, à quie<lb/>te e&longs;t initium: omnia autem cùm in motu &longs;unt, quàm cùm <lb/>quie&longs;cunt, faciliùs mouentur. </s>

<s id="N14733">An & eam ob cau&longs;am est, &longs;ed<emph.end type="italics"/><pb pagenum="150" xlink:href="005/01/158.jpg"/><emph type="italics"/>nec minus etiam, quia in fundæ v&longs;u manus quidem fit cen<lb/>trum: &longs;unda verò, quod à centro exit? </s>

<s id="N14733">An & eam ob cau&longs;am est, &longs;ed <emph.end type="italics"/><pb pagenum="150" xlink:href="005/01/158.jpg"/><emph type="italics"/>nec minus etiam, quia in fundæ v&longs;u manus quidem fit cen<lb/>trum: funda verò, quod à centro exit? </s>

<s id="N14741">Quanto autem pro<lb/>ductius fuerit id, quod à centro e&longs;t, tantò citiùs mouetur. <lb/></s>

<s id="N14747">Toctus autem, qui manu fit, fundæ re&longs;pectu breuis e&longs;t.<emph.end type="italics"/></s>

<s id="N14747">Tactus autem, qui manu fit, fundæ re&longs;pectu breuis e&longs;t.<emph.end type="italics"/></s>

<s id="N1474E">COMMENTARIVS.</s>

<s id="N14754">Dvas hic Ariftoreles rationes dubitandi proponit, <lb/>vt explicet cau&longs;am cur longius ferantur mi&longs;silia <lb/>funda, quàm manu mi&longs;&longs;a. </s>

<s id="N14754">Dvas hic Aristoreles rationes dubitandi proponit, <lb/>vt explicet cau&longs;am cur longius ferantur mi&longs;silia <lb/>funda, quàm manu mi&longs;&longs;a. </s>

<s id="N1475B">Prima e&longs;t, quia proie<lb/>ctor melius mi&longs;&longs;ilia ip&longs;a manu comprehendit, quàm cum <lb/>funda &longs;u&longs;pendit: Quod autem melius comprehenditur, va<lb/>lidius iacitur ac propterea longius mittitur: Potius itaque <lb/>manu mi&longs;&longs;a, quàm funda proiecta mi&longs;silia longius ferri de<lb/>berent. </s>

<s id="N14768">Secunda verò ratio e&longs;t, nam <expan abbr="c&utilde;">cum</expan> funda quis proijcit; <lb/>duo &longs;imul mouet <expan abbr="põdera">pondera</expan>; fundá nempe <expan abbr="ipsã">ipsam</expan>, & mi&longs;sile, quod <lb/>proijcit; <expan abbr="ab&longs;q;">ab&longs;que</expan> autem funda <expan abbr="nõ">non</expan> mouet ni&longs;i proiectum: At am<lb/>plius quilibet mouere valet quando <expan abbr="totã">totam</expan> eius vim applicat <lb/>in vnum, quàm cum di&longs;tribuit in plura: Ergo magis ac remo<lb/>tius proiector manu mittet, ac proijciet, quàm funda. </s>

Line 2152

<s id="N147A9">Omnia autem cum in motu &longs;unt, <lb/>facilius vlterius per nouum impul&longs;um feruntur, quàm cum <lb/>quie&longs;cunt, ac tunc primò moueri coguntur. </s>

<s id="N147B2">Quocirca vt hæc doctrina iuxta rei veritatem clarius elu<lb/>ce&longs;cat, ob&longs;eruandum e&longs;t, proiecta in rigore loquendo non <lb/>&longs;tatim po&longs;t quietem è manu iaculantis elabi; &longs;ed aliquan<lb/>tulum &longs;altem prius manu ip&longs;a comitante moueri antequam <lb/>cmittantur. </s>

<s id="N147BD">Motus enim brachij iaculantis arcum quen<lb/>dam &longs;emper de&longs;cribit, in cuius fine, non autem in principio <lb/>mi&longs;silia proijciuntur; & quò longius proijcienda &longs;unt eò <pb pagenum="151" xlink:href="005/01/159.jpg"/>maiorem arcum brachium ip&longs;um efficit; magis nimirum <lb/>prius retrocedendo, magi&longs;que po&longs;tea antror&longs;um &longs;e exten<lb/>dendo, atque in fine exten&longs;ionis è manu mi&longs;silia dimitten<lb/>do. </s>

<s id="N147CF">Alioqui ni&longs;i manus imò etiam brachium &longs;imul cum il<lb/>lis antea moueretur, nec impetum inferre, nec proijcere <lb/>ip&longs;a valeret. </s>

