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version 1.1, 2002/06/18 09:37:13

version 1.4, 2002/06/27 17:26:48

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<?xml version="1.0"?>

<!DOCTYPE archimedes [

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<info>

<author>Aristotle</author>

<author>Monantheuil, Henri</author>

<title>Mechanica</title>

<title>Aristotelis Mechanica</title>

<place>Paris</place>

</info>

<text>

<front>

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<s>Ex vno duo ferrea brachia nodo <lb/>Iunxit, vt æquali &longs;patio di&longs;tanti<lb/>

<arrow.to.target n="fig1"></arrow.to.target><lb/>busip&longs;is</s>

<figure id="fig1"></figure><lb/>busip&longs;is</s>

<s>Altera pars &longs;taret, pars altera du<lb/>ceret orbem.</s>

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<s>Primum &longs;iquidem.] <emph type="italics"/>Vetu&longs;tatis iniuria multas veterum li<lb/>bris, & huic &longs;ane irrep&longs;i&longs;&longs;e mendas, non e&longs;t res dubia, vt hoc loco<emph.end type="italics"/><lb/><foreign lang="greek">w_rw/ton</foreign> <emph type="italics"/>pro<emph.end type="italics"/> <foreign lang="greek">deu/teron.</foreign> <emph type="italics"/>Namque hîcnon prima, vtiam patuit: &longs;ed &longs;e<lb/>cunda e&longs;t in circulo repugnantia. Eaque ex eo quod cum circuli peri<lb/>pheria &longs;ir vna linea def. 15. lib. 1. elem. & idcirco latitudinis expers <lb/>def. 2. lib. eiu&longs;dem: habeat tamen in &longs;econtraria conuexum &longs;cilicet, <lb/>& concauum: illud quidem quà &longs;pectat foras: hoc vero quà intra. <lb/>vbinota Ari&longs;totelem dixi&longs;&longs;e hæe<emph.end type="italics"/> <foreign lang="greek">en)an<gap/>ia w_<gap/>s</foreign> <emph type="italics"/>contraria quodam<lb/>modo. Nec enim vere contraria &longs;unt, quia vere contraria &longs;untea, <lb/>quæ &longs;ecundum &longs;eip&longs;a &longs;umpta, ex &longs;eip&longs;is extreme di&longs;tant, & vnde &longs;e <lb/>expellere nata &longs;int, habent: at hæc conuexum & concauum non &longs;ic <lb/>extreme di&longs;tant: &longs;ed ratione &longs;itus partium in diuer&longs;is locorum diffe<lb/>rentÿs, quod &longs;cilicet aliæ alÿs &longs;int al-<emph.end type="italics"/><lb/>

<arrow.to.target n="fig2"></arrow.to.target><lb/><emph type="italics"/>tiores, vel depreßiores. Cum enim re<lb/>ctum &longs;it id in lineis quod ex æquo iacet <lb/>inter &longs;ua extrema def. 2. lib. 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"/>

<figure id="fig2"></figure><lb/><emph type="italics"/>tiores, vel depreßiores. Cum enim re<lb/>ctum &longs;it id in lineis quod ex æquo iacet <lb/>inter &longs;ua extrema def. 2. lib. 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. Quemadmodum magnum & paruum con<lb/>traria &longs;unt, quia di&longs;tant, inter &longs;e per medium, quod e&longs;t æquale, & <lb/>cum commutantur in inuicem nece&longs;&longs;e e&longs;t prius æquale fieri: &longs;ic con<lb/>uexum & concauum contraria erunt, quia di&longs;tant inter &longs;e per me<lb/>dium, quod e&longs;t rectum, & cum commutantur in inuicem prius re<lb/>ctum etiam fierinece&longs;&longs;um e&longs;t. &longs;unt igitur conuexum & concauum <lb/>contraria. Sed & hic a&longs;&longs;umemus per eandem definitionem contra<lb/>riorum ante po&longs;itam, & ex &longs;ententia Ari&longs;totelis in categ. Quanti<lb/>tatis, magnum & paruum apparenter duntaxat e&longs;&longs;e contraria. Ap<lb/>parenter dico vt illa priora, quia habent aliquid de definitione con<lb/>trariorum, quod &longs;ibi conueniat, &longs;cilicet di&longs;tare inter&longs;e in eodem ge<lb/>nere, & habere medium: &longs;ed non vere tamen e&longs;&longs;e. Quia non habent <lb/>omnes prædictæ definitionis particulas &longs;ibi conuenientes. Hæc <lb/>enim cum &longs;int in Relatis, vnum idemque non ex&longs;e dicitur magnum <lb/>aut paruum: &longs;ed re&longs;pectu alicuius, vt canis re&longs;pectu elephantis paruus <lb/>e&longs;t, at idem re&longs;pectu mu&longs;cæ magnus e&longs;t. C&oelig;terum hic notandum e&longs;t <lb/>re&longs;pectum i&longs;tum licet fieri poßit ad quodlibet obuium, cum tamen <lb/>hæc vocabula, magnum, paruum, &longs;impliciter dicuntur, fieri ad &longs;ym<lb/>metrum &longs;ui cuiu&longs;que generis. Symmetrum appello, quod iu&longs;tam ma<lb/>gnitudinem in &longs;uo genere adeptum e&longs;t. Et hoc e&longs;t quod hic dicitur <lb/>æquale, medium &longs;cilicet inter <expan abbr="magn&utilde;">magnum</expan> tanquam excedens, & paruum <lb/>tanquam deficiens, neutrobique igitur iu&longs;tum. Vt e&longs;to, quod aiunt <lb/>multi, iu&longs;ta hominis magnitudo &longs;ex pedum. Qui igitur inter homi<lb/>nes &longs;eptempedalis e&longs;t, magnus: qui quintumpedalis, paruus &longs;implici<lb/>ter dicetur. Hinc intellige, vt id obiter annotem, quod apud Ari&longs;to<lb/>telem memini me legi&longs;&longs;e, nullam paruam mulierem pulchram e&longs;&longs;e, <lb/>quia, quod prima pars e&longs;t pulchritudinis non habet, &longs;ymmetrum &longs;ui <lb/>generis.<emph.end type="italics"/></s>

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<s><emph type="italics"/>Centrum enim in plano circundatur quatuor loci differentÿs, <lb/>propter duas quæ in ip&longs;o ad rectos &longs;e &longs;ecant dimen&longs;iones, vt in circu<lb/>lo B C D E, e&longs;to linea fabricans ip&longs;um A B, ibique e&longs;to ante <lb/>B. igitur cum erit in D, erit ponè: & cum in C, &longs;ur&longs;um: & <lb/>in E, deor&longs;um, & perueniens ad A B, eidem loco re&longs;tituetur, <lb/>à quo c&oelig;perat moueri, quod e&longs;t vltimum<emph.end type="italics"/><lb/>

<arrow.to.target n="fig3"></arrow.to.target><lb/><emph type="italics"/>fieri primum. Vnde cum circulu<gap/>oue<lb/>tur, pote&longs;t dici ire, & reuerti &longs;imul: &longs;ic <lb/>cum &longs;phæricum corpus mouetur, in fine <lb/>&longs;emper, & principio motus &longs;ui, etiam tum <lb/>ire, tum reuerti veri&longs;imiliter dicetur.<emph.end type="italics"/></s>

<figure id="fig3"></figure><lb/><emph type="italics"/>fieri primum. Vnde cum circulu<gap/>oue<lb/>tur, pote&longs;t dici ire, & reuerti &longs;imul: &longs;ic <lb/>cum &longs;phæricum corpus mouetur, in fine <lb/>&longs;emper, & principio motus &longs;ui, etiam tum <lb/>ire, tum reuerti veri&longs;imiliter dicetur.<emph.end type="italics"/></s>

<s><emph type="italics"/>Cæterum notandum quod motiones dictæ <lb/>e&longs;&longs;e in circulo, in&longs;unt quidem: &longs;ed non &longs;i<lb/>mul &longs;ecundum eandem partem. Nam cum B, mouetur &longs;ur&longs;um ver<lb/>&longs;us C, idem B, eodem tempore non fertur deor&longs;um ver&longs;us E, &longs;ed <lb/>tunc quidem D, altera pars in circulo oppo&longs;ita ip&longs;i B, fertur ver<lb/>&longs;us E: vt autem verè e&longs;&longs;ent motiones contrariæ deberent fieri &longs;e<lb/>cundum ea&longs;dem partes. E&longs;t hæc igitur vt aliæ in circulo non vera <lb/>&longs;ed apparens repugnantia. ex cuius tamen natura magnorum effe<lb/>ctuum po&longs;tea cau&longs;æ repetuntur, cum diametri B D, vt inflexilis <lb/>circa A, centrum fixum motæ, &longs;i B, deprimatur, nece&longs;&longs;e e&longs;t a<gap/>e<lb/>rum extremum D, attolli: & contra.<emph.end type="italics"/></s>

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<s><emph type="italics"/>E&longs;to A B C, peripheria &longs;emidiametri maioris A E: item <lb/>D F G, peripheria &longs;emidiametri D H minoris. Dico periphe<lb/>riam A B C maiorem peripheria D F G. Producatur enim A E <lb/>recta vt &longs;it A C <lb/>diameter po&longs;tul.<emph.end type="italics"/><lb/>

<arrow.to.target n="fig4"></arrow.to.target><lb/>2. <emph type="italics"/><expan abbr="it&etilde;">item</expan> D H vt &longs;it <lb/>& D G diame<lb/>ter. 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. 3. lib. de dimen&longs;. circuli, & <lb/>vicißim proportionales erunt A C diameter ad D G diametrum: <lb/>vt peripheria A B C ad peripheriam D F G prop. 16. lib. 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. 5. ergo & peripheria A B C ad peri<lb/>pheriam D F G: vt A E ad D H prop. 11. lib. eiu&longs;dem. E&longs;t <lb/>autem A E maior: quam D H ex hypothe&longs;i. Erit igitur peri<lb/>pheria A B C maior: quam peripheria D F G. Et &longs;ic peripheria <lb/>remotioris puncti à centro maior e&longs;t peripheria puncti centro pro<lb/>pinquioris, quod fuit demon&longs;trandum.<emph.end type="italics"/></s>

<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. 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. 3. lib. de dimen&longs;. circuli, & <lb/>vicißim proportionales erunt A C diameter ad D G diametrum: <lb/>vt peripheria A B C ad peripheriam D F G prop. 16. lib. 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. 5. ergo & peripheria A B C ad peri<lb/>pheriam D F G: vt A E ad D H prop. 11. lib. eiu&longs;dem. E&longs;t <lb/>autem A E maior: quam D H ex hypothe&longs;i. Erit igitur peri<lb/>pheria A B C maior: quam peripheria D F G. Et &longs;ic peripheria <lb/>remotioris puncti à centro maior e&longs;t peripheria puncti centro pro<lb/>pinquioris, quod fuit demon&longs;trandum.<emph.end type="italics"/></s>

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<s>Qvod autem circulus.] <emph type="italics"/>Tertia repugnantia in vnius cir<lb/>culi contrarÿs motionibus ante po&longs;ita amplius declaratur, ab <lb/>exemplo plurium: &longs;ed contiguorum ab vnica vi primaria &longs;ecundum <lb/>motus contrarios motorum. Vt &longs;unto tres circuli contingentes quod<lb/>que ferè fit denticulis pectinis in&longs;tar &longs;e&longs;e &longs;ubingredientibus in peri<lb/>phcria præditi, quorum primus A B, moueatur antror&longs;um, &longs;eu&longs;e<lb/>cundum &longs;uperiorem peripheriam, vt A feratur ver&longs;us C: alter<emph.end type="italics"/>

<pb pagenum="25"/><emph type="italics"/>G D ad illius motum nece&longs;&longs;ario mouebitur propter denticulos, &longs;ed <lb/><expan abbr="retrors&utilde;">retrorsum</expan><emph.end type="italics"/><lb/>

<arrow.to.target n="fig5"></arrow.to.target><lb/><emph type="italics"/>&longs;eu <expan abbr="&longs;ec&utilde;-dum">&longs;ecun<lb/>dum</expan> <expan abbr="in-ferior&etilde;">in<lb/>feriorem</expan> <lb/><expan abbr="periphe-riã">periphe<lb/>riam</expan>, vt <lb/>G ad B: <lb/>tum ter<lb/>tius E Z ad &longs;ecundi motum mouebitur etiam, &longs;ed antror&longs;um, vt E <lb/>ad F, & &longs;int deinceps alternatim infiniti denticulis &longs;e&longs;e &longs;ubinui<lb/>cem ingredientibus, &longs;emper mouebuntur. Vnde tunc à Fabro dato <lb/>principio motionis, vertebra vertebram continenter mouet, vltimá<lb/>que ab illis &longs;imulacrorum excita fit præteruectio, non aliter quans in <lb/>animalium genere à &longs;en&longs;u, vel intellectione motionum exorto prin<lb/>cipio intrin&longs;ecis commotis cau&longs;is, &longs;eque inuicem mouentibus, vt alij <lb/>po&longs;tmodum extrin&longs;ecus, cum partium ip&longs;arum, tum etiam vniuer&longs;i <lb/>corporis vi&longs;untur motus.<emph.end type="italics"/></s>

<figure id="fig5"></figure><lb/><emph type="italics"/>&longs;eu <expan abbr="&longs;ec&utilde;-dum">&longs;ecun<lb/>dum</expan> <expan abbr="in-ferior&etilde;">in<lb/>feriorem</expan> <lb/><expan abbr="periphe-riã">periphe<lb/>riam</expan>, vt <lb/>G ad B: <lb/>tum ter<lb/>tius E Z ad &longs;ecundi motum mouebitur etiam, &longs;ed antror&longs;um, vt E <lb/>ad F, & &longs;int deinceps alternatim infiniti denticulis &longs;e&longs;e &longs;ubinui<lb/>cem ingredientibus, &longs;emper mouebuntur. Vnde tunc à Fabro dato <lb/>principio motionis, vertebra vertebram continenter mouet, vltimá<lb/>que ab illis &longs;imulacrorum excita fit præteruectio, non aliter quans in <lb/>animalium genere à &longs;en&longs;u, vel intellectione motionum exorto prin<lb/>cipio intrin&longs;ecis commotis cau&longs;is, &longs;eque inuicem mouentibus, vt alij <lb/>po&longs;tmodum extrin&longs;ecus, cum partium ip&longs;arum, tum etiam vniuer&longs;i <lb/>corporis vi&longs;untur motus.<emph.end type="italics"/></s>

<s>Hinc architecti.] <emph type="italics"/>Sicuti ante ex vnius circuli contrarÿs mo<lb/>tibus libram, vectem, mechanicáque in&longs;trumenta magnam habere <lb/>vim ad onera mouendum &longs;ubindicauit: &longs;ic nunc ex circulorum con<lb/>tiguorum & variè multiplicatorum contrarÿs motionibus machi<lb/>nas quamplurimas effici <expan abbr="o&longs;t&etilde;dit">o&longs;tendit</expan>, quibus credibile e&longs;t veteres paganos, <lb/>qui veris miraculis <expan abbr="de&longs;tituebãtur">de&longs;tituebantur</expan>, in templis &longs;uorum <expan abbr="deor&utilde;">deorum</expan> collocatis, <lb/>& etiam per vrbium vicos, & plateas ge&longs;tatis, <expan abbr="authoritat&etilde;">authoritatem</expan> dÿs &longs;uis <lb/><expan abbr="cõflaui&longs;&longs;e">conflaui&longs;&longs;e</expan>, & ignaro vulgo mirificis modis ita impo&longs;ui&longs;&longs;e. 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. cap. 6. lib. de <lb/>f&oelig;t. format. Herodotus hi&longs;toria &longs;ecunda videtur ex his aliqua<emph.end type="italics"/> <foreign lang="greek">neu<lb/>ro/dpasa</foreign> <emph type="italics"/>appella&longs;&longs;e: qua&longs;i diceremus, per funiculos tanquam neruos <lb/>circa rotulas inuolutos, varÿs motibus agitata. Eiu&longs;modij erant adeò <lb/>celebratæ Dædali &longs;tatuæ, quæ inquit Plato ni&longs;i ligatæ aufugiebant,<emph.end type="italics"/><lb/>

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<s>Cum igitur in.] <emph type="italics"/>Aggreditur demon&longs;trare radÿ duas lationes <lb/>nullam habere rationem inter &longs;e. Syllog. &longs;ic e&longs;t. Omne duabus latio<lb/>nibus rationem aliquam inter &longs;e &longs;eruantibus latum, fertur &longs;ecundum<emph.end type="italics"/>

<pb pagenum="30"/><emph type="italics"/>rectam. Radius de&longs;cribens circulum duabus &longs;uis lationibus, non <lb/>Jertur &longs;ecundum rectam. Radij igitur iationes in nulla &longs;unt ra<lb/>tione. Propo&longs;itio confirmatur cum| &longs;equenti diagrammate. <lb/>E&longs;to rectangulum<emph.end type="italics"/> <foreign lang="greek">a b h g</foreign> <emph type="italics"/>com-<emph.end type="italics"/><lb/>

<arrow.to.target n="fig6"></arrow.to.target><lb/><emph type="italics"/>prehen&longs;um &longs;ub rectis<emph.end type="italics"/> <foreign lang="greek">a b, a g,</foreign><lb/><emph type="italics"/>quæ &longs;int inter &longs;e in ratione, quam <lb/>duæ lationes ip&longs;ius<emph.end type="italics"/> <foreign lang="greek">a</foreign> <emph type="italics"/>habent. <lb/>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. 1. lib. 6. & proinde circa eandem dimentientem conuer&longs;. prop.<emph.end type="italics"/><lb/>24. <emph type="italics"/>lib. 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. Huic con<lb/>&longs;entit quod à Proclo ex Gemino acceptum &longs;ic expo&longs;itum e&longs;t. 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. 2. comm. in def. rectæ <lb/>lineæ. Nunc igitur ponatur<emph.end type="italics"/> <foreign lang="greek">a</foreign> <emph type="italics"/>extremum radij duabus lationibus <lb/>de&longs;cribere circulum non digrediens à recta producere rectam, quod <lb/>e&longs;t contra naturam circuli. Non igitur duæ lationes ip&longs;ius<emph.end type="italics"/> <foreign lang="greek">a</foreign> <emph type="italics"/>ferun<lb/>tur 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"/>Sed hîc obiici pote&longs;t quod Sol motu pri<lb/>mi mobilis mouetur ab Oriente in Occidentem in 24. horis, & motu <lb/>proprio ab Occidente in Orientem in aliquo tempore quantum e&longs;t <lb/>quod re&longs;pondet æquatori coa&longs;cendenti cum 59'. 8". Eclypticæ. Et &longs;ic <lb/>eius duæ lationes &longs;unt in ratione aliqua, nec tamen Sol fertur &longs;ecun<lb/>dum rectam &longs;ed <expan abbr="&longs;ecund&utilde;">&longs;ecundum</expan> arcum Eclypticæ. Ita e&longs;t, ob id <expan abbr="dicend&utilde;">dicendum</expan> hic <lb/>dictas ab Ari&longs;totele duæ lationes non &longs;impliciter <expan abbr="intellig&etilde;das">intelligendas</expan>: &longs;ed ta<lb/>les, quæ <expan abbr="ferãtur">ferantur</expan> ambæ <expan abbr="&longs;ecund&utilde;">&longs;ecundum</expan> rectam. Et &longs;it manebit demon&longs;tratio.<emph.end type="italics"/></s>

<figure id="fig6"></figure><lb/><emph type="italics"/>prehen&longs;um &longs;ub rectis<emph.end type="italics"/> <foreign lang="greek">a b, a g,</foreign><lb/><emph type="italics"/>quæ &longs;int inter &longs;e in ratione, quam <lb/>duæ lationes ip&longs;ius<emph.end type="italics"/> <foreign lang="greek">a</foreign> <emph type="italics"/>habent. <lb/>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. 1. lib. 6. & proinde circa eandem dimentientem conuer&longs;. prop.<emph.end type="italics"/><lb/>24. <emph type="italics"/>lib. 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. Huic con<lb/>&longs;entit quod à Proclo ex Gemino acceptum &longs;ic expo&longs;itum e&longs;t. 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. 2. comm. in def. rectæ <lb/>lineæ. Nunc igitur ponatur<emph.end type="italics"/> <foreign lang="greek">a</foreign> <emph type="italics"/>extremum radij duabus lationibus <lb/>de&longs;cribere circulum non digrediens à recta producere rectam, quod <lb/>e&longs;t contra naturam circuli. Non igitur duæ lationes ip&longs;ius<emph.end type="italics"/> <foreign lang="greek">a</foreign> <emph type="italics"/>ferun<lb/>tur 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"/>Sed hîc obiici pote&longs;t quod Sol motu pri<lb/>mi mobilis mouetur ab Oriente in Occidentem in 24. horis, & motu <lb/>proprio ab Occidente in Orientem in aliquo tempore quantum e&longs;t <lb/>quod re&longs;pondet æquatori coa&longs;cendenti cum 59'. 8". Eclypticæ. Et &longs;ic <lb/>eius duæ lationes &longs;unt in ratione aliqua, nec tamen Sol fertur &longs;ecun<lb/>dum rectam &longs;ed <expan abbr="&longs;ecund&utilde;">&longs;ecundum</expan> arcum Eclypticæ. Ita e&longs;t, ob id <expan abbr="dicend&utilde;">dicendum</expan> hic <lb/>dictas ab Ari&longs;totele duæ lationes non &longs;impliciter <expan abbr="intellig&etilde;das">intelligendas</expan>: &longs;ed ta<lb/>les, quæ <expan abbr="ferãtur">ferantur</expan> ambæ <expan abbr="&longs;ecund&utilde;">&longs;ecundum</expan> rectam. Et &longs;it manebit demon&longs;tratio.<emph.end type="italics"/></s>

<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. 1. lib. 6. elem.<emph.end type="italics"/></s>

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<s>Si enim in alia.] <emph type="italics"/>Locus hic paulo ob&longs;curior, debet &longs;ic intelligi, <lb/>vt &longs;i excmpli gratia, a duabus lationibus latum non feratur in <lb/>ratione quidem data<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"/>&longs;ed<emph.end type="italics"/><lb/>

<arrow.to.target n="fig7"></arrow.to.target><lb/><emph type="italics"/>in alia, non feretur &longs;ecundum diame<lb/>trum<emph.end type="italics"/> <foreign lang="greek">a h,</foreign> <emph type="italics"/>nihilominus tamen feretur <lb/>&longs;ecundum rectam, quæ erit diameter <lb/>figuræ à lateribus alterius rationis <lb/>con&longs;titutæ, vt e&longs;t in præ&longs;enti dia<lb/>grammate<emph.end type="italics"/> <foreign lang="greek">a x</foreign> <emph type="italics"/>diameter quadrilateri <lb/>&longs;ub<emph.end type="italics"/> <foreign lang="greek">a d, a e</foreign> <emph type="italics"/>comprehen&longs;i.<emph.end type="italics"/></s>

<figure id="fig7"></figure><lb/><emph type="italics"/>in alia, non feretur &longs;ecundum diame<lb/>trum<emph.end type="italics"/> <foreign lang="greek">a h,</foreign> <emph type="italics"/>nihilominus tamen feretur <lb/>&longs;ecundum rectam, quæ erit diameter <lb/>figuræ à lateribus alterius rationis <lb/>con&longs;titutæ, vt e&longs;t in præ&longs;enti dia<lb/>grammate<emph.end type="italics"/> <foreign lang="greek">a x</foreign> <emph type="italics"/>diameter quadrilateri <lb/>&longs;ub<emph.end type="italics"/> <foreign lang="greek">a d, a e</foreign> <emph type="italics"/>comprehen&longs;i.<emph.end type="italics"/></s>

<s>Si vero mobilis.] <emph type="italics"/>Conclu&longs;io e&longs;t confirmata reiterato propo&longs;i<lb/>tionis præcedentis pro&longs;yllogi&longs;mo, &longs;ic. Si duæ lationes puncti mobilis <lb/>&longs;unt in nulla ratione, nulloque in tempore, impoßibile e&longs;t mobile hoc <lb/>latum e&longs;&longs;e &longs;ecundum rectam: atqui puncti de&longs;cribentis circulum duæ <lb/>lationes &longs;unt in nulla ratione, nullóque in tempore. Ergo impoßibile <lb/>e&longs;t punctum, quod de&longs;cribit circulum, ferri &longs;ecundum rectam. Sint <lb/>enim lationes illæ in aliqua ratione. Ergo punctum feretur &longs;ecun<lb/>dum rectam: at non fertur &longs;ecundum rectam. Peripheria enim non <lb/>e&longs;t recta: &longs;ed curua. Non igitur in aliqua ratione &longs;unt illius lationes. <lb/>Et &longs;i non in vlla ratione. nec igitur in tempore, quia tempora moti<lb/>bus analoga &longs;unt. Hîc duo occurrunt valde difficilia. Prius de <lb/>tempore. Demon&longs;trauit enim Ari&longs;toteles in Phy&longs;icis, omnem mo<lb/>tum e&longs;&longs;e in tempore: alterum, cum ambæ lationes &longs;int in eodem ge<lb/>nere motus, &longs;cilicet localis, quî fiet, vt rationem non habeant. Hoc <lb/>enim repugnat def. 3. lib. 5. elem. quantitas enim motus vnius mul<lb/>tiplicata, alterius vicißim quantitatem &longs;uperare pote&longs;t. Dicimus <lb/>ergo quod ad hoc po&longs;terius attinet, rationem illas habere: &longs;ed<emph.end type="italics"/> <foreign lang="greek">a)/r)r(n<gap/>ov,</foreign><lb/><emph type="italics"/>& non &longs;olum indicibilem, quod numeris exprimi nequeat: &longs;ed & <lb/>quod rectis lineis geometricè id e&longs;t exactè, exprimi non poßit, qualis <lb/>non e&longs;t inter duas lationes è quibus recta creatur, cum hæc &longs;i nume<lb/>ris non poßit exprimi, at rectis lineis &longs;altem geometricè exprimitur. <lb/>vt cum duarum rectarum, quæ parallelogrammum con&longs;tituunt, vna <lb/>e&longs;t latus quadrati alicuius, altera e&longs;t eius diameter. Tunc enim ratio <lb/>e&longs;t rectis illis licet incommen&longs;erabilibus prop. 116. lib. 10. expre&longs;&longs;a. <lb/>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. kuk,</foreign> <emph type="italics"/>& Ptol. lib. 1.<emph.end type="italics"/> <foreign lang="greek">me/gal. 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. Cæterum duas has motiones facile ani<lb/>mo concipiet, qui viderit pueros no&longs;trates &longs;ub medio vere, quo genus <lb/>hoc in&longs;ecti in ro&longs;arÿs no&longs;tris abundat, captam vnam grandiorem <lb/>mu&longs;cam viridem Cathelinam ip&longs;i vocant, pede adfuniculum alliga-<emph.end type="italics"/>

