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version 1.10, 2002/08/05 20:41:03

version 1.15, 2002/08/08 08:32:07

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<!DOCTYPE archimedes SYSTEM "../dtd/archimedes.dtd" ><archimedes> <info> <author>Monantheuil, Henri</author> <title>Aristotelis Mechanica</title> <date>1599</date>

<place>Paris</place> <editor></editor> <publisher></publisher> <translator></translator> <lang>la</lang> <chunk unit="page*">page</chunk><locator>0000000035</locator> </info> <text> <front> </front> <body> <chap> <pb/>

<place>Paris</place> <translator></translator> <lang>la</lang> <cvs_file>monan_mecha_01_la_1599.xml</cvs_file><cvs_version>1.10</cvs_version><locator>0000000035</locator> </info> <text> <front> </front> <body> <chap> <pb/>

<s>ARISTOTELIS <lb/>MECHANICA <lb/>Græca, emendata, Latina facta, & <lb/>Commentariis illu&longs;trata. <lb/></s>

Line 440

<s>Ita con&longs;ilio habito, cum omnis conatus ludibrio <lb/>e&longs;&longs;et: ab&longs;i&longs;tere oppugnatione atque ob&longs;idendo tantum ar<lb/>cere terra marique commeatibus ho&longs;tem placuit. </s>

<s>Hæc Ti<lb/>tus Liuius lib. </s>

<s>Hæc Ti<lb/>tus Liuius lib.

<s>4. decad. </s>

4. decad. </s>

<s>3. Vilium igitur, &longs;ordidorum que ho<lb/>minum ne dixerimus ea e&longs;&longs;e in&longs;trumenta, quæ vel à dijs, vel <pb/>à nobili&longs;&longs;imis hominibus inuenta, & v&longs;urpata &longs;unt, & nunc <lb/>ad v&longs;us humanos perquam nece&longs;&longs;aria hone&longs;ti&longs;&longs;imum quæ<lb/>&longs;tum, & qualem agricultura dominis agricolis &longs;uppeditant. <lb/></s>

Line 630

<s><margin.target id="marg5"></margin.target>Cap.

2. lib. </s>

2. lib.

<s>2. <lb/>Metaph.</s>

2. <lb/>Metaph.</s>

<s><margin.target id="marg6"></margin.target>Cap.

6. lib. </s>

6. lib.

<s>5. <lb/>De benefic.</s>

5. <lb/>De benefic.</s>

<s>Quorum cau&longs;a ign.] <emph type="italics"/>In rebus naturalibus cau&longs;arum omne <lb/>genus ine&longs;t, materia, efficiens, forma, finis. </s>

Line 682

<s>Siquidem Natura.] <emph type="italics"/>Naturalia principium in &longs;e habent &longs;ui <lb/>motus, quo &longs;i &longs;implicia &longs;unt, ad vnum & vno modo &longs;impliciter <lb/>mouentur: &longs;i commixta prædominantis vnius motum &longs;equuntur, <lb/>&longs;icque ad vnum feruntur. </s>

<s>Hæc &longs;unt demon&longs;trata ab Aristotele<emph.end type="italics"/><pb pagenum="7"/><emph type="italics"/>lib. </s>

<s>Hæc &longs;unt demon&longs;trata ab Aristotele<emph.end type="italics"/><pb pagenum="7"/><emph type="italics"/>lib.

<s>de C&oelig;lo & de generat. </s>

de C&oelig;lo & de generat. </s>

<s>& corrupt.<emph.end type="italics"/></s>

Line 938

<s>Primum quod vna linea terminetur, eâque &longs;implici, &longs;imilari <lb/>vniformi, & carente principio, & fine, neque tamen infinita, vt <lb/>cuius, cum partes aliquot &longs;umptæ &longs;unt, quæ re&longs;tant, minus &longs;int, quam <lb/>ante quam &longs;umptæ e&longs;&longs;ent, quod repugnat infinito in magnitudine: &longs;ed <lb/>tota e&longs;t, & perfecta: vnde circulus figura e&longs;t planarum &longs;implicißi<lb/>ma, regularißima, perfectißima: Deinde quod ea linea non &longs;it an<lb/>gulus, ad angulum tamen proxime accedat, vt o&longs;tendimus in no&longs;tro <lb/>libello de angulo contactus, & ob id quod&abreve;modo vndequaque angu<lb/>lata, cum nu&longs;quam &longs;it, dici poßit, & figura<emph.end type="italics"/> <foreign lang="greek">w_an/gwnos & o(lo/gwnos,</foreign><lb/><emph type="italics"/>tum prima figurarum & vltima: po&longs;tea, quod ex infinitis punctis <lb/>quæ in &longs;patio ab ea comprehen&longs;o &longs;unt, vnum e&longs;t tantum, à quo omnes <lb/>rectæ ad peripheriam ductæ, &longs;unt æquales: quod Diametro bifariam <lb/>&longs;ecetur: quod hinc &longs;emicirculus circa Diametrum manentem <lb/>voluens, quou&longs;que redierit ad eum locum vnde moueri c&oelig;pit, &longs;phæ<lb/>ram constituat, corporum &longs;implicißimum, capacißimum, mobilißi<lb/>mum, mouentißimum: quod circulus omnium figurarum eiu&longs;dem <lb/>perimetri &longs;it capacißima: quod vno puncto lineam rectam attin<lb/>gat, &longs;icque o&longs;&longs;en&longs;ationibus & occur&longs;ationibus minimum pateat, <lb/>&longs;icque in&longs;i&longs;tens dimidia &longs;ui totius parte nutet, vnde propen&longs;ißimus <lb/>e&longs;t ad motum, & dimotus cum moueat annexa, aptißimus quoque<emph.end type="italics"/><pb pagenum="17"/><emph type="italics"/>erit ad mouendum: po&longs;tremò quod inter rectam circulum tangen<lb/>tem, & circuli peripheriam altera recta &longs;ine &longs;ectione cadere non <lb/>poßit. </s>

<s>quod 16. prop.

lib.

3. elem. </s>

<s>e&longs;t demon&longs;tratum.<emph.end type="italics"/></s>

Line 980

<s>Eaque ex eo quod cum circuli peri<lb/>pheria &longs;ir vna linea def. </s>

<s>15. lib.

1. elem. </s>

<s>& idcirco latitudinis expers <lb/>def. </s>

Line 996

<s>Cum enim re<lb/>ctum &longs;it id in lineis quod ex æquo iacet <lb/>inter &longs;ua extrema def. </s>

<s>2. lib.

<s>1. & vt <lb/>linea A B, curuum erit quod non ex <lb/>æquo iacebit, &longs;ed altius aut depreßius: <lb/>idque &longs;i inter extrema vbique attollatur: <lb/>conuexum vt C E D: &longs;i vero vbique <lb/>deprimatur concauum, vt C F D quæ eadem e&longs;t linea ex &longs;e, &longs;ed <lb/>ex locis E E & F F partium mutata, Cum igitur ab eadem C D<emph.end type="italics"/><pb pagenum="19"/><emph type="italics"/>non &longs;e expellant non erunt verè contraria: qualia tamen apparent ex <lb/>di&longs;tantia & differentiis locorum &longs;ur&longs;um deor&longs;um.<emph.end type="italics"/></s>

1. & vt <lb/>linea A B, curuum erit quod non ex <lb/>æquo iacebit, &longs;ed altius aut depreßius: <lb/>idque &longs;i inter extrema vbique attollatur: <lb/>conuexum vt C E D: &longs;i vero vbique <lb/>deprimatur concauum, vt C F D quæ eadem e&longs;t linea ex &longs;e, &longs;ed <lb/>ex locis E E & F F partium mutata, Cum igitur ab eadem C D<emph.end type="italics"/><pb pagenum="19"/><emph type="italics"/>non &longs;e expellant non erunt verè contraria: qualia tamen apparent ex <lb/>di&longs;tantia & differentiis locorum &longs;ur&longs;um deor&longs;um.<emph.end type="italics"/></s>

<s>Hæc autem ita.] <emph type="italics"/>Similitudine comprobatur conuexum & <lb/>concauum contraria e&longs;&longs;e. </s>

Line 1104

<s>Producatur enim A E <lb/>recta vt &longs;it A C <lb/>diameter po&longs;tul.<emph.end type="italics"/><lb/><figure id="fig4"></figure><lb/>2. <emph type="italics"/><expan abbr="it&etilde;">item</expan> D H vt &longs;it <lb/>& D G diame<lb/>ter. </s>

<s>Quia igi<lb/>tur vt diameter <lb/>A C ad <expan abbr="&longs;uã">&longs;uam</expan> <expan abbr="pe-ripheriã">pe<lb/>ripheriam</expan> A B C: <lb/>ita & D G diameter ad &longs;uam peripheriam D F G, per ea quæ <lb/>demon&longs;trata &longs;unt ab Archimede prop. </s>

3. lib.

<s>de dimen&longs;. </s>

de dimen&longs;. </s>

<s>circuli, & <lb/>vicißim proportionales erunt A C diameter ad D G diametrum: <lb/>vt peripheria A B C ad peripheriam D F G prop. </s>

<s>16. lib.

<s>5. & <lb/>quia A E & D H partes &longs;unt pariter multiplicium A C, D G <lb/>vtpote &longs;emidiametri &longs;uarum diametrorum, erit A E ad D H vt <lb/>A C ad D G prop. </s>

5. & <lb/>quia A E & D H partes &longs;unt pariter multiplicium A C, D G <lb/>vtpote &longs;emidiametri &longs;uarum diametrorum, erit A E ad D H vt <lb/>A C ad D G prop.

15. lib.

<s>5. ergo & peripheria A B C ad peri<lb/>pheriam D F G: vt A E ad D H prop. </s>

5. ergo & peripheria A B C ad peri<lb/>pheriam D F G: vt A E ad D H prop. </s>

Line 1152

<s>Huius rci <lb/>fecit mentionem Galenus, qui miracula inquit moliuntur principio <lb/>motionis exhibito di&longs;cedunt, Machinæ vero ip&longs;æ aliquanti&longs;per, non <lb/>multo tamen tempore per &longs;e ip&longs;æ arti&longs;iciosè impelluntur. </s>

<s>cap.

6. lib.

<s>de <lb/>f&oelig;t. </s>

de <lb/>f&oelig;t. </s>

<s>format. </s>

Line 1216

<s>Huius vero.] <emph type="italics"/>Cau&longs;a exactiorum librarum refertur ad circuli<emph.end type="italics"/><pb pagenum="28"/><emph type="italics"/>radios longiores, qui celerius feruntur minoribus, id e&longs;t qui æquali <lb/>tempore maius &longs;patium, & proinde &longs;en &longs;ibilius tran&longs;eunt.<emph.end type="italics"/></s>

<s>Celerius enim.] <emph type="italics"/>Celeritatis lationum duos modos adfert &longs;i<lb/>miles ÿs quos cap. </s>

<s>Celerius enim.] <emph type="italics"/>Celeritatis lationum duos modos adfert &longs;i<lb/>miles ÿs quos cap.

2. lib.

<s>6. de Phy&longs;. </s>

6. de Phy&longs;. </s>

<s>auditu attulit, vt vtro longioris <lb/>radÿ celeritas accipi debeat, intelligatur.<emph.end type="italics"/></s>

Line 1228

<s>Cum <expan abbr="itaq;">itaque</expan> totum <lb/>maius &longs;it &longs;ua parte ex 9. axiom. </s>

<s>lib.

1. ele. </s>

<s>externus circulus interno <lb/>concentrico erit maior. </s>

<s>Præterea <expan abbr="c&utilde;">cum</expan> circuli æquales &longs;int, <expan abbr="quor&utilde;">quorum</expan> &longs;emi<lb/>diametri &longs;int æquales def. </s>

<s>1. lib.

3. ele. </s>

<s>Illi quorum &longs;emidiametri &longs;unt <lb/>inæquales, erunt & inæquales, & ille maior, euius &longs;emidiameter <lb/>maior. </s>

<s>Quæ licet vera &longs;int non tamen &longs;tatim &longs;equitur figuræ planæ <lb/>cuius area maior e&longs;t, e&longs;&longs;e & perimetrum maiorem vt ex 36. 37. <lb/>prop. </s>

<s>Quæ licet vera &longs;int non tamen &longs;tatim &longs;equitur figuræ planæ <lb/>cuius area maior e&longs;t, e&longs;&longs;e & perimetrum maiorem vt ex 36. 37. <lb/>prop.

lib.

1. elem. </s>

<s>demon&longs;trari facile pote&longs;t: neque &longs;i rur&longs;us perimeter <lb/>contineat perimetrum, vt continens contento &longs;it maior, vt patere <lb/>pote&longs;t ex eo, quod e&longs;t à Proclo adductum ad prop. </s>

21. lib.

1. elem. </s>

<s>De <lb/>duabus rectis intra triangulum, rectangulum vel amblygonium <lb/>comprehen&longs;is, quæ maiores con&longs;titui po&longs;&longs;unt ÿs à quibus ambiuntur. <lb/></s>

Line 1304

<s>Et intelligatur a latum ver&longs;us<emph.end type="italics"/><lb/><foreign lang="greek">b</foreign> <emph type="italics"/>perueni&longs;&longs;e ad<emph.end type="italics"/> <foreign lang="greek">d,</foreign> <emph type="italics"/>& ver&longs;us<emph.end type="italics"/><lb/><foreign lang="greek">g</foreign> <emph type="italics"/>perueni&longs;&longs;e ad<emph.end type="italics"/> <foreign lang="greek">e</foreign>: <emph type="italics"/>&longs;icque cum <lb/>lationum ip&longs;ius<emph.end type="italics"/> <foreign lang="greek">a</foreign> <emph type="italics"/>ratio &longs;it vt<emph.end type="italics"/><lb/><foreign lang="greek">a b</foreign> <emph type="italics"/>ad<emph.end type="italics"/> <foreign lang="greek">a g,</foreign> <emph type="italics"/>ergo erit &<emph.end type="italics"/> <foreign lang="greek">a d</foreign><lb/><emph type="italics"/>ad<emph.end type="italics"/> <foreign lang="greek">a e</foreign>: <emph type="italics"/>vt<emph.end type="italics"/> <foreign lang="greek">a <gap/></foreign> <emph type="italics"/>ad<emph.end type="italics"/> <foreign lang="greek">a y,</foreign> <emph type="italics"/>& rectrangulum minus<emph.end type="italics"/> <foreign lang="greek">a d z e</foreign> <emph type="italics"/>com<lb/>munem angulum<emph.end type="italics"/> <foreign lang="greek">a</foreign> <emph type="italics"/>cum maiori<emph.end type="italics"/> <foreign lang="greek">a b h g</foreign> <emph type="italics"/>habens & &longs;imile erit <lb/>def. </s>

<s>1. lib.

<s>6. & proinde circa eandem dimentientem conuer&longs;. </s>

6. & proinde circa eandem dimentientem conuer&longs;. </s>

<s>prop.<emph.end type="italics"/><lb/>24. <emph type="italics"/>lib.

<s>6. Et &longs;ic<emph.end type="italics"/> <foreign lang="greek">a</foreign> <emph type="italics"/>duabus &longs;uis &longs;ic lationibus latum erit in<emph.end type="italics"/> <foreign lang="greek">z,</foreign> <emph type="italics"/>vt vbi<lb/>cumque lationes ip&longs;ius<emph.end type="italics"/> <foreign lang="greek">a</foreign> <emph type="italics"/>&longs;i&longs;tentur, &longs;emper &longs;int &longs;upra diametrum<emph.end type="italics"/><lb/><foreign lang="greek">a h.</foreign> <emph type="italics"/>&longs;iquidem lationes i&longs;tæ &longs;unt in ratione<emph.end type="italics"/> <foreign lang="greek">a b</foreign> <emph type="italics"/>ad<emph.end type="italics"/> <foreign lang="greek">a g.</foreign> <emph type="italics"/>proinde <lb/>&longs;upra rectam, quia omnis diameter rectanguli recta e&longs;t. </s>

6. Et &longs;ic<emph.end type="italics"/> <foreign lang="greek">a</foreign> <emph type="italics"/>duabus &longs;uis &longs;ic lationibus latum erit in<emph.end type="italics"/> <foreign lang="greek">z,</foreign> <emph type="italics"/>vt vbi<lb/>cumque lationes ip&longs;ius<emph.end type="italics"/> <foreign lang="greek">a</foreign> <emph type="italics"/>&longs;i&longs;tentur, &longs;emper &longs;int &longs;upra diametrum<emph.end type="italics"/><lb/><foreign lang="greek">a h.</foreign> <emph type="italics"/>&longs;iquidem lationes i&longs;tæ &longs;unt in ratione<emph.end type="italics"/> <foreign lang="greek">a b</foreign> <emph type="italics"/>ad<emph.end type="italics"/> <foreign lang="greek">a g.</foreign> <emph type="italics"/>proinde <lb/>&longs;upra rectam, quia omnis diameter rectanguli recta e&longs;t. </s>

<s>Huic con<lb/>&longs;entit quod à Proclo ex Gemino acceptum &longs;ic expo&longs;itum e&longs;t. </s>

<s>Si qua<lb/>drangulum duo&longs;que motus qui æquali celeritate fiant, alterum qui<lb/>dem per longitudinem: alterum vero per latitudinem intellexeris <lb/>dimetiens producetur recta exi&longs;tens linea, lib. </s>

2. comm. </s>

Line 1334

<s>Simile e&longs;t enim.] <foreign lang="greek">tw_ lo/gw,</foreign> <emph type="italics"/>id e&longs;t ratione, redundat quia quæ <lb/>&longs;imilia &longs;unt quadrangula, habent latera, quæ circum æquales angu<lb/>los propertionalia, ex def. </s>

<s>1. lib.

6. elem.<emph.end type="italics"/></s><pb pagenum="31"/>

Line 1380

<s>Hoc <lb/>enim repugnat def. </s>

<s>3. lib.

5. elem. </s>

<s>quantitas enim motus vnius mul<lb/>tiplicata, alterius vicißim quantitatem &longs;uperare pote&longs;t. </s>

Line 1390

<s>vt cum duarum rectarum, quæ parallelogrammum con&longs;tituunt, vna <lb/>e&longs;t latus quadrati alicuius, altera e&longs;t eius diameter. </s>

<s>Tunc enim ratio <lb/>e&longs;t rectis illis licet incommen&longs;erabilibus prop. </s>

<s>Tunc enim ratio <lb/>e&longs;t rectis illis licet incommen&longs;erabilibus prop.