<s id="N147D6">Quare cum ait Ari&longs;toteles, nullam antecede<lb/>re commotionem in proiectione, quæ fit &longs;ola manu, intelli<lb/>gendus non e&longs;t de commotione immediata coniuncta, & <lb/>qua&longs;i e&longs;&longs;entialiter pertinente ad eundem actum proiectio<lb/>nis: &longs;ed de commotione di&longs;po&longs;itiua accidentali, & qua&longs;i re<lb/>mota ad ip&longs;um actum iaculandi, vt e&longs;t præcedens illa irro<lb/>tatio, & agitatio fundæ. </s>

Line 2217

<s id="N14966">Cvm plura iugum de &longs;e po&longs;&longs;it &longs;ignificare, hoc loco &longs;u<lb/>mitur ab Ari&longs;totele pro <expan abbr="in&longs;trum&etilde;to">in&longs;trumento</expan> quodam ligneo, <lb/>quo textores in machina textoria. </s>

<s id="N14971">vtuntur, vt &longs;ta<lb/>men <expan abbr="telasq.">telasque</expan> conuoluant. </s>

<s id="N1497A">Oblongum itaque ac teres quod<lb/>dam lignum e&longs;t &longs;uper tran&longs;uer&longs;a ip&longs;ius textrinæ locatum, <pb pagenum="155" xlink:href="005/01/163.jpg"/>bina circa <lb/><figure id="id.005.01.163.1.jpg" xlink:href="005/01/163/1.jpg"/><lb/><expan abbr="vtramq.">vtramque</expan> ex<lb/>tremitatem <lb/><expan abbr="hab&etilde;s">habens</expan> fora<lb/>mina, qui<lb/>bus toti<lb/>dem collo<lb/>pes, &longs;eu fu<lb/>&longs;tes infigun<lb/>tur, vt faci<lb/>liùs iugum ip&longs;um eorum beneficio cum opus fuerit conuer<lb/>tatur, vt præ&longs;efert &longs;ub&longs;trata figura. </s>

<s id="N149A8">Sucula item quamuis alia po&longs;&longs;it &longs;ignificare, hic tamen <lb/>machinam &longs;ignificat tractorij generis, quæ ex tereti ligno, <lb/>aut lignorum compagine con&longs;tat, adiuncto axe &longs;uffulta <lb/>æquidi&longs;tante à plano horizontis, duobus, vel pluribus col<lb/>lopibus pari longitudine vtrinque immobiliter ad&longs;tantibus <lb/>tanquam rotæ radijs circa modiolum, quibus admota ma<lb/>nu, &longs;ucula ip&longs;a circa proprium axem obuoluitur, <expan abbr="funeq.">funeque</expan> cir<lb/>cumducto, pondera &longs;ubleuat, vt præoculis hic e&longs;t videre <lb/>in eius figura. </s>

Line 2227

<s id="N149D7"><expan abbr="Itemq.">Itemque</expan> cur gracilio<lb/>res &longs;ucculæ facilius <lb/>pariter ab <expan abbr="ead&etilde;">eadem</expan> po<lb/>tentia circumuoluantur, quàm cra&longs;&longs;iores. </s>

<s id="N149E7">Vtriu&longs;que &longs;ubin<lb/>de cau&longs;am e&longs;&longs;e inquit, quod in vtraque machina quilibet <lb/>collops tanquam vectis &longs;e habet, cuius <expan abbr="centr&utilde;">centrum</expan>, ac fulcimen<lb/>tum e&longs;t in medio iugi, vel &longs;uculæ, &longs;iue in intimo axe coniun<lb/>cto, aut &longs;altem in ip&longs;is concepto: potentia verò in extremi-<pb pagenum="156" xlink:href="005/01/164.jpg"/>tate, quæ extra ip&longs;um iugum, vel &longs;uculam prominet, vbi <lb/>manus communiter adhibetur: ac onus con&longs;tituitur in exti<lb/>ma ip&longs;a vtriu&longs;que corporis &longs;uperficie, quam fortiter præ<lb/>mendo vbi è foramine prodit, &longs;ecum conuoluit, ac ver&longs;at. <lb/></s>

<s id="N14A02">Cuius quippe vectis &longs;imilitudinem, & operationem hacte<lb/>nus etiam in malo expre&longs;simus loquendo de motione nauis <lb/>vento agitatæ. </s>

<s id="N14A09">Cum itaque plus atque celerius transfera<lb/>tur ab eadem potentia extremum &longs;emidiametri, quod ma<lb/>gis à centro di&longs;tat in de&longs;criptione circuli, nec non plus, ac <lb/>facilius mouere valeat extremum vectis, quod longius à <lb/>fulcimento re&longs;pectu oneris leuandi protenditur, quò lon<lb/>giores fuerint collopes, &longs;emidiametri, ac vectis rationem <lb/>adepti, <expan abbr="magisq.">magisque</expan> eorum extrema à fulcimento, &longs;eu centro <lb/>in &longs;uperficie conuoluenda di&longs;tauerint, eò faciliùs iugum, aut <lb/>&longs;uculam contorquendo ver&longs;abune. </s>