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<s>Qvod vero recta.] <emph type="italics"/>Quia &longs;uperioris &longs;yllogi&longs;mi a&longs;&longs;umptio a&longs;&longs;u<lb/>mebat <expan abbr="Radi&utilde;">Radium</expan> duabus &longs;imul ferri lationibus, id ip&longs;um hîc breui<lb/>ter, ideo valde ob&longs;curè confirmatur. Confirmatio apertior &longs;ic erit. <lb/>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. 2. lib. 1. de C&oelig;lo) Quinetiam &longs;i &longs;ic. Idem radius à diametro cir-<emph.end type="italics"/><lb/>

<arrow.to.target n="fig8"></arrow.to.target><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. Con&longs;equitur autem vt cum <lb/>e&longs;t in L<emph.end type="italics"/> <foreign lang="greek">g</foreign> <emph type="italics"/>diagrammatis hic de&longs;cri<lb/>pti. Non igitur vna latione tantum fer<lb/>tur: fertur ergo pluribus. Et quidem vna, vt <lb/>antror&longs;um: qua qua &longs;i diffunditur, & ab&longs;ce<lb/>dit foras, vt<emph.end type="italics"/> <foreign lang="greek">b</foreign> <emph type="italics"/>ver&longs;us E in hoc diagrammate: altera vt retror-<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. Con&longs;equitur autem vt cum <lb/>e&longs;t in L<emph.end type="italics"/> <foreign lang="greek">g</foreign> <emph type="italics"/>diagrammatis hic de&longs;cri<lb/>pti. Non igitur vna latione tantum fer<lb/>tur: fertur ergo pluribus. Et quidem vna, vt <lb/>antror&longs;um: qua qua &longs;i diffunditur, & ab&longs;ce<lb/>dit foras, vt<emph.end type="italics"/> <foreign lang="greek">b</foreign> <emph type="italics"/>ver&longs;us E in hoc diagrammate: altera vt retror-<emph.end type="italics"/><lb/>

<arrow.to.target n="fig9"></arrow.to.target><lb/><emph type="italics"/>&longs;um ver&longs;us centrum: qua retrahitur, ne euage<lb/>tur longius, quam æqualitas di&longs;tantiæ vndi<lb/>que à centro &longs;eruandæ permittit, vt idem<emph.end type="italics"/> <foreign lang="greek">b</foreign><lb/><emph type="italics"/>ver&longs;us L. V traque autem hæc latio quanta &longs;it <lb/>men&longs;uraturlineisrectis, quarum altera in po&longs;te<lb/>riore diaorammate e&longs;t &longs;inus rectus<emph.end type="italics"/> <foreign lang="greek">g e,</foreign> <emph type="italics"/>altera <lb/>verò e&longs;t &longs;inus ver&longs;us<emph.end type="italics"/> <foreign lang="greek">b g.</foreign></s>

<figure id="fig9"></figure><lb/><emph type="italics"/>&longs;um ver&longs;us centrum: qua retrahitur, ne euage<lb/>tur longius, quam æqualitas di&longs;tantiæ vndi<lb/>que à centro &longs;eruandæ permittit, vt idem<emph.end type="italics"/> <foreign lang="greek">b</foreign><lb/><emph type="italics"/>ver&longs;us L. V traque autem hæc latio quanta &longs;it <lb/>men&longs;uraturlineisrectis, quarum altera in po&longs;te<lb/>riore diaorammate e&longs;t &longs;inus rectus<emph.end type="italics"/> <foreign lang="greek">g e,</foreign> <emph type="italics"/>altera <lb/>verò e&longs;t &longs;inus ver&longs;us<emph.end type="italics"/> <foreign lang="greek">b g.</foreign></s>

<s>Demon&longs;tremus.] <emph type="italics"/>Dee&longs;t hoc vocabulum in Græco &longs;ine quo <lb/>&longs;en&longs;us e&longs;t imperfectus.<emph.end type="italics"/></s>

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<arrow.to.target n="fig10"></arrow.to.target><lb/>&longs;itio.</s>

<figure id="fig10"></figure><lb/>&longs;itio.</s>

<s><emph type="italics"/>Sunto <lb/>duo cir <lb/>culi in<lb/>æqua<lb/>les A <lb/>B C ma <lb/>ior & <lb/>D E F <lb/>minor, perpendiculares &longs;int B K, E I & ablatæ A K, D I.<emph.end type="italics"/></s>

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<s><emph type="italics"/>Sit datus circulus A B K C maior, ab A per D centrum reper<lb/>tum prop. 1. lib. 3. ducatur A k diameter. De&longs;cribendus autem &longs;it eo <lb/>minor, cuius accipiatur E <expan abbr="centr&utilde;">centrum</expan><emph.end type="italics"/><lb/>

<arrow.to.target n="fig11"></arrow.to.target><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. Nam &longs;i <lb/>& &longs;ecet, vt in puncto H, ducta <lb/>H E. erit æqualis ip&longs;i E A def. <lb/>15. lib. 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/>7. lib. 3. non erat igitur H punctum commune vtrique circulo, & <lb/>&longs;ic de alÿs. Circulus igitur A F G, tangit circulum A B K C <lb/>in puncto A prop. 11. lib. 3. quod oportuit facere.<emph.end type="italics"/></s>

<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. Nam &longs;i <lb/>& &longs;ecet, vt in puncto H, ducta <lb/>H E. erit æqualis ip&longs;i E A def. <lb/>15. lib. 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/>7. lib. 3. non erat igitur H punctum commune vtrique circulo, & <lb/>&longs;ic de alÿs. Circulus igitur A F G, tangit circulum A B K C <lb/>in puncto A prop. 11. lib. 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. 3. lib. 1. centro H interuallo A H de&longs;<lb/>cribatur circulus A M L po&longs;tul. 3. qui erit æqualis dato D E F. <lb/>def. 1. lib. 3. Et tanget intus circulum A B C in puncto A exprobl. <lb/>præ&longs;umpto. per punctum B ducaeur parallela B M prop. 31. lib. 1. <lb/>& per eandem parallela M N quæ per 34. lib. eiu&longs;dem cum &longs;it <lb/>æqualis ip&longs;i B K erit & æqualis ip&longs;i. E I ax. 1. connectantur M H, <lb/>E H po&longs;t. 1.<emph.end type="italics"/></s>

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<s>Agina fit cen<lb/>

<arrow.to.target n="fig12"></arrow.to.target><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>. Quod <lb/>vt intelligaturprius <lb/>in libra A D B C <lb/>H I partes notan<lb/>dæ &longs;unt. Sit igitur <lb/>libræ librile, &longs;eu<emph.end type="italics"/>

<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>. Quod <lb/>vt intelligaturprius <lb/>in libra A D B C <lb/>H I partes notan<lb/>dæ &longs;unt. Sit igitur <lb/>libræ librile, &longs;eu<emph.end type="italics"/>

<pb pagenum="46"/><emph type="italics"/>&longs;capus &longs;eu iugum A B, & C D trutina, &longs;eu an&longs;a, quæ pro com<lb/>muni more &longs;emper e&longs;t perpendicularis ad horizontis planum: pun<lb/>ctum vero C e&longs;t agina,<emph.end type="italics"/> <foreign lang="greek"><gap/>ar/tion</foreign> <emph type="italics"/>vocatur ab Ari&longs;totele, & e&longs;t cen<lb/>trum libræ circa quod brachia C A, C B moueri intelliguntur <lb/>pro ponderibus impo&longs;itis in H vel I lancibus, quas<emph.end type="italics"/> <foreign lang="greek">pla/<gap/>as</foreign> <emph type="italics"/>Ari<lb/>&longs;toteles appellabit, quo etiam nomine appellat librile, &longs;eu &longs;capum, &longs;eu <lb/>iugum A B. E&longs;t etiam recta E C F &longs;emper perpendicularis ip&longs;i <lb/>A B vtcunque moueatur. proinde perpendiculum appellatur, ab <lb/>alÿs æquamentum, ab alÿs trutina. His ita declaratis, ilico ex præ<lb/>cedentibus con&longs;tat, quod C centro fixo, &longs;i A C vel C B lineæ quæ <lb/>ex centro, moueantur, de&longs;cribent circulum pro &longs;uo interuallo, in <lb/>minore librili, minorem: in maiore maiorem: &longs;icque cum magnitudo <lb/>&longs;patÿ motu tran&longs;iti, quò maior, eò vi&longs;ibilior, & quò etiam librilis <lb/>pars maior, eò mobilior, citius ex æquali pondere, & magis mouebitur <lb/>librile maius: <expan abbr="quã">quam</expan> minus, proinde etiam erit exactius. id e&longs;t minores <lb/>ponderum differentias patefaciet.<emph.end type="italics"/></s>

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<s>Propter quid.] <emph type="italics"/>In hoc capite proponitur aliud di&longs;cutiendum <lb/>problema de libra. De qua quæruntur duo. Primum cur &longs;i cen<lb/>trum libræ &longs;it in &longs;uperiori parte librilis &longs;itum, cum pondere impo&longs;ito <lb/>deor&longs;um venerit librilis vna pars, altera &longs;ur&longs;um, eodem &longs;ublato, & <lb/>librili libero relicto brachia librilis redeant ad pri&longs;tinum locum.<emph.end type="italics"/>

<pb pagenum="50"/><emph type="italics"/>Secundum, cur &longs;i centrum eius &longs;it in inferiori parte librilis &longs;itum, <lb/>& pondere impo&longs;ito, parteque librilis vna deor&longs;um demi&longs;&longs;a, eodem <lb/>&longs;ublato librile liberum relictum non redeat: &longs;ed in eo &longs;itu maneat. <lb/>Tertium adiungitur à Guido V baldo (è quo quæ hîc dicemus omnia <lb/>ferè depromp &longs;imus) non minus quæ&longs;itu dignum. Cur &longs;i centrum &longs;it <lb/>exqui&longs;ite librilis medium, librile retinebit &longs;itum quemlibet datum. <lb/>Quæ vt intelligantur &longs;cire conuenit vel libram hic capi, cuius librile <lb/>latitudinem aliquam effatu dignam habet, vel cum quo trutina ita <lb/>connexa e&longs;t, vt ad vnius motum moueatur alterum, & contra: quia <lb/>totum continuum e&longs;t. In extremo autem trutinæ, non eo quidem, <lb/>quod e&longs;t ei cum librili <expan abbr="cõ-">con-</expan><emph.end type="italics"/><lb/>

<arrow.to.target n="fig13"></arrow.to.target><lb/><emph type="italics"/>mune: &longs;ed altero, <expan abbr="c&etilde;trum">centrum</expan> <lb/>circa quod <expan abbr="tanquã">tanquam</expan> <expan abbr="fix&utilde;">fixum</expan>, <lb/>ip&longs;a moueantur, <expan abbr="&longs;it&utilde;">&longs;itum</expan> &longs;it. <lb/>Sine horum enim altero <lb/>modo intelligi <expan abbr="nõ">non</expan> pote&longs;t, <lb/>quomodo librile, quod <lb/>&longs;ecundum longitudinem <lb/>e&longs;t, vt vna recta li<lb/>nea, admittat dif-<emph.end type="italics"/><lb/>

<figure id="fig13"></figure><lb/><emph type="italics"/>mune: &longs;ed altero, <expan abbr="c&etilde;trum">centrum</expan> <lb/>circa quod <expan abbr="tanquã">tanquam</expan> <expan abbr="fix&utilde;">fixum</expan>, <lb/>ip&longs;a moueantur, <expan abbr="&longs;it&utilde;">&longs;itum</expan> &longs;it. <lb/>Sine horum enim altero <lb/>modo intelligi <expan abbr="nõ">non</expan> pote&longs;t, <lb/>quomodo librile, quod <lb/>&longs;ecundum longitudinem <lb/>e&longs;t, vt vna recta li<lb/>nea, admittat dif-<emph.end type="italics"/><lb/>

<arrow.to.target n="fig14"></arrow.to.target><lb/><emph type="italics"/>ferentias illas loci <lb/><expan abbr="&longs;urs&utilde;">&longs;ursum</expan> deor&longs;um. At <lb/>&longs;iue hoc: &longs;iue illo <lb/>modo librile con<lb/>&longs;tituaturproblema <lb/>hîc ab Ari&longs;totele <lb/><expan abbr="po&longs;it&utilde;">po&longs;itum</expan> habebit non <lb/>&longs;olum <expan abbr="experientiã">experientiam</expan>, <lb/>&longs;ed & rationem <lb/>&longs;ibi &longs;uffragantem, <lb/>Exemplum igitur <lb/>librilis primi mo<lb/>di <expan abbr="c&utilde;">cum</expan> latitudine &longs;it <lb/>A B, cuius <expan abbr="centr&utilde;">centrum</expan> <lb/>in &longs;uperiori parte <lb/>latitudinis &longs;it C,<emph.end type="italics"/>

<figure id="fig14"></figure><lb/><emph type="italics"/>ferentias illas loci <lb/><expan abbr="&longs;urs&utilde;">&longs;ursum</expan> deor&longs;um. At <lb/>&longs;iue hoc: &longs;iue illo <lb/>modo librile con<lb/>&longs;tituaturproblema <lb/>hîc ab Ari&longs;totele <lb/><expan abbr="po&longs;it&utilde;">po&longs;itum</expan> habebit non <lb/>&longs;olum <expan abbr="experientiã">experientiam</expan>, <lb/>&longs;ed & rationem <lb/>&longs;ibi &longs;uffragantem, <lb/>Exemplum igitur <lb/>librilis primi mo<lb/>di <expan abbr="c&utilde;">cum</expan> latitudine &longs;it <lb/>A B, cuius <expan abbr="centr&utilde;">centrum</expan> <lb/>in &longs;uperiori parte <lb/>latitudinis &longs;it C,<emph.end type="italics"/>

<pb pagenum="51"/><emph type="italics"/>cum &longs;uo &longs;u&longs;pen&longs;orio &longs;eu trutina C D: vel &longs;it & in inferiori parte C <lb/>centrum cum &longs;uo fulcro quod pro trutina e&longs;t etiam C D, & <lb/>in vtroque in-<emph.end type="italics"/><lb/>

<arrow.to.target n="fig15"></arrow.to.target><lb/><emph type="italics"/>telligatur linea <lb/>recta per cen<lb/>trum tran&longs;ire <lb/>perpendiculari<lb/>ter ad planum <lb/><expan abbr="horizõtis">horizontis</expan> D E.<emph.end type="italics"/></s>

<figure id="fig15"></figure><lb/><emph type="italics"/>telligatur linea <lb/>recta per cen<lb/>trum tran&longs;ire <lb/>perpendiculari<lb/>ter ad planum <lb/><expan abbr="horizõtis">horizontis</expan> D E.<emph.end type="italics"/></s>

<s><emph type="italics"/>Exemplum li<lb/>brilis <expan abbr="c&utilde;">cum</expan> truti<lb/>na immobiliter <lb/>connexi &longs;it vbi<emph.end type="italics"/><lb/>

<arrow.to.target n="fig16"></arrow.to.target><lb/><emph type="italics"/>e&longs;t librile GH, <lb/>& trutina K <lb/>L, & centrum <lb/>libræ L.<emph.end type="italics"/></s>

<figure id="fig16"></figure><lb/><emph type="italics"/>e&longs;t librile GH, <lb/>& trutina K <lb/>L, & centrum <lb/>libræ L.<emph.end type="italics"/></s>

<s>An quia &longs;u<lb/>perne.] <emph type="italics"/>In<lb/>tellectis libræ <lb/>generibus ad propo&longs;itum problema accommodatis, nunc eius partis <lb/>prioris adfertur &longs;olutio. quia in vtroque genere librilis cum centrum <lb/>libræ &longs;upernam partem occupat, & à perpendiculari intellecta per <lb/>admotum pondus librile à paralleli&longs;mo cum horizonte di&longs;ce&longs;&longs;erit, <lb/>pars quæ &longs;uperior fit, maior e&longs;t parte inferiore. Maior autem grauior <lb/>e&longs;t. Totum enim librile &longs;upponitur e&longs;&longs;e materiæ vnigeneris. Redit <lb/>igitur libera relicta, &longs;itumquerecuperat, vbi paria momenta <expan abbr="æqui-ponderãt">æqui<lb/>ponderant</expan>. Talis <expan abbr="aut&etilde;">autem</expan> e&longs;t is &longs;itus in quo llbrile <expan abbr="parallel&utilde;">parallelum</expan> fit horizonti. <lb/>Contra &longs;i centrum infernam partem occupet, pars inferior librilis <lb/>maior e&longs;t. præponderat igitur. Non itaque per &longs;eredibit: &longs;ed &longs;itum <lb/>detracta decliuem retinebit: alias id graue, quo excedit, &longs;ur&longs;um &longs;ua <lb/>&longs;ponte a&longs;cenderet, contra def. grauis.<emph.end type="italics"/></s>

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<s>Itaque librilis <foreign lang="greek">e z.</foreign>] <emph type="italics"/>Quod pars &longs;uperior librilis in vno &longs;itu <lb/>centri &longs;it maior, in altero &longs;it minor, non e&longs;t probatum ab Ari&longs;totele: <lb/>&longs;ed ex fabrica librilis vtriu&longs;que generis res ilico fit euidens, etiam <lb/>pro Ari&longs;totelis characteribus no&longs;tris ad diagrammata adiunctis.<emph.end type="italics"/>

<pb pagenum="52"/><emph type="italics"/>Nam in librili primi modi cum obliquatur C F perpendiculum li<lb/>brilis, quod ip&longs;um perpetuò bifariam &longs;ecat, digreditur à perpendicu<lb/>lari intellecta, quam &longs;ecat<emph.end type="italics"/><lb/>

<arrow.to.target n="fig17"></arrow.to.target><lb/><emph type="italics"/>in centro, &longs;icque triangu<lb/>lum con&longs;tituit comprehen<lb/>dens aliquam partem al<lb/>terutrius brachÿ nempe F <lb/>C E, vel R C F, quæ &longs;ic <lb/>detracta vni, & alteri ad<lb/>dita, reddit hoc à quo de<lb/>trahitur minus, & eius <lb/>detractæ partis duplo alte<lb/>rum <expan abbr="brachi&utilde;">brachium</expan> maius. At<lb/>que hic modus conuenit <lb/>&longs;en&longs;ui Ari&longs;totelis, vt qui <lb/>eo v&longs;urus &longs;it capite &longs;equen<lb/>ti in problemate de vecte. <lb/>Et etiam pulchrè re&longs;pon-<emph.end type="italics"/><lb/>

<figure id="fig17"></figure><lb/><emph type="italics"/>in centro, &longs;icque triangu<lb/>lum con&longs;tituit comprehen<lb/>dens aliquam partem al<lb/>terutrius brachÿ nempe F <lb/>C E, vel R C F, quæ &longs;ic <lb/>detracta vni, & alteri ad<lb/>dita, reddit hoc à quo de<lb/>trahitur minus, & eius <lb/>detractæ partis duplo alte<lb/>rum <expan abbr="brachi&utilde;">brachium</expan> maius. At<lb/>que hic modus conuenit <lb/>&longs;en&longs;ui Ari&longs;totelis, vt qui <lb/>eo v&longs;urus &longs;it capite &longs;equen<lb/>ti in problemate de vecte. <lb/>Et etiam pulchrè re&longs;pon-<emph.end type="italics"/><lb/>

<arrow.to.target n="fig18"></arrow.to.target><lb/><emph type="italics"/>det cau&longs;æ iam dictæ ex <lb/>proprietate circuli, quate<lb/>nus eius radÿ breuiores <lb/>&longs;unt aut longiores, & pro<lb/>pter i&longs;tam inæqualitatem <lb/>tardiores aut velociores.<emph.end type="italics"/></s>

<figure id="fig18"></figure><lb/><emph type="italics"/>det cau&longs;æ iam dictæ ex <lb/>proprietate circuli, quate<lb/>nus eius radÿ breuiores <lb/>&longs;unt aut longiores, & pro<lb/>pter i&longs;tam inæqualitatem <lb/>tardiores aut velociores.<emph.end type="italics"/></s>

<s><emph type="italics"/>In librili vero &longs;ecundi <lb/>modi res erit adhuc aper<lb/>tior. Centro &longs;iquidem L, <lb/>& interuallo L K circu<lb/>lus de&longs;cribatur, & K <lb/><expan abbr="mot&utilde;">motum</expan> &longs;it in P propter vim <lb/>allatam: tum L K per<lb/>pendicularis intellecta pro<lb/>ducta &longs;ecabit brachium <lb/>P H, id e&longs;t K H, vt in <lb/>M: &longs;icque P M accre&longs;cet pro longitudine ideo & grauitate ad <lb/>P G, redibit igitur G P M.<emph.end type="italics"/></s>

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<s><emph type="italics"/>Contra in alte<lb/>ro diagrammate <lb/>eiu&longs;modi &longs;ectio <lb/>fiet, vt in O, & <lb/>&longs;ic pars O P ac<lb/>cre&longs;cet ad P H: <lb/>&longs;icque tota O P <lb/>H vt longior, ita <lb/>grauior O G. <lb/>Manebit igitur <lb/>(præ&longs;uppo&longs;ito hoc <lb/>quod ab H <expan abbr="app&etilde;&longs;a">appen&longs;a</expan><emph.end type="italics"/><lb/>

<arrow.to.target n="fig19"></arrow.to.target><lb/><emph type="italics"/>lanx in&longs;ideat ter<lb/>ræ vel alicui ful<lb/>cro. 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. quod e&longs;t demon&longs;tratum ab V baldo prop. 1. lib. de lib. <lb/>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. 4. lib. 1. <lb/>Archimed. de æquipond. L K vero linea e&longs;t perpendicularis ad pla<lb/>num horizontis. Non igitur P liberum relictum manebit ita vt e&longs;t <lb/>G P M H: Sed & redibit ex natura grauium quou&longs;que occupe<gap/><lb/>punctum k in perpendiculari horizontis, à qua quia per extre<lb/>mum L fixa e&longs;t, &longs;u&longs;tinebitur. At G O P H manebit &longs;ic, nec <lb/>redibit ad G k H, quia, quod e&longs;&longs;et contra naturam, a&longs;cenderet. <lb/>Vbiautem centrum librilis e&longs;t exqui&longs;itè medium, vt C ip&longs;ius A B <lb/>cum trutina C D mobili, &longs;eu &longs;upra, &longs;eu infra po&longs;ita &longs;it, quocunqu<gap/><emph.end type="italics"/>

<figure id="fig19"></figure><lb/><emph type="italics"/>lanx in&longs;ideat ter<lb/>ræ vel alicui ful<lb/>cro. 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. quod e&longs;t demon&longs;tratum ab V baldo prop. 1. lib. de lib. <lb/>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. 4. lib. 1. <lb/>Archimed. de æquipond. L K vero linea e&longs;t perpendicularis ad pla<lb/>num horizontis. Non igitur P liberum relictum manebit ita vt e&longs;t <lb/>G P M H: Sed & redibit ex natura grauium quou&longs;que occupe<gap/><lb/>punctum k in perpendiculari horizontis, à qua quia per extre<lb/>mum L fixa e&longs;t, &longs;u&longs;tinebitur. At G O P H manebit &longs;ic, nec <lb/>redibit ad G k H, quia, quod e&longs;&longs;et contra naturam, a&longs;cenderet. <lb/>Vbiautem centrum librilis e&longs;t exqui&longs;itè medium, vt C ip&longs;ius A B <lb/>cum trutina C D mobili, &longs;eu &longs;upra, &longs;eu infra po&longs;ita &longs;it, quocunqu<gap/><emph.end type="italics"/>

<arrow.to.target n="fig20"></arrow.to.target><lb/><emph type="italics"/>in &longs;itu fuerit A B vt <lb/>in G H manebit, tum <lb/>quia brachia manent <lb/>æqualia, tum quia cen<lb/>trum grauitatis C &longs;em<lb/>per erit in perpendicu<lb/>lari horizontis, &longs;ecun<lb/>dum quam & ad quam <lb/>magnitudo compo&longs;ita <lb/>exbrachÿs C A, C B & lancibus & ponderibus æquiponderan<lb/>tibus, &longs;i impo&longs;ita &longs;int, fertur, &longs;ed &longs;u&longs;tinetur linea C D vel C E <lb/>fixa. Et &longs;ic patet &longs;olutio tertiæ partis huius problematis ab Ari&longs;totele <lb/>prætermi&longs;&longs;æ. Rarò tamen huic demon&longs;trationi licet veræ, experien<lb/>tia re&longs;pondet, propter in&longs;trumentorum materiam Phy&longs;icam, in qua <lb/>exacte medium con&longs;tituere non datur in puncto geometrico, vtcum<lb/>que tamen alias re&longs;pondet.<emph.end type="italics"/></s>