116. lib.

<s>10. expre&longs;&longs;a. <lb/></s>

10. expre&longs;&longs;a. <lb/></s>

<s>At hîc vt inter peripheriam & diametrum &longs;it aliqua ratio, veluti <lb/>inter arcum & &longs;ubtendentem: hæc tamen neque numeris exprimi <lb/>pote&longs;t, nec rectis lineis Geometrice vt videre e&longs;t ex Archimede <lb/>lib.<emph.end type="italics"/> <foreign lang="greek">w_<gap/>i\ uetsh/d. </foreign></s>

<s>lib.

1.<emph.end type="italics"/> <foreign lang="greek">me/gal. </foreign></s>

<s><foreign lang="greek">dw<gap/>.</foreign> <emph type="italics"/>quod autem ad <lb/>prius attinet in lationibus illis tempus admittitur, &longs;ed hoc e&longs;t eiu&longs;mo<lb/>di, vt nullum eius detur in&longs;tans, quo vna latio fiat, quo etiam non <lb/>& altera itidem fiat: quod prioribus licet commune e&longs;&longs;e poßit: pro<lb/>pter tamen laterum inæqualitatem vbi in æqualia dantur, non ita <lb/>&longs;implex & indiui&longs;ibile e&longs;t. </s>

Line 1436

<s>Confirmatio apertior &longs;ic erit. <lb/></s>

<s>Radius de&longs;cribens circulum vna tantum latione fertur, aut pluri<lb/>bus: non vna tantum, quia ad vnam tantum loci differentiam, <lb/>cum &longs;it quid &longs;implicißimum, ferretur (probat enim hoc Ari&longs;toteles <lb/>cap. </s>

2. lib.

<s>1. de C&oelig;lo) Quinetiam &longs;i &longs;ic. </s>

1. de C&oelig;lo) Quinetiam &longs;i &longs;ic. </s>

<s>Idem radius à diametro cir-<emph.end type="italics"/><lb/><figure id="fig8"></figure><lb/><emph type="italics"/>culi digrediens in tran&longs;itu ab vna &longs;emidia<lb/>metro ad alteram numquam con&longs;equeretur <lb/>cum &longs;itum, per quem ip&longs;i à centro perpen<lb/>dicularis e&longs;&longs;et. </s>

Line 1546

<s><emph type="italics"/>A puncto<emph.end type="italics"/> <foreign lang="greek">a</foreign> <emph type="italics"/>ad punctum<emph.end type="italics"/> <foreign lang="greek">q</foreign> <emph type="italics"/>ducatur recta<emph.end type="italics"/> <foreign lang="greek">a q,</foreign> <emph type="italics"/>& producatur in<emph.end type="italics"/><lb/><foreign lang="greek">h</foreign> <emph type="italics"/>&longs;itque<emph.end type="italics"/> <foreign lang="greek">a q h.</foreign></s>

<s><emph type="italics"/>Tum à puncto<emph.end type="italics"/> <foreign lang="greek">q</foreign> <emph type="italics"/>excitetur perpendicularis lineæ<emph.end type="italics"/> <foreign lang="greek">a x</foreign> <emph type="italics"/>prop. </s>

12. <lb/>lib.

<s>1. &longs;itque<emph.end type="italics"/> <foreign lang="greek">q z.</foreign></s><pb pagenum="39"/>

1. &longs;itque<emph.end type="italics"/> <foreign lang="greek">q z.</foreign></s><pb pagenum="39"/>

<s><emph type="italics"/>Et per punctum<emph.end type="italics"/> <foreign lang="greek">q</foreign> <emph type="italics"/>ducatur parallela rectæ<emph.end type="italics"/> <foreign lang="greek">a b</foreign> <emph type="italics"/>prop. </s>

31. lib.

<s>1. <lb/>quæ &longs;it<emph.end type="italics"/> <foreign lang="greek">q w.</foreign></s><figure></figure>

1. <lb/>quæ &longs;it<emph.end type="italics"/> <foreign lang="greek">q w.</foreign></s><figure></figure>

<s><emph type="italics"/>Rur&longs;us à puncto<emph.end type="italics"/> <foreign lang="greek">w</foreign> <emph type="italics"/>excitetur perpendicularis lineæ<emph.end type="italics"/> <foreign lang="greek">a b,</foreign> <emph type="italics"/>&longs;itque<emph.end type="italics"/><lb/><foreign lang="greek">w n</foreign>: <emph type="italics"/>& &longs;ic parallelogrammum erit<emph.end type="italics"/> <foreign lang="greek">w n z q</foreign> <emph type="italics"/>ex def. </s>

Line 1566

<s>Sint autem<emph.end type="italics"/> <foreign lang="greek">w n, q z</foreign> <emph type="italics"/>perpendiculares ex fab. </s>

<s>& æquales, quia late<lb/>ra oppo&longs;ita in parallelogrammo<emph.end type="italics"/> <foreign lang="greek">w n z q</foreign> <emph type="italics"/>prop. </s>

<s>& æquales, quia late<lb/>ra oppo&longs;ita in parallelogrammo<emph.end type="italics"/> <foreign lang="greek">w n z q</foreign> <emph type="italics"/>prop.

34. lib.

<s>1. Erant vtro<lb/>bique &longs;patia<emph.end type="italics"/> <foreign lang="greek">b w & x q</foreign> <emph type="italics"/>æqualia.<emph.end type="italics"/></s>

1. Erant vtro<lb/>bique &longs;patia<emph.end type="italics"/> <foreign lang="greek">b w & x q</foreign> <emph type="italics"/>æqualia.<emph.end type="italics"/></s>

<s><foreign lang="greek">b n</foreign> <emph type="italics"/>vero eadem ratione metitur &longs;patium motus præter naturam <lb/>ip&longs;ius<emph.end type="italics"/> <foreign lang="greek">b, & x z</foreign> <emph type="italics"/>ip&longs;ius<emph.end type="italics"/> <foreign lang="greek">x.</foreign> <emph type="italics"/>&longs;i igitur<emph.end type="italics"/> <foreign lang="greek">x z</foreign> (<emph type="italics"/>quod po&longs;tea demon&longs;tra<lb/>bitur) maior &longs;it quam<emph.end type="italics"/> <foreign lang="greek">b n,</foreign> <emph type="italics"/>erit puncti<emph.end type="italics"/> <foreign lang="greek">x</foreign> <emph type="italics"/>motus præter naturam <lb/>maior in eodem &longs;patio motus naturalis: quam puncti<emph.end type="italics"/> <foreign lang="greek">b.</foreign></s><pb pagenum="40"/>

Line 1580

<s><foreign lang="greek">a q h</foreign>] <emph type="italics"/><expan abbr="Punct&utilde;">Punctum</expan><emph.end type="italics"/> <foreign lang="greek">q</foreign> <emph type="italics"/>vbi libet in peripheria accipitur ad de&longs;ignandum <lb/>quoduis <expan abbr="&longs;pati&utilde;">&longs;patium</expan>, quod confecerit<emph.end type="italics"/> <foreign lang="greek">x</foreign> <emph type="italics"/><expan abbr="extrem&utilde;">extremum</expan> mobile minoris radÿ<emph.end type="italics"/> <foreign lang="greek">a x.</foreign></s>

<s>Et <foreign lang="greek">a q</foreign> excitetur.] <emph type="italics"/>A puncto<emph.end type="italics"/> <foreign lang="greek">q</foreign> <emph type="italics"/>extra lineam<emph.end type="italics"/> <foreign lang="greek">a x</foreign> <emph type="italics"/>dato ex<lb/>citatur in ip&longs;am perpendicularis, quæ e&longs;t<emph.end type="italics"/> <foreign lang="greek">q z</foreign> <emph type="italics"/>prop. </s>

12. lib.

1. elem.<emph.end type="italics"/></s>

<s>Et rur&longs;us per <foreign lang="greek">q</foreign>] <emph type="italics"/>Per punctum<emph.end type="italics"/> <foreign lang="greek">q</foreign> <emph type="italics"/>datum datæ rectæ<emph.end type="italics"/> <foreign lang="greek">a b</foreign> <emph type="italics"/>duci<lb/>tur parallela prop. </s>

31. lib.

1. elem.<emph.end type="italics"/></s>

<s>Et <foreign lang="greek">w n</foreign> perpend.] <emph type="italics"/>prop. </s>

<s>12. lib.

1. elem.<emph.end type="italics"/></s>

<s>Sunt vero <foreign lang="greek">w n</foreign> &] <emph type="italics"/>Quia<emph.end type="italics"/> <foreign lang="greek">q w</foreign> <emph type="italics"/>parallela e&longs;t ip&longs;i<emph.end type="italics"/> <foreign lang="greek">z n</foreign> <emph type="italics"/>ex fabrica: <lb/>tùm<emph.end type="italics"/> <foreign lang="greek">w n</foreign> <emph type="italics"/>etiam parallela e&longs;t ip&longs;i<emph.end type="italics"/> <foreign lang="greek">q z,</foreign> <emph type="italics"/>quia in eas incidens<emph.end type="italics"/> <foreign lang="greek">z n</foreign> <emph type="italics"/>facit an<lb/>gulos internos ad <expan abbr="ea&longs;d&etilde;">ea&longs;dem</expan> partes rectos, ex fab. </s>

<s>proinde æquales ax. </s>

<s>10. <lb/><expan abbr="itaq;">itaque</expan> parallelæ prop. </s>

<s>10. <lb/><expan abbr="itaq;">itaque</expan> parallelæ prop.

28. lib.

<s>1. <expan abbr="parallelogrãm&utilde;">parallelogrammum</expan> erit<emph.end type="italics"/> <foreign lang="greek">w n z <expan abbr="q.">que</expan></foreign> <emph type="italics"/>per def. </s>

1. <expan abbr="parallelogrãm&utilde;">parallelogrammum</expan> erit<emph.end type="italics"/> <foreign lang="greek">w n z <expan abbr="q.">que</expan></foreign> <emph type="italics"/>per def. </s>

<s>quare eius latera oppo&longs;ita<emph.end type="italics"/> <foreign lang="greek">w n & q z</foreign> <emph type="italics"/><expan abbr="er&utilde;t">erunt</expan> æqualia prop. </s>

<s>quare eius latera oppo&longs;ita<emph.end type="italics"/> <foreign lang="greek">w n & q z</foreign> <emph type="italics"/><expan abbr="er&utilde;t">erunt</expan> æqualia prop.

34. lib.

1.<emph.end type="italics"/></s>

<s>In circulis.] <emph type="italics"/>Ex hoc loco elicitur hoc theorema. </s>

Line 1630

<s><emph type="italics"/>De&longs;cribere circulum minorem qui alterum datum maiorem <lb/>interius tangat.<emph.end type="italics"/></s>

<s><emph type="italics"/>Sit datus circulus A B K C maior, ab A per D centrum reper<lb/>tum prop. </s>

<s><emph type="italics"/>Sit datus circulus A B K C maior, ab A per D centrum reper<lb/>tum prop.

1. lib.

<s>3. ducatur A k diameter. </s>

3. ducatur A k diameter. </s>

<s>De&longs;cribendus autem &longs;it eo <lb/>minor, cuius accipiatur E <expan abbr="centr&utilde;">centrum</expan><emph.end type="italics"/><lb/><figure id="fig11"></figure><lb/><emph type="italics"/>inter A & D, & interuallo <lb/>E A de&longs;cribatur A F G. hic <lb/>tanget interius circulum A B k <lb/>C datum in puncto A. </s>

<s>Nam &longs;i <lb/>& &longs;ecet, vt in puncto H, ducta <lb/>H E. erit æqualis ip&longs;i E A def. <lb/></s>

<s>15. lib.

<s>1. non erit igitur E A mi<lb/>nima omnium quæ ab E puncto <lb/>extra D centrum circuli A B <lb/>K C cadunt in eius concauam pe<lb/>ripheriam, quod e&longs;t contra prop. <lb/></s>

1. non erit igitur E A mi<lb/>nima omnium quæ ab E puncto <lb/>extra D centrum circuli A B <lb/>K C cadunt in eius concauam pe<lb/>ripheriam, quod e&longs;t contra prop. <lb/></s>

<s>7. lib.

<s>3. non erat igitur H punctum commune vtrique circulo, & <lb/>&longs;ic de alÿs. </s>

3. non erat igitur H punctum commune vtrique circulo, & <lb/>&longs;ic de alÿs. </s>

<s>Circulus igitur A F G, tangit circulum A B K C <lb/>in puncto A prop. </s>

<s>Circulus igitur A F G, tangit circulum A B K C <lb/>in puncto A prop.

11. lib.

<s>3. quod oportuit facere.<emph.end type="italics"/></s>

3. quod oportuit facere.<emph.end type="italics"/></s>

<s><emph type="italics"/>Iam nunc de A G maiori &longs;emidiametro detrahatur portio A H <lb/>æqualis D H minori prop. </s>

<s><emph type="italics"/>Iam nunc de A G maiori &longs;emidiametro detrahatur portio A H <lb/>æqualis D H minori prop.

3. lib.

<s>1. centro H interuallo A H de&longs;<lb/>cribatur circulus A M L po&longs;tul. </s>

1. centro H interuallo A H de&longs;<lb/>cribatur circulus A M L po&longs;tul. </s>

<s>3. qui erit æqualis dato D E F. <lb/>def. </s>

<s>1. lib.

<s>3. Et tanget intus circulum A B C in puncto A exprobl. <lb/></s>

3. Et tanget intus circulum A B C in puncto A exprobl. <lb/></s>

<s>præ&longs;umpto. </s>

<s>per punctum B ducaeur parallela B M prop. </s>

<s>per punctum B ducaeur parallela B M prop.

31. lib.

<s>1. <lb/>& per eandem parallela M N quæ per 34. lib. </s>

1. <lb/>& per eandem parallela M N quæ per 34. lib. </s>

<s>eiu&longs;dem cum &longs;it <lb/>æqualis ip&longs;i B K erit & æqualis ip&longs;i. </s>

Line 1686

<s>3. A N, D I æquales &longs;unt quia reli<lb/>quæ ex æqualibus A H, D H ex fab. </s>

<s>demptis æqualibus N H, <lb/>I H quæ latera &longs;unt &longs;ub æqualibus angulis duorum triangulorum <lb/>M N H & I E H habentium duos angulos duobus angulis <lb/>æquales, & latus lateri æquale vt e&longs;t in 26. prop. </s>

lib.

<s>1. nempe angu<lb/>lus qui ad N rectus e&longs;t prop. </s>

1. nempe angu<lb/>lus qui ad N rectus e&longs;t prop. </s>

<s>29. lib.

<s>1. & qui ad I, rectus ex hypoth. <lb/></s>

1. & qui ad I, rectus ex hypoth. <lb/></s>

<s>ideo æquales ax. </s>

<s>10. tum angulus M H N ad centrum con&longs;titutus<emph.end type="italics"/><pb pagenum="42"/><emph type="italics"/>& angulus E H I ad centrum con&longs;titutus in æqualibus circulis ex <lb/>fab. </s>

<s>&longs;unt æquales prop. </s>

<s>&longs;unt æquales prop.

27. lib.

<s>3. quia æquales &longs;unt peripheriæ A M, <lb/>D E ablatæ &longs;cilicet ab æqualibus &longs;emißibus M N & E I ex <lb/>fab. </s>

3. quia æquales &longs;unt peripheriæ A M, <lb/>D E ablatæ &longs;cilicet ab æqualibus &longs;emißibus M N & E I ex <lb/>fab. </s>

<s>prop.

3. & 29. lib.

<s>3. & &longs;icreliquum latus N H æquale e&longs;t re<lb/>liquo I H. </s>

3. & &longs;icreliquum latus N H æquale e&longs;t re<lb/>liquo I H. </s>

<s>Ergo cum tota A N æqualis D I &longs;it maior A K <lb/>parte &longs;ua ax. </s>

Line 1760

<s>Ab <foreign lang="greek">h</foreign> enim e&longs;t.] <emph type="italics"/>Curuas lineas perpendicularis &longs;ola vt breui&longs;<lb/>&longs;ima, quantum fieri pote&longs;t exacte metitur. </s>

<s>vt &longs;cribit autem Ptolo<lb/>mæus in lib. </s>

<s>vt &longs;cribit autem Ptolo<lb/>mæus in lib.

<s>de Analemmate, & Simplicius in lib. </s>

de Analemmate, & Simplicius in lib. </s>

<s>de Dimen&longs;ione, <lb/>men&longs;ura cuiu&longs;cunque rei debet e&longs;&longs;e &longs;tata, determinata, & non indefi<lb/>nita. </s>

Line 1772

<s>Nam, qui anguli ad<emph.end type="italics"/> <foreign lang="greek"><gap/> & k,</foreign> <emph type="italics"/>&longs;unt recti ex fab. </s>

<s>qui vero <lb/>ad<emph.end type="italics"/> <foreign lang="greek">x & b</foreign> <emph type="italics"/>&longs;unt externus & internus ad ea&longs;dem partes facti à re<lb/>cta<emph.end type="italics"/> <foreign lang="greek">a b</foreign> <emph type="italics"/>incidente in parallelas<emph.end type="italics"/> <foreign lang="greek">x q, b h</foreign> <emph type="italics"/>prop. </s>

3. lib.