<s id="N14A20">Quoniam verò in omni <lb/>vecte maior, aut minor di&longs;tantia, quàm à centro, vel fulci<lb/>mento habet extremum, in quo applicatur potentia, atten<lb/>ditur &longs;olummodo re&longs;pectu di&longs;tantiæ, quam &longs;imul habet onus <lb/>ab eodem centro, vel fulcimento; hinc fit, vt in graciliori<lb/>bus &longs;uculis, minore exi&longs;tente di&longs;tantia à centro ad circum<lb/>ferentiam, &longs;eu extimam &longs;uperficiem conuexam vbi con&longs;ti<lb/>tuitur onus, & vbi fit collopis præ&longs;sio, maior di&longs;tantia relin<lb/>quatur v&longs;que ad alterum extremum eiu&longs;dem collopis, quod <lb/>e&longs;t extra; ac iuxtamaiorem hanc proporrionem, magis pa<lb/>riter collops ip&longs;e mouere &longs;uculam valeat. </s>

<s id="N14A20">Quoniam verò in omni <lb/>vecte maior, aut minor di&longs;tantia, quàm à centro, vel fulci<lb/>mento habet extremum, in quo applicatur potentia, atten<lb/>ditur &longs;olummodo re&longs;pectu di&longs;tantiæ, quam &longs;imul habet onus <lb/>ab eodem centro, vel fulcimento; hinc fit, vt in graciliori<lb/>bus &longs;uculis, minore exi&longs;tente di&longs;tantia à centro ad circum<lb/>ferentiam, &longs;eu extimam &longs;uperficiem conuexam vbi con&longs;ti<lb/>tuitur onus, & vbi fit collopis præ&longs;sio, maior di&longs;tantia relin<lb/>quatur v&longs;que ad alterum extremum eiu&longs;dem collopis, quod <lb/>e&longs;t extra; ac iuxta maiorem hanc proportionem, magis pa<lb/>riter collops ip&longs;e mouere &longs;uculam valeat. </s>

<s id="N14A39">Quod &longs;i contra hanc expo&longs;itionem obijciatur, quòd Ari<lb/>&longs;toteles palàm & ab&longs;olutè docuerit, tàm &longs;uculam, quàm iu<lb/>gum <expan abbr="cõ&longs;titui">con&longs;titui</expan> centrum in collopum motione; ex quo a&longs;&longs;um<lb/>pto minus concluderentur, quæ de ip&longs;ius mente relata &longs;unt; <lb/>Occurrendum e&longs;t, id &longs;ano modo e&longs;&longs;e intelligendum. </s>

Line 2241

<s id="N14A73">C<emph type="italics"/>vr eiu&longs;dem magnitudinis lignum faciliùs <lb/>genu. </s>

<s id="N14A7B">frangitur, &longs;i qui&longs;piam æquè deductis <lb/>manibus extrema comprehendens fregerie, <lb/>quàm &longs;i iuxta genu: & &longs;i terræ illud appli<lb/>cans pelle &longs;uperimpo&longs;ito, manu longè didu<lb/>cta confregerit, quàm propè? </s>

<s id="N14A7B">frangitur, &longs;i qui&longs;piam æquè deductis <lb/>manibus extrema comprehendens fregerit, <lb/>quàm &longs;i iuxta genu: & &longs;i terræ illud appli<lb/>cans pelle &longs;uperimpo&longs;ito, manu longè didu<lb/>cta confregerit, quàm propè? </s>

<s id="N14A86">An quia ibi <lb/>quidem genu centr<gap/> e&longs;t, bìs verò ip&longs;e pes. </s>

<s id="N14A8D">Quantò autem <lb/>remotiùs à centro fuerit, faciliùs mouetur quodcunque. </s>

<s id="N14A92">Mo<lb/>ueri autem quod frangitur, nece&longs;&longs;e est.<emph.end type="italics"/></s>

Line 2262

<s id="N14B05"><expan abbr="Cumq.">Cumque</expan> ex hac motione, & <lb/>inclinatione vtriu&longs;que dimidij procedat ip&longs;a fractio ligni, &longs;e<lb/>quitur etiam facilius longè quàm propè diductis manibus <lb/>ip&longs;um lignum confringi. </s>

<s id="N14B13">Cur autem non ob&longs;tante prædicta di&longs;paritate in modo, <lb/>quo frangitur lignum, cæteris paribus<gap/>difficilius <expan abbr="fuãgatur">fuangatur</expan> <lb/>&longs;i cra&longs;sius ip&longs;um &longs;it, quàm &longs;i gracilius, non docet Ari&longs;tote<lb/>les. </s>

<s id="N14B13">Cur autem non ob&longs;tante prædicta di&longs;paritate in modo, <lb/>quo frangitur lignum, cæteris paribus difficilius <expan abbr="fuãgatur">frangatur</expan> <lb/>&longs;i cra&longs;sius ip&longs;um &longs;it, quàm &longs;i gracilius, non docet Ari&longs;tote<lb/>les. </s>