<figure id="fig20"></figure><lb/><emph type="italics"/>in &longs;itu fuerit A B vt <lb/>in G H manebit, tum <lb/>quia brachia manent <lb/>æqualia, tum quia cen<lb/>trum grauitatis C &longs;em<lb/>per erit in perpendicu<lb/>lari horizontis, &longs;ecun<lb/>dum quam & ad quam <lb/>magnitudo compo&longs;ita <lb/>exbrachÿs C A, C B & lancibus & ponderibus æquiponderan<lb/>tibus, &longs;i impo&longs;ita &longs;int, fertur, &longs;ed &longs;u&longs;tinetur linea C D vel C E <lb/>fixa. Et &longs;ic patet &longs;olutio tertiæ partis huius problematis ab Ari&longs;totele <lb/>prætermi&longs;&longs;æ. Rarò tamen huic demon&longs;trationi licet veræ, experien<lb/>tia re&longs;pondet, propter in&longs;trumentorum materiam Phy&longs;icam, in qua <lb/>exacte medium con&longs;tituere non datur in puncto geometrico, vtcum<lb/>que tamen alias re&longs;pondet.<emph.end type="italics"/></s>

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<s>

<arrow.to.target n="marg19"></arrow.to.target><lb/>lus validus per mediam machinam traiectus, quo manuducto <lb/>machina, dum ver&longs;atur, funem ductarium aduoluit. Hæc definitio <lb/><expan abbr="nimi&utilde;">nimium</expan> angu&longs;ta e&longs;t, neque huic loco <expan abbr="cõuenit">conuenit</expan>, neque &longs;atis rei ip&longs;i. vectis <lb/>enim per &longs;e machina e&longs;t. E&longs;tigitur vectis palus oblongior vno <expan abbr="&longs;uor&utilde;">&longs;uorum</expan> <lb/>extremorum acutus, altero obtu&longs;us ex ligno vel ferro inflexibi<lb/>lis ad <expan abbr="commou&etilde;-">commouen-</expan><emph.end type="italics"/><lb/>

<arrow.to.target n="fig21"></arrow.to.target><lb/><emph type="italics"/>da onera factus, <lb/>vt e&longs;t A B. pars <lb/>obtu&longs;a caput: pars acuta lingula vocatur. Hoc vtendi modus duplex <lb/>e&longs;t. Primus cum lingula &longs;ubditur oneri commouendo, & vecti ip&longs;i <lb/>quam proxime lingulæ &longs;ubditur corpu&longs;culum firmum, quod Græcis<emph.end type="italics"/><lb/><foreign lang="greek">(w_omo/xlion,</foreign> <emph type="italics"/>Vitruuio preßio dicitur. Huius figura e&longs;t ferè quæ<lb/>uis obuia: expeditior tamen e&longs;t, &longs;i &longs;it pri&longs;mation, cuius aduer&longs;a duo <lb/>plana æqualia &longs;imilia, parallela, &longs;int trian-<emph.end type="italics"/><lb/>

<figure id="fig21"></figure><lb/><emph type="italics"/>da onera factus, <lb/>vt e&longs;t A B. pars <lb/>obtu&longs;a caput: pars acuta lingula vocatur. Hoc vtendi modus duplex <lb/>e&longs;t. Primus cum lingula &longs;ubditur oneri commouendo, & vecti ip&longs;i <lb/>quam proxime lingulæ &longs;ubditur corpu&longs;culum firmum, quod Græcis<emph.end type="italics"/><lb/><foreign lang="greek">(w_omo/xlion,</foreign> <emph type="italics"/>Vitruuio preßio dicitur. Huius figura e&longs;t ferè quæ<lb/>uis obuia: expeditior tamen e&longs;t, &longs;i &longs;it pri&longs;mation, cuius aduer&longs;a duo <lb/>plana æqualia &longs;imilia, parallela, &longs;int trian-<emph.end type="italics"/><lb/>

<arrow.to.target n="fig22"></arrow.to.target><lb/><emph type="italics"/>gula, vte&longs;t A D B C E F. Huius enim <lb/>pri&longs;matis lateri vni tanquam centro, &longs;i <lb/>vectis innitentis caput deprimatur, nece&longs;&longs;e <lb/>erit ilico lingulam, & con&longs;equenter lin<lb/>guæ innixum onus attolli, & ideo com<lb/>moueri. Atque hic e&longs;t primus modus vtendi vecte frequentißimus: <lb/>&longs;ed & e&longs;t alter non multò infrequentior, cum lingula oneri, vt an<lb/>tè, &longs;ubdita nullo &longs;ubdito præter &longs;olum immobile vecti ip&longs;i hypo<lb/>mochlio, vectis caput attollitur. Hoc enim &longs;ur&longs;um lato omnes etiam <lb/>vectis partes attolli nece&longs;&longs;e e&longs;t præter extremum lingulæ fixum, quo<gap/><lb/>centri immobilis rationem &longs;umit, & terræ vel alÿ corpori immobili <lb/>tanquam hypomachlio innititur. 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"/>

<figure id="fig22"></figure><lb/><emph type="italics"/>gula, vte&longs;t A D B C E F. Huius enim <lb/>pri&longs;matis lateri vni tanquam centro, &longs;i <lb/>vectis innitentis caput deprimatur, nece&longs;&longs;e <lb/>erit ilico lingulam, & con&longs;equenter lin<lb/>guæ innixum onus attolli, & ideo com<lb/>moueri. Atque hic e&longs;t primus modus vtendi vecte frequentißimus: <lb/>&longs;ed & e&longs;t alter non multò infrequentior, cum lingula oneri, vt an<lb/>tè, &longs;ubdita nullo &longs;ubdito præter &longs;olum immobile vecti ip&longs;i hypo<lb/>mochlio, vectis caput attollitur. Hoc enim &longs;ur&longs;um lato omnes etiam <lb/>vectis partes attolli nece&longs;&longs;e e&longs;t præter extremum lingulæ fixum, quo<gap/><lb/>centri immobilis rationem &longs;umit, & terræ vel alÿ corpori immobili <lb/>tanquam hypomachlio innititur. 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. Vtrumque vectis v&longs;um Vitruuius cap. 8. lib. 10. &longs;ic <lb/>explicuit. 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. Item &longs;i &longs;ub onus vectis ferrei lingula &longs;ubiecta fuerit, neque <lb/>caput eius preßione in imum: &longs;ed aduer&longs;us in altitudinem extolletur, <lb/>lingula fulcta in areæ &longs;olo habebit eam pro onere, oneris <expan abbr="aut&etilde;">autem</expan> ip&longs;ius <lb/>angulum pro preßione: ita non tam faciliter quam per preßionem, <lb/>&longs;ed aduer&longs;us nihilominus in pondus oneris erit <expan abbr="excitat&utilde;">excitatum</expan>. Hæc Vitr. <lb/>à quo parum di&longs;&longs;entimus dum in &longs;ecundo v&longs;u vectis ponit &longs;olum &longs;eu <lb/>aream pro onere, nos pro centro & hypomochlio, quor&longs;um, dicemus<emph.end type="italics"/><lb/>

<arrow.to.target n="marg20"></arrow.to.target><lb/><emph type="italics"/>alibi. Galenus comparauit mu&longs;culum, qui e&longs;t in&longs;trumentum motus <lb/>voluntarÿ vecti. vtque pondera, inquit, quæ mouere manibus nequi<lb/>mus, vectibus admotis mouere &longs;olemus. Ita cum membra corporis <lb/>mouere neruis non poßimus, ad ea mouenda mu&longs;culi nobis &longs;unt dati. <lb/>neruus enim in &longs;ingulis mu&longs;culis in fibras di&longs;&longs;olutus, ita cum fibris <lb/>copulatur atque coniungitur, vt ex vtri&longs;que vnum quoddam neruo<lb/>&longs;um corpus effectum è corpore mu&longs;culi prodeat, qui tendo nomina<lb/>tur. Atque hic quidem tendo ex in&longs;trumentis exoriens, habet illius <lb/>extremæ partis vectis rationem quæ ponderibus admouetur. Itaque <lb/>hic ÿs qui anatomen corporis humani re&longs;pexerunt <expan abbr="iucund&utilde;">iucundum</expan> e&longs;t ip&longs;ius <lb/>membra, tanquam onera &longs;excentis mu&longs;culis, tanquam vectibus, tam <lb/>varie flecti, intendi &longs;ur&longs;um, ferri deor&longs;um, demitti ad latera, contor<lb/>queri, circumuolui, & ad omnes motus, quos voluntas humana vti<lb/>litate incitata præ&longs;cribit, educi, immo vero ÿ&longs;dem agentibus in quie<lb/>te, & quam medici appellant in media figura, retineri.<emph.end type="italics"/></s>

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<s>Cur vires exiguæ.] <emph type="italics"/>Machina libræ duobus problematis expe<lb/>dita e&longs;t: vectis deinde duodecim di&longs;&longs;eritur, è quibus primum e&longs;t ge<lb/>nerale. Quæritur ergo hîc, cur homo verbi gratia pu&longs;illis viribus <lb/>amoueat vecte magna onera, coloßica vocat Vitruuius, id e&longs;t ma<lb/>gnæ molis, quales &longs;unt coloßi. Et apud eundem coloßicotera compa<lb/>ratiuum e&longs;t Græcum pro grandiora, va&longs;tiora, coloßi in&longs;tar ha<lb/>bentia.<emph.end type="italics"/></s>

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<s><emph type="italics"/>Locus hic breuißimè totam vectis rationem explicat, vt &longs;ciatur <lb/>vectis v&longs;us, & quæ vires, ad quod onus mouendum &longs;ufficiant, <lb/>vel non &longs;ufficiant. Quæres vt intelligatur proponemus hoc theore<lb/>ma. Vte&longs;t potentia ad pondus &longs;u&longs;tentum: ita e&longs;t pars vectis ab hypo<lb/>mochlio ver&longs;us linguam, ad partem ab eodem hypomochlio ver&longs;us <lb/>caput, quod vt demon&longs;tretur. Sit vectis A B, & huius hypo<lb/>mochlium C:<emph.end type="italics"/><lb/>

<arrow.to.target n="fig23"></arrow.to.target><lb/><emph type="italics"/><expan abbr="&longs;icq;">&longs;icque</expan> vectis duæ <lb/>partes C A ver<lb/>&longs;us linguam, C <lb/>B ver&longs;us caput: <lb/>&longs;it quoque pon<lb/>dus D &longs;u&longs;pen&longs;um ex perpendiculari A D: potentia autem &longs;u&longs;tinens <lb/>&longs;it in B. 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. 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. 6. lib. 1. <lb/>Archim. de æquipond. 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"/>

<figure id="fig23"></figure><lb/><emph type="italics"/><expan abbr="&longs;icq;">&longs;icque</expan> vectis duæ <lb/>partes C A ver<lb/>&longs;us linguam, C <lb/>B ver&longs;us caput: <lb/>&longs;it quoque pon<lb/>dus D &longs;u&longs;pen&longs;um ex perpendiculari A D: potentia autem &longs;u&longs;tinens <lb/>&longs;it in B. 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. 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. 6. lib. 1. <lb/>Archim. de æquipond. 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. Nam æqualia ad idem eandem rationem <lb/>habent prop. 7. lib. 5. el. Sed E habet eam ad D, quam A C and B C, ex <lb/>fab. ergo potentia in B ad pondus D eam rationem habebit, quam <lb/>A C ad B C. Itaque vt e&longs;t potentia ad pondus &longs;u&longs;tentum: ita e&longs;t <lb/>pars vectis &c. quod fuit demon&longs;trandum. Ex quo duo corollaria <lb/>&longs;tatim eliciuntur.<emph.end type="italics"/></s>

<s>Primum. <emph type="italics"/>Hypomochlio bifariam diuidente vectem, potentia <lb/>æqualis requiritur: inæqualiter vero inæqualis. Et quidem &longs;i pars ab <lb/>hypomochlio ad caput &longs;it maius &longs;egmentum, potentia minor: &longs;i con<lb/>tra pars ab eodem ad lingulam, potentia maior.<emph.end type="italics"/></s>

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<s>Sit vectis <foreign lang="greek">a b</foreign>] <emph type="italics"/>huius diagrammatis expo&longs;itio &longs;i non imperfe<lb/>cta e&longs;t, adfertur tantum ad o&longs;tendendum quod pondus<emph.end type="italics"/> <foreign lang="greek">g</foreign> <emph type="italics"/>ab eo cum<emph.end type="italics"/><lb/>

<arrow.to.target n="fig24"></arrow.to.target><lb/><emph type="italics"/>erat in<emph.end type="italics"/> <foreign lang="greek">a</foreign> <emph type="italics"/>per depreßionem<emph.end type="italics"/> <foreign lang="greek">b</foreign> <emph type="italics"/>ad<emph.end type="italics"/> <foreign lang="greek">h</foreign> <emph type="italics"/>tran&longs;latum e&longs;t ad<emph.end type="italics"/> <foreign lang="greek">k.</foreign> <emph type="italics"/>Sed adhuc <lb/>paulo ob&longs;curius. Apertius igitur &longs;ic. 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. 1. huius lib. 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. 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. Et ex his denique contendit Ari&longs;toteles o&longs;tendere circula<lb/>rem motum omnium machinationum principia in &longs;e continere, vt <lb/>multis po&longs;tea &longs;pecialibus exemplis declarabit, in quibus & alijs om<lb/>nibus, qui &longs;citè di&longs;tinguet, quid oneri re&longs;pondeat, pro quo &longs;it vectis, <lb/>quale &longs;it hypomochlium, vnde vis mouens habeatur, hic habebit <lb/>abundè, quid &longs;entiendum &longs;it.<emph.end type="italics"/></s>

<figure id="fig24"></figure><lb/><emph type="italics"/>erat in<emph.end type="italics"/> <foreign lang="greek">a</foreign> <emph type="italics"/>per depreßionem<emph.end type="italics"/> <foreign lang="greek">b</foreign> <emph type="italics"/>ad<emph.end type="italics"/> <foreign lang="greek">h</foreign> <emph type="italics"/>tran&longs;latum e&longs;t ad<emph.end type="italics"/> <foreign lang="greek">k.</foreign> <emph type="italics"/>Sed adhuc <lb/>paulo ob&longs;curius. Apertius igitur &longs;ic. 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. 1. huius lib. 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. 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. Et ex his denique contendit Ari&longs;toteles o&longs;tendere circula<lb/>rem motum omnium machinationum principia in &longs;e continere, vt <lb/>multis po&longs;tea &longs;pecialibus exemplis declarabit, in quibus & alijs om<lb/>nibus, qui &longs;citè di&longs;tinguet, quid oneri re&longs;pondeat, pro quo &longs;it vectis, <lb/>quale &longs;it hypomochlium, vnde vis mouens habeatur, hic habebit <lb/>abundè, quid &longs;entiendum &longs;it.<emph.end type="italics"/></s>

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<s><emph type="italics"/>Tullius tamen in 1. Tu&longs;cula. dicit nominatam Argô, quia Argiui in <lb/>ea delecti viri vecti petebant Arietis pellem inauratam. Ante Ar<lb/>goratibus, & paruis acatÿs homines tantum vehi &longs;olere, te&longs;tis e&longs;t <lb/>Diodorus &longs;iculus. Sed po&longs;t hanc, vt e&longs;t hominum ingenium ferax, <lb/>naues variæ confectæ &longs;unt: quarum aliæ velis, quæ onerariæ: aliæ <lb/>remis, quæ actuariæ: aliæ velis & remis, quæ longæ dictæ &longs;unt. Om<lb/>nium præcipuæ partes &longs;unt anterior, quæ prora: po&longs;terior quæ puppis: <lb/>latus, quicquid dextra & &longs;ini&longs;tra inter proram & puppim in<lb/>teriacens prominet: Ima, quæ in aqua immer&longs;a alueus & carina di<lb/>citur. Sunt & in omnium ambitu fori, per quos nautæ cur&longs;itant, & <lb/>in proiecturis laterum tran&longs;tra, &longs;edes &longs;cilicet quibus acturi nauem <lb/>actuariam, vel longam in&longs;ident. Hi à remo Remiges dicti. E&longs;t au<lb/>tem Remus palus longus & validus parte vna latior, quæ palmula <lb/>dicitur, reliqua <expan abbr="rot&utilde;dus">rotundus</expan>, cuius extremum, manubrium dicitur. Remi <lb/>fuerunt diuer&longs;æ magnitudinis pro proportione nauis agendæ, & in <lb/>eadem naui inæqualis, tractabilis tamen vnius validi remigis viri<lb/>bus, propter libramentum, quod à plumbatis manubrÿs accedebat ni<lb/>xus impellentium brachiorum adiuuans. Athenæus recitat inter <lb/>remos quo&longs;dam fui&longs;&longs;e tantæ longitudinis vt duodequadraginta cu<lb/>bitos explerent, quod non erit incredibile memoria repetenti quarun<lb/>dam nauium à veteribus fabricatarum va&longs;titatem, cuiu&longs;modi idem, <lb/>& Plutarchus memorant fui&longs;&longs;e illam dictam fluuialem Thalame<lb/>gon, quam Ptolomæus Philopator in delicÿs habuit, non tam ad <lb/>v&longs;um: quam ad o&longs;tentationem, vt quæ in longitudinem ducentos ac <lb/>octoginta: & ab imo v&longs;que ad tran&longs;tra duodequinquaginta cubitos <lb/>pateret. Quæ amplitudo remi & nauis (quod alioqui e&longs;t nunc nobis <lb/>incredibile videntibus tantum naues, quæ à numero remigum in <lb/>vnoquoque tran&longs;tro &longs;edentium &longs;unt vniremes, triremes, quadrire<lb/>mes, quinquiremes) probabile facit fui&longs;&longs;e in v&longs;u apud antiquos naues <lb/>multo plurium remigum decem, vndecim, viginti, multò plurium, in <lb/>vnoquoque tran&longs;tro & tran&longs;trorum multos, ordines vnde idem<emph.end type="italics"/>

<pb pagenum="64"/><emph type="italics"/>Athenæus recen&longs;et Philadelphum ad v&longs;um habui&longs;&longs;e trieconteres, id <lb/>e&longs;t tricenûm ordinum duas: I co&longs;erem vndm, quæ vicenûm erat, qua<lb/>tuor quæ ternûm denûm, duas quæ duodenûm, quatuordecim quæ <lb/>vndenûm, & alias infra multas. Illam autem, quæ Philopatoris fuit, <lb/>fui&longs;&longs;e quinquaginta ordinum, & in &longs;ingulis tran&longs;tris quadraginta <lb/>remis, id e&longs;t, remigibus (nam & horum po&longs;tea numerum aßignat to<lb/>tius fui&longs;&longs;e 4000.) agi. Remigum autem antiquitus, vt & hodie, <lb/>alÿ voluntarÿ: alÿ mercede <expan abbr="cõducti">conducti</expan>: alÿ vt adacti, vt in bello capti, <lb/>aut ab Archipyratis in locis maritimis <expan abbr="compreh&etilde;&longs;i">comprehen&longs;i</expan>, aut ob &longs;celera ad <lb/>remos à iudicibus damnati, <expan abbr="cõpediti">compediti</expan>, & alligati &longs;ine mercede etiam <lb/>nudi &longs;ub flagellis remigant. Omnes intres ordines reduxit quidam <lb/>Scholia&longs;tes Ari&longs;tophanis in Ranis locum illum,<emph.end type="italics"/> <foreign lang="greek">*kai\ <gap/>popa<gap/>d<gap/>_n e)s <lb/>to\ <gap/>o/ma tw_| <gap/>ala/maxi,</foreign> <emph type="italics"/>interpretans, dum dicit eos, qui in inferiore <lb/>parte nauis <expan abbr="eß&etilde;t">eßent</expan><emph.end type="italics"/> <foreign lang="greek"><gap/>alami_tas</foreign> <emph type="italics"/>&longs;eu<emph.end type="italics"/> <foreign lang="greek"><gap/>ala/maxas,</foreign> <emph type="italics"/>qui in medio<emph.end type="italics"/> <foreign lang="greek"><gap/>ou_tas,</foreign><lb/><emph type="italics"/>qui in &longs;uperiore<emph.end type="italics"/> <foreign lang="greek"><gap/>ani_tas</foreign> <emph type="italics"/>appellatos fui&longs;&longs;e. V nde nonnulli exi&longs;tima<lb/>runt fui&longs;&longs;e naues, quæ in parte laterali &longs;upra aquas eminente, tria fo<lb/>ramina<emph.end type="italics"/> <foreign lang="greek">xa<gap/>) i)/sin</foreign> <emph type="italics"/>eius partis habui&longs;&longs;e, <expan abbr="quor&utilde;">quorum</expan> &longs;ingula &longs;uum remum <lb/>haberet alligatum. Vnde cum hiremi &longs;itu pro differentia loci &longs;ur<lb/>&longs;um & deor&longs;um e&longs;&longs;ent di&longs;tincti: ita quoque &longs;uos remiges haberen<gap/><lb/>di&longs;tinctos: &longs;ed eam mentem non fui&longs;&longs;e &longs;cholia&longs;tis illius indicat, <lb/>quod paulò pò&longs;t &longs;ubiunxit.<emph.end type="italics"/> <foreign lang="greek"><gap/>ani/ths )<gap/>,</foreign> <emph type="italics"/>inquit<emph.end type="italics"/> <foreign lang="greek">o( w_ro\s ti/w\ w_ru/mnan, <lb/><gap/>ugi/ths o( meoos, <gap/>alami/ths o( w_ro\s ti/w\ w_rw/<gap/>an.</foreign> <emph type="italics"/>Thranites e&longs;t is, <lb/>qui ad puppim remigat, Zygites qui in media naui, Thalamites qui <lb/>ad proram, vbi manife&longs;tè &longs;uperiorem nauis partem explicat ad pup<lb/>pim in qua &longs;edet gubernator, vt quæ altior e&longs;t: inferiorem ad proram, <lb/>quæ inferior e&longs;t, ne gubernatoris ob&longs;truat luminibus: ideo inter istos <lb/><gap/>gitæ &longs;unt, quos hic Ari&longs;toteles vocabulo compo&longs;ito<emph.end type="italics"/> <foreign lang="greek">e)x meoh_s kai\ <lb/>ne/ws</foreign> <emph type="italics"/>vocat me&longs;oneos. Sed hic non leuis obrepit controuer &longs;ia, & pro<lb/>pter præ&longs;entem Ari&longs;totelis contextumante di&longs;&longs;oluenda, &longs;i pote&longs;t, ex <lb/>duobus locis, altero Thucydidis, altero Galeni. Ille enim li. 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. Hic verò cap. 24. lib. 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. Galen. citato, vt manus digiti inæ quales &longs;unt, <lb/>& medius longißimus ad firmam rerum apprehen &longs;ionem, & ap<lb/>prehen&longs;arum retentionem, quod illius munus e&longs;t, quod non aliter fit <lb/>quam quum digitorum extremitates ad æqualitatem perueniunt: &longs;ic <lb/>ob nauigationis perfectionem in valido & faciliori nauis, quâ prora <lb/>&longs;pectat impul&longs;u po&longs;itam, remi facti &longs;unt inæquales, & corum me<lb/>dius maximus: & horum quidem i&longs;ta inæqualitas ob eandem cau<lb/>&longs;am, vt &longs;cilicet remorum extremitates &longs;imul omnes in remigatione <lb/>ad æqualitatem peruenirent. Ex his locis <expan abbr="vtriq;">vtrique</expan> conueniunt eiu&longs;dem <lb/>lateris remos e&longs;&longs;e inæquales: &longs;ed in hoc in &longs;igniter di&longs;crepant, quod <lb/>Galenus a&longs;&longs;erat medios, id e&longs;t remos Zygitarum, &longs;eu<emph.end type="italics"/> <foreign lang="greek">meoune/wn</foreign> <emph type="italics"/>e&longs;&longs;e <lb/>maximos: Ari&longs;toteles non hos, &longs;ed <expan abbr="Thranitar&utilde;">Thranitarum</expan>. Et <expan abbr="ver&utilde;">verum</expan> dicere Gale<lb/>num cogno&longs;cemus &longs;i prius intellexerimus quomodo remorum extre<lb/>mitates in remigationis ictu ad æqualitatem perueniant. 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/>

<arrow.to.target n="fig25"></arrow.to.target><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/>Sed &longs;i &longs;ic præterquam <lb/>quod Thalamitarum <lb/>Zygitarum & Thra-<emph.end type="italics"/>

<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/>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. I. elem. Eucl. quod <lb/>e&longs;t contra omnium &longs;ententiam, nauigatio e&longs;&longs;et valde impedita, eo <lb/>quod cum aqua ante nauim immota, ideoque difficilius cedens: tum <lb/>po&longs;t nauim etiam immota, minimeque eo rediens non compelleret. <lb/>Moueretur enim aqua &longs;ecundum rectam E F remorum extremita<lb/>tes excipientem. Po&longs;terior igitur e&longs;t &longs;i de&longs;inant &longs;ecundum lineam pa<lb/>rallelam &longs;pondæ nauis quæ &longs;emper e&longs;t<emph.end type="italics"/> <foreign lang="greek">w_<gap/>e<gap/>xoeidh\s.</foreign> <emph type="italics"/>Sic enim <lb/>Galenus <expan abbr="digitor&utilde;">digitorum</expan> corpus valde <expan abbr="&longs;phæric&utilde;">&longs;phæricum</expan> omnium à manu <expan abbr="appreh&etilde;-dendor&utilde;">apprehen<lb/>dendorum</expan> <expan abbr="difficillim&utilde;">difficillimum</expan>, <expan abbr="apprehendenti&utilde;">apprehendentium</expan> extremitates vult de &longs;inere in <lb/>eandem circuli ip&longs;um &longs;ecantis <expan abbr="peripheriã">peripheriam</expan>. Quomodo &longs;i pro E F recta <lb/>con&longs;tituamus pe-<emph.end type="italics"/><lb/>

<arrow.to.target n="fig26"></arrow.to.target><lb/><emph type="italics"/><expan abbr="riphericã">riphericam</expan> Q L N <lb/>P R ad quam <expan abbr="de-&longs;inãt">de<lb/>&longs;inant</expan> prædicti re<lb/>mi, non &longs;olum re<lb/>morum erit inæ<lb/>qualitas, & me<lb/>dius erit maxi<lb/>mus, vt in manu <lb/>digitus medius: <lb/>&longs;ed & nauigatio <lb/>facilius procedet <lb/>propter <expan abbr="cõtrarias">contrarias</expan> <lb/>cau&longs;as, quippè ve<lb/>luti circulationes <lb/><expan abbr="vndar&utilde;">vndarum</expan> circa na<lb/>uim fient, vnde <lb/>quæ ante e&longs;t pro<lb/>pul&longs;a aqua viam <lb/>aperiet nauigio, <lb/>& retro compre&longs;&longs;a, comprimen&longs; que nauigium propellet. 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. Sic enim <lb/>æquales &longs;unt G K, S M, I O prop. 33. & 34. lib. 1. æquales item <lb/>propter paralleli&longs;mum G L, H N, & I P. totæ igitur ex his <lb/>æquales axiom. 2. lib. 1. & ad earum vnam nempe ex S M, H N<emph.end type="italics"/>