<s>6. Nam<emph.end type="italics"/> <foreign lang="greek">x q</foreign><lb/><emph type="italics"/>proportionaliter &longs;ecat<emph.end type="italics"/> <foreign lang="greek">a b & a h</foreign> <emph type="italics"/>latera trianguli<emph.end type="italics"/> <foreign lang="greek">b a h.</foreign> <emph type="italics"/>Sunt enim<emph.end type="italics"/><lb/><foreign lang="greek">a x, a q</foreign> <emph type="italics"/>æquales radj,<emph.end type="italics"/> & <foreign lang="greek">x b, q h</foreign> <emph type="italics"/>item æquales lineæ, quia re<lb/>liquæ ex æqualibus radÿs<emph.end type="italics"/> <foreign lang="greek">a b, a h</foreign>: <emph type="italics"/>habent autem æquales ad <lb/>æquales eandem rationem E&longs;t igitur<emph.end type="italics"/> <foreign lang="greek">x q</foreign> <emph type="italics"/>parallela ba&longs;i<emph.end type="italics"/> <foreign lang="greek">b h,</foreign> <emph type="italics"/>& &longs;ic <lb/>anguli qui ad<emph.end type="italics"/> <foreign lang="greek">x</foreign> <emph type="italics"/>externus, & qui ad<emph.end type="italics"/> <foreign lang="greek">b</foreign> <emph type="italics"/>internus erunt æquales <lb/>prop. </s>

6. Nam<emph.end type="italics"/> <foreign lang="greek">x q</foreign><lb/><emph type="italics"/>proportionaliter &longs;ecat<emph.end type="italics"/> <foreign lang="greek">a b & a h</foreign> <emph type="italics"/>latera trianguli<emph.end type="italics"/> <foreign lang="greek">b a h.</foreign> <emph type="italics"/>Sunt enim<emph.end type="italics"/><lb/><foreign lang="greek">a x, a q</foreign> <emph type="italics"/>æquales radj,<emph.end type="italics"/> & <foreign lang="greek">x b, q h</foreign> <emph type="italics"/>item æquales lineæ, quia re<lb/>liquæ ex æqualibus radÿs<emph.end type="italics"/> <foreign lang="greek">a b, a h</foreign>: <emph type="italics"/>habent autem æquales ad <lb/>æquales eandem rationem E&longs;t igitur<emph.end type="italics"/> <foreign lang="greek">x q</foreign> <emph type="italics"/>parallela ba&longs;i<emph.end type="italics"/> <foreign lang="greek">b h,</foreign> <emph type="italics"/>& &longs;ic <lb/>anguli qui ad<emph.end type="italics"/> <foreign lang="greek">x</foreign> <emph type="italics"/>externus, & qui ad<emph.end type="italics"/> <foreign lang="greek">b</foreign> <emph type="italics"/>internus erunt æquales <lb/>prop.

29. lib.

<s>1. Ergo & reliqui qui ad<emph.end type="italics"/> <foreign lang="greek">q & h</foreign> <emph type="italics"/>prop. </s>

1. Ergo & reliqui qui ad<emph.end type="italics"/> <foreign lang="greek">q & h</foreign> <emph type="italics"/>prop. </s>

<s>32. lib.

<s>1. Hæc <lb/>igitur duo triangula circa æquales angulos habebunt latera propor<lb/>tionalia prop. </s>

1. Hæc <lb/>igitur duo triangula circa æquales angulos habebunt latera propor<lb/>tionalia prop.

4. lib.

<s>6. Sicque erit vt<emph.end type="italics"/> <foreign lang="greek">q z</foreign> <emph type="italics"/>ad<emph.end type="italics"/> <foreign lang="greek">x z</foreign>: <emph type="italics"/>&longs;ic<emph.end type="italics"/> <foreign lang="greek">h k</foreign> <emph type="italics"/>ad<emph.end type="italics"/> <foreign lang="greek">k b,</foreign><lb/><emph type="italics"/>& alternatim vt<emph.end type="italics"/> <foreign lang="greek">q z</foreign> <emph type="italics"/>ad<emph.end type="italics"/> <foreign lang="greek">h k</foreign><emph type="italics"/>: &longs;ic<emph.end type="italics"/> <foreign lang="greek">x z</foreign> <emph type="italics"/>ad<emph.end type="italics"/> <foreign lang="greek">k b</foreign> <emph type="italics"/>prop. </s>

6. Sicque erit vt<emph.end type="italics"/> <foreign lang="greek">q z</foreign> <emph type="italics"/>ad<emph.end type="italics"/> <foreign lang="greek">x z</foreign>: <emph type="italics"/>&longs;ic<emph.end type="italics"/> <foreign lang="greek">h k</foreign> <emph type="italics"/>ad<emph.end type="italics"/> <foreign lang="greek">k b,</foreign><lb/><emph type="italics"/>& alternatim vt<emph.end type="italics"/> <foreign lang="greek">q z</foreign> <emph type="italics"/>ad<emph.end type="italics"/> <foreign lang="greek">h k</foreign><emph type="italics"/>: &longs;ic<emph.end type="italics"/> <foreign lang="greek">x z</foreign> <emph type="italics"/>ad<emph.end type="italics"/> <foreign lang="greek">k b</foreign> <emph type="italics"/>prop.

16. lib.

5.<emph.end type="italics"/></s>

<s>Ob hanc igitur cau&longs;am.] <emph type="italics"/>Conclu&longs;io qua tandem concludi<lb/>tur punctum à centro di&longs;tantius, vt eadem vi &longs;it motum, celerius <lb/>ferri, id e&longs;t eodem tempore maius loci &longs;patium conficere.<emph.end type="italics"/></s>

Line 1814

<s>Qvod vero propterea libræ.] <foreign lang="greek"><gap/>u<gap/>s</foreign> <emph type="italics"/>vel<emph.end type="italics"/> <foreign lang="greek"><gap/>u<gap/>n</foreign> <emph type="italics"/>præter iu<lb/>gum, remigum &longs;edes, & tran&longs;tra curruum & nauium &longs;ignifi<lb/>cat etiam libram & &longs;tateram, hinc illud Pythagoræ<emph.end type="italics"/> <foreign lang="greek">mh\zu<gap/>n u(per<lb/><gap/>a/inein</foreign> <emph type="italics"/>&longs;tateram ne tran&longs;grediaris & vt annotat Budæus<emph.end type="italics"/> <foreign lang="greek">zu<gap/>a/<lb/>tai</foreign> <emph type="italics"/>&longs;unt libripendes per vrbes con&longs;tituti, qui <expan abbr="põderibus">ponderibus</expan> præfecti ap<lb/>pellantur, vnde Zygo&longs;tatica fides pro plena & examinata æquitate <lb/>à Zygo quod e&longs;t libra publice temperata & con&longs;tituta, vt quemad<lb/>modum ait Vitruuius, vindicet ab iniquitate iu&longs;tis moribus vitam.<emph.end type="italics"/><lb/><arrow.to.target n="marg14"></arrow.to.target><lb/><emph type="italics"/>Statera enim dolo&longs;a, vt dixit Sapiens, abhominatio e&longs;t apud Deum, <lb/>& pondus æquum voluntas eius.<emph.end type="italics"/></s>

<s><margin.target id="marg14"></margin.target>Initio <lb/>cap. </s>

<s><margin.target id="marg14"></margin.target>Initio <lb/>cap.

<s>11. <lb/>Prouerb.</s>

11. <lb/>Prouerb.</s>

<s>Agina fit cen<lb/><figure id="fig12"></figure><lb/><expan abbr="tr&utilde;">trum</expan>.] <emph type="italics"/><expan abbr="Tand&etilde;">Tandem</expan> Ari<lb/>&longs;toteles <expan abbr="accõmodat">accommodat</expan> <lb/>problema <expan abbr="propo&longs;it&utilde;">propo&longs;itum</expan> <lb/>de libra ad circuli <lb/><expan abbr="proprietat&etilde;">proprietatem</expan> vltimò <lb/><expan abbr="demon&longs;tratã">demon&longs;tratam</expan>. </s>

Line 2000

<s>Sed & in li<lb/>brilibus huius ge<lb/>neris reditus & <lb/>non reditus alia <lb/><expan abbr="etiã">etiam</expan> cau&longs;a e&longs;t, &longs;ci<lb/>licet quia <expan abbr="null&utilde;">nullum</expan> <expan abbr="c&etilde;">cem</expan> <lb/><expan abbr="tr&utilde;">trum</expan> grauitatis ma<lb/>net ni&longs;i &longs;u&longs;tinea<lb/>tur à linea <expan abbr="per-p&etilde;diculari">per<lb/>pendiculari</expan> ad pla<lb/>num horizontis. </s>

<s>quod e&longs;t demon&longs;tratum ab V baldo prop. </s>

<s>quod e&longs;t demon&longs;tratum ab V baldo prop.

1. lib.

de lib. <lb/></s>

<s>Atque P e&longs;t centrum grauitatis magnitudinis compo&longs;itæ è duobus <lb/>brachÿs librilis G H, & lancibus ponderibu&longs;que vtrimque æqui<lb/>ponderantibus, &longs;i intelligantur admota, vt patet ex prop. </s>

4. lib.

<s>1. <lb/>Archimed. </s>

1. <lb/>Archimed. </s>

<s>de æquipond. </s>

Line 2072

<s>Proinde etiam onus ad partis ve<lb/>ctis cui impo&longs;itum e&longs;t, motionem mouebitur, & tunc non &longs;olum ele<lb/>uatur: &longs;ed & &longs;i opus e&longs;t, fiatque vectis perpendicularis &longs;olo, &longs;ecundum<emph.end type="italics"/><pb pagenum="56"/><emph type="italics"/>latus impellitur. </s>

<s>Vtrumque vectis v&longs;um Vitruuius cap. </s>

<s>Vtrumque vectis v&longs;um Vitruuius cap.

8. lib.

<s>10. &longs;ic <lb/>explicuit. </s>

10. &longs;ic <lb/>explicuit. </s>

<s>Ferreus vectis cum e&longs;t commotus ad onus, quod manuum <lb/>multitudo non pote&longs;t mouere, &longs;uppo&longs;ita vti centro cito porrecta pre&longs;<lb/>&longs;ione, quòd Græci<emph.end type="italics"/> <foreign lang="greek">(w_omo/xlion</foreign> <emph type="italics"/>appellant, & vectis lingua &longs;ub <lb/>onus &longs;ubdita, caput eius vnius hominis viribus pre&longs;&longs;um, id onus ex<lb/>tollet. </s>

Line 2168

<s>Dico potentiam in B e&longs;&longs;e ad pondus D: vt A C ad B <lb/>C (quod hic vocatur reciprocè) fiat ergo vt B C ad A C: ita <lb/>pondus D ad aliud, vt E. hoc igitur pondus E loco potentiæ ap<lb/>pen&longs;um in B, ip&longs;um D pondere æquabit. </s>

<s>Magnitudines enim in gra<lb/>uitate commen&longs;urabiles æquiponderant, &longs;i permutatim &longs;u&longs;pendantur <lb/>in di&longs;tantijs &longs;ecundum grauitatum rationem <expan abbr="cõ&longs;titutæ">con&longs;titutæ</expan> prop. </s>

6. lib.

<s>1. <lb/>Archim. </s>

1. <lb/>Archim. </s>

<s>de æquipond. </s>

<s>Et &longs;ic potentia æqualis ip&longs;i E ibidem con&longs;ti<lb/>tuta pondere æquabit ip&longs;um D, id e&longs;t ne D deor&longs;um vergat, quod fa-<emph.end type="italics"/><pb pagenum="59"/><emph type="italics"/>eit pondus E, prohibebit. </s>

<s>Nam æqualia ad idem eandem rationem <lb/>habent prop. </s>

<s>Nam æqualia ad idem eandem rationem <lb/>habent prop.

7. lib.

5. el. </s>

<s>Sed E habet eam ad D, quam A C and B C, ex <lb/>fab. </s>

Line 2204

<s>2. lib.

<s>6. vbi reciprocæ figuræ definiuntur cum in <lb/>vtraque figura antecedentes & con&longs;equentes rationum termini fue<lb/>rint, id e&longs;t quando in altera quidem e&longs;t terminus antecedens primæ <lb/>rationis, & con&longs;equens &longs;ecundæ: in altera vero e&longs;t con&longs;equens pri<lb/>mæ, & antecedens &longs;ecundæ. </s>

6. vbi reciprocæ figuræ definiuntur cum in <lb/>vtraque figura antecedentes & con&longs;equentes rationum termini fue<lb/>rint, id e&longs;t quando in altera quidem e&longs;t terminus antecedens primæ <lb/>rationis, & con&longs;equens &longs;ecundæ: in altera vero e&longs;t con&longs;equens pri<lb/>mæ, & antecedens &longs;ecundæ. </s>

<s>Quæ vt conuenire huic loco intelligan<lb/>tur, &longs;umendum e&longs;t pondus mouendum &longs;imul cum parte vectis ab hy<lb/>pomochlio ad lingulam cui appenditur pro vna figura: & potentia <lb/>mouens cum reliqua parte vectis pro altera figura. </s>

Line 2222

<s>Et <lb/>&longs;ic &longs;i minor potentia ad &longs;u&longs;tinendum vel dimouendum &longs;ufficiet, <lb/>etiam alia quæuis paulo maior vis tanto facilius &longs;u&longs;tinebit, aut mo<lb/>uebit pondus: quanto pars ad caput maior erit. </s>

<s>Inæqualium enim <lb/>maior ad eandem maiorem rationem habet prop. </s>

<s>Inæqualium enim <lb/>maior ad eandem maiorem rationem habet prop.

8. lib.

<s>5. Sed & <lb/>huius rei cau&longs;a adfertur ex his quæ ante demon&longs;trata &longs;unt, nempt à <lb/>radio maiore maiorem de&longs;cribi circulum. </s>

5. Sed & <lb/>huius rei cau&longs;a adfertur ex his quæ ante demon&longs;trata &longs;unt, nempt à <lb/>radio maiore maiorem de&longs;cribi circulum. </s>

<s>Pars enim vectis ab hy<lb/>pomochlio ad caput radÿ in&longs;tar e&longs;t maioris, qui depre&longs;&longs;us & ideo vo<lb/>lutus circa hypomochlium fixum tanquam <expan abbr="c&etilde;trum">centrum</expan>, de&longs;cribit arcum <lb/>tanto maiorem: quanto ip&longs;e radius maior erat. </s>

Line 2244

<s>Apertius igitur &longs;ic. </s>

<s>Sit vectis<emph.end type="italics"/> <foreign lang="greek">a b,</foreign> <emph type="italics"/>pondus vero<emph.end type="italics"/> <foreign lang="greek">g,</foreign><lb/><emph type="italics"/>mouens autem<emph.end type="italics"/> <foreign lang="greek">d,</foreign> <emph type="italics"/>preßio<emph.end type="italics"/> <foreign lang="greek">e.</foreign> <emph type="italics"/>Cum ip&longs;um<emph.end type="italics"/> <foreign lang="greek">d,</foreign> <emph type="italics"/>quod moueat, &longs;it vbi<emph.end type="italics"/> <foreign lang="greek">h</foreign><emph type="italics"/>: <lb/>& pondus<emph.end type="italics"/> <foreign lang="greek">g</foreign> <emph type="italics"/>motum erit vbi<emph.end type="italics"/> <foreign lang="greek">k.</foreign> <emph type="italics"/>quod ita &longs;e habere o&longs;tendit tertia <lb/>proprietas circuli, ex qua cap. </s>

<s>1. huius lib. </s>

1. huius lib.

<s>o&longs;ten&longs;um e&longs;t diametri ex<lb/>tremo vno deor&longs;um moto, alterum eodem tempore &longs;ur&longs;um moueri. </s>

o&longs;ten&longs;um e&longs;t diametri ex<lb/>tremo vno deor&longs;um moto, alterum eodem tempore &longs;ur&longs;um moueri. </s>

<s>E&longs;t <lb/>autem hic vectis<emph.end type="italics"/> <foreign lang="greek">b a,</foreign> <emph type="italics"/>vt diameter circuli cuius extremum<emph.end type="italics"/> <foreign lang="greek">b</foreign> <emph type="italics"/>deor<lb/>&longs;um cum ad<emph.end type="italics"/> <foreign lang="greek">h</foreign> <emph type="italics"/>mouetur, alterum<emph.end type="italics"/> <foreign lang="greek">a</foreign> <emph type="italics"/>&longs;ur&longs;um &longs;imul moueri vt ad<emph.end type="italics"/> <foreign lang="greek">k,</foreign> <emph type="italics"/>ne<lb/>ce&longs;&longs;um e&longs;t. </s>

Line 2364

<s>6. hæc hæ<lb/>bet.<emph.end type="italics"/> <foreign lang="greek"><gap/>pihra/fxwn )<gap/>pi<gap/>o<gap/>a\s w_ro\s tw_| )ex dimwoi/ou mi<gap/>w_| dido/ntwn <lb/>pi_s <gap/>ari/tais,</foreign> <emph type="italics"/>Thranitæ præter &longs;tipendium publicum à trierarchis <lb/>donatiuum con&longs;equebantur, cuius rei cau&longs;a &longs;ubdita e&longs;t à &longs;choliaste, <lb/><expan abbr="quoniãremos">quoniarremos</expan> longiores trahebant, grauioreque labore vexabantur, <lb/>& adhuc hodie eò loci remigant ex omnibus delecti robu&longs;tiores, à <lb/>largis &longs;patulis Gallis dicti Eppaliers. </s>

<s>Hic verò cap.

24. lib. </s>

<s>I, de v&longs;u<emph.end type="italics"/><pb pagenum="65"/><emph type="italics"/>partium &longs;ic ait, In triremibus <expan abbr="remor&utilde;">remorum</expan> extremitates ad vnam æqua<lb/>litatem perueniunt, cum tamen ip&longs;i omnes non &longs;int æquales, etenim <lb/>etiam ibi medios eandem ob cau&longs;am maximos efficiunt, id e&longs;t, vt vi<lb/>dere licet ex i&longs;to cap. </s>

Line 2380

<s>Ad hane <lb/>enim peruenire po&longs;&longs;unt duobus tantum modis, priore &longs;i intelligamus <lb/>tran&longs;trorum ordines<emph.end type="italics"/><lb/><figure id="fig25"></figure><lb/><emph type="italics"/>po&longs;itos e&longs;&longs;e ita, vt de<lb/>&longs;inant &longs;ecundum re<lb/>ctam A B parallelam <lb/>rectæ, quæ in naui ex<lb/>tenderetur à prora ad <lb/>puppim cuiu&longs;modi e&longs;to <lb/>C D, cui etiam altera <lb/>E F in mari parallela <lb/>ad quam extremitates <lb/>peruenirent, ita vt <lb/>&longs;ponda nauis ad cuius <lb/>G H T &longs;calmos e&longs;&longs;ent <lb/>alligati remi K G P, <lb/>M H N, O T P. <lb/></s>

<s>Sed &longs;i &longs;ic præterquam <lb/>quod Thalamitarum <lb/>Zygitarum & Thra-<emph.end type="italics"/><pb pagenum="66"/><emph type="italics"/>nitarum Remi e&longs;&longs;ent æquales prop. </s>

<s>Sed &longs;i &longs;ic præterquam <lb/>quod Thalamitarum <lb/>Zygitarum & Thra-<emph.end type="italics"/><pb pagenum="66"/><emph type="italics"/>nitarum Remi e&longs;&longs;ent æquales prop.