<s id="N14B23">Ex ip&longs;a <expan abbr="tam&etilde;">tamen</expan> rei natura qui&longs;que &longs;tatim intelliget ab&longs;que <lb/>eo, quod recurrat cum Baldo ad rationem illam angulati <lb/>vectis, quam dicit habere <expan abbr="vtrumq.">vtrumque</expan> dimidium ligni prærupti. <lb/></s>

<s id="N14B33">Siquidem cum tota difficultas, quæ reperitur in fractione <lb/>ligni oriatur ex re&longs;i&longs;tentia partium &longs;eparandarum, eo quod <lb/>hæ inter &longs;e naturali nexu coniunctæ, nece&longs;&longs;ariò ob&longs;tent &longs;e<lb/>parationi ab inuicem: quo plures fuerint ip&longs;æ partes, eo ma<lb/>gis ob&longs;tabunt, <expan abbr="difficiliusq.">difficiliusque</expan> proinde per earum diui&longs;ionem <lb/>lignum quodlibet ex ip&longs;is compo&longs;itum confringetur. </s>

<s id="N14B46">Illud etiam hic quæri po&longs;&longs;et, quod Ari&longs;toteles prætermi<lb/>&longs;it, cur prius ex parte &longs;uperiori, ac extra angulum, quem effi<lb/>ciunt dimidia ligni inclinata, quàm ex parte inferiori in cu<lb/>&longs;pide ip&longs;ius anguli vbi <expan abbr="c&etilde;trum">centrum</expan> motionis con&longs;tituitur, fractio <lb/>ip&longs;a ligni &longs;equatur. </s>

<s id="N14B55">Facilisque erit re&longs;pon&longs;io &longs;i dicamus id <lb/>&longs;ieri, quia illæ partes continui in fractione prius ab inuicem <lb/>&longs;eparantur, quæ & citius & longius coguntur di&longs;cedere: In <lb/>fractione autem ligni per inclinationem, & complicationem <lb/>vtriu&longs;que dimidij, ex partibus cra&longs;sitiei, quæ ab inuicem di-<pb pagenum="159" xlink:href="005/01/167.jpg"/>uelluntur, illæ citius ac longius ab inuicem coguntur di&longs;ce<lb/>dere, quæ magis di&longs;tant à puncto, quod con&longs;tituitur cen<lb/>trum in hac motione; quia nimirum illæ di&longs;cedendo, maio<lb/>rem &longs;emper arcum de&longs;cribunt eodem tempore, quam quæ <lb/>propinquiores &longs;unt centro. </s>

<s id="N14B55">Facilisque erit re&longs;pon&longs;io &longs;i dicamus id <lb/>fieri, quia illæ partes continui in fractione prius ab inuicem <lb/>&longs;eparantur, quæ & citius & longius coguntur di&longs;cedere: In <lb/>fractione autem ligni per inclinationem, & complicationem <lb/>vtriu&longs;que dimidij, ex partibus cra&longs;sitiei, quæ ab inuicem di-<pb pagenum="159" xlink:href="005/01/167.jpg"/>uelluntur, illæ citius ac longius ab inuicem coguntur di&longs;ce<lb/>dere, quæ magis di&longs;tant à puncto, quod con&longs;tituitur cen<lb/>trum in hac motione; quia nimirum illæ di&longs;cedendo, maio<lb/>rem &longs;emper arcum de&longs;cribunt eodem tempore, quam quæ <lb/>propinquiores &longs;unt centro. </s>

<s id="N14B6D">Illæ igitur ip&longs;æ partes cra&longs;&longs;itiei <lb/>di&longs;tantiores a centro prius, ac citius ab inuicem &longs;eparantur, <lb/>ac proinde fractio non ab ip&longs;o centro, vel parte inferiori vbi <lb/>fulcitur, &longs;ed à parte &longs;uperiori, ac remotiori ab illo, initium <lb/>&longs;umere debet. </s>

Line 2277

<s id="N14B91">Partes <lb/>verò quæ ab in<lb/>uicem &longs;eparan<lb/>tur &longs;int illæ, quæ <lb/>exi&longs;tunt in lineis <lb/>DC, & EC re<lb/>pr&etail;&longs;entantes la<lb/>titudinem, vel <lb/>cra&longs;sitiem ligni. <lb/></s>

<s id="N14BA5">Dicimus ergo ex <lb/>huiu&longs;modi par<lb/>tibus, quæ &longs;unt in ip&longs;is lineis DC, & EC, illas quæ magis <lb/>di&longs;tant à puncto C citius moueri, ac per maius interuallum <lb/>ab inuicem &longs;eparari: quod e&longs;t prius confringi, quàm quæ <lb/>prop inquiores &longs;unt puncto C. </s>