<figure id="fig26"></figure><lb/><emph type="italics"/><expan abbr="riphericã">riphericam</expan> Q L N <lb/>P R ad quam <expan abbr="de-&longs;inãt">de<lb/>&longs;inant</expan> prædicti re<lb/>mi, non &longs;olum re<lb/>morum erit inæ<lb/>qualitas, & me<lb/>dius erit maxi<lb/>mus, vt in manu <lb/>digitus medius: <lb/>&longs;ed & nauigatio <lb/>facilius procedet <lb/>propter <expan abbr="cõtrarias">contrarias</expan> <lb/>cau&longs;as, quippè ve<lb/>luti circulationes <lb/><expan abbr="vndar&utilde;">vndarum</expan> circa na<lb/>uim fient, vnde <lb/>quæ ante e&longs;t pro<lb/>pul&longs;a aqua viam <lb/>aperiet nauigio, <lb/>& retro compre&longs;&longs;a, comprimen&longs; que nauigium propellet. 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. Sic enim <lb/>æquales &longs;unt G K, S M, I O prop. 33. & 34. lib. 1. æquales item <lb/>propter paralleli&longs;mum G L, H N, & I P. totæ igitur ex his <lb/>æquales axiom. 2. lib. 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. 4. Ergo maximus, quod <lb/>fuit probandum. Dicemus igitur &longs;cholia&longs;tis & Thucydidis locos <lb/>debere intelligi, non de totis remis: &longs;ed remorum partibus, quæ &longs;unt à <lb/>&longs;calmo ad mare proportione habita ad eas partes, quæ &longs;unt à &longs;calmo <lb/>ad manubrium. Thranitæ enim remus à &longs;calmo ad <expan abbr="extrem&utilde;">extremum</expan> palmu<lb/>læ maiorem longè rationem habet ad partem, quæ e&longs;t ab eodem &longs;cal<lb/>mo ad manubrium, id e&longs;t I P ad I O: quam zygitæ pars H N ad <lb/>partem H S M vt docebitur po&longs;tea. Et ea e&longs;t cau&longs;a cur zygites fa<lb/>cilius & plus promoueat nauim: contra Thranites laborio&longs;ius & <lb/>minus, vt docebitur etiam. Atque &longs;ic &longs;int hi duo loci meo iudicio ex<lb/>plicati. Cæterum Remiges, vt & hoc notatu pulchrum adÿciamus, <lb/>Remigando artificiosè &longs;imul omnes, quamuis quater mille, inter &longs;e <lb/>con&longs;entientes, alioqui illis corium fiagris tam fit maculo&longs;um quam <lb/>nutricis pallium, vel cur&longs;um nauis accelerant, vel inhibent, vel &longs;u&longs;ti<lb/>nent, & vt ait Poeta,<emph.end type="italics"/></s>

<s>Intentaque brachia remís</s>

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<s>Theorema. <emph type="italics"/>Si chorda rectas in circulo in&longs;criptas ad rectos &longs;e<lb/>cet: &longs;ectarum pars, quæ de diametro ab&longs;cinditur, e&longs;t maxima, reli<lb/>quarum quæ diametro propinquior remotiore maior e&longs;t. E&longs;to circu<lb/>lus A D B E, in quo rectam A B diametrum &longs;ecet chorda D <lb/>E ad rectos vt & K I, L H: & &longs;int &longs;egmenta C B, è dia<lb/>metro: F I è propinquiore: G H è remotiore. Dico C B e&longs;&longs;e <lb/>maiorem quam F I: & F I quam G H. Per punctum M cen<lb/>trum circuli repertum prop. 1. lib. 3. ducatur parallela M N O P<emph.end type="italics"/>

<pb pagenum="69"/><emph type="italics"/>rectæ C D prop. 31. lib. 1. &longs;icque parallelogramma &longs;unt O F &<emph.end type="italics"/><lb/>

<arrow.to.target n="fig27"></arrow.to.target><lb/><emph type="italics"/>N C. 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. 3. harum <lb/>quoque dimidiæ M B, N I, O <lb/>H prop. 3. lib. eiu&longs;dem erunt in<lb/>æquales & M B maior quam <lb/>N I, & N I quam O H. 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. 1. reliquæ C| B, <lb/>F I, G H erunt iuæquales ax. 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. Igitur &longs;i chorda rectas, &c. quod fuit <expan abbr="demon&longs;trand&utilde;">demon&longs;trandum</expan>.<emph.end type="italics"/></s>

<figure id="fig27"></figure><lb/><emph type="italics"/>N C. 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. 3. harum <lb/>quoque dimidiæ M B, N I, O <lb/>H prop. 3. lib. eiu&longs;dem erunt in<lb/>æquales & M B maior quam <lb/>N I, & N I quam O H. 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. 1. reliquæ C| B, <lb/>F I, G H erunt iuæquales ax. 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. Igitur &longs;i chorda rectas, &c. quod fuit <expan abbr="demon&longs;trand&utilde;">demon&longs;trandum</expan>.<emph.end type="italics"/></s>

<s>Itaque mouetur nauis.] <emph type="italics"/>Cau&longs;a efficiens motum nauis actua<lb/>riæ, & modus quo efficitur, hic exprimitur e&longs;&longs;e impul&longs;io remi à re<lb/>mige, mouente animato. Modus e&longs;t cum remi palmula aquam ingre&longs;<lb/>&longs;a, & aquæ ob &longs;ui copiam, tanquam &longs;olo, firmiter renitenti innixu <lb/>manubrium antror&longs;um propellitur à remige, & proinde totus remus <lb/>vnum continuum & validum inflexileque exi&longs;tens, excepto palmu<lb/>læ extremo quod ob aquæ renixum vtcumque immobile manet, & <lb/>per con&longs;equens alligata remo, eò quò manubrium, promouentur. <lb/>Nauis autem per &longs;calmum alligata e&longs;t remo. Nauis igitur promouebi<lb/>tur antror&longs;um, &longs;i eò manubrium <expan abbr="promot&utilde;">promotum</expan> &longs;it. Dixi &longs;i eò manubrium <lb/>promotum &longs;it, quia concitato nauigio, quum remiges inhibent, contra <lb/>fit. Manubrium &longs;iquidem mouetur retror&longs;um, proinde vna cum eo <lb/>& nauis. Ad huius rei fidem locus e&longs;t apud Tullium luculentus. <lb/>Nunc vt ad rem redeam, inquit, inhibere illud tuum, quod valde <lb/>mihi arri&longs;erat, vehementer di&longs;plicet. E&longs;t enim verbum totum nauti<lb/>cum: quanquam id quidem &longs;ciebam: &longs;ed arbitrabar &longs;u&longs;tineri remos, <lb/>quum inhibere e&longs;&longs;ent remiges iußi. Id non e&longs;&longs;e eiu&longs;modi, didici heri, <lb/>quum ad villam no&longs;tram nauis appelleretur: non enim &longs;u&longs;tinent, &longs;ed <lb/>alio modo remigant, id ab<emph.end type="italics"/> <foreign lang="greek">e)poxh_s</foreign> <emph type="italics"/>remotißimum e&longs;t. Et po&longs;tea &longs;ubdit. <lb/>Inhibitio autem remigum motum habet, & <expan abbr="vehem&etilde;tiorem">vehementiorem</expan> quidem<emph.end type="italics"/>

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<s><emph type="italics"/>Si duo I&longs;o&longs;celia æqualia angulis, inæqualium crurum fuerint: <lb/>erunt & inæqualia<emph.end type="italics"/><lb/>

<arrow.to.target n="fig28"></arrow.to.target><lb/><emph type="italics"/>ba&longs;ibus: & huius ba<lb/>&longs;is maior, cuius crura <lb/>maiora. Sint A B E <lb/>& A D C duo i&longs;o&longs;<lb/>celia æqualia angulis <lb/>qui ad A, & A D <lb/>crus e&longs;to maius crure <lb/>A B &longs;icut & A C <lb/>ip&longs;o A E. Dico ba&longs;im D C maiorem e&longs;&longs;e ba&longs;i B E. Nam quia<emph.end type="italics"/>

<figure id="fig28"></figure><lb/><emph type="italics"/>ba&longs;ibus: & huius ba<lb/>&longs;is maior, cuius crura <lb/>maiora. Sint A B E <lb/>& A D C duo i&longs;o&longs;<lb/>celia æqualia angulis <lb/>qui ad A, & A D <lb/>crus e&longs;to maius crure <lb/>A B &longs;icut & A C <lb/>ip&longs;o A E. Dico ba&longs;im D C maiorem e&longs;&longs;e ba&longs;i B E. Nam quia<emph.end type="italics"/>

<pb pagenum="79"/><emph type="italics"/>tres anguli vnius triangulorum &longs;unt æquales tribus alterius prop. <lb/>32. lib. 1. & anguli qui ad A æquales ex hypothe&longs;i, anguli ad ba<lb/>&longs;im duo duobus &longs;unt æquales ax. 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. 1. & per <lb/>eandem anguli A B E & A E B. 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. 6. & per idem reliquus reliquo. Sunt igitur A B E & <lb/>A D C triangula æquiangula, proinde circum æquales angulos la<lb/>tera habebunt proportionalia. prop. 4. lib. 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. 16. lib. 5. E&longs;t autem maius A D ip&longs;o A B <lb/>ex hypothe&longs;i. Ergo Ba&longs;is D C maior erit ip&longs;a B E. Igitur &longs;i duo <lb/>I&longs;o&longs;celia æqualia angulis, inæqualia cruribus fuerint &c. quod <lb/>fuit demonstrandum.<emph.end type="italics"/></s>

<s><emph type="italics"/>Patet igitur ex his quod cum B C &longs;it vt longitudo nauis, &longs;i pup<lb/>pis B peruenerit ad E manente A cardine. Tunc C erit in D. <lb/>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. 1. Et inæqualia cruri<lb/>bus. 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. Peragrabit igitur prora D lineam C B <lb/>longè maiorem, cum B peragrabit B E multo minorem.<emph.end type="italics"/></s>

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<s><emph type="italics"/>Hoc autem quanquam verum &longs;it, quor&longs;um tamen, dubium e&longs;t. <lb/>Exi&longs;timauit Nonius ideò hîc po&longs;itum e&longs;&longs;e, vt o&longs;tendatur B per remi-<emph.end type="italics"/><lb/>

<arrow.to.target n="fig29"></arrow.to.target><lb/><emph type="italics"/>gationem factam, non e&longs;&longs;e <lb/>in E: &longs;ed vltra vt in K, <lb/>vnde nouam hane de&longs;cri<lb/>bit figuram. qua demon<lb/>&longs;trat cum A caput remi <lb/>remigatione facta e&longs;t in <lb/>D, palmulam B remi A <lb/>B e&longs;&longs;e non in E: &longs;ed in K <lb/>vltra E. Nihilominu&longs;que <lb/>B K motum palmulæ B <lb/>retror&longs;um minorem e&longs;&longs;e A <lb/>D motu capitis A an<lb/>tror&longs;um, &longs;ecundum &longs;enten<lb/>tiam Ari&longs;totelis. Et &longs;ic <lb/>Nonius remigatione facta <lb/>& tran&longs;uecta naui ponit <lb/>&longs;calmum C tran&longs;uectum e&longs;&longs;e in T: vel ex &longs;uperiori Victoris figura<emph.end type="italics"/>

<figure id="fig29"></figure><lb/><emph type="italics"/>gationem factam, non e&longs;&longs;e <lb/>in E: &longs;ed vltra vt in K, <lb/>vnde nouam hane de&longs;cri<lb/>bit figuram. qua demon<lb/>&longs;trat cum A caput remi <lb/>remigatione facta e&longs;t in <lb/>D, palmulam B remi A <lb/>B e&longs;&longs;e non in E: &longs;ed in K <lb/>vltra E. Nihilominu&longs;que <lb/>B K motum palmulæ B <lb/>retror&longs;um minorem e&longs;&longs;e A <lb/>D motu capitis A an<lb/>tror&longs;um, &longs;ecundum &longs;enten<lb/>tiam Ari&longs;totelis. Et &longs;ic <lb/>Nonius remigatione facta <lb/>& tran&longs;uecta naui ponit <lb/>&longs;calmum C tran&longs;uectum e&longs;&longs;e in T: vel ex &longs;uperiori Victoris figura<emph.end type="italics"/>

<pb pagenum="83"/><emph type="italics"/>ex<emph.end type="italics"/> <foreign lang="greek">g</foreign> <emph type="italics"/>in<emph.end type="italics"/> <foreign lang="greek"><expan abbr="q.">que</expan></foreign> <emph type="italics"/>Sed &longs;i &longs;ice&longs;&longs;et, T idem &longs;calmus qui C, propior cum &longs;it <lb/>aquæ: quam ip&longs;e C, &longs;equeretur vt in vnius remigationis principio, <lb/>medio, fine nauis plus & minus mergeretur. quod &longs;i quando fiat, fit <lb/>exaccidenti, nec citra naufragÿ periculum: imo vero &longs;ic non tam <lb/>nauis ferretur antror&longs;um: quam in profundum. 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/>

<arrow.to.target n="fig30"></arrow.to.target><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. Et quidem cum anguli qui ad E &longs;int &longs;emper <lb/>æquales prop. 15. lib. 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. 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. vt in figuræ no&longs;træ pun<lb/>cto F. Sicque caput A multo anterius latum erit, quam B retrò. <lb/>E&longs;t enim A F maior quam A D axiom. 9. quæ demon&longs;trata e&longs;t<emph.end type="italics"/>

<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. Et quidem cum anguli qui ad E &longs;int &longs;emper <lb/>æquales prop. 15. lib. 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. 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. vt in figuræ no&longs;træ pun<lb/>cto F. Sicque caput A multo anterius latum erit, quam B retrò. <lb/>E&longs;t enim A F maior quam A D axiom. 9. quæ demon&longs;trata e&longs;t<emph.end type="italics"/>

<arrow.to.target n="fig31"></arrow.to.target><lb/><emph type="italics"/>e&longs;&longs;e maior ip&longs;a B E: &longs;ic <lb/>etiam C &longs;calmus erit in O, <lb/>æquedi&longs;tanter cum C ab <lb/>aqua. quod fieri oportet in <lb/>artificio&longs;a & pro&longs;pera na<lb/>uigatione. An &longs;ic rectè <lb/>&longs;entiamus aliorum e&longs;to iu<lb/>dicium: &longs;ed in hoc conueni<lb/>mus cum Nonio quod remi <lb/>motus in vna remigatione <lb/>duplex e&longs;t: proprius, & alie<lb/>nus: & ille quidem circularis circa &longs;calmum tanquam centrum, <lb/>cuius motus &longs;calmus expers e&longs;t: hic vero contingit & ob motum <lb/>&longs;calmi delati vna cum nauigio. Et quod totus motus remi ex his duo<lb/>bus maior e&longs;t motu nauigÿ. Sed & cætera quæ in hoc problema <lb/>animaduertit & annotauit Nonius. Hîc &longs;ubÿciemus.<emph.end type="italics"/></s>

<figure id="fig31"></figure><lb/><emph type="italics"/>e&longs;&longs;e maior ip&longs;a B E: &longs;ic <lb/>etiam C &longs;calmus erit in O, <lb/>æquedi&longs;tanter cum C ab <lb/>aqua. quod fieri oportet in <lb/>artificio&longs;a & pro&longs;pera na<lb/>uigatione. An &longs;ic rectè <lb/>&longs;entiamus aliorum e&longs;to iu<lb/>dicium: &longs;ed in hoc conueni<lb/>mus cum Nonio quod remi <lb/>motus in vna remigatione <lb/>duplex e&longs;t: proprius, & alie<lb/>nus: & ille quidem circularis circa &longs;calmum tanquam centrum, <lb/>cuius motus &longs;calmus expers e&longs;t: hic vero contingit & ob motum <lb/>&longs;calmi delati vna cum nauigio. Et quod totus motus remi ex his duo<lb/>bus maior e&longs;t motu nauigÿ. Sed & cætera quæ in hoc problema <lb/>animaduertit & annotauit Nonius. Hîc &longs;ubÿciemus.<emph.end type="italics"/></s>

<s><emph type="italics"/>Primum dicit Ari&longs;totelis ratiocinationem ob&longs;curam e&longs;&longs;e.<emph.end type="italics"/></s>

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<s><emph type="italics"/>In&longs;uper Nonius a&longs;&longs;erit nauim interdum maius &longs;patium percurrere:<emph.end type="italics"/><lb/>

<arrow.to.target n="fig32"></arrow.to.target><lb/><emph type="italics"/>quam caput remi: interdum minus, iuxta <lb/>remigum vires, & provt mariremi pal<lb/>mula immer&longs;a fuerit: Quæ omnia vt con<lb/>&longs;picua fiant, demon&longs;trat quinque <expan abbr="&longs;equ&etilde;tes">&longs;equentes</expan> <lb/>propo&longs;itiones.<emph.end type="italics"/></s>

<figure id="fig32"></figure><lb/><emph type="italics"/>quam caput remi: interdum minus, iuxta <lb/>remigum vires, & provt mariremi pal<lb/>mula immer&longs;a fuerit: Quæ omnia vt con<lb/>&longs;picua fiant, demon&longs;trat quinque <expan abbr="&longs;equ&etilde;tes">&longs;equentes</expan> <lb/>propo&longs;itiones.<emph.end type="italics"/></s>

<s>Propo&longs;itio prima.</s>

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<s><emph type="italics"/>Ante remigationem remi existentis in &longs;calmo B &longs;it nauis prora C <lb/>po&longs;t remigationem &longs;it B<emph.end type="italics"/><lb/>

<arrow.to.target n="fig33"></arrow.to.target><lb/><emph type="italics"/>in E & prora in D &longs;ic<lb/>que C D erit nauis pro<lb/>motio, & B E &longs;calmi. <lb/>Dico igitur C D & B E æquales, quia reliquæ &longs;unt ex æqualibus <lb/>B C, E D dempto communi E C axio. 3. Ergo nauis tantùm de<lb/>currit quantùm &longs;calmus.<emph.end type="italics"/></s>

<figure id="fig33"></figure><lb/><emph type="italics"/>in E & prora in D &longs;ic<lb/>que C D erit nauis pro<lb/>motio, & B E &longs;calmi. <lb/>Dico igitur C D & B E æquales, quia reliquæ &longs;unt ex æqualibus <lb/>B C, E D dempto communi E C axio. 3. Ergo nauis tantùm de<lb/>currit quantùm &longs;calmus.<emph.end type="italics"/></s>

<s>Propo&longs;itio &longs;ecunda.</s>

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<s><emph type="italics"/>Inter hos duo &longs;unt medÿ, vnus tran&longs;uer&longs;us ad latera nauis perpendi<lb/>culariter incidens: alter obliquus <lb/>

<arrow.to.target n="fig34"></arrow.to.target><lb/>qui medius e&longs;t inter &longs;ecundum & <lb/>tran&longs;uer&longs;um, velinter aduer&longs;um & <lb/>tran&longs;uer&longs;um. Vt e&longs;to nauis G H, <lb/>& prora &longs;it G puppis H, ventus <lb/>ex B &longs;ecundus erit, ex A aduer<lb/>&longs;us, ex C vel D tran&longs;uer&longs;us, ex E <lb/>vel F obliquus. Horum autem mo<lb/>tuum Galenus obliquos per pulchrè<emph.end type="italics"/>

<figure id="fig34"></figure><lb/>qui medius e&longs;t inter &longs;ecundum & <lb/>tran&longs;uer&longs;um, velinter aduer&longs;um & <lb/>tran&longs;uer&longs;um. Vt e&longs;to nauis G H, <lb/>& prora &longs;it G puppis H, ventus <lb/>ex B &longs;ecundus erit, ex A aduer<lb/>&longs;us, ex C vel D tran&longs;uer&longs;us, ex E <lb/>vel F obliquus. Horum autem mo<lb/>tuum Galenus obliquos per pulchrè<emph.end type="italics"/>

<pb pagenum="97"/><emph type="italics"/>declarauit &longs;umpta primùm hac propo&longs;itione. In vniuer&longs;um quando <lb/>à duobus motibus ex tran&longs;uer&longs;o &longs;ibi inuicem occurrentibus trahitur <lb/>corpus, &longs;i multò quidem &longs;upereminet alter, nece&longs;&longs;arium e&longs;t ob&longs;curari, <lb/>di&longs;pareréue reliquum: pauca verò cum e&longs;t exuperantia alterius: aut <lb/>ambo æqualiter po&longs;&longs;unt, mixtum ex vtri&longs;que fieri eum corporis mo<lb/>tum oportet. Videntur autem omnia i&longs;ta propemodum quotidie in <lb/>&longs;excentis exemplis, exempli gratia in remigantibus, &longs;imul & naui<lb/>bus ventum tran&longs;uer&longs;um habentibus. Si enim æquipollet venti & <lb/>remigantium robur, mixtum fieri motum nece&longs;&longs;e e&longs;t. Cum neque <lb/>antror&longs;um &longs;olum, neque ad tran&longs;uer&longs;um naues ferantur, &longs;ed ad am<lb/>borum medium (vbi malè legitur Medicum) &longs;i vero remigantium <lb/>robur maius fuerit, antror&longs;um magis, quam ad tran&longs;uer&longs;um. Si au<lb/>tem venti violentia vincat, ad tran&longs;uer&longs;um magis, quam antror<lb/>&longs;um. Multus autem &longs;i fuerit exce&longs;&longs;us, adeo vt alterius vires omnino <lb/>vincantur, nauigantium quidem ob&longs;curatis viribus, ad tran&longs;uer<lb/>&longs;um: venti vero, antror&longs;um magis naues ferentur. Quid tandem &longs;i <lb/>tenuis omnino aura fuerit, nauis verò prælonga, & leuis, quamplu<lb/>rimos habens nautas, poterit aliquando motus ab aura e&longs;&longs;e manife<lb/>&longs;tus? 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. cap. 19. lib. 1. de v&longs;. partium.<emph.end type="italics"/></s>

<s>An quia gubernaculum.] <emph type="italics"/>Solutio e&longs;t problematis propo&longs;iti, <lb/>quod &longs;ic fiet euidentius. Cur qui è cornu nauigaturi vento &longs;cilicet <lb/>non &longs;ecundo exi&longs;tente: &longs;ed obliquo vel tran&longs;uer&longs;o eam veli partem, <lb/>quæ ver&longs;us gubernatorem e&longs;t, contrahunt id e&longs;t &longs;tringunt, & circa <lb/>antemnam implicant. Eam vero, quæ ad proram, relaxant, quod ap<lb/>pellant pedem facere. Re&longs;pon&longs;io. Quia obliquè vel tran&longs;uer&longs;im naui<lb/>gari non pote&longs;t, ni&longs;i tunc gubernaculum auertat, atque obliquet na<lb/>uim. Eò enim fertur nauis, quò prora dirigitur. Obliquare autem <lb/>nauim vel tran&longs;uertere tantò facilius gubernaculum pote&longs;t: quantò <lb/>ventus paucior e&longs;t. Paucior autem fit contracto velo, quod &longs;pectat ad <lb/>puppim, & relaxato eo quod e&longs;t ad proram. Sufficiens tamen pro<lb/>pellere. Obliquus enim veli relaxati &longs;inubus totis excipitur. I deo <expan abbr="c&utilde;">cum</expan> <lb/>& &longs;ufficiat gubernaculum auertere atque propellere mare, vocatis <lb/>ad id in auxilium, &longs;i opus e&longs;t, nautis in contrariam vento partem ni<lb/>tentibus, fit vt ex obliquo vel tran&longs;uer&longs;o vento feratur nauis. Sic<emph.end type="italics"/>

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<s>At &longs;i rectilineum e&longs;&longs;et.] <emph type="italics"/>Difficultas motus in mobili pendet <lb/>ab eius internis aut externis. Interna e&longs;t naturalis cuiu&longs;que <expan abbr="prop&etilde;&longs;io">propen&longs;io</expan>, <lb/>qua extra locum exi&longs;tens, &longs;i liberum &longs;inatur mobile, ad <expan abbr="e&utilde;">eum</expan> per &longs;e fe<lb/>ratur. Atque vt ibi vi retineatur, eò tamen quodam motu occulro <lb/>tendit, vt graue deor&longs;um, leue &longs;ur&longs;um, & &longs;emper &longs;ecundum rectam <lb/>perpendicularem in qua e&longs;t centrum grauitatis mobilis: aliò nun<lb/>quam, ni&longs;i vi contraria nixus ille vincatur, vt cum graue &longs;ur&longs;um: <lb/>aut leue deor&longs;um: aut vtrumque ad latera propellitur. Itaque prima<emph.end type="italics"/>