33. & 34. lib. </s>

Line 2398

<s>Quod autem <lb/>M H N medius remus &longs;it longior remis O I P & K G L fa<lb/>cile demon&longs;tratur ducta recta G I parallela ip&longs;i K. O. </s>

<s>Sic enim <lb/>æquales &longs;unt G K, S M, I O prop. </s>

<s>Sic enim <lb/>æquales &longs;unt G K, S M, I O prop.

33. & 34. lib.

<s>1. æquales item <lb/>propter paralleli&longs;mum G L, H N, & I P. totæ igitur ex his <lb/>æquales axiom. </s>

1. æquales item <lb/>propter paralleli&longs;mum G L, H N, & I P. totæ igitur ex his <lb/>æquales axiom. </s>

<s>2. lib.

<s>1. & ad earum vnam nempe ex S M, H N<emph.end type="italics"/><pb pagenum="67"/><emph type="italics"/>cum addatur in&longs;uper S H erit ip&longs;a M S H N remus medius <lb/>inæqualis, & vtrolibet aliorum maior ax. </s>

1. & ad earum vnam nempe ex S M, H N<emph.end type="italics"/><pb pagenum="67"/><emph type="italics"/>cum addatur in&longs;uper S H erit ip&longs;a M S H N remus medius <lb/>inæqualis, & vtrolibet aliorum maior ax. </s>

<s>4. Ergo maximus, quod <lb/>fuit probandum. </s>

Line 2480

<s>Dico C B e&longs;&longs;e <lb/>maiorem quam F I: & F I quam G H. </s>

<s>Per punctum M cen<lb/>trum circuli repertum prop. </s>

<s>Per punctum M cen<lb/>trum circuli repertum prop.

1. lib.

<s>3. ducatur parallela M N O P<emph.end type="italics"/><pb pagenum="69"/><emph type="italics"/>rectæ C D prop. </s>

3. ducatur parallela M N O P<emph.end type="italics"/><pb pagenum="69"/><emph type="italics"/>rectæ C D prop. </s>

<s>31. lib.

<s>1. &longs;icque parallelogramma &longs;unt O F &<emph.end type="italics"/><lb/><figure id="fig27"></figure><lb/><emph type="italics"/>N C. </s>

1. &longs;icque parallelogramma &longs;unt O F &<emph.end type="italics"/><lb/><figure id="fig27"></figure><lb/><emph type="italics"/>N C. </s>

<s>Quoniam igitur diame<lb/>ter A B maxima e&longs;t in&longs;cripta<lb/>rum in circulo, & K I propin<lb/>quior centro ip&longs;i L H remotiore <lb/>maior e&longs;t prop. </s>

<s>Quoniam igitur diame<lb/>ter A B maxima e&longs;t in&longs;cripta<lb/>rum in circulo, & K I propin<lb/>quior centro ip&longs;i L H remotiore <lb/>maior e&longs;t prop.

15. lib.

<s>3. harum <lb/>quoque dimidiæ M B, N I, O <lb/>H prop. </s>

3. harum <lb/>quoque dimidiæ M B, N I, O <lb/>H prop. </s>

<s>eiu&longs;dem erunt in<lb/>æquales & M B maior quam <lb/>N I, & N I quam O H. </s>

<s>Ab <lb/>his igitur &longs;ublatis æqualibus M <lb/>C, N F, O G parallelogram<lb/>morum O F, N C lateribus oppo&longs;itis prop. </s>

<s>Ab <lb/>his igitur &longs;ublatis æqualibus M <lb/>C, N F, O G parallelogram<lb/>morum O F, N C lateribus oppo&longs;itis prop.

34. lib.

<s>1. reliquæ C| B, <lb/>F I, G H erunt iuæquales ax. </s>

1. reliquæ C| B, <lb/>F I, G H erunt iuæquales ax. </s>

<s>5. Et quidem reliqua C B à maiore M <lb/>B maior: quam F I: & F I eadem ratione maior quam G H, & <lb/>&longs;ic de cæteris. </s>

Line 2792

<s>Quemadmodum eorum quæ vi <lb/>feruntur latio ad finem deficit, & imbecillior e&longs;t: &longs;ic continui lati <lb/>extremum imbecillius mouetur.<emph.end type="italics"/></s>

<s>Et quoniam exigua.] <emph type="italics"/>Similis &longs;ententia e&longs;t apud Ari&longs;totelem <lb/>lib. </s>

<s>Et quoniam exigua.] <emph type="italics"/>Similis &longs;ententia e&longs;t apud Ari&longs;totelem <lb/>lib.

<s>de animalium motu. </s>

de animalium motu. </s>

<s>Nec vero dubium e&longs;t, inquit, quin parua ad<lb/>modum initio facta mutatione in corpore multiplices è longinquo <lb/>varietates &longs;uboriantur, vt cum per temonem paululum tralatum <lb/>longè diuer&longs;a proræ po&longs;itio vi&longs;itur. </s>

Line 2810

<s>Nam quia<emph.end type="italics"/><pb pagenum="79"/><emph type="italics"/>tres anguli vnius triangulorum &longs;unt æquales tribus alterius prop. <lb/></s>

<s>32. lib.

<s>1. & anguli qui ad A æquales ex hypothe&longs;i, anguli ad ba<lb/>&longs;im duo duobus &longs;unt æquales ax. </s>

1. & anguli qui ad A æquales ex hypothe&longs;i, anguli ad ba<lb/>&longs;im duo duobus &longs;unt æquales ax. </s>

<s>3. & quia A D C & A C D <lb/>&longs;unt ad ba&longs;im I&longs;o&longs;celis, ÿ inter &longs;e erunt æquales prop. </s>

<s>3. & quia A D C & A C D <lb/>&longs;unt ad ba&longs;im I&longs;o&longs;celis, ÿ inter &longs;e erunt æquales prop.

5. lib.

<s>1. & per <lb/>eandem anguli A B E & A E B. </s>

1. & per <lb/>eandem anguli A B E & A E B. </s>

<s>Sicque A E B dimidius <lb/>cum &longs;it horum <expan abbr="duor&utilde;">duorum</expan>, angulo A C D etiam dimidio <expan abbr="æquali&utilde;">æqualium</expan> æ qua<lb/>lis erit ax. </s>

Line 2826

<s>Sunt igitur A B E & <lb/>A D C triangula æquiangula, proinde circum æquales angulos la<lb/>tera habebunt proportionalia. </s>

<s>prop.

4. lib.

<s>6. ideo vt A D ad D C: <lb/>&longs;ic A B ad B E: & vicißim vt A D ad A B: &longs;ic D C ba<lb/>&longs;is ad ba&longs;im B E prop. </s>

6. ideo vt A D ad D C: <lb/>&longs;ic A B ad B E: & vicißim vt A D ad A B: &longs;ic D C ba<lb/>&longs;is ad ba&longs;im B E prop. </s>

<s>16. lib.

<s>5. E&longs;t autem maius A D ip&longs;o A B <lb/>ex hypothe&longs;i. </s>

5. E&longs;t autem maius A D ip&longs;o A B <lb/>ex hypothe&longs;i. </s>

<s>Ergo Ba&longs;is D C maior erit ip&longs;a B E. </s>

Line 2846

<s>Sicque fiunt duo triangula I&longs;o&longs;celia A B E & A D C æqualia <lb/>angulis ad verticem A oppo&longs;itis prop. </s>

<s>Sicque fiunt duo triangula I&longs;o&longs;celia A B E & A D C æqualia <lb/>angulis ad verticem A oppo&longs;itis prop.

15. lib.

<s>1. Et inæqualia cruri<lb/>bus. </s>

1. Et inæqualia cruri<lb/>bus. </s>

<s>Namrectæ ab A puncto Cardini re&longs;pondente in ima parte na<lb/>uis propè puppis extremum ad extremum proræ id e&longs;t A D, A C <lb/>longè maiores &longs;unt breuißimis ÿs, quæ &longs;unt ab <expan abbr="eod&etilde;">eodem</expan> puncto A ad ex<lb/>tremum puppis A B, A E. </s>

Line 2942

<s>fiunt duo triangula<emph.end type="italics"/> <foreign lang="greek">a g d & b g e,</foreign><lb/><emph type="italics"/>quorum anguli quiad<emph.end type="italics"/> <foreign lang="greek">g,</foreign> <emph type="italics"/>quia ad <expan abbr="vertic&etilde;">verticem</expan> oppo&longs;iti, &longs;unt æquales prop. <lb/></s>

<s>15. lib.

<s>1. Tum latera, quæ ip&longs;os continent<emph.end type="italics"/> <foreign lang="greek">a g, d g,</foreign> <emph type="italics"/>duobus<emph.end type="italics"/> <foreign lang="greek"><gap/> g, <lb/><gap/> g</foreign> <emph type="italics"/>&longs;unt æqualia, quia partes &longs;unt dimidiæ eiu&longs;dem remi<emph.end type="italics"/> <foreign lang="greek">a b</foreign> <emph type="italics"/>ax. </s>

1. Tum latera, quæ ip&longs;os continent<emph.end type="italics"/> <foreign lang="greek">a g, d g,</foreign> <emph type="italics"/>duobus<emph.end type="italics"/> <foreign lang="greek"><gap/> g, <lb/><gap/> g</foreign> <emph type="italics"/>&longs;unt æqualia, quia partes &longs;unt dimidiæ eiu&longs;dem remi<emph.end type="italics"/> <foreign lang="greek">a b</foreign> <emph type="italics"/>ax. </s>

<s>6. <lb/>eruntigitur ba&longs;es<emph.end type="italics"/> <foreign lang="greek">a d, b e</foreign> <emph type="italics"/>æquales, vt reliqui anguli prop. </s>

<s>6. <lb/>eruntigitur ba&longs;es<emph.end type="italics"/> <foreign lang="greek">a d, b e</foreign> <emph type="italics"/>æquales, vt reliqui anguli prop.

4. lib.

<s>1.<emph.end type="italics"/><pb pagenum="82"/><emph type="italics"/>Et &longs;ic palmula perducta ad<emph.end type="italics"/> <foreign lang="greek">e</foreign> <emph type="italics"/>cum<emph.end type="italics"/> <foreign lang="greek">a</foreign> <emph type="italics"/>caput prouectum e&longs;&longs;et ad<emph.end type="italics"/> <foreign lang="greek">d</foreign><lb/><emph type="italics"/>æqualiter moueretur, &longs;ed in i&longs;to ca&longs;u<emph.end type="italics"/> <foreign lang="greek">g</foreign> <emph type="italics"/>&longs;calmo manente nauis immo<lb/>ta e&longs;&longs;et, <expan abbr="c&utilde;">cum</expan> tamen prouecta e&longs;&longs;e &longs;upponatur. </s>

1.<emph.end type="italics"/><pb pagenum="82"/><emph type="italics"/>Et &longs;ic palmula perducta ad<emph.end type="italics"/> <foreign lang="greek">e</foreign> <emph type="italics"/>cum<emph.end type="italics"/> <foreign lang="greek">a</foreign> <emph type="italics"/>caput prouectum e&longs;&longs;et ad<emph.end type="italics"/> <foreign lang="greek">d</foreign><lb/><emph type="italics"/>æqualiter moueretur, &longs;ed in i&longs;to ca&longs;u<emph.end type="italics"/> <foreign lang="greek">g</foreign> <emph type="italics"/>&longs;calmo manente nauis immo<lb/>ta e&longs;&longs;et, <expan abbr="c&utilde;">cum</expan> tamen prouecta e&longs;&longs;e &longs;upponatur. </s>

<s>Intelligatur igitur mini<lb/>mùm, vt ad<emph.end type="italics"/> <foreign lang="greek">z</foreign> <emph type="italics"/>e&longs;&longs;e perducta palmula<emph.end type="italics"/> <foreign lang="greek">b.</foreign> <emph type="italics"/>Ex hoc rur&longs;us <expan abbr="cõcludit">concludit</expan> Ari<lb/>&longs;toteles ex figura à Victore Fau&longs;to & ab alÿs paßim rectam<emph.end type="italics"/> <foreign lang="greek">d q</foreign><lb/><emph type="italics"/>maiorem e&longs;&longs;e: quam<emph.end type="italics"/> <foreign lang="greek">q z.</foreign> <emph type="italics"/>Et ita e&longs;&longs;e o&longs;tendamus, quia duorum trian<lb/>gulorum<emph.end type="italics"/> <foreign lang="greek">a q d & b q z</foreign> <emph type="italics"/>anguli, qui ad<emph.end type="italics"/> <foreign lang="greek">q</foreign> <emph type="italics"/>ad verticem oppo&longs;iti, <lb/>&longs;unt æquales prop. </s>

15. lib.

<s>1. tum<emph.end type="italics"/> <foreign lang="greek">q a d</foreign> <emph type="italics"/>æqualis e&longs;t<emph.end type="italics"/> <foreign lang="greek">q b z</foreign> <emph type="italics"/>vel quia <lb/>&longs;unt alterni facti à recta<emph.end type="italics"/> <foreign lang="greek">a b</foreign> <emph type="italics"/>incidente in parallelas<emph.end type="italics"/> <foreign lang="greek">a d, <gap/> e.</foreign> <emph type="italics"/>Ex <lb/>præcedenti <expan abbr="demõ&longs;tratione">demon&longs;tratione</expan>. </s>

1. tum<emph.end type="italics"/> <foreign lang="greek">q a d</foreign> <emph type="italics"/>æqualis e&longs;t<emph.end type="italics"/> <foreign lang="greek">q b z</foreign> <emph type="italics"/>vel quia <lb/>&longs;unt alterni facti à recta<emph.end type="italics"/> <foreign lang="greek">a b</foreign> <emph type="italics"/>incidente in parallelas<emph.end type="italics"/> <foreign lang="greek">a d, <gap/> e.</foreign> <emph type="italics"/>Ex <lb/>præcedenti <expan abbr="demõ&longs;tratione">demon&longs;tratione</expan>. </s>

<s>Ergo reliquus<emph.end type="italics"/> <foreign lang="greek">q d a</foreign> <emph type="italics"/>reliquo<emph.end type="italics"/> <foreign lang="greek">b z q</foreign> <emph type="italics"/>æqua<lb/>lis erit prop. </s>

32. lib.

<s>1. Et &longs;ic triangula<emph.end type="italics"/> <foreign lang="greek">a q d & b q z</foreign> <emph type="italics"/>&longs;unt æquian<lb/>gula, proinde & circum æquales angulos latera proportionalia prop. <lb/></s>

1. Et &longs;ic triangula<emph.end type="italics"/> <foreign lang="greek">a q d & b q z</foreign> <emph type="italics"/>&longs;unt æquian<lb/>gula, proinde & circum æquales angulos latera proportionalia prop. <lb/></s>

<s>4. lib.

<s>6. E&longs;t igitur vt<emph.end type="italics"/> <foreign lang="greek">a q</foreign> <emph type="italics"/>ad<emph.end type="italics"/> <foreign lang="greek">q d</foreign>: <emph type="italics"/>&longs;ic<emph.end type="italics"/> <foreign lang="greek">b q</foreign> <emph type="italics"/>ad<emph.end type="italics"/> <foreign lang="greek">q z,</foreign> <emph type="italics"/>& vicißim <lb/>prop. </s>

6. E&longs;t igitur vt<emph.end type="italics"/> <foreign lang="greek">a q</foreign> <emph type="italics"/>ad<emph.end type="italics"/> <foreign lang="greek">q d</foreign>: <emph type="italics"/>&longs;ic<emph.end type="italics"/> <foreign lang="greek">b q</foreign> <emph type="italics"/>ad<emph.end type="italics"/> <foreign lang="greek">q z,</foreign> <emph type="italics"/>& vicißim <lb/>prop.

16. lib.

<s>5. vt<emph.end type="italics"/> <foreign lang="greek">a q</foreign> <emph type="italics"/>ad<emph.end type="italics"/> <foreign lang="greek">q b</foreign>: <emph type="italics"/>&longs;ic<emph.end type="italics"/> <foreign lang="greek">d q</foreign> <emph type="italics"/>ad<emph.end type="italics"/> <foreign lang="greek">q z.</foreign> <emph type="italics"/>E&longs;t <expan abbr="aut&etilde;">autem</expan><emph.end type="italics"/> <foreign lang="greek">a q</foreign> <emph type="italics"/>maior: <lb/>quam<emph.end type="italics"/> <foreign lang="greek">q b,</foreign> <emph type="italics"/>quia<emph.end type="italics"/> <foreign lang="greek">a b</foreign> <emph type="italics"/>erat bi&longs;&longs;ecta in<emph.end type="italics"/> <foreign lang="greek">g,</foreign> <emph type="italics"/>& detracta e&longs;t de dimi<lb/>dia<emph.end type="italics"/> <foreign lang="greek">g b</foreign> <emph type="italics"/>portio<emph.end type="italics"/> <foreign lang="greek">q g,</foreign> <emph type="italics"/>quæ additur ip&longs;i dimidiæ<emph.end type="italics"/> <foreign lang="greek">a g.</foreign> <emph type="italics"/>E&longs;t igitur<emph.end type="italics"/><lb/><foreign lang="greek">d q</foreign> <emph type="italics"/>maior quam<emph.end type="italics"/> <foreign lang="greek">q z.</foreign></s>

5. vt<emph.end type="italics"/> <foreign lang="greek">a q</foreign> <emph type="italics"/>ad<emph.end type="italics"/> <foreign lang="greek">q b</foreign>: <emph type="italics"/>&longs;ic<emph.end type="italics"/> <foreign lang="greek">d q</foreign> <emph type="italics"/>ad<emph.end type="italics"/> <foreign lang="greek">q z.</foreign> <emph type="italics"/>E&longs;t <expan abbr="aut&etilde;">autem</expan><emph.end type="italics"/> <foreign lang="greek">a q</foreign> <emph type="italics"/>maior: <lb/>quam<emph.end type="italics"/> <foreign lang="greek">q b,</foreign> <emph type="italics"/>quia<emph.end type="italics"/> <foreign lang="greek">a b</foreign> <emph type="italics"/>erat bi&longs;&longs;ecta in<emph.end type="italics"/> <foreign lang="greek">g,</foreign> <emph type="italics"/>& detracta e&longs;t de dimi<lb/>dia<emph.end type="italics"/> <foreign lang="greek">g b</foreign> <emph type="italics"/>portio<emph.end type="italics"/> <foreign lang="greek">q g,</foreign> <emph type="italics"/>quæ additur ip&longs;i dimidiæ<emph.end type="italics"/> <foreign lang="greek">a g.</foreign> <emph type="italics"/>E&longs;t igitur<emph.end type="italics"/><lb/><foreign lang="greek">d q</foreign> <emph type="italics"/>maior quam<emph.end type="italics"/> <foreign lang="greek">q z.</foreign></s>

<s><emph type="italics"/>Hoc autem quanquam verum &longs;it, quor&longs;um tamen, dubium e&longs;t. <lb/></s>

Line 2986

<s>At contrà latum <lb/>pro&longs;perè nauigium &longs;eruat eundem &longs;calmum, &longs;eu &longs;pondam &longs;uam &longs;em<lb/>per æquidi&longs;tantem aquæ, ni&longs;i quod verius e&longs;t, arcum peripheriæ, &longs;ed <lb/>non &longs;implicem, vt po&longs;tea docebimus, de&longs;cribat, cuius extrema &longs;unt in <lb/>&longs;uperficie aquæ.<emph.end type="italics"/><lb/><figure id="fig30"></figure><lb/><emph type="italics"/>vt, &longs;it &longs;ponda <lb/>nauis G H, & <lb/>&longs;calmus C, cui <lb/>alligatus remus <lb/>per medium &longs;it <lb/>A B exi&longs;tens in <lb/>principio remi<lb/>gationis, & in <lb/>fine &longs;it vbi D E, <lb/>tran&longs;lato C per <lb/>motum nauigij <lb/>impul&longs;i in T: <lb/>&longs;icque motionis <lb/>intra aquam pal<lb/>mulæ B &longs;patium erit B E: nauigij vero erit C T: tum capitis <lb/>remi A erit A D. </s>

<s>Et quidem cum anguli qui ad E &longs;int &longs;emper <lb/>æquales prop. </s>

<s>Et quidem cum anguli qui ad E &longs;int &longs;emper <lb/>æquales prop.