<s id="N14BB3">Siquidem ip&longs;um C non <lb/>modo con&longs;tituitur centrum in hac motione re&longs;pectu &longs;emi<lb/>circuli AFB; &longs;ed etiam re&longs;pectu &longs;emicirculi GDEH, qui <lb/>efficitur à punctis DE, vt tandem DA po&longs;t ab&longs;olutam <lb/>complicationem ligni reperiatur in GI; & EB in HK. </s>

<s id="N14BBE">Qua<lb/>propter lineæ DC, & EC con&longs;tituuntur tanquam duo &longs;e<lb/>midiametri, cuius partes quo remotiores fuerint à centro <lb/>C, eo velocius ab eadem potentia mouentur, maiusq &longs;pa<lb/>tium in æquali tempore percurrunt, vt &longs;&etail;pius probatum e&longs;t. </s>

<s id="N14BBE">Qua<lb/>propter lineæ DC, & EC con&longs;tituuntur tanquam duo &longs;e<lb/>midiametri, cuius partes quo remotiores fuerint à centro <lb/>C, eo velocius ab eadem potentia mouentur, <expan abbr="maiusq">maiusque</expan> &longs;pa<lb/>tium in æquali tempore percurrunt, vt &longs;&etail;pius probatum e&longs;t. </s>

<s id="N14BCB">Diximus autem prius &longs;eparari partes di&longs;tantiores à pun-<pb pagenum="160" xlink:href="005/01/168.jpg"/>cto C in ip&longs;is lineis DC, & EC, loquendo de illis prout <lb/>repræ&longs;entant materialem cra&longs;sitiem ligni, quæ non &longs;tatim <lb/>ac tota &longs;imul di&longs;rumpitur. </s>

Line 2305

<s id="N14C38">Crocæ apud Græcosidem &longs;ignificant, ac apud Lati<lb/>nos vmbilici, quorum meminit Cicero 2. de Orato<lb/>re; <expan abbr="&longs;untq.">&longs;untque</expan> expoliti illi calculi, qui in littoribus repe<lb/>riuntur continua maris agitatione attriti, ac inorbicularem, <lb/>vel rotundam figuram redacti, vt qui in glarea arenis vi&longs;un-<pb pagenum="161" xlink:href="005/01/169.jpg"/>tur admi&longs;ti. </s>

<s id="N14C4C">De ijs igitur hic loquens Ari&longs;toteles, quærit, <lb/>qua de cau&longs;a rotundam potius quam aliam figuram per at<lb/>tritionem ac perpetuam illam agitationem adipi&longs;cantur, <lb/>cum frequentius ex lapidibus, ac fragmentis alterius figuræ <lb/>efficiantur. </s>

<s id="N14C57">Quod enim &longs;ecundum omnes &longs;ui partes paula<lb/>tim conteritur, ac minuitur, vniformiter difformiter contun<lb/>di debet, ac &longs;en&longs;im attenuari, eadem partium proportione <lb/>&longs;eruata, <expan abbr="eademq.">eademque</expan> proinde figura. </s>

<s id="N14C64">Non igitur &longs;atis apparet <lb/>cur ex tot tanquam ex diuer&longs;is &longs;iguris te&longs;tarum o&longs;treorum <lb/><expan abbr="concarumq.">concarumque</expan> ac lapidum angularium non ni&longs;i rotundam, & <lb/>orbicularem formam eorum reliquiæ videantur &longs;eruare, <lb/><expan abbr="eiu&longs;demq.">eiu&longs;demque</expan> figuræ penè omnes euadant cuius non erant. </s>

<s id="N14C64">Non igitur &longs;atis apparet <lb/>cur ex tot tanquam ex diuer&longs;is figuris te&longs;tarum o&longs;treorum <lb/><expan abbr="concarumq.">concarumque</expan> ac lapidum angularium non ni&longs;i rotundam, & <lb/>orbicularem formam eorum reliquiæ videantur &longs;eruare, <lb/><expan abbr="eiu&longs;demq.">eiu&longs;demque</expan> figuræ penè omnes euadant cuius non erant. </s>

<s id="N14C77">Huic autem quæ&longs;tioni Ari&longs;toteles re&longs;pondet, partes, quæ <lb/>magis à centro, &longs;eu puncto medio circumlati corporis rece<lb/>dunt, cum celerius in eius circumuolutione ferantur (maius <lb/>videlicet in æquali tempore &longs;patium in rotatione conficien<lb/>do) vehementius impetere, <expan abbr="vicinaq.">vicinaque</expan> corpora rotando per<lb/>cutere, quàm partes centro propinquiores; velocitas enim <lb/>auget impul&longs;um: Quæ autem partes <expan abbr="vehem&etilde;tius">vehementius</expan> impetunt, <lb/>atque impingunt, &longs;i fragiles in &longs;e &longs;int, facilius etiam refran<lb/>guntur. </s>