<pb pagenum="102"/><emph type="italics"/>difficultas in <expan abbr="viol&etilde;tis">violentis</expan> pendet è renixu. Externa vero &longs;unt <expan abbr="&longs;ubiect&utilde;">&longs;ubiectum</expan>, <lb/>& occur&longs;ans, & mobilis figura. Subiectum appello, cui mobile &longs;u<lb/>perincumbit, aut primo in&longs;i&longs;tit, & huic tantò magis qua &longs;i inhæret <lb/>& in&longs;i&longs;tit: quantò pluribus punctis ab eo &longs;imul tangitur. Tot enim <lb/>&longs;unt lineæ in mobili ad rectos angulos in&longs;i&longs;tentes &longs;ubiecto, quæ vt <lb/>vires vnitæ &longs;e mutuo &longs;tabiliunt, & fulciunt, ne facile deÿciantur: <lb/>contrà id, quod antè de Sphærico, vbi cum vna e&longs;&longs;et <expan abbr="tãtum">tantum</expan> quæ in<lb/>&longs;i&longs;teret plano ad rectos, facillima ab illo &longs;tatu erat deiectio. Maior <lb/>igitur inhærentia, maius e&longs;t impedimentum. Occur&longs;ans autem dico <lb/>quodlibet corpus aliud, vel contra motum, vel cum locum ibi habe<lb/>at, minimè <expan abbr="ced&etilde;s">cedens</expan>. Talia &longs;unt fortuita omnia, quæ vt &longs;ubiectum, quò <lb/>pluribus mobilis punctis occurrunt propter eandem cau&longs;am, eò plus. <lb/>ne fiat inuer&longs;io vel volutatio, impediunt. Tale quoque medium e&longs;t <lb/>nece&longs;&longs;arium, per quod fit motus, <expan abbr="rar&utilde;">rarum</expan>, den&longs;um, vtrumque impariter. <lb/>Hoc enim magis, illud minus: re&longs;i&longs;tit partibus obuijs. Re&longs;i&longs;tens in<lb/>&longs;uper ob loci, in quo e&longs;t, <expan abbr="&longs;eruãdi">&longs;eruandi</expan> cupiditatem naturalem, & etiam, ne <lb/>admittatur vacuum. Mobilis denique figura quæ quò propius ac<lb/>cedit ad &longs;phæricam vt mobilißimam, eò ad motum pronior: contra <lb/>quò remotior. Atque ea &longs;unt impedimenta, quorum duo &longs;ublatis for<lb/>tuitis è figurarum &longs;uperficialibus rectilineæ, è &longs;olidis cubo in&longs;unt. <lb/>Sit enim <lb/>ABCD <lb/>

<arrow.to.target n="fig35"></arrow.to.target><lb/><expan abbr="rectili-ne&utilde;">rectili<lb/>neum</expan> pla<lb/>no E F <lb/><expan abbr="in&longs;i&longs;t&etilde;s">in&longs;i&longs;tens</expan>, <lb/>& <expan abbr="qui-d&etilde;">qui<lb/>dem</expan> &longs;ina<lb/>turale e&longs;t <lb/>in&longs;ita grauitate verget ver&longs;us G, & ad rectos in&longs;i&longs;tet rectis A C <lb/>& B D & omnibus inter illas interiectis vt H I, K L, M N, <lb/>&longs;icque totidem momentis ver&longs;us G contendit. Præterea aër vel <lb/>aqua medium occurrens lateri A C, quantum in &longs;e, e&longs;t impedit tot <lb/>punctis, quot &longs;unt in A C.<emph.end type="italics"/></s>

<figure id="fig35"></figure><lb/><expan abbr="rectili-ne&utilde;">rectili<lb/>neum</expan> pla<lb/>no E F <lb/><expan abbr="in&longs;i&longs;t&etilde;s">in&longs;i&longs;tens</expan>, <lb/>& <expan abbr="qui-d&etilde;">qui<lb/>dem</expan> &longs;ina<lb/>turale e&longs;t <lb/>in&longs;ita grauitate verget ver&longs;us G, & ad rectos in&longs;i&longs;tet rectis A C <lb/>& B D & omnibus inter illas interiectis vt H I, K L, M N, <lb/>&longs;icque totidem momentis ver&longs;us G contendit. Præterea aër vel <lb/>aqua medium occurrens lateri A C, quantum in &longs;e, e&longs;t impedit tot <lb/>punctis, quot &longs;unt in A C.<emph.end type="italics"/></s>

<s><emph type="italics"/>Sit & cubus A D, planum K L, vna &longs;uperficierum &longs;uarum <lb/>E D attingens, tum habeat rectas A E, C F, B D, H G, ad<emph.end type="italics"/>

<pb pagenum="103"/><emph type="italics"/>rectos in&longs;i&longs;ten-<emph.end type="italics"/><lb/>

<arrow.to.target n="fig36"></arrow.to.target><lb/><emph type="italics"/>tes, vt totidem <lb/>alias, quot &longs;unt <lb/>puncta in &longs;u<lb/>perficie E D <lb/>nixu naturali <lb/>coniunctæ. Tot <lb/>vires nullo <expan abbr="t&etilde;-poris">ten<lb/>poris</expan> momento alio inclinantes &longs;e à &longs;uo &longs;tatu dimoueri &longs;inent: medio <lb/>etiam obuio &longs;eu aëre, &longs;eu aqua totidem ad latus punctis propter æqua<lb/>litatem &longs;uperficierum impediente. Ex quo fit vt figurarum planum <lb/>pro vertice habentium &longs;tabilißima dicatur cubus. Et quia talis e&longs;t, <lb/>eius figuram Plato affinxit terræ in loco &longs;uo pror&longs;us immobili. Ob id <lb/>etiam pictores <expan abbr="Virtut&etilde;">Virtutem</expan> quæ &longs;olacon&longs;tans e&longs;t animi &longs;tatus, vel etiam <lb/>Mercurium qui &longs;uos &longs;ectatores numquam de&longs;erit cubo in&longs;identem <lb/>repræ&longs;entant: &longs;icut ob contrariam cau&longs;am Fortunam.<emph.end type="italics"/></s>

<figure id="fig36"></figure><lb/><emph type="italics"/>tes, vt totidem <lb/>alias, quot &longs;unt <lb/>puncta in &longs;u<lb/>perficie E D <lb/>nixu naturali <lb/>coniunctæ. Tot <lb/>vires nullo <expan abbr="t&etilde;-poris">ten<lb/>poris</expan> momento alio inclinantes &longs;e à &longs;uo &longs;tatu dimoueri &longs;inent: medio <lb/>etiam obuio &longs;eu aëre, &longs;eu aqua totidem ad latus punctis propter æqua<lb/>litatem &longs;uperficierum impediente. Ex quo fit vt figurarum planum <lb/>pro vertice habentium &longs;tabilißima dicatur cubus. Et quia talis e&longs;t, <lb/>eius figuram Plato affinxit terræ in loco &longs;uo pror&longs;us immobili. Ob id <lb/>etiam pictores <expan abbr="Virtut&etilde;">Virtutem</expan> quæ &longs;olacon&longs;tans e&longs;t animi &longs;tatus, vel etiam <lb/>Mercurium qui &longs;uos &longs;ectatores numquam de&longs;erit cubo in&longs;identem <lb/>repræ&longs;entant: &longs;icut ob contrariam cau&longs;am Fortunam.<emph.end type="italics"/></s>

<s>Quæ tantùm con&longs;tans in leuitate &longs;ua e&longs;t. <lb/><emph type="italics"/>globo mobilißimo. Sed quod ad figuram attinet quia pluribus planis <lb/>clauditur quam tetraedrum, vel pentaedrum, vt qui &longs;it hexaedrum, <lb/>& ideo propius accedit ad &longs;phæram, ad volutationem adhuc procli<lb/>uior e&longs;t, quam illa &longs;int. hinc te&longs;&longs;erarum talorumque in alueo per hanc <lb/><expan abbr="figurã">figuram</expan> planum vnum pro vertice, & planum vnum pro ba&longs;i &longs;emper <lb/><expan abbr="&longs;eruant&etilde;">&longs;eruantem</expan> ludus. Sed hîc non immeritò<emph.end type="italics"/><lb/>

<arrow.to.target n="fig37"></arrow.to.target><lb/><emph type="italics"/>quæri pote&longs;t. cur terræ &longs;tare debenti na<lb/>tura figuram attribuit &longs;phæricam, vt <lb/><expan abbr="doc&etilde;t">docent</expan> a&longs;tronomi. vnum enim e&longs;t ex <expan abbr="ar-gum&etilde;tis">ar<lb/>gumentis</expan> Copernici terram moueri pro<lb/>bare volentis. Sed id nullum locum ha<lb/>bet, quia quæ hactenus dicta &longs;unt im<lb/>pedimenta figurarum, &longs;unt <expan abbr="figurar&utilde;">figurarum</expan> in <lb/>plano <expan abbr="nõ">non</expan> <expan abbr="aut&etilde;">autem</expan> in concauo &longs;imili & <expan abbr="cõ-">con-</expan><emph.end type="italics"/><lb/>

<figure id="fig37"></figure><lb/><emph type="italics"/>quæri pote&longs;t. cur terræ &longs;tare debenti na<lb/>tura figuram attribuit &longs;phæricam, vt <lb/><expan abbr="doc&etilde;t">docent</expan> a&longs;tronomi. vnum enim e&longs;t ex <expan abbr="ar-gum&etilde;tis">ar<lb/>gumentis</expan> Copernici terram moueri pro<lb/>bare volentis. Sed id nullum locum ha<lb/>bet, quia quæ hactenus dicta &longs;unt im<lb/>pedimenta figurarum, &longs;unt <expan abbr="figurar&utilde;">figurarum</expan> in <lb/>plano <expan abbr="nõ">non</expan> <expan abbr="aut&etilde;">autem</expan> in concauo &longs;imili & <expan abbr="cõ-">con-</expan><emph.end type="italics"/><lb/>

<arrow.to.target n="fig38"></arrow.to.target><lb/><emph type="italics"/>gruenti <expan abbr="exi&longs;tenti&utilde;">exi&longs;tentium</expan>, cuiu&longs;modi e&longs;t terra, <lb/>cuiu&longs;que omnes partes <expan abbr="rot&utilde;dæ">rotundæ</expan> exi&longs;ten<lb/>tis æquabilius coniuncto nixu ad cen<lb/>trum contendunt: quam &longs;i alterius e&longs;&longs;et <lb/>cuiu&longs;cunque figuræ. Sit enim cubica <lb/>cuius centrum A & B punctum an-<emph.end type="italics"/>

<figure id="fig38"></figure><lb/><emph type="italics"/>gruenti <expan abbr="exi&longs;tenti&utilde;">exi&longs;tentium</expan>, cuiu&longs;modi e&longs;t terra, <lb/>cuiu&longs;que omnes partes <expan abbr="rot&utilde;dæ">rotundæ</expan> exi&longs;ten<lb/>tis æquabilius coniuncto nixu ad cen<lb/>trum contendunt: quam &longs;i alterius e&longs;&longs;et <lb/>cuiu&longs;cunque figuræ. Sit enim cubica <lb/>cuius centrum A & B punctum an-<emph.end type="italics"/>

<pb pagenum="104"/><emph type="italics"/>gulare, & ita remotius quam C laterale, non tanto nixu contendet: <lb/>quam ip&longs;um C. Quò enim mobile naturale propius e&longs;t, eò obnixius <lb/>incumbit. Eadem e&longs;t ratio cuiu&longs;cumque figuræ præterquam &longs;phæri<lb/>cæ, cuius puncta B, C, D, in eadem &longs;uperficie æqualiter à centro <lb/>&longs;emper di&longs;tant. Itaque terra, vt medium vndiquaque obtineret, & <lb/>vt quæ in ea omnia puncta æquali nixu ad eius centrum niteren<lb/>tur, debuit e&longs;&longs;e &longs;phærica: ob idque immobilißima e&longs;t, nullibique <lb/>nutat, contrà quam dixit Poëta,<emph.end type="italics"/></s>

<s>A&longs;pice nutantem conuexo pondere mundum. <lb/><emph type="italics"/>Nutus enim hic e&longs;t inclinatio aliò facta: quam id, à quo &longs;u&longs;penditur, <lb/>vel &longs;u&longs;tinetur, inclinet. Cuiu&longs;modi nihil e&longs;t in mundo, aut in terra: <lb/>&longs;ed omne punctum eò fertur, quò id à quo &longs;u&longs;tinetur, rectà &longs;cilicet ad <lb/>centrum, non vt D ad E, hoc enim e&longs;&longs;et contra naturam grauis, <lb/>quippe in diuer&longs;um per ambitum. Quærenti verò cur igitur c&oelig;lum <lb/>exacte &longs;phæricum moueatur. Re&longs;pondent moueri in loco non na<lb/>turaliter: &longs;ed voluntariè. Omnis enim motus naturalis e&longs;t per rectam <lb/>de centro ad locum. V oluntas illa e&longs;t intelligentiæ, quæ c&oelig;lo vt mens <lb/>corpori præe&longs;t. 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. 1. lib. 1.<emph.end type="italics"/> <foreign lang="greek">meg. <lb/>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. Intelligetur quoque quomodo illius c&oelig;li <lb/>motus &longs;it omnium motuum <expan abbr="m&etilde;&longs;ura">men&longs;ura</expan>. Nam cum men&longs;ura &longs;it in vno<lb/>quoque genere minimum, vt e&longs;t cap. 4. lib. 2. de C&oelig;l. 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>

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<s>Rectà in&longs;i&longs;tit.] <emph type="italics"/>Diameter circuli rectà in&longs;i&longs;tere in plano di<lb/>citur cum ad omnes rectas lineas à quibus tangitur in ip&longs;o plano<emph.end type="italics"/>

<pb pagenum="106"/><emph type="italics"/>rectos angulos ef-<emph.end type="italics"/><lb/>

<arrow.to.target n="fig39"></arrow.to.target><lb/><emph type="italics"/>ficit ex def. 3. lib. <lb/>11. vt A B dia<lb/>meter ad B O, B D, <lb/>B E, B F. Et A B <lb/>quia diameter e&longs;t <lb/>circulum &longs;uum bi<lb/>fariam diuidit ex <lb/>def. 17. lib. 1. Sic<lb/>que tanta pars e&longs;t <lb/>ad G, quanta ad H. 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>

<figure id="fig39"></figure><lb/><emph type="italics"/>ficit ex def. 3. lib. <lb/>11. vt A B dia<lb/>meter ad B O, B D, <lb/>B E, B F. Et A B <lb/>quia diameter e&longs;t <lb/>circulum &longs;uum bi<lb/>fariam diuidit ex <lb/>def. 17. lib. 1. Sic<lb/>que tanta pars e&longs;t <lb/>ad G, quanta ad H. 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>

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<s>Vt maioribus circulis.] <emph type="italics"/>Nutus &longs;eu perpetua propen &longs;io con<lb/>firmatur e&longs;&longs;e &longs;emper in circulo. quia quicunque &longs;it &longs;emper in &longs;e habet <lb/>concentricos minores infinitos, & maior tum celerius mouetur ab <lb/>æquali vi, & cum eo etiam pondera: tum angulus maioris nutum <lb/>habet ad angulum æqualem, qui e&longs;t in minori circulo. quia angull <lb/>maioris crura maiora &longs;unt, &longs;empérque e&longs;t, vt diameter ad diame<lb/>trum. Sunt enim circulorum &longs;emidiametri. Partes autem cum pari<lb/>ter multiplicibus &longs;unt in eadem ratione prop. 15. lib. 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/>

<arrow.to.target n="fig40"></arrow.to.target><lb/><emph type="italics"/><expan abbr="lõgitudine">longitudine</expan>. hæc autem figura hac cir<lb/>culorum concentricorum & à cen<lb/>tris angulorum illu&longs;trantur.<emph.end type="italics"/></s>

<figure id="fig40"></figure><lb/><emph type="italics"/><expan abbr="lõgitudine">longitudine</expan>. hæc autem figura hac cir<lb/>culorum concentricorum & à cen<lb/>tris angulorum illu&longs;trantur.<emph.end type="italics"/></s>

<s>Nutum habet.] <foreign lang="greek">ro/ph</foreign> <emph type="italics"/>Nutus <lb/>vis e&longs;t cuiu&longs;que impre&longs;&longs;a à Deo & <lb/>natura, qua in loco &longs;uo naturali quie&longs;<lb/>cit, & volentiab eo di&longs;pellere, re&longs;i&longs;tit. <lb/>vnde<emph.end type="italics"/> <foreign lang="greek">an)t<gap/><gap/>sis</foreign> <emph type="italics"/>renixus. Extra locum verò ad eum per breuißi<lb/>mam viam mouetur. Deus enim ne omnia in omnibus e&longs;&longs;ent, vni<lb/>cuique a<gap/> initio proprium locum tribuit, in quo & circa quem con<lb/>globatur, & ibi hæret. Hinc etiam &longs;ingulæ partes &longs;uis totis natura <lb/>inhærent, & in ÿs certum quendam &longs;itum habent, àquo remotæ ad <lb/>ip&longs;um redeunt, vt in arcubus & balli&longs;tis videre licet. Nutus autem <lb/>naturalis e&longs;t: vel non naturalis: vel mixtus. Naturalis e&longs;t is, quo res <lb/>quælibet natura &longs;ua mouetur: aut <expan abbr="mou&etilde;ti">mouenti</expan> re&longs;i&longs;tit habita ratione loci <lb/>&longs;ui naturalis, & &longs;itus &longs;uarum partium. Non naturalis e&longs;t is, quo nec <lb/>ratione loci naturalis, nec &longs;itus partium mouetur, vt fortuitus vel <lb/>voluntarius. Ille vt ventorum, hic vt animalium. Mixtus parti<lb/>ceps e&longs;t vtriu&longs;que. Nutus voluntarÿ mille &longs;unt modi <expan abbr="nõ">non</expan> aliter, quam <lb/>voluntatis decreto determinabiles. At naturalis vnius tantum e&longs;t <lb/>à loco non naturali ad naturalem. Hinc linea recta, quæ e&longs;t à termi<lb/>no à quo incipit moueri ad terminum in quo quie&longs;cit, linea nutus, <lb/>& eadem in terminis contrarÿs renixus dicitur, vt &longs;i ab eo in quo <lb/>quie&longs;cit aliena vis ad alium moueret: linea verò ip&longs;am &longs;ecans ad an<lb/>gulos inæquales e&longs;t linea obliqui nutus, vel renixus: & &longs;ecans ad <lb/>rectos nec ad nutum e&longs;t, nec ad renixum. Nunc igitur hoc cum ve<lb/>rum e&longs;&longs;e experiamur, & ratio conuincat, quantò quodque remotius <lb/>e&longs;t à loco, in quo naturaliter quie&longs;ceret, tantò ad eum magis conari, <lb/>remotioris maior erit nutus. In peripheria maiori punctum A re<lb/>motius puncto D. Magis igitur nutat. E&longs;t enim linea A C maior <lb/>quam D E vt ex &longs;imilibus triangulis A B C, D B E demon&longs;trari <lb/>facile pote&longs;t. Et &longs;ic angulus ad angulum nutare dicitur, cum in an<lb/>gulorum æqualitate crurum e&longs;t inæqualitas.<emph.end type="italics"/></s>

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<s>Infiniti autem.] <emph type="italics"/>Quod infiniti circuli minores concentrici in<lb/>&longs;int in quouis dato circulo &longs;ic demon&longs;trabimus. Sit circulus C B, <lb/>cuius &longs;emidiameter D B bifariam<emph.end type="italics"/><lb/>

<arrow.to.target n="fig41"></arrow.to.target><lb/><emph type="italics"/>&longs;ecetur, vt in puncto E prop. 10. <lb/>lib. 1. Et centro D interuallo D E <lb/>de&longs;criptus circulus po&longs;t. 3. Hic <lb/>erit concentricus & minor ip&longs;o <lb/>C B def. 1. lib. 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. Et eadem ra<lb/>tione deinceps ad infinitum, cum rectam lineam &longs;emper bi&longs;&longs;ecare li<lb/>ceat prop. 10. lib. 1. Et &longs;ic infiniti erunt circuli concentrici minores <lb/>in quouis circulo. quod erat demon&longs;trandum.<emph.end type="italics"/></s>

<figure id="fig41"></figure><lb/><emph type="italics"/>&longs;ecetur, vt in puncto E prop. 10. <lb/>lib. 1. Et centro D interuallo D E <lb/>de&longs;criptus circulus po&longs;t. 3. Hic <lb/>erit concentricus & minor ip&longs;o <lb/>C B def. 1. lib. 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. Et eadem ra<lb/>tione deinceps ad infinitum, cum rectam lineam &longs;emper bi&longs;&longs;ecare li<lb/>ceat prop. 10. lib. 1. Et &longs;ic infiniti erunt circuli concentrici minores <lb/>in quouis circulo. quod erat demon&longs;trandum.<emph.end type="italics"/></s>

<s>Etiam&longs;i curuatura.] <emph type="italics"/>Repetit cau&longs;am perpetui motus, aut nu<lb/>tus ad motum, quæ in circulo e&longs;t, cum &longs;ua ab&longs;ide id e&longs;t curuatura at<lb/>tingit planum, ine&longs;&longs;e, etiam&longs;i non attingat, vtfit in rotis figulorum, <lb/>& in trochleis. de quibus po&longs;tea.<emph.end type="italics"/></s>

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<s><emph type="italics"/>Hinc collige ex leuiori materia facta, dummodo firma, agiliora e&longs;&longs;e, <lb/>& exactiora. vnde petorita no&longs;tra rotis in orbita ferreis prædita <lb/>difficilius trahuntur, quam<emph.end type="italics"/><lb/>

<arrow.to.target n="fig42"></arrow.to.target><lb/><emph type="italics"/>nobilium Polonorum, quæ ex <lb/>ligno &longs;olo compacta &longs;unt.<emph.end type="italics"/></s>

<figure id="fig42"></figure><lb/><emph type="italics"/>nobilium Polonorum, quæ ex <lb/>ligno &longs;olo compacta &longs;unt.<emph.end type="italics"/></s>

<s>Non propendet.] <emph type="italics"/>Linea <lb/>nutus grauis alicuius deor<lb/>&longs;um e&longs;t recta perpendicularis <lb/><expan abbr="in&longs;i&longs;t&etilde;s">in&longs;i&longs;tens</expan> plano horizontis, <expan abbr="hãc">hanc</expan> <lb/>quæ &longs;ecat ad inæquales an<lb/>gulos, e&longs;t obliqua, cuiu&longs;mo<lb/>di e&longs;t arcus B F ad rectam <lb/>B G lineam nutus puncti <lb/>B.<emph.end type="italics"/></s>

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<s>Cvr onera.] <emph type="italics"/>Secundum genus &longs;cytalæ e&longs;t lignum ferrumue <lb/>cylindricum oblongum in extremis rotulas habens intra annu<lb/>los currui<emph.end type="italics"/><lb/>

<arrow.to.target n="fig43"></arrow.to.target><lb/><emph type="italics"/>affixos <lb/>ver&longs;atile, <lb/>vt e&longs;t fi<lb/>gura A <lb/>B quæ <lb/>mota iu<lb/>go rotis annexo, contrà, quam in curribus, in quibus non rotis: &longs;ed <lb/>currui annectitur, omnibus &longs;uis partibus mouetur duobus motibus <lb/>&longs;imul, circumcirca, & antror&longs;um. quod cau&longs;a e&longs;t vt leuius vertatur, <lb/>quam rota in curru. vt cuius axis procedendo tantùm antror&longs;um <lb/>moueatur, non autem circum circa vertatur. Vnde fit vt axis etiam <lb/>premat magis, & veluti rotam affigat plano, &longs;icque remoretur: con<lb/>tra in &longs;cytala rotæ dummodo maiores &longs;int, quam vt terra obruantur <lb/>à &longs;ubiecta planicie inferne ip&longs;am circunferentiam atterente impel<lb/>luntur. Supernè etiam ab onere cylindricum premente. Ob has itaque<emph.end type="italics"/>

<figure id="fig43"></figure><lb/><emph type="italics"/>affixos <lb/>ver&longs;atile, <lb/>vt e&longs;t fi<lb/>gura A <lb/>B quæ <lb/>mota iu<lb/>go rotis annexo, contrà, quam in curribus, in quibus non rotis: &longs;ed <lb/>currui annectitur, omnibus &longs;uis partibus mouetur duobus motibus <lb/>&longs;imul, circumcirca, & antror&longs;um. quod cau&longs;a e&longs;t vt leuius vertatur, <lb/>quam rota in curru. vt cuius axis procedendo tantùm antror&longs;um <lb/>moueatur, non autem circum circa vertatur. Vnde fit vt axis etiam <lb/>premat magis, & veluti rotam affigat plano, &longs;icque remoretur: con<lb/>tra in &longs;cytala rotæ dummodo maiores &longs;int, quam vt terra obruantur <lb/>à &longs;ubiecta planicie inferne ip&longs;am circunferentiam atterente impel<lb/>luntur. Supernè etiam ab onere cylindricum premente. Ob has itaque<emph.end type="italics"/>

<pb pagenum="115"/><emph type="italics"/>cau&longs;as &longs;cytala commodior erit, & expeditior ad onera conuehenda, <lb/>licet minores, quam currus habeat rotas, quod non repugnat ÿs quæ <lb/>ante 10. cap. dicta <expan abbr="s&utilde;t">sunt</expan> derotis maioribus. Aliud enim facilius attol<lb/>lere, & trahere quæcunque pondera, aliud conuehere. Scytala tamen <lb/>pote&longs;t e&longs;&longs;e illud curriculi genus quod Galli vocant<emph.end type="italics"/> Traineau, <emph type="italics"/>Itali<emph.end type="italics"/><lb/>Stra&longs;cino, <emph type="italics"/>apud quendam non ineruditum legi dici po&longs;&longs;e traham. <lb/>Hæc autem annexa ligno cylindrico &longs;olas rotas habet ver&longs;atiles, quæ <lb/>quantò minores, tantò minus occur&longs;ant &longs;ubiecto pauimento. vt enim <lb/>quò circulus rotæ maior e&longs;t, eò eius cum recta à qua tangitur in pla<lb/>no minor e&longs;t an-<emph.end type="italics"/><lb/>

<arrow.to.target n="fig44"></arrow.to.target><lb/><emph type="italics"/>gulus. Et contrà <lb/>quò circulus mi<lb/>nor, eò angulus <lb/>contactus maior <lb/>euadit. vt angu<lb/>lus A B C ro<lb/>tæ maioris mi<lb/>nor e&longs;t angulo <lb/>A B D rotæ <lb/>minoris: & con<lb/>trà vtrolibet <lb/>maior e&longs;t angu<lb/>lus A B E rotæ minoris.<emph.end type="italics"/></s>