15. lib.

<s>1. Ba&longs;es erunt æquales, &longs;i triangula fiant æqui <lb/>crura, &longs;i iniquicrura, illius trianguli ba&longs;is erit maior, cuius latera <lb/>angulum continentia &longs;unt maiora, vt antea ostendimus. </s>

1. Ba&longs;es erunt æquales, &longs;i triangula fiant æqui <lb/>crura, &longs;i iniquicrura, illius trianguli ba&longs;is erit maior, cuius latera <lb/>angulum continentia &longs;unt maiora, vt antea ostendimus. </s>

<s>Hæcigi<lb/>tur cum expendo cogor aliud &longs;entire quam Nonius licet timidè (quia <lb/>viro huic propter &longs;cientiam præ&longs;tantem, & quod in loco natus &longs;it, <lb/>vixeritque ad nauigandum opportunißimo, multò plura quam mihi <lb/>tribuere &longs;oleo) dicam tamen quod &longs;entio nempe conclu&longs;ionem i&longs;tam<emph.end type="italics"/><lb/><foreign lang="greek">d q</foreign> <emph type="italics"/>maiorem e&longs;&longs;e<emph.end type="italics"/> <foreign lang="greek">q z,</foreign> <emph type="italics"/>pertinere eò, vt inferatur caput remi A <lb/>tran&longs;uecti non con&longs;i&longs;tere in<emph.end type="italics"/> <foreign lang="greek">d</foreign>: <emph type="italics"/>&longs;ed vltra. </s>

Line 3034

<s>Secet enim re<lb/>cta A C rectam E F in G. </s>

<s>Quia igitur A G E, & B G D <lb/>triangula &longs;unt æquiangula, erit &longs;icut A G ad B G: &longs;ic A E <lb/>ad B D prop. </s>

<s>Quia igitur A G E, & B G D <lb/>triangula &longs;unt æquiangula, erit &longs;icut A G ad B G: &longs;ic A E <lb/>ad B D prop.

4. lib.

<s>6. Maior e&longs;t autem A G ip&longs;a B G, ax. </s>

6. Maior e&longs;t autem A G ip&longs;a B G, ax. </s>

<s>9. <lb/>Erit igitur A E maior quam B D. </s>

Line 3046

<s>quod erat demon&longs;trandum.<emph.end type="italics"/></s><figure></figure>

<s><emph type="italics"/>Quod &longs;i per punctum B rectam duca<lb/>mus H K æqualem remo, & ad rectos <lb/>cum recta B D, & in&longs;uper &longs;ecantem A<emph.end type="italics"/><lb/>3 <emph type="italics"/>in puncto I, manife&longs;tè intelligemus <lb/>ip&longs;am rectam A E (quæ e&longs;t totus motus <lb/>capitis remi in vna remigatione) con&longs;tare <lb/>ex A I, & I E, quarum prior re&longs;pon<lb/>det curuæ A H de&longs;criptæ per capitis remi <lb/>motum proprium: po&longs;terior vero æqualis <lb/>e&longs;trectæ B D (&longs;unt enim latera parallelo<lb/>grammi oppo&longs;ita prop. </s>

34. lib.

<s>1.) quæ motu <lb/>nauis decur&longs;a e&longs;t.<emph.end type="italics"/></s>

1.) quæ motu <lb/>nauis decur&longs;a e&longs;t.<emph.end type="italics"/></s>

<s><emph type="italics"/>Et quia Nonius &longs;ine demon&longs;tratione a&longs;<lb/>&longs;umit nauim tantùm decurrere, quantùm <lb/>&longs;calmus, id quoque demonstremus. </s>

Line 3070

<s>Et <lb/>eadem recta C G producatur v&longs;que <lb/>ad E, ita vt G E &longs;it æqualis rectæ <lb/>B A (quæ e&longs;t dimidium remi) rur<lb/>&longs;us per punctum B ducatur recta Q <lb/>B F ad rectos cum ip&longs;a B G, & in <lb/>Q B F incidant perpendiculares A <lb/>Q C F. </s>

<s>Quoniam igitur triangu<lb/>lorum A B Q & F B C anguli, <lb/>qui ad B ad verticem oppo&longs;iti &longs;unt <lb/>æquales, prop. </s>

<s>Quoniam igitur triangu<lb/>lorum A B Q & F B C anguli, <lb/>qui ad B ad verticem oppo&longs;iti &longs;unt <lb/>æquales, prop.

15. lib.

<s>1. & anguli qui ad Q & F recti &longs;unt, tum <lb/>latus A B lateri B C, &longs;unt enim dimidia remi, æquale e&longs;t, erit & <lb/>latus A Q æquale lateri F C prop. </s>

1. & anguli qui ad Q & F recti &longs;unt, tum <lb/>latus A B lateri B C, &longs;unt enim dimidia remi, æquale e&longs;t, erit & <lb/>latus A Q æquale lateri F C prop.

26. lib.

<s>1. Ip&longs;i autem F C recta <lb/>B G, latus parallelogrammi oppo&longs;itum, æqualis e&longs;t prop. </s>

1. Ip&longs;i autem F C recta <lb/>B G, latus parallelogrammi oppo&longs;itum, æqualis e&longs;t prop. </s>

<s>34. lib.

<s>1. <lb/>A Qigitur erit æqualis ip&longs;i B G ax. </s>

1. <lb/>A Qigitur erit æqualis ip&longs;i B G ax. </s>

<s>1. Atque tantum &longs;patium B <lb/>&longs;calmus: quantum nauis. </s>

Line 3110

<s><emph type="italics"/>Manife&longs;ta e&longs;t, quia &longs;i remi palmula dimota non fuerit à loco &longs;uo, <lb/>ibique tandiu per&longs;i&longs;tat, donec remus &longs;itum rectitudinis obtineat, tan<lb/>tum &longs;patium conficiet caput remi motu proprio: quantum nauis. <lb/></s>

<s>Recta enim C F æqualis e&longs;t A Q prop. </s>

<s>Recta enim C F æqualis e&longs;t A Q prop.

26. lib.

<s>1. æqualis etiam <lb/>B G prop. </s>

1. æqualis etiam <lb/>B G prop. </s>

<s>34. lib.

<s>1. igitur A Q & B G æquales erunt ax. </s>

1. igitur A Q & B G æquales erunt ax. </s>

Line 3130

<s>Et &longs;ic &longs;calmus B pro<lb/>pter nauis motum conficiet interual<lb/>lum B D. </s>

<s>Excitetur igitur à puncto <lb/>B in vtramque partem perpendicu<lb/>laris E E, prop. </s>

<s>Excitetur igitur à puncto <lb/>B in vtramque partem perpendicu<lb/>laris E E, prop.

11. lib.

<s>1. In quam <lb/>perpendiculares incidant à punctis <lb/>A & C, quæ &longs;int A E, C E prop. <lb/></s>

1. In quam <lb/>perpendiculares incidant à punctis <lb/>A & C, quæ &longs;int A E, C E prop. <lb/></s>

<s>12. lib.

<s>1. Et &longs;it interuallum A E <lb/>quod e&longs;t decur&longs;um à capite remi A <lb/>proprio motu, duplum interualli B <lb/>D, & recta linea C H re&longs;pondeat <lb/>curuæ C G à remi palmula de&longs;cri<lb/>ptæ. </s>

1. Et &longs;it interuallum A E <lb/>quod e&longs;t decur&longs;um à capite remi A <lb/>proprio motu, duplum interualli B <lb/>D, & recta linea C H re&longs;pondeat <lb/>curuæ C G à remi palmula de&longs;cri<lb/>ptæ. </s>

<s>Dico rectas lineas B D, C H <lb/>æquales e&longs;&longs;e. </s>

<s>Nam triangulorum B <lb/>A E & C B E rectæ A E, C E prop. </s>

<s>Nam triangulorum B <lb/>A E & C B E rectæ A E, C E prop.

26. lib.

<s>1. & in parallelo<lb/>grammo B H rectæ oppo&longs;itæ B D, E H etiam æquales prop. </s>

1. & in parallelo<lb/>grammo B H rectæ oppo&longs;itæ B D, E H etiam æquales prop. </s>

<s>34. <lb/>lib.

<s>1. Atqui recta A E dupla e&longs;t rectæ B D ex hypothe&longs;i. </s>

1. Atqui recta A E dupla e&longs;t rectæ B D ex hypothe&longs;i. </s>

<s>Dupla <lb/>igitur & C E rectæ H E, quapropter C H & E H æqual<gap/>s <lb/>erunt ax. </s>

Line 3170

<s><emph type="italics"/>Si enim C H æqualis ponatur B D, quoniam eidem B D æqua<lb/>lis e&longs;t H E in parallelogrammo, æquales igitur erunt C H & <lb/>H E ax. </s>

<s>1. Et &longs;ic dupla erit C E ip&longs;ius H E: & eadem C E <lb/>dupla ip&longs;ius B D. æquales porro &longs;unt C E & A E prop 26. lib. </s>

<s>1. Et &longs;ic dupla erit C E ip&longs;ius H E: & eadem C E <lb/>dupla ip&longs;ius B D. æquales porro &longs;unt C E & A E prop 26. lib.

<s>1. <lb/>Dupla ergo erit A E rectæ B D. &longs;ed recta A E decur&longs;a e&longs;t à ca<lb/>pite remi, & B D à &longs;calmo, quantùm autem prouehitur &longs;calmus, <lb/>tantùm & nauis. </s>

1. <lb/>Dupla ergo erit A E rectæ B D. &longs;ed recta A E decur&longs;a e&longs;t à ca<lb/>pite remi, & B D à &longs;calmo, quantùm autem prouehitur &longs;calmus, <lb/>tantùm & nauis. </s>

<s>Igitur &longs;i nauis tantùm fuerit prouecta, quantùm <lb/>remi palmula retroceßit, duplum conficit caput remi motu proprio <lb/>eius interualli, quod nauis conficit. </s>

Line 3424

<s>Prior venit in men<lb/>tem ob duos locos apud Galenum à perpaucis intellectos. </s>

<s>Alter e&longs;t <lb/>cap. </s>

<s>Alter e&longs;t <lb/>cap.

9. lib.

<s>2. de mu&longs;c. </s>

2. de mu&longs;c. </s>

<s>motu: alter com. </s>

<s>4. in lib.

6.<emph.end type="italics"/> <foreign lang="greek">e(pid.</foreign> <emph type="italics"/>in Aph. </s>

<s>24. <lb/>vbi dicit tibicines, præcones, nuncupatum<emph.end type="italics"/> <foreign lang="greek">po/da,</foreign> <emph type="italics"/>id e&longs;t, pedem cane<lb/>re. </s>

Line 3460

<s><arrow.to.target n="marg25"></arrow.to.target><pb pagenum="96"/><emph type="italics"/>detrahitur his velum, & vocantur<emph.end type="italics"/> <foreign lang="greek">mesouri/ai</foreign>: <emph type="italics"/>aut intenditur vtrin<lb/>que ad proram, & &longs;unt<emph.end type="italics"/> <foreign lang="greek">w_<gap/>/tonoi</foreign>: <emph type="italics"/>aut conuertitur & laxatur, hi <lb/>&longs;unt<emph.end type="italics"/> <foreign lang="greek"><gap/>\ ta\s gwni/as</foreign> <emph type="italics"/>ad angulos, & dicuntur<emph.end type="italics"/> <foreign lang="greek">po/des</foreign> <emph type="italics"/>& ante hos<emph.end type="italics"/><lb/><foreign lang="greek">w_<gap/>/podes</foreign> <emph type="italics"/>quo &longs;en&longs;u dixi&longs;&longs;e Plinius videtur lib. </s>

2. cap.

<s>47. Ii&longs;dem <lb/>autem ventis in contrarium nauigatur prolatis pedibus vt noctu <lb/>plerumque vela concurrant.<emph.end type="italics"/></s>

47. Ii&longs;dem <lb/>autem ventis in contrarium nauigatur prolatis pedibus vt noctu <lb/>plerumque vela concurrant.<emph.end type="italics"/></s>

Line 3516

<s>Sed neque &longs;i maximus quidem &longs;uerit ventus, nauis autem & <lb/>maxima & grauis, & duo &longs;olum aut tres remigent, remigum actio<lb/>nem apparere poßibile e&longs;t. </s>

<s>cap.

19. lib.

<s>1. de v&longs;. </s>

1. de v&longs;. </s>

<s>partium.<emph.end type="italics"/></s>

Line 3566

<s>Neuter enim cum &longs;uo impul&longs;u præualeat, medium teneat A G ne<lb/>ce&longs;&longs;e e&longs;t, quod &longs;i ventus præualet, adiungitur remigum renixus, qui <lb/>&longs;i non &longs;atis &longs;it, vento cedendum, aut anchora iacienda. </s>

<s>Tum autem <lb/>vix remiges re&longs;i&longs;tunt, <expan abbr="c&utilde;">cum</expan> nauis e&longs;t in centro, vel radio perpendicula<lb/>ri venti, quo in loco propter vim venti maiorem, & anguli per te-<emph.end type="italics"/><pb pagenum="99"/><emph type="italics"/>monem faciendi magnitudinem, vt qui rectum æquare debeat, dif<lb/>ficillimè ad locum de&longs;tinatum dirigitur: at quantò fuerit remotior <lb/>à puncto D, velocius & facilius feretur, quia ventus rectius tan<lb/>get puppim, minor enim erit &longs;emper angulus per temonem facien<lb/>dus, vt intelligitur ex G P Q minore: quam G A E, & G I <lb/>M minore: quam G P <expan abbr="q.">que</expan> Sunt enim duo C A G & G A E, <lb/>quia facti à recta G A in rectam C E duobus rectis æquales <lb/>prop. </s>

13. lib.

<s>1. & per eandem etiam duo C P G & G P Q duobus <lb/>rectis æquales. </s>

1. & per eandem etiam duo C P G & G P Q duobus <lb/>rectis æquales. </s>

<s>Ergo duo C A G & G A E duobus C P G & <lb/>G P Q &longs;unt æquales axiom. </s>

<s>1. E&longs;t autem C P G externus oppo<lb/>&longs;ito interno C A G maior, prop. </s>

<s>1. E&longs;t autem C P G externus oppo<lb/>&longs;ito interno C A G maior, prop.

16. lib.

<s>1. Reliquus igitur G P Q <lb/>reliquo G A E minor erit, & ita de cæteris. </s>

1. Reliquus igitur G P Q <lb/>reliquo G A E minor erit, & ita de cæteris. </s>

<s>Sicque nauis proce&longs;&longs;u <lb/>&longs;uo mutabit &longs;en&longs;im temonem, vt & vela.<emph.end type="italics"/></s>

Line 3644

<s>quod demon&longs;tratum e&longs;t de <lb/>illo quidem à Theodo&longs;. </s>

<s>prop.

2. lib.

<s>1. de Sphær. </s>

1. de Sphær. </s>

<s>de hoc vero ab Eucli<lb/>de prop. </s>

<s>16. lib.

3.<emph.end type="italics"/></s>

<s>Et quia non off.] <emph type="italics"/>Secunda cau&longs;a e&longs;t de occur&longs;antibus, quæ <lb/>rur&longs;us cum minimam partem rotundorum attingant, & atterant, <lb/>minus impediunt, quam quæ plus attingunt, pluribu&longs;que occur&longs;ant.<emph.end type="italics"/></s>

<s>Di&longs;tat enim angulus.] <emph type="italics"/>Cum rotundum incumbit plano ad <lb/>omnes rectas à quibus tangitur in ip&longs;o plano angulos facit contin<lb/>gentiæ, quorum &longs;inguli quia &longs;unt minores quouis acuto angulo re<lb/>ctilineo, vt e&longs;t demon&longs;tratum prop. </s>

16. lib.

<s>3. procliues &longs;unt maxime <lb/>ad motum. </s>

3. procliues &longs;unt maxime <lb/>ad motum. </s>

<s>Latus enim curuum anguli vnius contactus &longs;emotum <lb/>quidem e&longs;t à plano: &longs;ed parum propter anguli angu&longs;tiam. </s>

Line 3752

<s>Et per &longs;e cum motum hunc creet &longs;ine defatigatione e&longs;t <lb/>hic motus in regularißimo corpore regularißimus, & facillimo ad <lb/>motum velocißimus, vt e&longs;t apud Ptolomæum concl. </s>

<s>1. lib.