Line 2315

<s id="N14CA5">Quod &longs;i ex hoc Ari&longs;totelis di&longs;cur&longs;u &longs;equatur maiores <lb/>croceas rotundiores fieri, quàm minores propter maiorem <lb/>à centro di&longs;tantiam, qua in rotatione prominentes partes <lb/>facilius contunduntur; id certè ab experientia non e&longs;t om<lb/>nino alienum, vt Baldus arbitratur; &longs;icut nec ip&longs;as croceas <lb/>circa centrum conuerti, quamuis alijs, ac diuer&longs;is etiam mo<lb/>tionibus agitentur. </s>

<s id="N14CB4">Si enim in pluribus littoribus attentius <lb/>ob&longs;erua&longs;&longs;et, vidi&longs;&longs;et vtique fluctuum iactatione fluxu, ac re<lb/>fluxu, non modo glareas, paruo&longs;que lapillos circa centrum <lb/>omnino conuolui, &longs;ed etiam maiores vmbilicos, & non me<pb pagenum="162" xlink:href="005/01/170.jpg"/>diocria &longs;axa &longs;imiliter in orbem ruere, <expan abbr="&longs;e&longs;eq.">&longs;e&longs;eque</expan> collidere, quæ <lb/>ni&longs;i magna valde &longs;int, vt rotari minus commodè po&longs;sint, <lb/>mutua ip&longs;orum colli&longs;ione, orbiculata euadunt, vel ad orbi<lb/>cularem figuram accedunt magis quàm minores lapilli, vel <lb/>te&longs;tæ. </s>

<s id="N14CCE">Vnde lati&longs;simæ plagæ vi&longs;untur his tantum rotundis <lb/>lapidibus &longs;tratæ, nulla ferè admi&longs;ta arena, parua te&longs;ta, vel <lb/>glarea. </s>

<s id="N14CD5">Quod verò non omnes lapides leuigatos, ac rotun<lb/>dos tanquam torno fabrefactos &longs;e videantur o&longs;tendere; id <lb/>potius materiæ varietati eribuendum e&longs;t, qua non omnes <lb/>partes æquè fiagiles con&longs;tituuntur, vt pariter po&longs;sint &longs;ua <lb/>volubilitate contundi. </s>

<s id="N14CD5">Quod verò non omnes lapides leuigatos, ac rotun<lb/>dos tanquam torno fabrefactos &longs;e videantur o&longs;tendere; id <lb/>potius materiæ varietati tribuendum e&longs;t, qua non omnes <lb/>partes æquè fragiles con&longs;tituuntur, vt pariter po&longs;sint &longs;ua <lb/>volubilitate contundi. </s>

<s id="N14CE0">Imò minores vmbilicos, vt plurimùm <lb/>fragiliorem adeptos e&longs;&longs;e materiam argumento e&longs;&longs;e pote&longs;t <lb/>ip&longs;a eorum paruitas. </s>

<s id="N14CE7">Non enim ex magnis parui facti e&longs;&longs;ent, <lb/>ni&longs;i materia, ex qua con&longs;tant facilè cederet, ac cedendo vni<lb/>formiter attenuaretur, ex quo prouenit leuitas. </s>

Line 2352

<s id="N14D9E">Ex ijs autem duobus quæ&longs;itis, &longs;ecundo tantum <expan abbr="re&longs;põdet">re&longs;pondet</expan> <lb/>Ari&longs;toteles, cum ex eius &longs;olutione facilè patere po&longs;sit &longs;olu<lb/>tio primi. </s>

<s id="N14DA9">Ait igitur ex hoc procedere maiorem inflexio<pb pagenum="164" xlink:href="005/01/172.jpg"/>nem ligni procerioris, quod cum lignum ita &longs;u&longs;pen&longs;um, &longs;i<lb/>mul con&longs;tituatur vectis, & onus, fulcimentum habens prope <lb/>alterum extremum in manu à qua eleuatur; quanto exten<lb/>&longs;ius fuerit id quod à fulcimento e&longs;t ver&longs;us alteram extremi<lb/>tatem, quæ con&longs;tituitur pondus; tanto magis ip&longs;um inflecti <lb/>nece&longs;&longs;e e&longs;t, &longs;uppo&longs;ito quod vectis ip&longs;a &longs;eu lignum, ex &longs;e fle<lb/>ctile &longs;it; id quod non contingit in breuibus lignis, aut vecti<lb/>bus etiam &longs;i eadem &longs;eruetur proportio: Porrò extremum, <lb/>quod grauitat parum &longs;emper di&longs;tat à fulcimento. </s>

<s id="N14DC1">Sit enim <lb/>&longs;ari&longs;&longs;a decem cubitorum longitudinis aliquantulum incli<lb/><figure id="id.005.01.172.1.jpg" xlink:href="005/01/172/1.jpg"/><lb/>nata ip&longs;a AB, cuius manubrium A, cu&longs;pis B, &longs;uffulta di<lb/>gitis vbi C, pollice præmente in A tanquam potentia <lb/>eleuante. </s>