<figure id="fig44"></figure><lb/><emph type="italics"/>gulus. Et contrà <lb/>quò circulus mi<lb/>nor, eò angulus <lb/>contactus maior <lb/>euadit. vt angu<lb/>lus A B C ro<lb/>tæ maioris mi<lb/>nor e&longs;t angulo <lb/>A B D rotæ <lb/>minoris: & con<lb/>trà vtrolibet <lb/>maior e&longs;t angu<lb/>lus A B E rotæ minoris.<emph.end type="italics"/></s>

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<s><emph type="italics"/>Et Pappus lib. 8. Mathemat collectionum fabricam in&longs;trumenti <lb/>docet, quod huc referri debet, e&longs;t autem eiu&longs;modi. vocat axem M B,<emph.end type="italics"/><lb/>

<arrow.to.target n="fig45"></arrow.to.target><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. Qui amplius videre volet, cur ab <lb/>hoc in&longs;trumento, quod axis in peritrochio vocatur, magna pondera <lb/>ab exigua virtute, quo ve etiam modo moueantur, quæ ratio tempo<lb/>ris, &longs;patÿ, potentiæ, ac moti ponderis inter &longs;e, & vt v&longs;us ip&longs;ius ad ve<lb/>ctem referatur. Videat apud Guidum V baldum in Mechanicis. Ad <lb/>hoc genus etiam in&longs;trumenti referantur ingentes illæ rotæ in vno <lb/>axe quarum vna labore vnius atque alterius hominis vertitur: alte<lb/>ra &longs;itulis quibus in &longs;ua circumferentia accommodate dispo&longs;itis con<lb/>ferta e&longs;t &longs;ui conuer&longs;ione ex vna parte aquam Sequanæ &longs;eptis contra<lb/>ctam exhau&longs;it, ex altera aliò refudit, vt ex lapide quadrato firma <lb/><expan abbr="iacer&etilde;tur">iacerentur</expan> fundamenta illius eximij pontis, qui magno ornamento & <lb/>commoditate celeberrimæ vrbium Lutetiæ, iu&longs;&longs;u Henrici III. Regis<emph.end type="italics"/>

<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. Qui amplius videre volet, cur ab <lb/>hoc in&longs;trumento, quod axis in peritrochio vocatur, magna pondera <lb/>ab exigua virtute, quo ve etiam modo moueantur, quæ ratio tempo<lb/>ris, &longs;patÿ, potentiæ, ac moti ponderis inter &longs;e, & vt v&longs;us ip&longs;ius ad ve<lb/>ctem referatur. Videat apud Guidum V baldum in Mechanicis. Ad <lb/>hoc genus etiam in&longs;trumenti referantur ingentes illæ rotæ in vno <lb/>axe quarum vna labore vnius atque alterius hominis vertitur: alte<lb/>ra &longs;itulis quibus in &longs;ua circumferentia accommodate dispo&longs;itis con<lb/>ferta e&longs;t &longs;ui conuer&longs;ione ex vna parte aquam Sequanæ &longs;eptis contra<lb/>ctam exhau&longs;it, ex altera aliò refudit, vt ex lapide quadrato firma <lb/><expan abbr="iacer&etilde;tur">iacerentur</expan> fundamenta illius eximij pontis, qui magno ornamento & <lb/>commoditate celeberrimæ vrbium Lutetiæ, iu&longs;&longs;u Henrici III. Regis<emph.end type="italics"/>

<pb pagenum="121"/><emph type="italics"/>no&longs;tri Chri&longs;tianißimi inchoatus, & maiori iam ex parte con&longs;tru<lb/>ctus perfectionem ab Henrico IIII. Rege nunc no&longs;tro magnifi<lb/>centißimo de&longs;iderat, ea in parte, qua flumen à &longs;chola S. Germani <lb/>ad plateam Augu&longs;tinorum traducitur. Hanc, vt &longs;pero, exorabit cla<lb/>rißimus vir dominus Marlyius rationum regiarum præ&longs;es, & mer<lb/>catorum præfectus dignißimus.<emph.end type="italics"/></s>

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<s>Cau&longs;a pote&longs;tatis cunei.] <emph type="italics"/>Cuneus e&longs;t in&longs;trumentum ex ma<lb/>teria firma in&longs;tar pyramidis à ba&longs;i lata in angu&longs;tum fa&longs;tigia-<emph.end type="italics"/>

<arrow.to.target n="fig46"></arrow.to.target><lb/><emph type="italics"/>tum. Vt A B C D E F. In <lb/>hac forma duo con&longs;ideranda &longs;unt, <lb/>alterum e&longs;t ex amplitudine ba&longs;is, <lb/>qua cuneus ad &longs;u&longs;cipiendam &longs;u&longs;ti<lb/>nendamque percußionem aptißi<lb/>mus e&longs;t: alterum e&longs;t ex vertice acu<lb/>to, qui ob id facile intrà corpora penetrans &longs;ibi viam facit. V&longs;us <lb/>eius e&longs;t ad magnos arborum truncos diuidendum, quod fit magna <lb/>cum facilitate <expan abbr="etiã">etiam</expan> à puero, beneficio ip&longs;ius cunei per rimulam primò <lb/>factam, qua parte acutior e&longs;t, immi&longs;si & qua parte oppo&longs;ita latior <lb/>e&longs;t à malleo percu&longs;si, quod à Milone licet athleta robu&longs;ti&longs;simo per &longs;e <lb/>fieri non potuit. Hic enim cum aliquando conspiceret adole&longs;centem <lb/>cuneis immißis findentem arbores, fertur &longs;ubri&longs;i&longs;&longs;e & &longs;ubmoui&longs;&longs;e. <lb/>Tum non alio vtens in&longs;trumento, quam &longs;uis manibus au&longs;us e&longs;t trun<lb/>cum diducere. 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. de <lb/>exhort. ad bonas artes. Hic e&longs;t de quo Iuuenalis,<emph.end type="italics"/></s>

<figure id="fig46"></figure><lb/><emph type="italics"/>tum. Vt A B C D E F. In <lb/>hac forma duo con&longs;ideranda &longs;unt, <lb/>alterum e&longs;t ex amplitudine ba&longs;is, <lb/>qua cuneus ad &longs;u&longs;cipiendam &longs;u&longs;ti<lb/>nendamque percußionem aptißi<lb/>mus e&longs;t: alterum e&longs;t ex vertice acu<lb/>to, qui ob id facile intrà corpora penetrans &longs;ibi viam facit. V&longs;us <lb/>eius e&longs;t ad magnos arborum truncos diuidendum, quod fit magna <lb/>cum facilitate <expan abbr="etiã">etiam</expan> à puero, beneficio ip&longs;ius cunei per rimulam primò <lb/>factam, qua parte acutior e&longs;t, immi&longs;si & qua parte oppo&longs;ita latior <lb/>e&longs;t à malleo percu&longs;si, quod à Milone licet athleta robu&longs;ti&longs;simo per &longs;e <lb/>fieri non potuit. Hic enim cum aliquando conspiceret adole&longs;centem <lb/>cuneis immißis findentem arbores, fertur &longs;ubri&longs;i&longs;&longs;e & &longs;ubmoui&longs;&longs;e. <lb/>Tum non alio vtens in&longs;trumento, quam &longs;uis manibus au&longs;us e&longs;t trun<lb/>cum diducere. 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. de <lb/>exhort. ad bonas artes. Hic e&longs;t de quo Iuuenalis,<emph.end type="italics"/></s>

<s>Viribus ille</s>

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<s>Præterea percu&longs;&longs;io.] <emph type="italics"/>Secunda e&longs;t cau&longs;a ad &longs;olutionem proble<lb/>matis, quod cuneus adigatur non &longs;implici pul&longs;u: &longs;ed percu&longs;&longs;u, qui ve<lb/>hemens & celer e&longs;t motus: iam motum autem mouendum vehemen<lb/>tius mouet. Percußio autem duobus fit modis, vel ex eo ip&longs;o &longs;olo quod <lb/>percutit tanquam graui<gap/> loco &longs;uperiori deor&longs;um incidente: at que hoc <lb/>quò grauius e&longs;t, eò maior fit percußio: quin & quò longius di&longs;titerit <lb/>primum incidens, magis percutit. Graue enim vnumquodque dum <lb/>mouetur grauitatis magis a&longs;&longs;umit motum: quam quie&longs;cens: & adhuc <lb/>magis quo longius mouet. quilibet enim aër addit &longs;uper motum iam <lb/>acqui&longs;itum. Inde ca&longs;us lapidis aut ictus ab altiore loco grauius per<lb/>cutit: vel ex eo quidem quod percutit, &longs;ed recto atque moto, ab aliqua <lb/>potentia percutiente, vt &longs;i per manubrium mallei, quod vna vel duæ <lb/>manus moueant. Certum e&longs;t quod quò grauior erit malleus, & quò <lb/>longius manubrium, eò maior fiet percu&longs;sio, vt ex præcedentibus &longs;atis <lb/>patere pote&longs;t, cum malleus tanquam pondus à centro, quod e&longs;t in ma-<emph.end type="italics"/>

<pb pagenum="129"/><emph type="italics"/>nubrio, vbi manus ip&longs;um comprehendunt, plus di&longs;tet. Præterea cer<lb/>tum e&longs;t quod quantò potentia percutiens validior e&longs;t, validiori tantò <lb/>impellet pul&longs;u. his adde quod e&longs;t ab Hippocrate<emph.end type="italics"/> <foreign lang="greek"><gap/>)n toi_s tsw/masi</foreign><lb/><emph type="italics"/>annotatum. Quantò impul&longs;us magis fiet<emph.end type="italics"/> <foreign lang="greek">ka(<gap/>) i)/cin</foreign> <emph type="italics"/>è directo, id e&longs;t vt <lb/>interpretor è perpendiculari. Cæterum percußionem vim habere ad <lb/>mouendum validißimam docebit Ari&longs;toteles prob. 19. huius libri: <lb/>&longs;ed ex multis colligere id ita e&longs;&longs;e po&longs;&longs;umus. Primum quod licet cuneo <lb/>ba&longs;i &longs;ua &longs;uper plano in&longs;i&longs;tenti, pondus alioqui valde ingens impona<lb/>tur, ip&longs;um non diuidet, aut parùm, &longs;i ad diui&longs;ionem percußione fa<lb/>ctam compares. Secundum &longs;i cuneo vel vectis vel cochlea vel aliud <lb/>aliquod in&longs;trumentum aptetur, vt ip&longs;e intimius propellatur, effectus <lb/>inde con&longs;equens parui erit momenti,<emph.end type="italics"/><lb/>

<arrow.to.target n="fig47"></arrow.to.target><lb/><emph type="italics"/>re&longs;pectu eius, qui à percußione pro<lb/>fici&longs;citur. Guidus V baldus commo<lb/>de hoc adfert exemplum. Sit A cor<lb/>pus lapideum ex quo angulus &longs;olidus <lb/>B &longs;it auferendus, mallei ferrei per<lb/>cu&longs;&longs;u facile id fit, &longs;ine percu&longs;&longs;u, nec <lb/>cum hoc, nec cum alio quouis in&longs;tru<lb/>mento, ni&longs;i cum maxima difficulta<lb/>te fieri poterit. Percu&longs;sio igitur cau&longs;a e&longs;t, cur magna &longs;cindantur <lb/>pondera.<emph.end type="italics"/></s>

<figure id="fig47"></figure><lb/><emph type="italics"/>re&longs;pectu eius, qui à percußione pro<lb/>fici&longs;citur. Guidus V baldus commo<lb/>de hoc adfert exemplum. Sit A cor<lb/>pus lapideum ex quo angulus &longs;olidus <lb/>B &longs;it auferendus, mallei ferrei per<lb/>cu&longs;&longs;u facile id fit, &longs;ine percu&longs;&longs;u, nec <lb/>cum hoc, nec cum alio quouis in&longs;tru<lb/>mento, ni&longs;i cum maxima difficulta<lb/>te fieri poterit. Percu&longs;sio igitur cau&longs;a e&longs;t, cur magna &longs;cindantur <lb/>pondera.<emph.end type="italics"/></s>

<s>Paruo verò.] <emph type="italics"/>Occurrit obiectioni, quæ fit propter exiguitatem <lb/>cunei, ob idque & vectis, &longs;ed hanc dicit compen&longs;ari vehementia & <lb/>celeritate percu&longs;sionis, & quanquam ratione motus, motor exiguus <lb/>videatur, & ita lateat, magnus e&longs;t tamen viribus. Sic in rebus natu-<emph.end type="italics"/><lb/>

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<s>E&longs;to cuneus.] <emph type="italics"/>Hîc e&longs;t demon&longs;tratio linearis ad ostenden<lb/>dum cuneum diuidendo ponderi duorum vectium vicem pror&longs;us ge<lb/>rere, eorumque &longs;ibi inuicem contrariorum. Sed hanc &longs;ic paulò am<lb/>plius & apertius repetemus. Sit cuneus A B C cuius vertex B: <lb/>& &longs;it A B æqualis B C, <lb/>quod autem diuidendum<emph.end type="italics"/><lb/>

<arrow.to.target n="fig48"></arrow.to.target><lb/><emph type="italics"/>e&longs;t, &longs;it D E F G, &longs;itque <lb/>pars cunei H B K intra <lb/>D E F G, & H B &longs;it <lb/>æqualis ip&longs;i B K. percu<lb/>tiatur vt fieri &longs;olet cuneus <lb/>in A C. Dum cuneus in <lb/>A C percutitur, A B fit <lb/>vectis, cuius hypomoch<lb/>lium e&longs;t H, & pondus in <lb/>B, eodemque modo C B <lb/>fit vectis, cuius hypomo<lb/>chlium e&longs;t K, & pondus &longs;imiliter in B. Sed dum percutitur cuneus <lb/>maiori adhuc ip&longs;ius portione, intra ip&longs;um D E F G ingreditur, <lb/>quam prius e&longs;&longs;et: &longs;it autem portio hæc M B L, &longs;itque M B ip&longs;i <lb/>B L æqualis. Et cum M B, B L &longs;int ip&longs;is H B, B K maiores: <lb/>erit M L maior H K. Dumigitur M L erit in &longs;itu H K, opor<lb/>tet vt fiat maior diui&longs;io, & D moueatur ver&longs;us O: G autem ver<lb/>&longs;us N, & quò maior pars cunei intra D E F G ingredietur, eò <lb/>maior fiet diui&longs;io: & D, G magis adhuc impellentur ver&longs;us O, <lb/>N. Parsigitur K G eius quod diuiditur mouebitur à vecte A B, <lb/>cuius hypomochlium e&longs;t H, & pondus in B, ita vt punctum B <lb/>ip&longs;ius vectis A B impellat partem k G: & pars H D mouebi<lb/>tur à vecte C B, cuius hypomochlium e&longs;t k, ita vt B vecte C B<emph.end type="italics"/>

<figure id="fig48"></figure><lb/><emph type="italics"/>e&longs;t, &longs;it D E F G, &longs;itque <lb/>pars cunei H B K intra <lb/>D E F G, & H B &longs;it <lb/>æqualis ip&longs;i B K. percu<lb/>tiatur vt fieri &longs;olet cuneus <lb/>in A C. Dum cuneus in <lb/>A C percutitur, A B fit <lb/>vectis, cuius hypomoch<lb/>lium e&longs;t H, & pondus in <lb/>B, eodemque modo C B <lb/>fit vectis, cuius hypomo<lb/>chlium e&longs;t K, & pondus &longs;imiliter in B. Sed dum percutitur cuneus <lb/>maiori adhuc ip&longs;ius portione, intra ip&longs;um D E F G ingreditur, <lb/>quam prius e&longs;&longs;et: &longs;it autem portio hæc M B L, &longs;itque M B ip&longs;i <lb/>B L æqualis. Et cum M B, B L &longs;int ip&longs;is H B, B K maiores: <lb/>erit M L maior H K. Dumigitur M L erit in &longs;itu H K, opor<lb/>tet vt fiat maior diui&longs;io, & D moueatur ver&longs;us O: G autem ver<lb/>&longs;us N, & quò maior pars cunei intra D E F G ingredietur, eò <lb/>maior fiet diui&longs;io: & D, G magis adhuc impellentur ver&longs;us O, <lb/>N. Parsigitur K G eius quod diuiditur mouebitur à vecte A B, <lb/>cuius hypomochlium e&longs;t H, & pondus in B, ita vt punctum B <lb/>ip&longs;ius vectis A B impellat partem k G: & pars H D mouebi<lb/>tur à vecte C B, cuius hypomochlium e&longs;t k, ita vt B vecte C B<emph.end type="italics"/>

<pb pagenum="131"/><emph type="italics"/>partem H D impellat. Atque hæc e&longs;t &longs;ententia Ari&longs;totelis de du<lb/>plici vecte in cuneo. Aliam habet Guidus Vbaldus, quam exi&longs;timat <lb/>meliorem. E&longs;t autem eiu&longs;modi, vt figuræ iam po&longs;itæ vectis A B <lb/>habeat hypomochlium B, & pondus mouendum H, &longs;icut vectis <lb/>C B, habeatitem hypomochlium B & pondus mouendum &longs;it K: it a <lb/>vt pars H D moueatur à vecte A B, & pars k G à vecte C B. <lb/>Ratio e&longs;t, quia in&longs;trumenta mouent per contactum: vectis autem A <lb/>B tangit partem H D motam in H, non &longs;imiliter tangit in B. <lb/>Id ip&longs;um in&longs;uper comprobat ex cuneo inter duas moles &longs;eparatas in<lb/>terpo&longs;ito: &longs;ed quod pace tanti viri dixerim certum e&longs;t, quod ni&longs;i B <lb/>vertex cunei tangeret molem in B, & ip&longs;am impelleret atque diui<lb/>deret, partes H D, K G non vtrinque cederent in O & N. Quod <lb/>igitur cedant motus is &longs;ecundarius e&longs;t, & priorem qui e&longs;t in B con<lb/>&longs;equens. Quod autem ad moles &longs;eparatas attinet, in his aër pondus e&longs;t <lb/>mouendum, quem &longs;i nequaquam cedere fingamus, non vltra ingre<lb/>diente cuneo, partes molium inter quas erit cuneus con&longs;i&longs;tent. Cæte<lb/>rum vt cuneus vectis e&longs;t multiplicatus: ita cochlea, cuius nullam <lb/><expan abbr="mention&etilde;">mentionem</expan> feci&longs;&longs;e <expan abbr="Ari&longs;totel&etilde;">Ari&longs;totelem</expan> totis his mechanicis miror, <expan abbr="c&umacr;">cum</expan> &longs;it cuneus <lb/>multiplicatus, vel vnus continuatus. E&longs;t enim cochlea (vt de hac <lb/>pauca quæ ex Pappo, Vbaldo, Mun&longs;tero &longs;elegimus, dicamus) cuneus <lb/>cylindro circumuolutus helicis in&longs;tar, percußionis quidem expers, <lb/>&longs;ed per vectem cylindri axi annexum ver&longs;us, faciens motionem ma<lb/>gnorum ponderum. Quod vt intelligatur. Sit cuneus A B C circa<emph.end type="italics"/></s>

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<s>Cochlea cum matrice.<lb/><emph type="italics"/>nexum: pondus <lb/>mouendum &longs;it <lb/>L M N O ex <lb/>parte M N im<lb/>mobile, vt in <lb/>his quæ <expan abbr="&longs;cind&umacr;-tur">&longs;cindun<lb/>tur</expan>, fieri &longs;olet: <lb/>cunei vero vertex A &longs;it intra rimam R S. Itaque facile e&longs;t videre <lb/>quod dum K F circumuer&longs;us erit vbi K P, vertex A non erit <lb/>amplius intra R S: &longs;ed cunei pars alia vt T V: quæ cum maior <lb/>&longs;it, quam R S. E&longs;t enim pars quæque cunei remotior à vertice, latior <lb/>propinquiore: ergo vt T V &longs;it intra K S, oportet vt R cedat, mo<lb/>ueaturque ver&longs;us X, & S ver&longs;us E vt faciunt ea quæ &longs;cindun<lb/>tur. Totum ergo L M N O &longs;cindetur. Nam dum rur&longs;us vectis K <lb/>P peruenerit ad K Q, tunc B C erit intra R S, erit R &longs;iquidem <lb/>in X & S in E, vt X E &longs;it æqualis B C: &longs;emperque conti<lb/>nuato cuneo progredienteque A vertice vltrà, pondus L M N O, <lb/>&longs;cindetur, vel pondus G mobile impelletur, attrahetur, attolletur,<emph.end type="italics"/><lb/>

<arrow.to.target n="fig49"></arrow.to.target><lb/><emph type="italics"/>prout cylindrus cochleæ po&longs;itus erit ad planum horizontis cum &longs;ua, <lb/>vel &longs;inefcemina &longs;eu matrice. Quod &longs;irur&longs;us cochleæ <expan abbr="tympan&umacr;rectè">tympanurrectè</expan><emph.end type="italics"/>

<figure id="fig49"></figure><lb/><emph type="italics"/>prout cylindrus cochleæ po&longs;itus erit ad planum horizontis cum &longs;ua, <lb/>vel &longs;inefcemina &longs;eu matrice. Quod &longs;irur&longs;us cochleæ <expan abbr="tympan&umacr;rectè">tympanurrectè</expan><emph.end type="italics"/>

<pb pagenum="133"/><emph type="italics"/>vel obliquè denticulatum, ita vt helici facilè congruat, aptetur: ma<lb/>nife&longs;tum e&longs;t, quod ad motum cochleæ etiam tympani C dentes &longs;uper <lb/>helicem cochleæ ad infinitum <expan abbr="circumuert&etilde;tur">circumuertentur</expan>. Vnde hæc cochlea di<lb/>citur infinita, id e&longs;t tandiu vertetur, quandiu quis volet. Eodem enim <lb/>modo &longs;emper &longs;e habebit tympanum ad cochleam. Porrò cochleæ vi <lb/>& beneficio admirabile certè quanta pondera moueantur. Refert<emph.end type="italics"/><lb/>

<arrow.to.target n="marg33"></arrow.to.target><lb/><emph type="italics"/>Mun&longs;terus Ba&longs;ileæ &longs;e vidi&longs;&longs;e longißimas &longs;udes præacutis ferreis ro<lb/>&longs;tris munitas olim in fundum profundi&longs;simè actas auelli. Quinetiam <lb/>aliquando integras domos ex lignis compaginatas in &longs;ublime &longs;uble<lb/>uari & cylindris aliquot &longs;ubmi&longs;sis aliò deferri: &longs;ed & homi&nacute;um <lb/>v&longs;u propemodum immen&longs;o quotidie experimur, quantum valeat <lb/>torquendo & premendo, dum vinum, oleum, &longs;uccos quo&longs;libet à <lb/>&longs;uis fructibus exprimimus, & hone&longs;tam v&longs;uram dominis &longs;uis <lb/>per&longs;oluere cogimus, ita ad vltimum quadrantem v&longs;que, vt à pu<lb/>mice po&longs;tea aquam citius extrahas: quam à fæcibus reliquis &longs;uc<lb/>cum aliquem. Immo verò, quæ laudari nunquam &longs;atis pote&longs;t, &longs;ine <lb/>cochlea ars Typographica quid e&longs;&longs;e po&longs;&longs;et, Duo autem efficiunt vt <lb/>cochlea tanta po&longs;sit. Primum quia e&longs;t helix circa cochleam, quæ quò <lb/>e&longs;t vertex cunei acutioris, eò facilius: &longs;ed tardius mouet. Alterum <lb/>quia e&longs;t vectis, quo cochlea circumuertitur, qui etiam quò longior, eò <lb/>facilius: &longs;ed etiam tardius mouet.<emph.end type="italics"/></s>

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<s>Quare &longs;i quis.] <emph type="italics"/>Problema de trochleis cur duabus magna one<lb/>ra parua vi trahuntur, proponitur, apertè quidem, ni&longs;i vbi de alliga<lb/>tione ip&longs;arum agitur. Tota enim particula contextus huius<emph.end type="italics"/> <foreign lang="greek">e)/xon to\ <lb/>ar)/thma e)k <gap/>ate/rou t<gap/> cu/lwn, <gap/>a/teron de\ h)_ w_<gap/>serhreimu/on h)\ w_<gap/><lb/>se<gap/>u/on <gap/> ta\s t<gap/>oxali/as,</foreign> <emph type="italics"/>mendo&longs;a meo iudicio e&longs;t. Quid enim <lb/>e&longs;t habere lorum quod dependeat, ab altero tignorum: alterum vero <lb/>e&longs;&longs;e infixum, & appo&longs;itum ad trochleas, quid e&longs;t illud alterum, quod <lb/>dicitur infigi, & apponi<emph.end type="italics"/><lb/>

<arrow.to.target n="fig50"></arrow.to.target><lb/><emph type="italics"/>ad trochleas, intelligi certè <lb/>non pote&longs;t. Si igitur quid <lb/>rei natura, & v&longs;us o&longs;ten<lb/>dat, ponamus: illam parti<lb/>culam &longs;ic <expan abbr="cõmutabimus">commutabimus</expan>, <lb/>vt dicamus vnam è dua<lb/>bus trochleis habere <expan abbr="lor&utilde;">lorum</expan>, <lb/>quod dependeat ab altero <lb/>vel vtroque tignorum: al<lb/>teri vero infixum & <expan abbr="ap-po&longs;it&utilde;">ap<lb/>po&longs;itum</expan> e&longs;&longs;e pondus trahen<lb/>dum vel attollendum. Vt <lb/>&longs;int duo tigna &longs;e&longs;e ex ad-<emph.end type="italics"/>

<figure id="fig50"></figure><lb/><emph type="italics"/>ad trochleas, intelligi certè <lb/>non pote&longs;t. Si igitur quid <lb/>rei natura, & v&longs;us o&longs;ten<lb/>dat, ponamus: illam parti<lb/>culam &longs;ic <expan abbr="cõmutabimus">commutabimus</expan>, <lb/>vt dicamus vnam è dua<lb/>bus trochleis habere <expan abbr="lor&utilde;">lorum</expan>, <lb/>quod dependeat ab altero <lb/>vel vtroque tignorum: al<lb/>teri vero infixum & <expan abbr="ap-po&longs;it&utilde;">ap<lb/>po&longs;itum</expan> e&longs;&longs;e pondus trahen<lb/>dum vel attollendum. Vt <lb/>&longs;int duo tigna &longs;e&longs;e ex ad-<emph.end type="italics"/>