1.<emph.end type="italics"/> <foreign lang="greek">meg. <lb/></foreign></s>

<s><foreign lang="greek">sun<gap/>.</foreign> <emph type="italics"/>Velocitatem autem intelliget, qui intellexerit quot millia<lb/>ria, habeat circulus in c&oelig;lo extimo maximus, & quot ex his vno<lb/>quoque momento conficiat. </s>

<s>Intelligetur quoque quomodo illius c&oelig;li <lb/>motus &longs;it omnium motuum <expan abbr="m&etilde;&longs;ura">men&longs;ura</expan>. </s>

<s>Nam cum men&longs;ura &longs;it in vno<lb/>quoque genere minimum, vt e&longs;t cap. </s>

<s>Nam cum men&longs;ura &longs;it in vno<lb/>quoque genere minimum, vt e&longs;t cap.

4. lib.

<s>2. de C&oelig;l. </s>

2. de C&oelig;l. </s>

<s>hic autem mo<lb/>tus minimus debet dici, qui per minimam lineam earum quæ æqua<lb/>les areas includunt fit, cuiu&longs;modi e&longs;t circularis, &longs;icque &longs;ecundum eam <lb/>motus erit celerrimus, quia minimus.<emph.end type="italics"/></s>

Line 3816

<s>Et A B <lb/>quia diameter e&longs;t <lb/>circulum &longs;uum bi<lb/>fariam diuidit ex <lb/>def. </s>

<s>17. lib.

<s>1. Sic<lb/>que tanta pars e&longs;t <lb/>ad G, quanta ad H. </s>

1. Sic<lb/>que tanta pars e&longs;t <lb/>ad G, quanta ad H. </s>

<s>Similiter maximus in &longs;phæra circulus recta <lb/>in&longs;i&longs;tens &longs;phæram bifariam di&longs;pe&longs;cit.<emph.end type="italics"/></s>

Line 3872

<s>Sunt enim circulorum &longs;emidiametri. </s>

<s>Partes autem cum pari<lb/>ter multiplicibus &longs;unt in eadem ratione prop. </s>

<s>Partes autem cum pari<lb/>ter multiplicibus &longs;unt in eadem ratione prop.

15. lib.

<s>5. Diameter au<lb/>tem maior celerius mouetur, hîc autem notandum e&longs;t angulos non<emph.end type="italics"/><pb pagenum="108"/><emph type="italics"/>&longs;umi pro inclinatione: &longs;ed pro crurum<emph.end type="italics"/><lb/><figure id="fig40"></figure><lb/><emph type="italics"/><expan abbr="lõgitudine">longitudine</expan>. </s>

5. Diameter au<lb/>tem maior celerius mouetur, hîc autem notandum e&longs;t angulos non<emph.end type="italics"/><pb pagenum="108"/><emph type="italics"/>&longs;umi pro inclinatione: &longs;ed pro crurum<emph.end type="italics"/><lb/><figure id="fig40"></figure><lb/><emph type="italics"/><expan abbr="lõgitudine">longitudine</expan>. </s>

<s>hæc autem figura hac cir<lb/>culorum concentricorum & à cen<lb/>tris angulorum illu&longs;trantur.<emph.end type="italics"/></s>

Line 3924

<s>Infiniti autem.] <emph type="italics"/>Quod infiniti circuli minores concentrici in<lb/>&longs;int in quouis dato circulo &longs;ic demon&longs;trabimus. </s>

<s>Sit circulus C B, <lb/>cuius &longs;emidiameter D B bifariam<emph.end type="italics"/><lb/><figure id="fig41"></figure><lb/><emph type="italics"/>&longs;ecetur, vt in puncto E prop. </s>

<s>Sit circulus C B, <lb/>cuius &longs;emidiameter D B bifariam<emph.end type="italics"/><lb/><figure id="fig41"></figure><lb/><emph type="italics"/>&longs;ecetur, vt in puncto E prop.

10. <lb/>lib.

<s>1. Et centro D interuallo D E <lb/>de&longs;criptus circulus po&longs;t. </s>

1. Et centro D interuallo D E <lb/>de&longs;criptus circulus po&longs;t. </s>

<s>3. Hic <lb/>erit concentricus & minor ip&longs;o <lb/>C B def. </s>

<s>1. lib.

<s>3. Rur&longs;us recta D <lb/>E bifariam &longs;ecetur, vt in puncto <lb/>F, & centro D eodem interuallo <lb/>D F de&longs;criptus circulus erit con<lb/>centricus & minor. </s>

3. Rur&longs;us recta D <lb/>E bifariam &longs;ecetur, vt in puncto <lb/>F, & centro D eodem interuallo <lb/>D F de&longs;criptus circulus erit con<lb/>centricus & minor. </s>

<s>Et eadem ra<lb/>tione deinceps ad infinitum, cum rectam lineam &longs;emper bi&longs;&longs;ecare li<lb/>ceat prop. </s>

<s>Et eadem ra<lb/>tione deinceps ad infinitum, cum rectam lineam &longs;emper bi&longs;&longs;ecare li<lb/>ceat prop.

10. lib.

<s>1. Et &longs;ic infiniti erunt circuli concentrici minores <lb/>in quouis circulo. </s>

1. Et &longs;ic infiniti erunt circuli concentrici minores <lb/>in quouis circulo. </s>

<s>quod erat demon&longs;trandum.<emph.end type="italics"/></s>

Line 4012

<s>De hoc autem genere lo<lb/>cus hic intelligi debet. </s>

<s>De altero dicetur cap. </s>

<s>De altero dicetur cap.

12.<emph.end type="italics"/></s>

<s>Vt diximus ctiam.] <emph type="italics"/>Confirmatio e&longs;t propo&longs;itionis præceden<lb/>tis &longs;yllogi&longs;mi per &longs;peciem libræ, quæ tantò exactior exi&longs;tit: quantò li<lb/>brile habet longius, è &longs;uperioribus repetitam. </s>

Line 4168

<s>In medio latior, & paululum excauatus, vt <lb/>ibi mißile contineatur, quod aliquoties circumacto in orbem funicu<lb/>lo, & ab vno capitum dimi&longs;&longs;o vehementer proÿcitur. </s>

<s>Inuentam à <lb/>Phenicibus fui&longs;&longs;e refert Plinius cap. </s>

<s>Inuentam à <lb/>Phenicibus fui&longs;&longs;e refert Plinius cap.

56. lib.

<s>7. ne manus iaculi a&longs;pe<lb/>rioris attrectatione læderetur, & vt longius atque validius proÿce<lb/>retur. </s>

7. ne manus iaculi a&longs;pe<lb/>rioris attrectatione læderetur, & vt longius atque validius proÿce<lb/>retur. </s>

<s>Quæ cum intelligeret pa&longs;tor ille exilis, &longs;ed Deo dilectus Dauid <lb/>funda aduer&longs;us Goliathem immanem gigantem non aliter, quam <lb/>&longs;ummo impetu pro&longs;ternendum, prudenter &longs;e&longs;e armauit. </s>

Line 4238

<s><emph type="italics"/>Igitur proiectio cum funda longior fiet.<emph.end type="italics"/><lb/><arrow.to.target n="marg28"></arrow.to.target></s>

<s><margin.target id="marg28"></margin.target>Cap 1. lib.

<s>2. <lb/>de v&longs;. </s>

2. <lb/>de v&longs;. </s>

Line 4292

<s>Huius fecit <lb/>mentionem Hippocrates &longs;ect. </s>

<s>3. lib.

<s>de fract. </s>

de fract. </s>

<s>Ex vniuer&longs;is inquit, <lb/>machinationibus, quæ ab hominibus excogitatæ &longs;unt, hæ tres om<lb/>nium valentißimæ,<emph.end type="italics"/> <foreign lang="greek">o)/nou</foreign> <emph type="italics"/>id e&longs;t axis ver&longs;atio, impul&longs;us per vectem, & <lb/>cuneus adactus. </s>

Line 4302

<s>Hæc Hipp.<emph.end type="italics"/><pb pagenum="120"/><emph type="italics"/>Succularum <expan abbr="tam&etilde;">tamen</expan> multa &longs;unt genera vt videre e&longs;t apud Vitruuium.<emph.end type="italics"/></s>

<s><emph type="italics"/>Et Pappus lib. </s>

<s><emph type="italics"/>Et Pappus lib.

<s>8. Mathemat collectionum fabricam in&longs;trumenti <lb/>docet, quod huc referri debet, e&longs;t autem eiu&longs;modi. </s>

8. Mathemat collectionum fabricam in&longs;trumenti <lb/>docet, quod huc referri debet, e&longs;t autem eiu&longs;modi. </s>

<s>vocat axem M B,<emph.end type="italics"/><lb/><figure id="fig45"></figure><lb/><emph type="italics"/><expan abbr="tympan&utilde;">tympanum</expan> C D, circa tympani <expan abbr="peripheriã&longs;cytalas">peripherian&longs;cytalas</expan> vel collopes in fora<lb/>minibus tympani F G, H F, & ct:ita, vt potentia quæ &longs;emper in <lb/>&longs;cytalis e&longs;t, vel in peripheria tympani vt in F, dum circumuertit <lb/>tympanum, & axem &longs;ur&longs;um quoque mouet pondus K axi appen&longs;um <lb/>fune M circa axem reuoluto. </s>

Line 4416

<s>cap.

8. <lb/>lib.

8.</s>

<s><margin.target id="marg30"></margin.target>Cap.

Line 4526

<s>Tum non alio vtens in&longs;trumento, quam &longs;uis manibus au&longs;us e&longs;t trun<lb/>cum diducere. </s>

<s>Mox quicquid habebat roboris in primo impetu colli<lb/>gens, diduxit hûc atque illûc partes, interim elap&longs;is cuneis, quoniam <lb/>reliquam arboris partem diducere non po&longs;&longs;et, diù quidem obnixus e&longs;t, <lb/>tandem victus educere non potuit: &longs;ed ab arboris partibus in &longs;e&longs;e cele<lb/>riter <expan abbr="co&etilde;untibus">coenuntibus</expan> comprehen&longs;æ, primum quidem ip&longs;æ contritæ &longs;unt, <lb/>mox & ip&longs;i mi&longs;erandi exitÿ fuere cau&longs;a, vt refert Galenus in lib. </s>

<s>de <lb/>exhort. </s>

de <lb/>exhort. </s>

<s>ad bonas artes. </s>

Line 4552

<s>Notandum autem quod inter <lb/>cuneos, qui angulum ad verticem <expan abbr="acutior&etilde;">acutiorem</expan> habet facilius mouet, ac <lb/>&longs;cindit: quam qui obtu&longs;iorem. </s>

<s>Mouetur enim cuneus anguli maioris<emph.end type="italics"/><pb pagenum="128"/><emph type="italics"/>per maius &longs;patium, quam minoris, &longs;iquidem maioris anguli maior e&longs;t <lb/>&longs;ubten&longs;a, cum anguli &longs;unt æquicruri prop. </s>

26. lib.

<s>1. A potentia verò <lb/>facilius eodem tempore mouetur aliquid per minus &longs;patium: quam <lb/>per maius cum cætera paria &longs;unt.<emph.end type="italics"/></s>

1. A potentia verò <lb/>facilius eodem tempore mouetur aliquid per minus &longs;patium: quam <lb/>per maius cum cætera paria &longs;unt.<emph.end type="italics"/></s>

<s>An quia.] <emph type="italics"/>Prior cau&longs;a e&longs;t ad &longs;olutionem problematis, quæ hoc <lb/>&longs;yllogi&longs;mo concludetur.<emph.end type="italics"/></s>

Line 4786

<s>Itaque quo<lb/>niam facilius e&longs;t mouere pondus vecte: quam manu, & trochlea ve<lb/>ctis e&longs;t, facilius erit trochlea: quam manu.<emph.end type="italics"/></s>

<s>Plu&longs;quam in dupla.] <emph type="italics"/>Quò plures &longs;unt orbiculi in trochleis, eò <lb/>quidem facilius, & minore vi pondus trahitur, vt e&longs;t demon&longs;tra<lb/>tum à Guido V baldo prop. </s>

<s>3. & aliquot &longs;equentibus in tractatu de <lb/>trochlea. </s>

3. & aliquot &longs;equentibus in tractatu de <lb/>trochlea. </s>

<s>Sed etiam vbi &longs;unt plures, ibi lentior e&longs;t tractio, quia po<lb/>tentia in æquali tempore, &longs;patio &longs;ecundum duplum, triplum, & &longs;ic <lb/>deinceps ampliori &longs;ine huiu&longs;modi trochleis idem pondus moueret: &longs;i <lb/>quidem per &longs;e &longs;ufficiat. </s>

Line 5156

<s>Notandum etiam pondus impo&longs;itum lanci e&longs;&longs;e perinde <lb/>atque &longs;i in puncto A imponeretur. </s>

<s>Sed de his qui multò plura vide<lb/>re volet, videat apud Cardanum lib. </s>

<s>Sed de his qui multò plura vide<lb/>re volet, videat apud Cardanum lib.

<s>1. de &longs;ubtilitate.<emph.end type="italics"/></s>

1. de &longs;ubtilitate.<emph.end type="italics"/></s>

Line 5228

<s>Vnde & apud Vitruuium legimus re-<emph.end type="italics"/><lb/><arrow.to.target n="marg36"></arrow.to.target><lb/><emph type="italics"/>demptorem ad tempus opus manufactum &longs;ubtiliter regi approba<lb/>ui&longs;&longs;e, & ad &longs;acoma pondus coronæ vi&longs;um e&longs;&longs;e præ&longs;titi&longs;&longs;e. </s>

<s>Cæterum <lb/>quam rationem habeat æquipondium ad &longs;e&longs;e pro varÿs inter&longs;titüs, <lb/>quibus remouetur ab an&longs;a, colligi pote&longs;t ex V baldo per corollarium <lb/>quod deduxit è prop. </s>

<s>6. tractatus de lib. </s>

6. tractatus de lib.

in Mech. </s>

<s>quod tale e&longs;t. </s>

Line 5262

<s>Demon&longs;t.</s>

<s><emph type="italics"/>Quia grauitas ponderis D e&longs;t æqualis grauitati ponderis E ex F <lb/>dependentis, & grauitas ponderis G e&longs;t æqualis grauitati ponderis <lb/>E ex B, erit grauitas ponderis D ad grauitatem E ex F: vt gra<lb/>uitas ponderis G ad grauitatem ponderis E ex B, & permutatim <lb/>prop. </s>

16. lib.

<s>5. vt grauitas ponderis D ad grauitatem ponderis G: <lb/>ita grauitas ip&longs;ius E ex F ad ip&longs;um E ex B. </s>

5. vt grauitas ponderis D ad grauitatem ponderis G: <lb/>ita grauitas ip&longs;ius E ex F ad ip&longs;um E ex B. </s>

<s>Grauitas autem pon<lb/>deris E ex F dependentis ad grauitatem ponderis E ex B e&longs;t: vt <lb/>C F ad C B, vt demon&longs;trat V baldus prop. </s>

<s>Grauitas autem pon<lb/>deris E ex F dependentis ad grauitatem ponderis E ex B e&longs;t: vt <lb/>C F ad C B, vt demon&longs;trat V baldus prop.

<s>6. tract. </s>

6. tract. </s>

<s>delib. </s>

<s>delib.

<s>vt igitur <lb/>grauitas ponderis D ad pondus G: ita e&longs;t C F ad C B. </s>

vt igitur <lb/>grauitas ponderis D ad pondus G: ita e&longs;t C F ad C B. </s>

<s>Si ergo <lb/>pars &longs;capi C B diuidatur in partes æquales &longs;olo pondere E, & pro<lb/>pius & longius à puncto C po&longs;ito, ponderum grauitates ex puncto <lb/>H appen&longs;æ notæ erunt. </s>

Line 5304

<s>COMMENTARIVS.</s>

<s>De dentiduco.] <foreign lang="greek">o)donta/<gap/>an h)\ o)donta/gw<gap/>n</foreign> <emph type="italics"/>vertit Cælius <lb/>Aurelianus cap. </s>

<s>De dentiduco.] <foreign lang="greek">o)donta/<gap/>an h)\ o)donta/gw<gap/>n</foreign> <emph type="italics"/>vertit Cælius <lb/>Aurelianus cap.

4. lib.

<s>2.<emph.end type="italics"/> <foreign lang="greek"><gap/>oniw_n</foreign> <emph type="italics"/>paßionum dentiducum: Cel<lb/>&longs;us forficem, & generaliter forcipem. </s>

2.<emph.end type="italics"/> <foreign lang="greek"><gap/>oniw_n</foreign> <emph type="italics"/>paßionum dentiducum: Cel<lb/>&longs;us forficem, & generaliter forcipem. </s>

<s>E&longs;t autem in&longs;trumentum, quo <lb/>dens eximitur. </s>

Line 5482

<s>Vtrumque problema vt intelligatur &longs;ciendum e&longs;t e def. <lb/></s>

<s>32. lib.

1. Eucl. </s>

<s>Rhombum e&longs;&longs;e quadrilaterum æquilaterum, & mini<lb/>mè rectangulum: Et tamen omnes eius angulos æquales e&longs;&longs;e quatuor <lb/>rectis per coroll. </s>

<s>prop.

32. li. </s>

Line 5516

<s>Sit enim vt<emph.end type="italics"/> <foreign lang="greek">a</foreign> <emph type="italics"/>proce&longs;&longs;erit per &longs;e v&longs;que ad<emph.end type="italics"/> <foreign lang="greek">e,</foreign> <emph type="italics"/>&<emph.end type="italics"/> <foreign lang="greek">a b</foreign> <emph type="italics"/>v&longs;que ad<emph.end type="italics"/><lb/><foreign lang="greek">z</foreign>: <emph type="italics"/>tunc quia motus illi &longs;unt in ratione laterum Rhombi id e&longs;t in ra<lb/>tione æqualitatis<emph.end type="italics"/> <foreign lang="greek">a e</foreign> <emph type="italics"/>&<emph.end type="italics"/> <foreign lang="greek">a z</foreign> <emph type="italics"/>erunt æquales. </s>

<s>Perficiatur <expan abbr="parallelo-gramm&utilde;">parallelo<lb/>grammum</expan> prop. </s>

<s>Perficiatur <expan abbr="parallelo-gramm&utilde;">parallelo<lb/>grammum</expan> prop.