<s id="N14DD2">Eodemq pacto con&longs;tituatur gracilior &longs;urculu<gap/><lb/>bicubitus DE fultus in F. </s>

<s id="N14DD2"><expan abbr="Eodemq">Eodemque</expan> pacto con&longs;tituatur gracilior &longs;urculus <lb/>bicubitus DE fultus in F. </s>

<s id="N14DD9">Dico igitur &longs;ari&longs;&longs;am magis in<lb/>clinari quàm &longs;urculum, eo quod licet vtiumque habeat ra<lb/>tionem vectis &longs;imul & oneris; pondus tamen con&longs;titutus in <lb/>B magis di&longs;tat à fulcimento C, quàm quod <expan abbr="cõ&longs;tituitur">con&longs;tituitur</expan> in E <lb/>ab ip&longs;o F; <expan abbr="magisq.">magisque</expan> propterea grauitat, & inclinat deor&longs;um, <lb/>paulatim recedendo à rectitudine, quam &longs;tans, vel in &longs;olo <lb/>iacens habebat. </s>

<s id="N14DD9">Dico igitur &longs;ari&longs;&longs;am magis in<lb/>clinari quàm &longs;urculum, eo quod licet vtrumque habeat ra<lb/>tionem vectis &longs;imul & oneris; pondus tamen con&longs;titutus in <lb/>B magis di&longs;tat à fulcimento C, quàm quod <expan abbr="cõ&longs;tituitur">con&longs;tituitur</expan> in E <lb/>ab ip&longs;o F; <expan abbr="magisq.">magisque</expan> propterea grauitat, & inclinat deor&longs;um, <lb/>paulatim recedendo à rectitudine, quam &longs;tans, vel in &longs;olo <lb/>iacens habebat. </s>

<s id="N14DF2">Quod non abs re fuerit aliundè etiam confirmare, ac vl<lb/>terius declarare, notando prius ad inflexionem <expan abbr="cõtinui">continui</expan> duo <lb/>nece&longs;&longs;ario requiri. </s>

<s id="N14DFD">Vnum e&longs;t determinata, ac proportiona<lb/>ta quædam virtus &longs;iue ponderis, &longs;iue motricis potentiæ, ita <lb/>vt ab alia minori nulla cau&longs;ari po&longs;&longs;it talis inflexio. </s>

<s id="N14E04"><expan abbr="Quõd">Quond</expan> <lb/>certè <expan abbr="cõmune">commune</expan> e&longs;t omnibus cau&longs;is naturalibus re&longs;pectu pro<lb/>priorum effectuum, ad quos ordinantur. </s>

<s id="N14E04"><expan abbr="Quõd">Quod</expan> <lb/>certè <expan abbr="cõmune">commune</expan> e&longs;t omnibus cau&longs;is naturalibus re&longs;pectu pro<lb/>priorum effectuum, ad quos ordinantur. </s>

<s id="N14E12">Alterum verò e&longs;t <pb pagenum="165" xlink:href="005/01/173.jpg"/>con&longs;tipatio quædam aliquarum partium, aliarumque laxa<lb/>tio in corporibus flexibilibus tanquam conden&longs;atio, ac ra<lb/>refactio. </s>

<s id="N14E1E">Non enim po&longs;&longs;et continuum inflecti ni&longs;i partes il<lb/>lius, quæ concauam &longs;uperficiem con&longs;tituunt vici&longs;&longs;im con&longs;ti<lb/>parentur; illæ verò quæ conuexam, laxarentur; &longs;eu quo fie<lb/>ri pote&longs;t extenderentur. </s>

<s id="N14E27">Cumque &longs;en&longs;im natura ab vno ad <lb/>aliud in omnibus gradum faciat; hinc e&longs;t, vt non in qualibet <lb/>longitudine &longs;iue di&longs;tantia æquè fieri po&longs;&longs;it inflexio, &longs;ed lon<lb/>gè facilius in ea, in qua paulatim procedendo, ita partes va<lb/>lent curuari, vt &longs;ingulæ à rectitudine non videantur recede<lb/>re. </s>

Line 2370

<s id="N14E4B">E contra verò quo bre<lb/>uiora extiterint, eo minor e&longs;t virtus huiu&longs;modi; quæ tandem <lb/>&longs;i minor &longs;it minima, quæ &longs;ufficere po&longs;sit ad motionem, nullo <lb/>pacto valet inflectere, vt patet in &longs;urculis calamis ac paleis, <lb/>quæ cum leuitate materiæ, tùm breuitate corporis, graui<lb/>tare non po&longs;&longs;unt quantum &longs;ufficiat ad motum inflexionis. <lb/></s>