<pb pagenum="135"/><emph type="italics"/>uer&longs;o fulcientia C D & E F<emph.end type="italics"/><lb/>

<arrow.to.target n="fig51"></arrow.to.target><lb/><emph type="italics"/>(plura duobus vt tria, & qua<lb/>tuor, vt &longs;e validius fulciant, vt <lb/>plurimum &longs;tatuuntur) &longs;int & <lb/>duæ trochleæ A & B, qua<lb/>rum altera A ad vtrumque ti<lb/>gnum reuinciatur loro H A, <lb/>alteri vero B appo&longs;itum &longs;it pon<lb/>dus G, tracto loro ab ini<lb/>tio vbi I, pondus G cum tro<lb/>chlea B attolletur ver&longs;us A.<emph.end type="italics"/></s>

<figure id="fig51"></figure><lb/><emph type="italics"/>(plura duobus vt tria, & qua<lb/>tuor, vt &longs;e validius fulciant, vt <lb/>plurimum &longs;tatuuntur) &longs;int & <lb/>duæ trochleæ A & B, qua<lb/>rum altera A ad vtrumque ti<lb/>gnum reuinciatur loro H A, <lb/>alteri vero B appo&longs;itum &longs;it pon<lb/>dus G, tracto loro ab ini<lb/>tio vbi I, pondus G cum tro<lb/>chlea B attolletur ver&longs;us A.<emph.end type="italics"/></s>

<s><emph type="italics"/>Vel etiam &longs;it trochlea in<lb/>ferior in qua orbiculi duo cui <lb/>pondus A per vncum apponi<lb/>tur, &longs;uperior in qua duo item or<lb/>biculi. funis primò alligari de<lb/>bet vnco, qui e&longs;t in ea, & cir<lb/>cum agi circa &longs;uperiorem orbicu<lb/>lorum inferioris trochleæ, ita vt <lb/>a&longs;cendens circum inferiorem &longs;u<lb/>perioris, deuoluatur po&longs;tea circa <lb/>inferiorem inferioris, & reuol<lb/>uatur adhuc circa &longs;uperiorem &longs;u<lb/>perioris, habens tandem initium <lb/>&longs;ui in G vbi motor intelligitur.<emph.end type="italics"/></s>

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<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. 3. & aliquot &longs;equentibus in tractatu de <lb/>trochlea. 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. Vnde arbitror hûc irrep&longs;i&longs;&longs;e mendum in vo<lb/>cabulo<emph.end type="italics"/> <foreign lang="greek">ta/xei</foreign> <emph type="italics"/>pro<emph.end type="italics"/> <foreign lang="greek">logw|</foreign> <emph type="italics"/>vel<emph.end type="italics"/> <foreign lang="greek">diplasi/w|.</foreign> <emph type="italics"/>pro<emph.end type="italics"/> <foreign lang="greek">(wodiplasi/w|</foreign> <emph type="italics"/>tollendo<emph.end type="italics"/><lb/><foreign lang="greek">ple/on h)\</foreign> <emph type="italics"/>vel potius pro<emph.end type="italics"/> <foreign lang="greek">h)\</foreign> <emph type="italics"/>reponendo<emph.end type="italics"/> <foreign lang="greek">mh\</foreign> <emph type="italics"/>&longs;ic enim &longs;ententia vera erit.<emph.end type="italics"/><lb/>Hoc vero duæ trochleæ plus non in dupla velocitate <expan abbr="at-toll&etilde;t">at<lb/>tollent</expan>. <emph type="italics"/><expan abbr="Cæter&utilde;">Cæterum</expan> quomodo per trochleas, quanto <expan abbr="t&etilde;pore">tempore</expan>, & &longs;patio, pon<lb/>dera moueantur, <expan abbr="quodnã">quodnam</expan> &longs;uperioris & inferioris trochleæ fuerit offi<lb/>cium, orbiculorum diametri vt moueantur, vt in omni ratione quæ <lb/>in numeris e&longs;t, pondus & potentia &longs;tatui po&longs;sint, quæ omnia certè <lb/>&longs;citu digni&longs;sima &longs;unt Geometricè demon&longs;trata, qui &longs;cire volet, vi<lb/>deat apud Guidum V baldum prædicto tractatu, ne maior pars il<lb/>lius præ&longs;tanti&longs;simi operis, quod edidit de mechanicis, mihi &longs;it hûc <lb/>transferenda. Huic verò loco non po&longs;&longs;um non in&longs;erere vnam ma<lb/>chinam e &longs;ex trochleis: & funiculis quinque compo&longs;itam (è pluri<lb/>bus componi, &longs;i v&longs;us po&longs;tulet, nihil obe&longs;t) mira celeritate, & funis <lb/>ductarÿ paucitate atque compendio pondus attollentem, quam mihi <lb/>communicauit Georgius Lhullierius vir &longs;ine honoris titulo <expan abbr="n&utilde;quam">nunquam</expan> <lb/>mihi nominandus, propter <expan abbr="&longs;u&utilde;">&longs;uum</expan> in artes mathematicas & <expan abbr="mathema-t&utilde;">mathema<lb/>tum</expan> <expan abbr="&longs;tudio&longs;osquãdiu">&longs;tudio&longs;osquandiu</expan> vixit &longs;ingularem <expan abbr="amor&etilde;">amorem</expan>. Machina e&longs;t eiu&longs;modi, <lb/>&longs;it tignum A B perpendiculariter in&longs;i&longs;tens, cui etiam ad rectos al<lb/>terum in &longs;i&longs;tat vt C D: &longs;int &longs;ex trochleæ E, F, G, H, I, K, <lb/>funiculi quinque L A, N M, Q P, S R, B T, quorum pri<lb/>mus circumuoluitur circa duos orbiculos E & F in extremis <gap/>i<lb/>gnorum circa &longs;uos axiculos mobiles reliquorum &longs;inguli circa &longs;inga<lb/>los à proximè antecedentibus funiculis &longs;u&longs;pen&longs;os. In X autem &longs;it <lb/>harpago ad apprehendendum pondus E attollendum vel deprimen<lb/>dum. Si eni<gap/> extremum L ab harpagone V liberetur, & ad A <lb/>traducatur, de&longs;cendet vno qua&longs;i nictu oculi pondus E, tantum<emph.end type="italics"/>

<arrow.to.target n="fig52"></arrow.to.target><lb/><emph type="italics"/>&longs;patÿ, quanti &longs;unt funiculi N M, Q P, <lb/>R S, B T. Tanti erunt autem, <lb/>quantos loci, ad quem de&longs;cendere, vel <lb/>è quo educere volumus, profunditas, <lb/>po&longs;tulat. Si autem attollere oporteat, <lb/>extremum L cum erit in A, traduce<lb/>tur ad harpagonem V.<emph.end type="italics"/></s>

<figure id="fig52"></figure><lb/><emph type="italics"/>&longs;patÿ, quanti &longs;unt funiculi N M, Q P, <lb/>R S, B T. Tanti erunt autem, <lb/>quantos loci, ad quem de&longs;cendere, vel <lb/>è quo educere volumus, profunditas, <lb/>po&longs;tulat. Si autem attollere oporteat, <lb/>extremum L cum erit in A, traduce<lb/>tur ad harpagonem V.<emph.end type="italics"/></s>

<s><emph type="italics"/>In hac machina igitur hæc duo in<lb/>&longs;unt, facilitas motionis ob multitudi<lb/>nem trochlearum, & celeritas motio<lb/>nis. quia quanto temporis &longs;patio extre<lb/>mum funiculi L ab A transfertur <lb/>ad harpagonem V, eodem pondus E <lb/>ex infimo loco &longs;ur&longs;um per decuplam <lb/>longitudinem & amplius, &longs;i quis vo<lb/>let, euehitur, aut contra.<emph.end type="italics"/></s>

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<s>De &longs;tateris.] <foreign lang="greek">fa/lagc</foreign> <emph type="italics"/>apud Græcos multa &longs;ignificat vt in<lb/>ternodium in digitis, ordinem & agmem militare longius <lb/>quam latius, ligna teretia, quibus naues in mare deuoluuntur: &longs;ed hîc<emph.end type="italics"/>

<pb pagenum="147"/><emph type="italics"/>&longs;ignificat libræ genus, quod trutina, ab alÿs &longs;tatera appellatur. Huitis <lb/>partes quatuor &longs;unt A B &longs;capus, C D an&longs;a, A E harpago vel <lb/>lanx, F G<emph.end type="italics"/><lb/>

<arrow.to.target n="fig53"></arrow.to.target><lb/><emph type="italics"/><expan abbr="æquipõdium">æquipondium</expan> <lb/>Græcis di<lb/>ctum<emph.end type="italics"/> <foreign lang="greek">sfai/<lb/>rwma</foreign> <emph type="italics"/>no&longs;tris <lb/>Marcum vel <lb/><expan abbr="Roman&utilde;">Romanum</expan>. Vi <lb/>truuius dixit inuentam fui&longs;&longs;e &longs;tateram, vt ab iniquitate iu&longs;tis mori<lb/>bus hominum vita vindicetur. Vnde e&longs;t apud &longs;apientem &longs;tatera do<lb/>lo&longs;a abhominatio e&longs;t apud Deum, & pondus æquum voluntas eius. <lb/>In rebus autem pretio&longs;is licet libra, non &longs;tatera v&longs;urpetur, quia tam <lb/>exacta e&longs;&longs;e non pote&longs;t: in vilioribus tamen, quia iniquitatis parua ia<lb/>ctura e&longs;t, frequentißimè v&longs;urpatur, propter operis commoditatem. <lb/>Nam libra vti non po&longs;&longs;umus, ni&longs;i paria pondera pen&longs;ionibus &longs;emper <lb/>habeantur, quarum apparatus atque tractatio e&longs;t magis opero&longs;a & <lb/>mole&longs;ta. In &longs;tater is autem quicquid appender is &longs;eu magnum, &longs;eu par<lb/>uum vnico pondere, hoc e&longs;t æquipondio: distinctione tamen puncto<lb/>rum in &longs;capo examinatur. Id cnim in &longs;capo ita impo&longs;itum e&longs;t, vt mo<lb/>dò ad an&longs;am, modò ab an&longs;a remoueatur, vt maiora & minora pon<lb/>dera libret, & vi mouenti re&longs;pondeat. Nam velut aliqua manus va<lb/>lida longiorem &longs;tateræ &longs;capum deprimit.<emph.end type="italics"/></s>

<figure id="fig53"></figure><lb/><emph type="italics"/><expan abbr="æquipõdium">æquipondium</expan> <lb/>Græcis di<lb/>ctum<emph.end type="italics"/> <foreign lang="greek">sfai/<lb/>rwma</foreign> <emph type="italics"/>no&longs;tris <lb/>Marcum vel <lb/><expan abbr="Roman&utilde;">Romanum</expan>. Vi <lb/>truuius dixit inuentam fui&longs;&longs;e &longs;tateram, vt ab iniquitate iu&longs;tis mori<lb/>bus hominum vita vindicetur. Vnde e&longs;t apud &longs;apientem &longs;tatera do<lb/>lo&longs;a abhominatio e&longs;t apud Deum, & pondus æquum voluntas eius. <lb/>In rebus autem pretio&longs;is licet libra, non &longs;tatera v&longs;urpetur, quia tam <lb/>exacta e&longs;&longs;e non pote&longs;t: in vilioribus tamen, quia iniquitatis parua ia<lb/>ctura e&longs;t, frequentißimè v&longs;urpatur, propter operis commoditatem. <lb/>Nam libra vti non po&longs;&longs;umus, ni&longs;i paria pondera pen&longs;ionibus &longs;emper <lb/>habeantur, quarum apparatus atque tractatio e&longs;t magis opero&longs;a & <lb/>mole&longs;ta. In &longs;tater is autem quicquid appender is &longs;eu magnum, &longs;eu par<lb/>uum vnico pondere, hoc e&longs;t æquipondio: distinctione tamen puncto<lb/>rum in &longs;capo examinatur. Id cnim in &longs;capo ita impo&longs;itum e&longs;t, vt mo<lb/>dò ad an&longs;am, modò ab an&longs;a remoueatur, vt maiora & minora pon<lb/>dera libret, & vi mouenti re&longs;pondeat. Nam velut aliqua manus va<lb/>lida longiorem &longs;tateræ &longs;capum deprimit.<emph.end type="italics"/></s>

<s>Cur &longs;tateræ.] <emph type="italics"/>Problema e&longs;t de &longs;tatera, quæ paruo æquipondio <lb/>magna appendit pondera. Et problematis difficultas hinc o&longs;tenditur, <lb/>quod &longs;tatera videatur tantum e&longs;&longs;e dimidia libra, vt in cuius vna <lb/>parte lanx e&longs;t vna dependens, ex altera vero &longs;capus. Rationi igitur <lb/>con&longs;entaneum e&longs;tne tanta pendat, quanta libra integra.<emph.end type="italics"/></s>

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<s><emph type="italics"/>Statera certe multæ &longs;unt libræ actu & pote&longs;tate. Et primum actu <lb/>cum an&longs;æ (&longs;ic enim<emph.end type="italics"/> <foreign lang="greek">ta\ <gap/>ar/tia</foreign> <emph type="italics"/>exprimi debere declarant multi <lb/>huius contextus loci inter &longs;e comparati) plures &longs;unt in vno &longs;capo, vt <lb/>duæ, quod frequentißimum, vel tres, quod rarius: cuiu&longs;modi &longs;unt in <lb/>A B &longs;capo<emph.end type="italics"/><lb/>

<arrow.to.target n="fig54"></arrow.to.target><lb/><emph type="italics"/>duæ C D, E F <lb/>quarum pro<lb/>piore lanci, <lb/>qui vtuntur, <lb/>pondera ad <lb/><expan abbr="craßior&etilde;">craßiorem</expan> tru<lb/>tinam &longs;e ex<lb/>pendere dicunt. quod huius notæ longius inter&longs;e di&longs;tent: qui vero re<lb/>motiore, ad &longs;ubtiliorem, vt in qua notæ minus di&longs;tent in lateribus <lb/>&longs;capi &longs;ignatæ. Deinde pote&longs;tate plures &longs;unt, cuman&longs;a vna e&longs;t, &longs;ed mi<lb/>nimè fixa, verum libero modo propius A, modo remotius colloca<lb/>tur. Semper autem in aliquo puncto inter A & B intermedio. <lb/>Vnde e&longs;t quod hîc dicat Ari&longs;toteles an&longs;am ad partes, vbi e&longs;t æqui<lb/>pondium, e&longs;&longs;e dimidium &longs;tateræ, non &longs;umendo dimidium exactè, <lb/>quandoquidem extremo, à quo lanx <expan abbr="dep&etilde;det">dependet</expan> &longs;emper propior &longs;it. Hinc <lb/>elicitur pulchra regula è qua po&longs;tea ferè omnia, quæ ad &longs;tateræ ratio<lb/>nem pertinent, dedueuntur. quæ e&longs;t eiu&longs;modi. Cum &longs;capus integer ad <lb/>pondus appen&longs;um, rationem eam habet: quam duplum partis, quæ e&longs;t <lb/>ab an&longs;a ver&longs;us lancem ad reliquum: tunc <expan abbr="põdus">pondus</expan> &longs;capum vniformem, <lb/>& omnibus &longs;uis partibus æqualem in æquilubrio con&longs;tituit. Vt e&longs;to <lb/>&longs;capus A B duodecim vnciarum, & pars A F <expan abbr="dudr&utilde;">dudrum</expan>: huius partis <lb/>duplum e&longs;t 4. & reliquum 8. Quemadmodum ergo 4. ad 8. &longs;ic &longs;ca<lb/>pus <gap/>otus id e&longs;t 12. erit ad pondus, quod per regulam trium inuenie<lb/>tur e&longs;&longs;e 4. vnciarum. Rur&longs;us &longs;it an&longs;a in D & A D &longs;it vna vn<lb/>cia. Huius duplum e&longs;t 2. Reliquum e&longs;t 10. Vtigitur 2. ad 10. &longs;ic 12. <lb/>totus &longs;capus erit ad pondus: quod per regulam trium inuenietur e&longs;&longs;e<emph.end type="italics"/>

<figure id="fig54"></figure><lb/><emph type="italics"/>duæ C D, E F <lb/>quarum pro<lb/>piore lanci, <lb/>qui vtuntur, <lb/>pondera ad <lb/><expan abbr="craßior&etilde;">craßiorem</expan> tru<lb/>tinam &longs;e ex<lb/>pendere dicunt. quod huius notæ longius inter&longs;e di&longs;tent: qui vero re<lb/>motiore, ad &longs;ubtiliorem, vt in qua notæ minus di&longs;tent in lateribus <lb/>&longs;capi &longs;ignatæ. Deinde pote&longs;tate plures &longs;unt, cuman&longs;a vna e&longs;t, &longs;ed mi<lb/>nimè fixa, verum libero modo propius A, modo remotius colloca<lb/>tur. Semper autem in aliquo puncto inter A & B intermedio. <lb/>Vnde e&longs;t quod hîc dicat Ari&longs;toteles an&longs;am ad partes, vbi e&longs;t æqui<lb/>pondium, e&longs;&longs;e dimidium &longs;tateræ, non &longs;umendo dimidium exactè, <lb/>quandoquidem extremo, à quo lanx <expan abbr="dep&etilde;det">dependet</expan> &longs;emper propior &longs;it. Hinc <lb/>elicitur pulchra regula è qua po&longs;tea ferè omnia, quæ ad &longs;tateræ ratio<lb/>nem pertinent, dedueuntur. quæ e&longs;t eiu&longs;modi. Cum &longs;capus integer ad <lb/>pondus appen&longs;um, rationem eam habet: quam duplum partis, quæ e&longs;t <lb/>ab an&longs;a ver&longs;us lancem ad reliquum: tunc <expan abbr="põdus">pondus</expan> &longs;capum vniformem, <lb/>& omnibus &longs;uis partibus æqualem in æquilubrio con&longs;tituit. Vt e&longs;to <lb/>&longs;capus A B duodecim vnciarum, & pars A F <expan abbr="dudr&utilde;">dudrum</expan>: huius partis <lb/>duplum e&longs;t 4. & reliquum 8. Quemadmodum ergo 4. ad 8. &longs;ic &longs;ca<lb/>pus <gap/>otus id e&longs;t 12. erit ad pondus, quod per regulam trium inuenie<lb/>tur e&longs;&longs;e 4. vnciarum. Rur&longs;us &longs;it an&longs;a in D & A D &longs;it vna vn<lb/>cia. Huius duplum e&longs;t 2. Reliquum e&longs;t 10. Vtigitur 2. ad 10. &longs;ic 12. <lb/>totus &longs;capus erit ad pondus: quod per regulam trium inuenietur e&longs;&longs;e<emph.end type="italics"/>

<pb pagenum="149"/>60. <emph type="italics"/>vnciarum. Vbi notandum lancem in hoc numero pro &longs;uo pon<lb/>dere includi. Notandum etiam pondus impo&longs;itum lanci e&longs;&longs;e perinde <lb/>atque &longs;i in puncto A imponeretur. Sed de his qui multò plura vide<lb/>re volet, videat apud Cardanum lib. 1. de &longs;ubtilitate.<emph.end type="italics"/></s>

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<pb pagenum="151"/><foreign lang="greek">sh/xw ma,</foreign> <emph type="italics"/>vt annotauit Budæus in Pandect. quod apponitur in libra <lb/>ad æquilibrium faciendum. 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. 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. 6. tractatus de lib. in Mech. quod tale e&longs;t. Ma<lb/>nife&longs;tum e&longs;t quò pondus à centro libræ magis di&longs;tat, eò grauius e&longs;&longs;e, <lb/>& per con&longs;equens velocius moueri. Et æquipondÿ grauitatem in <lb/>vno loco ad grauitatem eiu&longs;dem in altero, eam rationem habere per <lb/>experientiam noui&longs;&longs;e &longs;e dicit Cardanus, quam habet remotio ad re-<emph.end type="italics"/><lb/>

<arrow.to.target n="marg37"></arrow.to.target><lb/><emph type="italics"/><expan abbr="motion&etilde;">motionem</expan>.<emph.end type="italics"/><lb/>

<arrow.to.target n="fig55"></arrow.to.target><lb/><emph type="italics"/>vt &longs;i æqui <lb/><expan abbr="pondi&utilde;">pondium</expan> K <lb/>in D ele<lb/>uet libras <lb/>20. & in <lb/>E 25. ele<lb/>uabit in F <lb/>30. In G 35. In H 40. Sic æquali &longs;patio æquale <expan abbr="acquir&etilde;s">acquirens</expan> <expan abbr="augment&utilde;">augmentum</expan>.<emph.end type="italics"/></s>

<figure id="fig55"></figure><lb/><emph type="italics"/>vt &longs;i æqui <lb/><expan abbr="pondi&utilde;">pondium</expan> K <lb/>in D ele<lb/>uet libras <lb/>20. & in <lb/>E 25. ele<lb/>uabit in F <lb/>30. In G 35. In H 40. Sic æquali &longs;patio æquale <expan abbr="acquir&etilde;s">acquirens</expan> <expan abbr="augment&utilde;">augmentum</expan>.<emph.end type="italics"/></s>

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<s><margin.target id="marg37"></margin.target>65. c. Arich</s>

<s><emph type="italics"/>Et quidem &longs;tateræ ratio demon&longs;trari pote&longs;t. Sit &longs;tateræ &longs;capus <lb/>H B cu-<emph.end type="italics"/><lb/>

<arrow.to.target n="fig56"></arrow.to.target><lb/><emph type="italics"/>ius an&longs;a <lb/>&longs;it A C, <lb/>& eius <lb/>æquipon<lb/>dium E, <lb/>appenda<lb/>tur vero <lb/>ex H <expan abbr="põ-dus">pon<lb/>dus</expan> D, <lb/>quod æquiponderet æquipondio E in F appen&longs;o. Aliud quoque pon<lb/>dus G appendatur in H, quod etiam æquipondio in B appen&longs;o. <lb/>æquiponderet.<emph.end type="italics"/></s>

<figure id="fig56"></figure><lb/><emph type="italics"/>ius an&longs;a <lb/>&longs;it A C, <lb/>& eius <lb/>æquipon<lb/>dium E, <lb/>appenda<lb/>tur vero <lb/>ex H <expan abbr="põ-dus">pon<lb/>dus</expan> D, <lb/>quod æquiponderet æquipondio E in F appen&longs;o. Aliud quoque pon<lb/>dus G appendatur in H, quod etiam æquipondio in B appen&longs;o. <lb/>æquiponderet.<emph.end type="italics"/></s>

<s><emph type="italics"/>Dico grauitatem ponderis D ad grauitatem ponderis G i<gap/><lb/>vt C F ad C B.<emph.end type="italics"/></s>

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<s>Cur medici facilius den<lb/>tes <expan abbr="exim&utilde;t">eximunt</expan> <expan abbr="accipi&etilde;tes">accipientes</expan> pon<lb/>dus, <expan abbr="d&etilde;tiducum">dentiducum</expan>: <expan abbr="quã">quam</expan> &longs;i &longs;ola <lb/>vtantur manu. Vtrum quia <lb/>dens magis manum præ<lb/>terlabitur, quam dentidu<lb/>cum? vel ferrum quidem <lb/>magis labitur manu, neque <lb/>ip&longs;um vndique <expan abbr="compreh&etilde;-dit">comprehen<lb/>dit</expan>. E&longs;t enim digitorum <lb/>caro mollis, & adhæret ma<lb/>gis, atque vndique con<lb/>gruit. Verum quia denti<lb/>ducus e&longs;t duo vectes aduer<lb/>&longs;i, vnum <expan abbr="hypomochli&utilde;">hypomochlium</expan> ha<lb/>bentes in concur&longs;u com<lb/>mi&longs;&longs;uræ. I gitur ad <expan abbr="ex&etilde;ptio-n&etilde;">exemptio<lb/>nem</expan>, vt facili^{9} <expan abbr="dimoueãt">dimoueant</expan>, hoc <lb/>vtuntur organo. Sit enim

<pb pagenum="153"/><gap/><lb/>dentiduci extremum alte<lb/>

<arrow.to.target n="fig57"></arrow.to.target><lb/>rum <foreign lang="greek">a,</foreign> alterum <foreign lang="greek">b,</foreign> quod <lb/>eximit, vectis vero <foreign lang="greek">a q z,</foreign><lb/>& alter vectis <foreign lang="greek">b g e</foreign>: hypo<lb/>mochlium verò <foreign lang="greek">q</foreign> vbi e&longs;t <expan abbr="cõ-mi&longs;&longs;ura">con<lb/>mi&longs;&longs;ura</expan>: <expan abbr="d&etilde;s">dens</expan> verò <expan abbr="põdus">pondus</expan> e&longs;t. <lb/>Vtroque igitur extremo <foreign lang="greek">b <lb/>& z</foreign> &longs;imul capiens dimouet: <lb/>quando vero emotus fuerit, manu facilius: quam in&longs;tru<lb/>mento eximetur.</s>

<figure id="fig57"></figure><lb/>rum <foreign lang="greek">a,</foreign> alterum <foreign lang="greek">b,</foreign> quod <lb/>eximit, vectis vero <foreign lang="greek">a q z,</foreign><lb/>& alter vectis <foreign lang="greek">b g e</foreign>: hypo<lb/>mochlium verò <foreign lang="greek">q</foreign> vbi e&longs;t <expan abbr="cõ-mi&longs;&longs;ura">con<lb/>mi&longs;&longs;ura</expan>: <expan abbr="d&etilde;s">dens</expan> verò <expan abbr="põdus">pondus</expan> e&longs;t. <lb/>Vtroque igitur extremo <foreign lang="greek">b <lb/>& z</foreign> &longs;imul capiens dimouet: <lb/>quando vero emotus fuerit, manu facilius: quam in&longs;tru<lb/>mento eximetur.</s>