31. lib.

<s>1. <expan abbr="n&etilde;pè">nempè</expan><emph.end type="italics"/> <foreign lang="greek">a e q z.</foreign> <emph type="italics"/>Hoc erit &longs;imile toti<emph.end type="italics"/> <foreign lang="greek">a b d g.</foreign><lb/><emph type="italics"/>prop. </s>

1. <expan abbr="n&etilde;pè">nempè</expan><emph.end type="italics"/> <foreign lang="greek">a e q z.</foreign> <emph type="italics"/>Hoc erit &longs;imile toti<emph.end type="italics"/> <foreign lang="greek">a b d g.</foreign><lb/><emph type="italics"/>prop.

24. lib.

<s>6. Ergo per conu <expan abbr="eiu&longs;d&etilde;">eiu&longs;dem</expan> prop. </s>

6. Ergo per conu <expan abbr="eiu&longs;d&etilde;">eiu&longs;dem</expan> prop. </s>

<s>&longs;unt circa <expan abbr="eand&etilde;">eandem</expan> <expan abbr="diametr&utilde;">diametrum</expan><emph.end type="italics"/><lb/><foreign lang="greek">a q d,</foreign> <emph type="italics"/>& &longs;ic<emph.end type="italics"/> <foreign lang="greek">a</foreign> <emph type="italics"/>duobus motibus motum prædictis delineauit<emph.end type="italics"/> <foreign lang="greek">a q</foreign><lb/><emph type="italics"/>cum<emph.end type="italics"/> <foreign lang="greek">a b</foreign> <emph type="italics"/>peruenit ad<emph.end type="italics"/> <foreign lang="greek">z h.</foreign> <emph type="italics"/>proinde &<emph.end type="italics"/> <foreign lang="greek">a</foreign> <emph type="italics"/>etiam delineauerit<emph.end type="italics"/> <foreign lang="greek">a d</foreign><lb/><emph type="italics"/>cum peruenerit<emph.end type="italics"/> <foreign lang="greek">a b</foreign> <emph type="italics"/>ad<emph.end type="italics"/> <foreign lang="greek">g d.</foreign> <emph type="italics"/>Simili ratiocinatione conficitur<emph.end type="italics"/> <foreign lang="greek">b</foreign> <emph type="italics"/>eo<lb/>dem tempore peragra&longs;&longs;e diametrum<emph.end type="italics"/> <foreign lang="greek">b g.</foreign> <emph type="italics"/>E&longs;t autem<emph.end type="italics"/> <foreign lang="greek">b g</foreign> <emph type="italics"/>minor: <lb/>quam<emph.end type="italics"/> <foreign lang="greek">a d</foreign> <emph type="italics"/>quia ba&longs;es &longs;unt duorum triangulorum<emph.end type="italics"/> <foreign lang="greek">g a b,</foreign> <emph type="italics"/>&<emph.end type="italics"/> <foreign lang="greek">a b d</foreign><lb/><emph type="italics"/>bina latera<emph.end type="italics"/> <foreign lang="greek">a g, a b</foreign> <emph type="italics"/>binis<emph.end type="italics"/> <foreign lang="greek">a b, b d</foreign> <emph type="italics"/>æqualia habentium. </s>

<s>quia &longs;unt <lb/>latera eiu&longs;dem Rhombi, & angulum<emph.end type="italics"/> <foreign lang="greek">a</foreign> <emph type="italics"/>vtpote acutum minorem <lb/>angulo<emph.end type="italics"/> <foreign lang="greek">b</foreign> <emph type="italics"/>vtpote obtu&longs;o. </s>

<s>Ergo prop.

24. lib.

<s>1. ba&longs;is<emph.end type="italics"/> <foreign lang="greek">a d</foreign> <emph type="italics"/>maior e&longs;t <lb/>ba&longs;i<emph.end type="italics"/> <foreign lang="greek">b g.</foreign> <emph type="italics"/>Et &longs;ic<emph.end type="italics"/> <foreign lang="greek">a</foreign> <emph type="italics"/>ab angulo acuto di&longs;cedens &longs;uis motibus maiorem <lb/>in Rhombo lineam tran&longs;it, quam<emph.end type="italics"/> <foreign lang="greek"><gap/>.</foreign></s>

1. ba&longs;is<emph.end type="italics"/> <foreign lang="greek">a d</foreign> <emph type="italics"/>maior e&longs;t <lb/>ba&longs;i<emph.end type="italics"/> <foreign lang="greek">b g.</foreign> <emph type="italics"/>Et &longs;ic<emph.end type="italics"/> <foreign lang="greek">a</foreign> <emph type="italics"/>ab angulo acuto di&longs;cedens &longs;uis motibus maiorem <lb/>in Rhombo lineam tran&longs;it, quam<emph.end type="italics"/> <foreign lang="greek"><gap/>.</foreign></s>

<s>Licet & hoc.] <emph type="italics"/>Hoc additur ad augendam &longs;ecundi problematis <lb/>difficultatem. </s>

Line 5542

<s>Nece&longs;&longs;e igitur.] <emph type="italics"/>Nam parallelogramma quæ toti & inter &longs;e<emph.end type="italics"/><pb pagenum="161"/><emph type="italics"/>&longs;unt &longs;imilia, &longs;unt circa eandem diametrum. </s>

<s>conu prop.

24. lib.

6.<emph.end type="italics"/></s>

<s>Æqualis enim e&longs;t.] <emph type="italics"/>Quia in ratione æqualitatis motum e&longs;t<emph.end type="italics"/> <foreign lang="greek">b</foreign><lb/><emph type="italics"/>ad<emph.end type="italics"/> <foreign lang="greek">e</foreign> <emph type="italics"/>&<emph.end type="italics"/> <foreign lang="greek">a b</foreign> <emph type="italics"/>ad<emph.end type="italics"/> <foreign lang="greek">h.</foreign></s>

Line 5554

<s>Etlatus <foreign lang="greek">b d.</foreign>] <emph type="italics"/>Attingit &longs;ecundum problema quod generaliter <lb/>verum non e&longs;t. </s>

<s>In Rhombo enim cuius, qui acutus e&longs;t angulus, maior <lb/>e&longs;t dimidio obtu&longs;i, vt in E<emph.end type="italics"/><lb/><figure id="fig60"></figure><lb/><emph type="italics"/>F G H: quia F H an<lb/>gulum E maiorem &longs;ubten<lb/>dit: quam E H, erit F H <lb/>maior E H prop. </s>

18. lib.

<s>1. <lb/>Sed verum e&longs;t in certo ca<lb/>&longs;u, eo nimirum (licet hîc <lb/>non &longs;it expre&longs;&longs;us) in quo <lb/>Rhombi acutus e&longs;&longs;et mi<lb/>nor: quam dimidius obtu<lb/>&longs;i, vt angulus A Rhombi <lb/>A B C D &longs;it minor: quam dimidius obtu&longs;i B, id e&longs;t quam A B C. <lb/></s>

1. <lb/>Sed verum e&longs;t in certo ca<lb/>&longs;u, eo nimirum (licet hîc <lb/>non &longs;it expre&longs;&longs;us) in quo <lb/>Rhombi acutus e&longs;&longs;et mi<lb/>nor: quam dimidius obtu<lb/>&longs;i, vt angulus A Rhombi <lb/>A B C D &longs;it minor: quam dimidius obtu&longs;i B, id e&longs;t quam A B C. <lb/></s>

<s>Dico latus A C maius e&longs;&longs;e diametro B C per eandem prop. </s>

<s>Dico latus A C maius e&longs;&longs;e diametro B C per eandem prop.

<s>18. <lb/>&longs;ubtendit enim trianguli A B C maiorem angulum. </s>

18. <lb/>&longs;ubtendit enim trianguli A B C maiorem angulum. </s>

<s>Po&longs;&longs;e autem <lb/>talem Rhombum con&longs;titui, patet. </s>

<s>quia angulus acutus &longs;eruata late<lb/>rum quorumuis a&longs;&longs;umptorum longitudine, infinitè minor fieri pote&longs;t, <lb/>prop. </s>

<s>quia angulus acutus &longs;eruata late<lb/>rum quorumuis a&longs;&longs;umptorum longitudine, infinitè minor fieri pote&longs;t, <lb/>prop.

9. lib.

<s>1. Ergo & tandem dabitur minor dimidio obtu&longs;i. </s>

1. Ergo & tandem dabitur minor dimidio obtu&longs;i. </s>

<s>Nam <lb/>& dimidius recti, qui acutus e&longs;t, e&longs;t eo minor prop. </s>

<s>15. lib.

<s>5. Ergo in <lb/>tali Rhombo latus A B per A C vna latione motum, plus &longs;patÿ <lb/>confecit: quam B, quod peragrans B C duabus lationibus ferebatur.<emph.end type="italics"/></s>

5. Ergo in <lb/>tali Rhombo latus A B per A C vna latione motum, plus &longs;patÿ <lb/>confecit: quam B, quod peragrans B C duabus lationibus ferebatur.<emph.end type="italics"/></s>

Line 5706

<s>Attamen quod circa.] <emph type="italics"/>Problematis propo &longs;iti veritas demon<lb/>&longs;tratur figura geometrica in vtroque modo. </s>

<s>Nam po&longs;ito quod<emph.end type="italics"/> <foreign lang="greek">a h z</foreign><lb/><emph type="italics"/>perpendiculariter in&longs;i&longs;tat pla-<emph.end type="italics"/><lb/><figure id="fig62"></figure><lb/><emph type="italics"/>no, & ad rectam<emph.end type="italics"/> <foreign lang="greek">z i.</foreign> <emph type="italics"/>Tum<emph.end type="italics"/> <foreign lang="greek">h q</foreign><lb/><emph type="italics"/>rectos angulos faciat, &longs;icque il<lb/>las tangat in punctis<emph.end type="italics"/> <foreign lang="greek">h</foreign> <emph type="italics"/>&<emph.end type="italics"/> <foreign lang="greek">z,</foreign><lb/><emph type="italics"/>cum quarta pars peripheriæ<emph.end type="italics"/> <foreign lang="greek">h b</foreign><lb/><emph type="italics"/>orit reuoluta: ita vt<emph.end type="italics"/> <foreign lang="greek">a b</foreign> <emph type="italics"/>rur<lb/>&longs;us ad rectos &longs;it ad rectam<emph.end type="italics"/> <foreign lang="greek">h q,</foreign><lb/><emph type="italics"/>ip&longs;amque tangat, vt in puncto<emph.end type="italics"/><lb/><foreign lang="greek">k</foreign>: <emph type="italics"/>tunc &<emph.end type="italics"/> <foreign lang="greek">a g</foreign> <emph type="italics"/>etiam ad re<lb/>ctos erit &longs;uper<emph.end type="italics"/> <foreign lang="greek">z i,</foreign> <emph type="italics"/>& &longs;it vt <lb/>tangat in puncto<emph.end type="italics"/> <foreign lang="greek">l.</foreign> <emph type="italics"/>Erunt pro <lb/>29. prop. </s>

lib.

<s>1. Duæ<emph.end type="italics"/> <foreign lang="greek">z h</foreign> <emph type="italics"/>&<emph.end type="italics"/> <foreign lang="greek">k l</foreign> <emph type="italics"/>parallelæ & æquales, ex hypoth. <lb/></s>

1. Duæ<emph.end type="italics"/> <foreign lang="greek">z h</foreign> <emph type="italics"/>&<emph.end type="italics"/> <foreign lang="greek">k l</foreign> <emph type="italics"/>parallelæ & æquales, ex hypoth. <lb/></s>

<s>Ergo quæ eas ad ea&longs;dem partes iungunt rectæ<emph.end type="italics"/> <foreign lang="greek">z l</foreign> <emph type="italics"/>&<emph.end type="italics"/> <foreign lang="greek">h k</foreign> <emph type="italics"/>erunt <lb/>æquales, prop 34. eiu&longs;dem. </s>

Line 5720

<s>Quæ autem ratio e&longs;t quartarum circulorum inter &longs;e, eadem <lb/>e&longs;t totorum. </s>

<s>Partes enim cum pariter multiplicibus eandem ratio<lb/>nem habent prop. </s>

<s>Partes enim cum pariter multiplicibus eandem ratio<lb/>nem habent prop.

15. lib.

<s>5. Igitur in vtroque modo orbitæ coneen<lb/>tricorum inæqualium &longs;unt æquales.<emph.end type="italics"/></s>

5. Igitur in vtroque modo orbitæ coneen<lb/>tricorum inæqualium &longs;unt æquales.<emph.end type="italics"/></s>

<s>Atque id nulla.] <emph type="italics"/>Cau&longs;am admirabilis huius aduentus, quæ <lb/>adferri potui&longs;&longs;et, In primò quidem modo ex tarditate & mora <lb/>maioris circuli in quibu&longs;dam rectæ lineæ punctis, dum minor <lb/>circulus ip&longs;am peragrat: In &longs;ecundo verò modo ex tran&longs;ultu minoris <lb/>qua&longs;i exiliat, nec &longs;imul omnia puncta rectæ attingat: &longs;ed tran&longs;iliat <lb/>minor, dum maior contra omnia attingat peragrando, reÿcit, mo<lb/>ramque nullam in hoc intercedere, neque tran&longs;ultum in i&longs;to: &longs;ed <lb/>vtriu&longs;que continuas motiones e&longs;&longs;e dicit, quia vnica latio e&longs;t.<emph.end type="italics"/></s>

Line 5794

<s>Secundum e&longs;t. </s>

<s>Motum <lb/>ab alio non plus moueri pote&longs;t: quam quod ip&longs;um mouet, vt quod non <lb/>&longs;uo: &longs;ed motu mouentis moueatur, tum mouens & motum &longs;unt &longs;i<lb/>mul, vt demon&longs;tratum e&longs;t ab Ari&longs;totele in lib. </s>

<s>de Phy&longs;. </s>

de Phy&longs;. </s>

<s>auditu. </s>

Line 5898

<s>Sicque M retroceßit per angulum M G H. </s>

<s>Contrà I an<lb/>teceßit per angulum I G F, qui &longs;unt anguli æquales prop. </s>

<s>Contrà I an<lb/>teceßit per angulum I G F, qui &longs;unt anguli æquales prop.

15. lib.

<s>1. <lb/>Et &longs;ic patet cur retrocedente vno tantum: quantum procedit alter, <lb/>moueantur æqualiter, id e&longs;t per æquale &longs;patium puncta peripheria<lb/>rum inæqualium ob centri communis æqualem motum. </s>

1. <lb/>Et &longs;ic patet cur retrocedente vno tantum: quantum procedit alter, <lb/>moueantur æqualiter, id e&longs;t per æquale &longs;patium puncta peripheria<lb/>rum inæqualium ob centri communis æqualem motum. </s>

<s>Hæc ex <lb/>Cardan. </s>

<s>prop.

196. lib.

<s>5. de proport.<emph.end type="italics"/></s>

5. de proport.<emph.end type="italics"/></s>

<s><margin.target id="marg40"></margin.target>Vide penul <lb/>timum dia <lb/>gramma.</s>

Line 5938

<s>Itaque ex def. </s>

<s>1. <lb/>lib.

<s>2. contineri &longs;ub duobus lateribus, quæ rectum angulum compre<lb/>hendunt. </s>

2. contineri &longs;ub duobus lateribus, quæ rectum angulum compre<lb/>hendunt. </s>

<s>Et hæc &longs;unt quæ hîc <expan abbr="con&longs;iderãtur">con&longs;iderantur</expan> in ratione dupla. </s>

Line 5992

<s>At &longs;i obliquè ex<lb/>tendantur, minus erunt: quam &longs;i &longs;ecundum diametrum. </s>

<s>I uxta ed quæ <lb/>demon&longs;trata &longs;unt cap. </s>

<s>I uxta ed quæ <lb/>demon&longs;trata &longs;unt cap.

15. lib.

<s>huius. </s>

huius. </s>

<s>Namque vt recta percußio ad <lb/>medium ligni oblongi facta facile ip&longs;um frangit: &longs;ic tractio firma <lb/>è directo à medio. </s>

Line 6076

<s>In hac lora &longs;ecundum diametrum &longs;int quidem <lb/>&longs;ecundum longitudinem tria K N. </s>

<s>L O, M P, & &longs;ic inter &longs;e<emph.end type="italics"/><pb pagenum="181"/><emph type="italics"/>& lateri A B æqualia prop. </s>

<s>L O, M P, & &longs;ic inter &longs;e<emph.end type="italics"/><pb pagenum="181"/><emph type="italics"/>& lateri A B æqualia prop.

34. lib.

<s>1. Sint & totidem G Q, <lb/>E F, H R &longs;ecundum latitudinem exten&longs;a, inter&longs;e quoque, & la<lb/>teri A C æqualia per eandem.<emph.end type="italics"/></s>

1. Sint & totidem G Q, <lb/>E F, H R &longs;ecundum latitudinem exten&longs;a, inter&longs;e quoque, & la<lb/>teri A C æqualia per eandem.<emph.end type="italics"/></s>

<s><emph type="italics"/>Sit &longs;ecunda forma<emph.end type="italics"/> <foreign lang="greek">a b g d</foreign> <emph type="italics"/>in eadem ratione laterum, & ea<lb/>dem magnitudine &longs;eruata, & linearum &longs;ed obliquarum æquali nu<lb/>mero, quæ &longs;int<emph.end type="italics"/> <foreign lang="greek">a c, h k, e d</foreign> <emph type="italics"/>tum.<emph.end type="italics"/> <foreign lang="greek">b c, q i, e g,</foreign> <emph type="italics"/>quæ quia pa-<emph.end type="italics"/><lb/><figure id="fig67"></figure><lb/><emph type="italics"/>rallelæ &longs;unt, & aduer&longs;æ in &longs;uis parallelogrammis, omnes inter &longs;e <lb/>æquales &longs;unt prop. </s>

34. lib.