<s id="N14E59">Quod &longs;i breuitas ligni compen&longs;etur magna cra&longs;&longs;itiei, ob&longs;ta<lb/>bit ex alio capite ip&longs;amet eadem cra&longs;sities propter maio<lb/>rem multitudinem partium, quarum aliæ con&longs;tipari, aliæ au<lb/>tem laxari debent cum fit ip&longs;a inflexio. </s>

<s id="N14E62">Secundo verò nam <lb/>quanto maior e&longs;t longitudo ip&longs;ius flexilis, tanto minor con<lb/>&longs;tituitur laxatio, & con&longs;tipatio &longs;ingularum partium, quæ ar<lb/>cum inflexionis efficiunt, meliu&longs;que valent &longs;en&longs;im inflecti. <lb/></s>

<s id="N14E6C">Vice autem ver&longs;a, quò breuior e&longs;t longitudo illius, eò magis <lb/>&longs;ingulæ partes curuari debent, vt totius continui &longs;iat infle<lb/>xio. </s>

<s id="N14E6C">Vice autem ver&longs;a, quò breuior e&longs;t longitudo illius, eò magis <lb/>&longs;ingulæ partes curuari debent, vt totius continui fiat infle<lb/>xio. </s>

<s id="N14E73"><expan abbr="Ideoq.">Ideoque</expan> difficilius curuantur, & inflectuntur etiam &longs;i gra<lb/>cile &longs;it ip&longs;um lignum, quod debet inflecti. </s>

Line 2385

<s id="N14ED1">Quare nihil determinari pote&longs;t quo ad hoc ni&longs;i per<lb/>&longs;pecta, vt diximus di&longs;po&longs;itione materiæ, <expan abbr="variaq.">variaque</expan> proportio<lb/>ne, quæ diuer&longs;imodè iuxta maiorem, aut minorem corpo<lb/>rum magnitudinem operatur. </s>

<s id="N14EE0">Denique vt dictum e&longs;t de eleuatione, ac &longs;u&longs;pen&longs;ione li<lb/>gni, vel alterius corporis oblongi &longs;umpti ab altera tantum <lb/>extremitate, vt exemplificauimus in &longs;ari&longs;&longs;a, idem dicendum <lb/>e&longs;t de eleuatione, ac &longs;u&longs;pen&longs;ione, quæ fit, vel ex ambabus <lb/>extremitatibus; vel ex medio inter illas: Nam &longs;i vtrinque ab <lb/>extremitatibus &longs;u&longs;pendatur aliquod lignum ad paralellum <lb/>horizonti, duo quidem in illo vectes fient in ip&longs;is extremita<lb/>tibus fulti, ponderaq in communi puncto intermedio gra<lb/>uitabunt tanquam in remoti&longs;simo &longs;itu ab vtriu&longs;que fultura. <lb/></s>

<s id="N14EE0">Denique vt dictum e&longs;t de eleuatione, ac &longs;u&longs;pen&longs;ione li<lb/>gni, vel alterius corporis oblongi &longs;umpti ab altera tantum <lb/>extremitate, vt exemplificauimus in &longs;ari&longs;&longs;a, idem dicendum <lb/>e&longs;t de eleuatione, ac &longs;u&longs;pen&longs;ione, quæ fit, vel ex ambabus <lb/>extremitatibus; vel ex medio inter illas: Nam &longs;i vtrinque ab <lb/>extremitatibus &longs;u&longs;pendatur aliquod lignum ad paralellum <lb/>horizonti, duo quidem in illo vectes fient in ip&longs;is extremita<lb/>tibus fulti, <expan abbr="ponderaq">ponderaque</expan> in communi puncto intermedio gra<lb/>uitabunt tanquam in remoti&longs;simo &longs;itu ab vtriu&longs;que fultura. <lb/></s>

<s id="N14EF4">Quapropter ibidem fiet vtriu&longs;que vectis, &longs;eu totius ligni in<lb/>flexio, &longs;uppo&longs;ita vt diximus flexibilitate materiæ, <expan abbr="ip&longs;aq.">ip&longs;aque</expan> ce-<pb pagenum="167" xlink:href="005/01/175.jpg"/>dente &longs;uomet ponderi. </s>

<s id="N14F02">Alioquin lignum ip&longs;um, aut non <lb/>recederet à &longs;ua rectitudine, aut frangeretur. </s>

<s id="N14F07">Quod &longs;i &longs;u<lb/>&longs;pendatur ex medio, in ip&longs;o medio fulcietur vtrumque di<lb/>midium, ceu duplex vectis vtrinque applicatus, extremita<lb/>tibus vtrinque pariter grauitantibus, ac propendentibus <lb/>tanquam in remoti&longs;&longs;imo loco à communi centro &longs;iue fùlci<lb/>mento. </s>

Legend:

Removed from v.1.8
changed lines
	Added in v.1.9