<s>1. Nam po&longs;ito quod<emph.end type="italics"/> <foreign lang="greek">a c</foreign> <emph type="italics"/>&longs;it ab angulo<emph.end type="italics"/> <foreign lang="greek">a</foreign><lb/><emph type="italics"/>ad<emph.end type="italics"/> <foreign lang="greek">c</foreign> <emph type="italics"/>medium lateris<emph.end type="italics"/> <foreign lang="greek">g d</foreign><emph type="italics"/>: erit hæc æqualis ip&longs;i<emph.end type="italics"/> <foreign lang="greek">b c,</foreign> <emph type="italics"/>quia latera <lb/>æqualium quadratorum. </s>

1. Nam po&longs;ito quod<emph.end type="italics"/> <foreign lang="greek">a c</foreign> <emph type="italics"/>&longs;it ab angulo<emph.end type="italics"/> <foreign lang="greek">a</foreign><lb/><emph type="italics"/>ad<emph.end type="italics"/> <foreign lang="greek">c</foreign> <emph type="italics"/>medium lateris<emph.end type="italics"/> <foreign lang="greek">g d</foreign><emph type="italics"/>: erit hæc æqualis ip&longs;i<emph.end type="italics"/> <foreign lang="greek">b c,</foreign> <emph type="italics"/>quia latera <lb/>æqualium quadratorum. </s>

<s>V trumque enim æquale e&longs;t duobus ex<emph.end type="italics"/> <foreign lang="greek">a g, <lb/>g c,</foreign> <emph type="italics"/>vel quod idem e&longs;tex<emph.end type="italics"/> <foreign lang="greek">c d, d <gap/></foreign> <emph type="italics"/>prop. </s>

47. lib.

1.<emph.end type="italics"/></s>

<s><emph type="italics"/>Dico ergo quod lorum K N cum G Q, id e&longs;t A C, A B ma<lb/>ius e&longs;t<emph.end type="italics"/> <foreign lang="greek">a c, c b,</foreign> <emph type="italics"/>& duo pariter accepta duobus pariter acceptis e&longs;&longs;e <lb/>maiora: &longs;icque totum lorum in lecto A B C D maius e&longs;&longs;e toto, <lb/>quod e&longs;t in lecto<emph.end type="italics"/> <foreign lang="greek">a b g d.</foreign></s>

<s><emph type="italics"/>Demon&longs;tratio. </s>

<s>Quia rectangulum &longs;ub A C, A B comprehen<lb/>&longs;um duplum e&longs;t quadrati ex A C prop. </s>

<s>Quia rectangulum &longs;ub A C, A B comprehen<lb/>&longs;um duplum e&longs;t quadrati ex A C prop.

1. lib.

<s>6. & rectangulum &longs;ub<emph.end type="italics"/><lb/><foreign lang="greek">a c, c b</foreign> <emph type="italics"/>duplum <expan abbr="it&etilde;">item</expan> e&longs;t quadrati ex A C. </s>

6. & rectangulum &longs;ub<emph.end type="italics"/><lb/><foreign lang="greek">a c, c b</foreign> <emph type="italics"/>duplum <expan abbr="it&etilde;">item</expan> e&longs;t quadrati ex A C. </s>

<s>Ip&longs;um enim <expan abbr="c&utilde;">cum</expan> quadratum <lb/>&longs;it. </s>

<s><expan abbr="Nã">Nam</expan><emph.end type="italics"/> <foreign lang="greek">a c</foreign> <emph type="italics"/>&<emph.end type="italics"/> <foreign lang="greek">c b</foreign> <emph type="italics"/>&longs;unt æquales ex fabrica, æquale e&longs;t prop. </s>

47. lib.

<s>1. <lb/>duobus quadratis ex A C & C F: &longs;ed quod idem e&longs;t ex<emph.end type="italics"/> <foreign lang="greek">a g</foreign> <emph type="italics"/>&<emph.end type="italics"/> <foreign lang="greek">g c,</foreign><lb/><emph type="italics"/>æqualibus ex hypoth, erit <expan abbr="rectangul&utilde;">rectangulum</expan> &longs;ub A C, A B comprehen&longs;um <lb/>rectangulo &longs;ub<emph.end type="italics"/> <foreign lang="greek">a c, c b</foreign> <emph type="italics"/>comprehen&longs;o. </s>

1. <lb/>duobus quadratis ex A C & C F: &longs;ed quod idem e&longs;t ex<emph.end type="italics"/> <foreign lang="greek">a g</foreign> <emph type="italics"/>&<emph.end type="italics"/> <foreign lang="greek">g c,</foreign><lb/><emph type="italics"/>æqualibus ex hypoth, erit <expan abbr="rectangul&utilde;">rectangulum</expan> &longs;ub A C, A B comprehen&longs;um <lb/>rectangulo &longs;ub<emph.end type="italics"/> <foreign lang="greek">a c, c b</foreign> <emph type="italics"/>comprehen&longs;o. </s>

<s>axiom. </s>

<s>6. & per idem rectan<lb/>gulum bis &longs;ub A C, A B comprehen&longs;um, rectangulo bis &longs;ub<emph.end type="italics"/> <foreign lang="greek">a c, c b</foreign><pb pagenum="182"/><emph type="italics"/>comprehen&longs;o æquale: &longs;ed & quadratum ex A B æquale e&longs;t quadratis <lb/>ex<emph.end type="italics"/> <foreign lang="greek">a z, zb</foreign> <emph type="italics"/>prop. </s>

47. lib.

<s>1. E&longs;t enim angulus<emph.end type="italics"/> <foreign lang="greek">a z b</foreign> <emph type="italics"/>rectus, cum &longs;it <lb/>reliquus trium<emph.end type="italics"/> <foreign lang="greek">a z g, a z b, b z d</foreign> <emph type="italics"/>duobus rectis æqualium prop. </s>

1. E&longs;t enim angulus<emph.end type="italics"/> <foreign lang="greek">a z b</foreign> <emph type="italics"/>rectus, cum &longs;it <lb/>reliquus trium<emph.end type="italics"/> <foreign lang="greek">a z g, a z b, b z d</foreign> <emph type="italics"/>duobus rectis æqualium prop.

13. <lb/>lib.

<s>1. &longs;ublatis duobus &longs;emirectis<emph.end type="italics"/> <foreign lang="greek">a z g, <gap/> z d</foreign> <emph type="italics"/>per coroll. </s>

1. &longs;ublatis duobus &longs;emirectis<emph.end type="italics"/> <foreign lang="greek">a z g, <gap/> z d</foreign> <emph type="italics"/>per coroll. </s>

<s>32. lib.

<s>1. <lb/>Erunt igitur quadrata ex A B, A C cum rectangulo bis &longs;ub A C, <lb/>A B comprehen&longs;o maiora quadratis ex<emph.end type="italics"/> <foreign lang="greek">a z, z <gap/></foreign> <emph type="italics"/>cum rectangulo <lb/>bis &longs;ub<emph.end type="italics"/> <foreign lang="greek">a z, z b</foreign> <emph type="italics"/>comprehen&longs;o per quantitatem quadrati ex A C: <lb/>&longs;ed quadrata ex A B, A C cum rectangulo bis comprehen&longs;o &longs;ub <lb/>A B, A C &longs;unt potentia lineæ C A B vtcunque &longs;ectæ in A, id e&longs;t <lb/>æqualia &longs;unt quadrato ex C A B prop. </s>

1. <lb/>Erunt igitur quadrata ex A B, A C cum rectangulo bis &longs;ub A C, <lb/>A B comprehen&longs;o maiora quadratis ex<emph.end type="italics"/> <foreign lang="greek">a z, z <gap/></foreign> <emph type="italics"/>cum rectangulo <lb/>bis &longs;ub<emph.end type="italics"/> <foreign lang="greek">a z, z b</foreign> <emph type="italics"/>comprehen&longs;o per quantitatem quadrati ex A C: <lb/>&longs;ed quadrata ex A B, A C cum rectangulo bis comprehen&longs;o &longs;ub <lb/>A B, A C &longs;unt potentia lineæ C A B vtcunque &longs;ectæ in A, id e&longs;t <lb/>æqualia &longs;unt quadrato ex C A B prop.

4. lib.

<s>2. & per eandem qua<lb/>drata ex<emph.end type="italics"/> <foreign lang="greek">a z, z <gap/></foreign> <emph type="italics"/>cum rectangulo bis comprehen&longs;o &longs;ub<emph.end type="italics"/> <foreign lang="greek">a z, z b</foreign> <emph type="italics"/>&longs;unt <lb/>potentia lineæ<emph.end type="italics"/> <foreign lang="greek">a z b</foreign> <emph type="italics"/>vtcunque &longs;ectæ in<emph.end type="italics"/> <foreign lang="greek">z.</foreign> <emph type="italics"/>E&longs;t ergo C A B maior <lb/>potentia quam<emph.end type="italics"/> <foreign lang="greek">a z b,</foreign> <emph type="italics"/>proinde erit & longitudine maior per coroll. <lb/></s>

2. & per eandem qua<lb/>drata ex<emph.end type="italics"/> <foreign lang="greek">a z, z <gap/></foreign> <emph type="italics"/>cum rectangulo bis comprehen&longs;o &longs;ub<emph.end type="italics"/> <foreign lang="greek">a z, z b</foreign> <emph type="italics"/>&longs;unt <lb/>potentia lineæ<emph.end type="italics"/> <foreign lang="greek">a z b</foreign> <emph type="italics"/>vtcunque &longs;ectæ in<emph.end type="italics"/> <foreign lang="greek">z.</foreign> <emph type="italics"/>E&longs;t ergo C A B maior <lb/>potentia quam<emph.end type="italics"/> <foreign lang="greek">a z b,</foreign> <emph type="italics"/>proinde erit & longitudine maior per coroll. <lb/></s>

<s>è prop.

47. lib.

<s>1. Similiter demon&longs;trabitur de reliquis. </s>

1. Similiter demon&longs;trabitur de reliquis. </s>

<s>E&longs;t ergo maior <lb/>lororum quantitas in lecto A B C D: quam in lecto<emph.end type="italics"/> <foreign lang="greek">a b d g,</foreign> <emph type="italics"/>quod <lb/>erat demon&longs;trandum.<emph.end type="italics"/></s>

Line 6162

<s>In parallelis enim.] <emph type="italics"/>Quod hic dicit Ari&longs;toteles<emph.end type="italics"/> <foreign lang="greek">i)/sas <gap/>a/mmas</foreign><lb/><emph type="italics"/>vertimus parallelas. </s>

<s>Sic enim etiam locutus e&longs;t cap. </s>

<s>Sic enim etiam locutus e&longs;t cap.

5. lib.

<s>1. po&longs;teriore <lb/>analytic. </s>

1. po&longs;teriore <lb/>analytic. </s>

<s>Si quis igitur inquit demon&longs;trauerit, quod rectæ non con<lb/>currant, videatur huius e&longs;&longs;e <expan abbr="demõ&longs;tratio">demon&longs;tratio</expan>. </s>

Line 6286

<s><emph type="italics"/>Sit & breuius<emph.end type="italics"/><lb/><figure id="fig72"></figure><lb/><emph type="italics"/>D E eiu&longs;dem pon<lb/>deris puta decem librarum è medio F ge&longs;tatum etiam. </s>

<s>Quia partes <lb/>cum pariter multiplicibus &longs;unt in eadem ratione prop. </s>

<s>Quia partes <lb/>cum pariter multiplicibus &longs;unt in eadem ratione prop.

15. lib.

<s>5. & <lb/>e&longs;t A B maior ip&longs;o D E, erit dimidium A C maius dimidio D F. <lb/></s>

5. & <lb/>e&longs;t A B maior ip&longs;o D E, erit dimidium A C maius dimidio D F. <lb/></s>

<s>Et &longs;ic extremum A magis di&longs;tans à centro C immoto plus mouet, <lb/>vel mouetur pro natura &longs;ua deor&longs;um. </s>

Line 6408

<s>Nam <expan abbr="ver&utilde;">verum</expan> e&longs;t quod è tertio co<lb/>roll. </s>

<s>prop.

<s>2. tractatus de vecte apud <expan abbr="Gvid&utilde;">Gvidum</expan> Vbaldum demon&longs;trate <lb/>deducitur. </s>

2. tractatus de vecte apud <expan abbr="Gvid&utilde;">Gvidum</expan> Vbaldum demon&longs;trate <lb/>deducitur. </s>

<s>Nempe &longs;i in extremis vectis duæ &longs;int potentiæ, inter quas <lb/>pondus &longs;it &longs;u&longs;pen&longs;um. </s>

Line 6436

<s><emph type="italics"/>Hanc rur&longs;us quæ&longs;tionem aliter &longs;oluere videtur Cardanus, nimi<lb/>rum quod E pondus alteri ferentium propius exi&longs;tens ip&longs;um premit <lb/>magis, quia de&longs;cendat magis re&longs;pectu B: quam A alterius feren<lb/>tium. </s>

<s>Nam cum de&longs;cendat &longs;ecundumrectam C E, &longs;i intelligamus à <lb/>puncto B ad Erectam ductam, <lb/>& ab A ad E item rectam,<emph.end type="italics"/><lb/><figure id="fig75"></figure><lb/><emph type="italics"/>con&longs;titutum erit triangulum A <lb/>B E, cuius quia A E maior <lb/>e&longs;t: quam E B, per prop. </s>

46. <lb/>& 47. lib.

<s>1. E&longs;t enim A di&longs;tans <lb/>magis ab C quam B ex hypo<lb/>the&longs;i: erit angulus B maior: quam A prop. </s>

1. E&longs;t enim A di&longs;tans <lb/>magis ab C quam B ex hypo<lb/>the&longs;i: erit angulus B maior: quam A prop. </s>

<s>18. lib.

<s>1. Et &longs;ic E plus <lb/>de&longs;cendit re&longs;pectu B: quam re&longs;pectu A. </s>

1. Et &longs;ic E plus <lb/>de&longs;cendit re&longs;pectu B: quam re&longs;pectu A. </s>

<s>Igitur E plus grauat B: <lb/>quam A &longs;eu ex cau&longs;a, quod magis premat: &longs;eu ex effectu, quod ma<lb/>gis de&longs;cenderit.<emph.end type="italics"/></s><pb pagenum="193"/>

Line 6520

<s><margin.target id="marg42"></margin.target>Cap.

1. & 3. <lb/>lib. </s>

1. & 3. <lb/>lib.

<s>3. de v&longs;u <lb/>part.</s>

3. de v&longs;u <lb/>part.</s>

<s><margin.target id="marg43"></margin.target>Cap.

2. lib. </s>

2. lib.

<s>1. <lb/>de v&longs;u part.</s>

1. <lb/>de v&longs;u part.</s>

<s>Re&longs;picio aduer&longs;us Olympum fronte intrepida.</s><pb pagenum="195"/>

Line 6578

<s><emph type="italics"/>Angulus rectus e&longs;t æqualitas, quia &longs;ibi & alÿs omnibus re<lb/>ctis rectilineis e&longs;t æqualis. </s>

<s>quod e&longs;t axioma 10. lib. </s>

<s>quod e&longs;t axioma 10. lib.

<s>1. In eo <lb/>&longs;cilicet rectæ ip&longs;um con&longs;tituentes &longs;ibi pariter incumbunt, <lb/>&longs;ibique inuicem perpendiculares &longs;unt. </s>

1. In eo <lb/>&longs;cilicet rectæ ip&longs;um con&longs;tituentes &longs;ibi pariter incumbunt, <lb/>&longs;ibique inuicem perpendiculares &longs;unt. </s>

<s>10. lib.

1.<emph.end type="italics"/></s>

<s><emph type="italics"/>Ergò angulus rectus e&longs;t cau&longs;a quietis.<emph.end type="italics"/></s>

Line 6782

<s>Hanc <lb/>Simplicius Ari&longs;totelis interpres<emph.end type="italics"/> <foreign lang="greek">)<gap/>pipo/laian</foreign> <emph type="italics"/>qua&longs;i diceres &longs;uperfi-<emph.end type="italics"/><pb pagenum="202"/><emph type="italics"/>ciariam appellat comment. </s>

<s>in lib.

<s>7. Phy&longs;. </s>

7. Phy&longs;. </s>

<s>Hæc autem tollitur autà <lb/>re&longs;i&longs;tentia medÿ per quod fertur. </s>

Line 6816

<s>Cæterum &longs;agitta & ha&longs;ta & quicquid <lb/>aliud tale e&longs;t ten&longs;a coria facilius, quam laxa penetrat quod illa qui<lb/>dem re&longs;i&longs;tunt: hæc autem cedentia paulatim eorum quæ incidunt, <lb/>violentiam exoluunt, Gal. </s>

<s>cap.

8. lib.

<s>2. de v&longs;. </s>

2. de v&longs;. </s>

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<s><emph type="italics"/>Neutrum igitur proiectum fertur, nedum procul.<emph.end type="italics"/></s>

<s><emph type="italics"/>Propo&longs;itionis huius &longs;yllogi&longs;mi prior pars per&longs;e clara e&longs;t, & illu&longs;trata <lb/>etiam ijs quæ à nobis cap. </s>

<s><emph type="italics"/>Propo&longs;itionis huius &longs;yllogi&longs;mi prior pars per&longs;e clara e&longs;t, & illu&longs;trata <lb/>etiam ijs quæ à nobis cap.

<s>32. dicta &longs;unt. </s>

32. dicta &longs;unt. </s>

<s>Po&longs;terior de re&longs;i&longs;tentia etiam <lb/>vera e&longs;t, quia &longs;i mobile motori non re&longs;i&longs;tat, motus non fiet in tempo<lb/>re, & &longs;ucceßione.: &longs;ed in in&longs;tanti quod e&longs;t contra demon&longs;trata ab <lb/>Ari&longs;totele lib. </s>

<s>4. de Phi&longs;ico audit. </s>

4. de Phi&longs;ico audit. </s>

<s>Vim enim motoris, &longs;i nihil retar<lb/>dat, quare non ageret ilico? </s>

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<s>Sed reuocare gradum, &longs;upera&longs;que euadere ad auras, <lb/>Hocopus hic labor e&longs;t.</s>

<s><emph type="italics"/>Sed rur&longs;us de vorticibus hæc quæ &longs;unt apud Cardanum cap. </s>

<s><emph type="italics"/>Sed rur&longs;us de vorticibus hæc quæ &longs;unt apud Cardanum cap.

6. lib.

<s>1. <lb/>de variet. </s>

1. <lb/>de variet. </s>

<s>rerum &longs;citu digna &longs;unt. </s>

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