<s>COMMENTARIVS.</s>

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<s>De in&longs;trumentis.] <emph type="italics"/>In&longs;trumentum ad frangendum nuces <lb/>pote&longs;t appellari nucifrangibulum, & hoc non differt à forcipe <lb/>ni&longs;i quia leuiter in extremis excauatur ad excipiendum nucem fran<lb/>gendam commodius, Huiu&longs;mo-<emph.end type="italics"/><lb/>

<arrow.to.target n="fig58"></arrow.to.target><lb/><emph type="italics"/>di e&longs;t F A C E A B.<emph.end type="italics"/></s>

<figure id="fig58"></figure><lb/><emph type="italics"/>di e&longs;t F A C E A B.<emph.end type="italics"/></s>

<s>Cur facilius.] <emph type="italics"/>Quæritur <lb/>cur nucifrangibulum ab&longs;que ictu <lb/>facillimè frangat nucem. Quod <lb/>problema, vt <expan abbr="anteced&etilde;s">antecedens</expan>, generale <lb/>e&longs;&longs;e pote&longs;t de quouis forcipe & forfice, ad capiendum &longs;cindendum <lb/>frangendum qualibus multis chirurgi, & quiuis manuales artifices <lb/>opera &longs;ua exercent & perficiunt.<emph.end type="italics"/></s>

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<s>Idem e&longs;t &longs;ermo.] <emph type="italics"/>Po&longs;terius e&longs;t cur vnum ê dictis punctis mo<lb/>tum prædictis duobus motibus minus aliquando &longs;patÿ conficiat: <expan abbr="quã">quam</expan> <lb/>latus &longs;uum. Vtrumque problema vt intelligatur &longs;ciendum e&longs;t e def. <lb/>32. lib. 1. Eucl. 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. prop. 32. li. 1. Eucl. <expan abbr="Cumq;">Cumque</expan> oppo&longs;iti in <expan abbr="parallelogrãmo">parallelogrammo</expan> <lb/>&longs;int æquales prop. 34. lib. <expan abbr="eiu&longs;d&etilde;">eiu&longs;dem</expan> duo &longs;unt acuti, reliqui obtu&longs;i, vt &longs;it <lb/><expan abbr="Rhõbus">Rhombus</expan><emph.end type="italics"/> <foreign lang="greek">a b d g,</foreign> <emph type="italics"/>cuius anguli oppo&longs;iti<emph.end type="italics"/> <foreign lang="greek">a</foreign> <emph type="italics"/>&<emph.end type="italics"/> <foreign lang="greek">d</foreign> <emph type="italics"/>&longs;int acuti:<emph.end type="italics"/> <foreign lang="greek">b</foreign> <emph type="italics"/>vero<emph.end type="italics"/>

<pb pagenum="160"/><emph type="italics"/>&<emph.end type="italics"/> <foreign lang="greek">g</foreign> <emph type="italics"/>obtu&longs;i. Coneipiamus ergo<emph.end type="italics"/> <foreign lang="greek">a</foreign> <emph type="italics"/>tan-<emph.end type="italics"/><lb/>

<arrow.to.target n="fig59"></arrow.to.target><lb/><emph type="italics"/>quam formicam ambulantem proprio <lb/>motu ver&longs;us<emph.end type="italics"/> <foreign lang="greek">b,</foreign> <emph type="italics"/>vt &<emph.end type="italics"/> <foreign lang="greek">b</foreign> <emph type="italics"/>proprio iti<lb/>dem motu ver&longs;us<emph.end type="italics"/> <foreign lang="greek">a.</foreign> <emph type="italics"/>Tum ip&longs;um<emph.end type="italics"/> <foreign lang="greek">a b</foreign><lb/><emph type="italics"/>latus ver&longs;us<emph.end type="italics"/> <foreign lang="greek">g d,</foreign> <emph type="italics"/>eadem etiam celerita<lb/>te moueri &longs;eruando paralleli&longs;mum, cum <lb/>ip&longs;o<emph.end type="italics"/> <foreign lang="greek">g d</foreign> <emph type="italics"/>quou&longs;que coniungatur ei. Ad <lb/>huius autem <expan abbr="mot&utilde;">motum</expan> moueri etiam<emph.end type="italics"/> <foreign lang="greek">a</foreign> <emph type="italics"/>ver<lb/>&longs;us<emph.end type="italics"/> <foreign lang="greek">g,</foreign> <emph type="italics"/>&<emph.end type="italics"/> <foreign lang="greek">b</foreign> <emph type="italics"/>ver&longs;us<emph.end type="italics"/> <foreign lang="greek">d.</foreign> <emph type="italics"/>Sicque<emph.end type="italics"/> <foreign lang="greek">a</foreign> <emph type="italics"/>&<emph.end type="italics"/> <foreign lang="greek">b</foreign><lb/><emph type="italics"/>mouebuntur duobus motibus, vno per &longs;e: <lb/>altero per accidens. Et po&longs;ito quod mo<lb/>ueantur in Rhombo. Id e&longs;t quod motus <lb/>illi &longs;int in ratione laterum quibus Rhombus continetur. E&longs;t autem <lb/>i&longs;ta certa, quia e&longs;t ratio æqualitatis vt<emph.end type="italics"/> <foreign lang="greek">i</foreign> <emph type="italics"/>ad<emph.end type="italics"/> <foreign lang="greek">i,</foreign> <emph type="italics"/>& in eadem celerita<lb/>te, id e&longs;t eodem tempore, non immeritò primum problema in medium <lb/>adducitur. quia &longs;i verum &longs;it, cau&longs;am habet minimè vulgarem.<emph.end type="italics"/></s>

<figure id="fig59"></figure><lb/><emph type="italics"/>quam formicam ambulantem proprio <lb/>motu ver&longs;us<emph.end type="italics"/> <foreign lang="greek">b,</foreign> <emph type="italics"/>vt &<emph.end type="italics"/> <foreign lang="greek">b</foreign> <emph type="italics"/>proprio iti<lb/>dem motu ver&longs;us<emph.end type="italics"/> <foreign lang="greek">a.</foreign> <emph type="italics"/>Tum ip&longs;um<emph.end type="italics"/> <foreign lang="greek">a b</foreign><lb/><emph type="italics"/>latus ver&longs;us<emph.end type="italics"/> <foreign lang="greek">g d,</foreign> <emph type="italics"/>eadem etiam celerita<lb/>te moueri &longs;eruando paralleli&longs;mum, cum <lb/>ip&longs;o<emph.end type="italics"/> <foreign lang="greek">g d</foreign> <emph type="italics"/>quou&longs;que coniungatur ei. Ad <lb/>huius autem <expan abbr="mot&utilde;">motum</expan> moueri etiam<emph.end type="italics"/> <foreign lang="greek">a</foreign> <emph type="italics"/>ver<lb/>&longs;us<emph.end type="italics"/> <foreign lang="greek">g,</foreign> <emph type="italics"/>&<emph.end type="italics"/> <foreign lang="greek">b</foreign> <emph type="italics"/>ver&longs;us<emph.end type="italics"/> <foreign lang="greek">d.</foreign> <emph type="italics"/>Sicque<emph.end type="italics"/> <foreign lang="greek">a</foreign> <emph type="italics"/>&<emph.end type="italics"/> <foreign lang="greek">b</foreign><lb/><emph type="italics"/>mouebuntur duobus motibus, vno per &longs;e: <lb/>altero per accidens. Et po&longs;ito quod mo<lb/>ueantur in Rhombo. Id e&longs;t quod motus <lb/>illi &longs;int in ratione laterum quibus Rhombus continetur. E&longs;t autem <lb/>i&longs;ta certa, quia e&longs;t ratio æqualitatis vt<emph.end type="italics"/> <foreign lang="greek">i</foreign> <emph type="italics"/>ad<emph.end type="italics"/> <foreign lang="greek">i,</foreign> <emph type="italics"/>& in eadem celerita<lb/>te, id e&longs;t eodem tempore, non immeritò primum problema in medium <lb/>adducitur. quia &longs;i verum &longs;it, cau&longs;am habet minimè vulgarem.<emph.end type="italics"/></s>

<s>Feratur enim.] <emph type="italics"/>Prioris problematis <expan abbr="veritat&etilde;">veritatem</expan> geometricè o&longs;ten<lb/>dit. 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. Perficiatur <expan abbr="parallelo-gramm&utilde;">parallelo<lb/>grammum</expan> prop. 31. lib. 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. 6. Ergo per conu <expan abbr="eiu&longs;d&etilde;">eiu&longs;dem</expan> prop. &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. 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. Ergo prop. 24. lib. 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>

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

<arrow.to.target n="fig60"></arrow.to.target><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. 18. lib. 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/>Dico latus A C maius e&longs;&longs;e diametro B C per eandem prop. 18. <lb/>&longs;ubtendit enim trianguli A B C maiorem angulum. Po&longs;&longs;e autem <lb/>talem Rhombum con&longs;titui, patet. quia angulus acutus &longs;eruata late<lb/>rum quorumuis a&longs;&longs;umptorum longitudine, infinitè minor fieri pote&longs;t, <lb/>prop. 9. lib. 1. Ergo & tandem dabitur minor dimidio obtu&longs;i. Nam <lb/>& dimidius recti, qui acutus e&longs;t, e&longs;t eo minor prop. 15. lib. 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>

<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. 18. lib. 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/>Dico latus A C maius e&longs;&longs;e diametro B C per eandem prop. 18. <lb/>&longs;ubtendit enim trianguli A B C maiorem angulum. Po&longs;&longs;e autem <lb/>talem Rhombum con&longs;titui, patet. quia angulus acutus &longs;eruata late<lb/>rum quorumuis a&longs;&longs;umptorum longitudine, infinitè minor fieri pote&longs;t, <lb/>prop. 9. lib. 1. Ergo & tandem dabitur minor dimidio obtu&longs;i. Nam <lb/>& dimidius recti, qui acutus e&longs;t, e&longs;t eo minor prop. 15. lib. 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>

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<s>Fere ad idem.] <emph type="italics"/>Particula<emph.end type="italics"/> <foreign lang="greek">sxedo\n</foreign> <emph type="italics"/>ferè ad-<emph.end type="italics"/><lb/>

<arrow.to.target n="fig61"></arrow.to.target><lb/><emph type="italics"/>iecta indicat non eundem e&longs;&longs;e terminum vtriu&longs;<lb/>que motionis, qua fertur<emph.end type="italics"/> <foreign lang="greek">a</foreign> <emph type="italics"/>: &longs;ed duos diuer&longs;os, ve<lb/>rum propiores, quam &longs;int termini ad quos<emph.end type="italics"/> <foreign lang="greek"><gap/></foreign><lb/><emph type="italics"/>fertur.<emph.end type="italics"/></s>

<figure id="fig61"></figure><lb/><emph type="italics"/>iecta indicat non eundem e&longs;&longs;e terminum vtriu&longs;<lb/>que motionis, qua fertur<emph.end type="italics"/> <foreign lang="greek">a</foreign> <emph type="italics"/>: &longs;ed duos diuer&longs;os, ve<lb/>rum propiores, quam &longs;int termini ad quos<emph.end type="italics"/> <foreign lang="greek"><gap/></foreign><lb/><emph type="italics"/>fertur.<emph.end type="italics"/></s>

<s>Rectior enim linea.] <emph type="italics"/>Id e&longs;t duo latera<emph.end type="italics"/> <foreign lang="greek"><gap/> a</foreign><lb/><emph type="italics"/>&<emph.end type="italics"/> <foreign lang="greek"><gap/> d</foreign> <emph type="italics"/>magis accedunt ad rectam vnam, vtpo<lb/>te quia angulus obtu&longs;us &longs;i augeatur plu&longs;culum, <lb/>latera ip&longs;um continentia fient è directo: & tunc<emph.end type="italics"/>

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

<arrow.to.target n="fig62"></arrow.to.target><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. lib. 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/>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. Sunt autem orbitæ ab vtri&longs;que confectæ <lb/>eadem celeritate motis. Eadem ratiocinatione cum<emph.end type="italics"/> <foreign lang="greek">a g</foreign> <emph type="italics"/>tanget in<emph.end type="italics"/>

<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. lib. 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/>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. Sunt autem orbitæ ab vtri&longs;que confectæ <lb/>eadem celeritate motis. Eadem ratiocinatione cum<emph.end type="italics"/> <foreign lang="greek">a g</foreign> <emph type="italics"/>tanget in<emph.end type="italics"/>

<pb pagenum="168"/><emph type="italics"/>puncto<emph.end type="italics"/> <foreign lang="greek">i</foreign> <emph type="italics"/>ex reuolutione maioris, &<emph.end type="italics"/> <foreign lang="greek">b</foreign> <emph type="italics"/>tanget in<emph.end type="italics"/> <foreign lang="greek">q</foreign>: <emph type="italics"/>&longs;icque<emph.end type="italics"/> <foreign lang="greek">q i</foreign> <emph type="italics"/>&<emph.end type="italics"/> <foreign lang="greek">h <lb/>z</foreign> <emph type="italics"/>cum &longs;int æquales & parallelæ, duæ rur&longs;us<emph.end type="italics"/> <foreign lang="greek">h q</foreign> <emph type="italics"/>&<emph.end type="italics"/> <foreign lang="greek">z i</foreign> <emph type="italics"/>erunt pa<lb/>rallelæ. Quæ autem ratio e&longs;t quartarum circulorum inter &longs;e, eadem <lb/>e&longs;t totorum. Partes enim cum pariter multiplicibus eandem ratio<lb/>nem habent prop. 15. lib. 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>

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<s>Qvod etiam dubit.] <emph type="italics"/>Antea de circulis ad vnum centrum <lb/>connexis <expan abbr="demõ&longs;tratum">demon&longs;tratum</expan> e&longs;t: perinde etiam in inæqualibus ad di<lb/>wer&longs;a puncta connexis &longs;e habere o&longs;tenditur, ni&longs;i <expan abbr="mend&utilde;">mendum</expan> &longs;ub&longs;it aliquod <lb/>in contextu è quo particulam<emph.end type="italics"/> <foreign lang="greek">ou)k</foreign> <emph type="italics"/>expunximus. Nam & eccentrici <lb/>connexi raptum motoris primi &longs;equuntur, & &longs;emper orbitarum <lb/>æqualitas reperietur &longs;eu centra &longs;int in eadem linea: &longs;iue in diuer&longs;is,<emph.end type="italics"/>

<arrow.to.target n="fig63"></arrow.to.target><lb/><emph type="italics"/>vtin A, B, <lb/>C, vbi lineæ <lb/>pro <gap/>rbitis <lb/>inæqualium <lb/><expan abbr="circulor&utilde;">circulorum</expan>, &longs;ed <lb/><expan abbr="annexor&utilde;">annexorum</expan> D <lb/>E, FG, HI <lb/>&longs;unt æquales <lb/>vt facile e&longs;t <lb/>demon&longs;trare <lb/>ex ad&longs;cripto <lb/>diagrammate.<emph.end type="italics"/></s>

<figure id="fig63"></figure><lb/><emph type="italics"/>vtin A, B, <lb/>C, vbi lineæ <lb/>pro <gap/>rbitis <lb/>inæqualium <lb/><expan abbr="circulor&utilde;">circulorum</expan>, &longs;ed <lb/><expan abbr="annexor&utilde;">annexorum</expan> D <lb/>E, FG, HI <lb/>&longs;unt æquales <lb/>vt facile e&longs;t <lb/>demon&longs;trare <lb/>ex ad&longs;cripto <lb/>diagrammate.<emph.end type="italics"/></s>

<s>Quod vero eodem.] <emph type="italics"/>Re&longs;pondet a&longs;&longs;umptioni præcedentis &longs;yllo<lb/>gi&longs;mi, in quo concludebatur ratio admirationis problematis. Negat<lb/>que idem etiam concentricorum circulorum ita vt dictum e&longs;t moto<lb/>rum, <expan abbr="c&etilde;trum">centrum</expan> e&longs;&longs;e, ni&longs;i captiose. Huius enim <expan abbr="centr&utilde;">centrum</expan>, e&longs;t quod primum <lb/>mouetur, non huius quod &longs;ecundario. Huius enim centrum feriatur: <lb/>illius verò <expan abbr="c&utilde;">cum</expan> &longs;it <expan abbr="principi&utilde;">principium</expan> motus, agit, &longs;eu in actu e&longs;t. Et &longs;ic non <expan abbr="vn&utilde;">vnum</expan> <lb/><expan abbr="idemq;">idemque</expan> centrum <expan abbr="vtriu&longs;q;">vtriu&longs;que</expan> e&longs;t, cum <expan abbr="alter&utilde;">alterum</expan> moueat, alterum moueatur. <lb/>Hæc tamen &longs;olutio quæ &longs;it, relinquo cogitandum. quomodo enim &longs;i <lb/><expan abbr="principi&utilde;">principium</expan> motus <expan abbr="concentricor&utilde;">concentricorum</expan> <expan abbr="circulor&utilde;">circulorum</expan> &longs;it ab axe, vt in mola mole<lb/>trinæ, & <expan abbr="vn&utilde;">vnum</expan> <expan abbr="idemq;">idemque</expan> <expan abbr="centr&utilde;">centrum</expan> cum &longs;it, puta, molæ minoris in maiore <lb/>de&longs;criptæ, non <expan abbr="id&etilde;">idem</expan> eodem <expan abbr="t&etilde;pore">tempore</expan> ab <expan abbr="eod&etilde;">eodem</expan> erit in actu & <expan abbr="principi&utilde;">principium</expan>, &longs;ui <lb/>mot^{9} habebit. Aliter igitur verè &longs;olueretur, &longs;i intelligamus aliud e&longs;&longs;e <lb/><expan abbr="mot&utilde;">motum</expan> <expan abbr="circular&etilde;">circularem</expan>: aliud <expan abbr="mot&utilde;">motum</expan> in circulo vel per circulum. Motus enim <lb/>circularis fit <expan abbr="c&etilde;tro">centro</expan> quie&longs;cente, & reliquis omnibus motis, talis e&longs;t mo<lb/>tus æquatoris in cælo. Motus verò per <expan abbr="circul&utilde;">circulum</expan> fit progrediente centro, <lb/>& huic accedit vt <expan abbr="circ&utilde;uertatur">circunuertatur</expan>, alioqui nihil aliud e&longs;&longs;et <expan abbr="quã">quam</expan> circu<lb/>lus progrediens, & vectio <expan abbr="quædã">quædam</expan>, vt hæc qua<emph.end type="italics"/> <foreign lang="greek">a</foreign> <emph type="italics"/><expan abbr="centr&utilde;">centrum</expan> perpetuò per<emph.end type="italics"/><lb/>

<arrow.to.target n="marg40"></arrow.to.target><lb/><emph type="italics"/>æquidi&longs;tantem <expan abbr="lineã">lineam</expan> fertur in<emph.end type="italics"/> <foreign lang="greek">g,</foreign> <emph type="italics"/>&longs;eu trahatur &longs;eu impellatur, & ideo <lb/>omnia puncta æqualiter <expan abbr="mou&etilde;tur">mouentur</expan>, & per æquale <expan abbr="&longs;pati&utilde;">&longs;patium</expan> perinde ac &longs;i <lb/>motus hic merè rectus e&longs;&longs;et, & &longs;ine vlla circumuer&longs;ione qua&longs;i fune <lb/>circulus traheretur. Cæterum cum <expan abbr="tã">tam</expan><emph.end type="italics"/> <foreign lang="greek">z g d,</foreign> <emph type="italics"/><expan abbr="quã">quam</expan><emph.end type="italics"/> <foreign lang="greek">h b e</foreign> <emph type="italics"/>moueantur &longs;u<lb/>per rectas<emph.end type="italics"/> <foreign lang="greek">zl, h q</foreign> <emph type="italics"/>& quidem ita vt &longs;ingula puncta<emph.end type="italics"/> <foreign lang="greek">z g d</foreign> <emph type="italics"/>tangant <lb/>&longs;ingula puncta<emph.end type="italics"/> <foreign lang="greek">z l</foreign><emph type="italics"/>: <expan abbr="t&utilde;">tum</expan><emph.end type="italics"/> <foreign lang="greek">h b e</foreign> <emph type="italics"/>&longs;ingula puncta ip&longs;ius<emph.end type="italics"/> <foreign lang="greek">h <expan abbr="q.">que</expan></foreign> <emph type="italics"/>Tamen peri<lb/>pheria<emph.end type="italics"/> <foreign lang="greek">z g d,</foreign> <emph type="italics"/>aut <expan abbr="nõ">non</expan> e&longs;t æqualis rectæ<emph.end type="italics"/> <foreign lang="greek">z l</foreign><emph type="italics"/>: aut peripheria<emph.end type="italics"/> <foreign lang="greek">z b e</foreign> <emph type="italics"/><expan abbr="nõ">non</expan> e&longs;t<emph.end type="italics"/>

<pb pagenum="174"/><emph type="italics"/>æqualis rectæ<emph.end type="italics"/> <foreign lang="greek">h q</foreign>: <emph type="italics"/>alioqui &longs;i<emph.end type="italics"/><lb/>

<arrow.to.target n="fig64"></arrow.to.target><lb/><emph type="italics"/>ambæ peripheriæ ambabus re<lb/>ctis e&longs;&longs;ent æquales, cum ip&longs;æ <lb/>&longs;int æquales rectæ, vt demon<lb/>&longs;tratume&longs;t, e&longs;&longs;ent & periphe<lb/>riæ æquales, maior minori, quod <lb/>ab&longs;urdum. Ex quo exploditur <lb/>ratio Bouilli, qui ex <expan abbr="circ&utilde;uolu-tione">circunuolu<lb/>tione</expan> circuli exactè rotundi &longs;u<lb/>per plano ad libellam facto pu<lb/>tabat inueni&longs;&longs;e rectam periphe<lb/>riæ æqualem. Quæritur ergo quod e&longs;t &longs;uperiori problemate diffici<lb/>lius, vt fieri poßit rectarum æqualium peragratio à circulis inæqua<lb/>libus. Sit igitur. vt rotæ axis<emph.end type="italics"/> <foreign lang="greek">a</foreign> <emph type="italics"/>tran&longs;eat in F. Et quia<emph.end type="italics"/> <foreign lang="greek">a h</foreign> <emph type="italics"/>& F G<emph.end type="italics"/><lb/>

<figure id="fig64"></figure><lb/><emph type="italics"/>ambæ peripheriæ ambabus re<lb/>ctis e&longs;&longs;ent æquales, cum ip&longs;æ <lb/>&longs;int æquales rectæ, vt demon<lb/>&longs;tratume&longs;t, e&longs;&longs;ent & periphe<lb/>riæ æquales, maior minori, quod <lb/>ab&longs;urdum. Ex quo exploditur <lb/>ratio Bouilli, qui ex <expan abbr="circ&utilde;uolu-tione">circunuolu<lb/>tione</expan> circuli exactè rotundi &longs;u<lb/>per plano ad libellam facto pu<lb/>tabat inueni&longs;&longs;e rectam periphe<lb/>riæ æqualem. Quæritur ergo quod e&longs;t &longs;uperiori problemate diffici<lb/>lius, vt fieri poßit rectarum æqualium peragratio à circulis inæqua<lb/>libus. Sit igitur. vt rotæ axis<emph.end type="italics"/> <foreign lang="greek">a</foreign> <emph type="italics"/>tran&longs;eat in F. Et quia<emph.end type="italics"/> <foreign lang="greek">a h</foreign> <emph type="italics"/>& F G<emph.end type="italics"/><lb/>

<arrow.to.target n="fig65"></arrow.to.target><lb/><emph type="italics"/>æquales &longs;unt. Radij enim &longs;unt eiu&longs;dem circuli minoris &<emph.end type="italics"/> <foreign lang="greek">h</foreign> <emph type="italics"/>G e&longs;t <lb/>æquidi&longs;tans<emph.end type="italics"/> <foreign lang="greek">a</foreign> <emph type="italics"/>F. Erit per demon&longs;trata punctum G in linea F H. <lb/>Et ponatur quod punctum fuerit M in maiori circulo, quod tran&longs;la<lb/>tum & retrò reuolutum peruenerit ad H, atque<emph.end type="italics"/> <foreign lang="greek">a</foreign> <emph type="italics"/>M &longs;ecet circulum <lb/>minorem<emph.end type="italics"/> <foreign lang="greek">h</foreign> <emph type="italics"/>F<emph.end type="italics"/> <foreign lang="greek">e,</foreign> <emph type="italics"/>vt in puncto I. Dico quod I e&longs;t punctum G. Nam <lb/>quia M e&longs;t H, & in linea F H: præterea I e&longs;t in linea<emph.end type="italics"/> <foreign lang="greek">a</foreign> <emph type="italics"/>M, <lb/>erit etiam in linea F H. E&longs;t etiam in circulo<emph.end type="italics"/> <foreign lang="greek">h</foreign> <emph type="italics"/>F<emph.end type="italics"/> <foreign lang="greek">e.</foreign> <emph type="italics"/>Ergo in puncto <lb/>communi vtrique. Nullum autem e&longs;t præter G. Igitur I peruenit<emph.end type="italics"/>

<figure id="fig65"></figure><lb/><emph type="italics"/>æquales &longs;unt. Radij enim &longs;unt eiu&longs;dem circuli minoris &<emph.end type="italics"/> <foreign lang="greek">h</foreign> <emph type="italics"/>G e&longs;t <lb/>æquidi&longs;tans<emph.end type="italics"/> <foreign lang="greek">a</foreign> <emph type="italics"/>F. Erit per demon&longs;trata punctum G in linea F H. <lb/>Et ponatur quod punctum fuerit M in maiori circulo, quod tran&longs;la<lb/>tum & retrò reuolutum peruenerit ad H, atque<emph.end type="italics"/> <foreign lang="greek">a</foreign> <emph type="italics"/>M &longs;ecet circulum <lb/>minorem<emph.end type="italics"/> <foreign lang="greek">h</foreign> <emph type="italics"/>F<emph.end type="italics"/> <foreign lang="greek">e,</foreign> <emph type="italics"/>vt in puncto I. Dico quod I e&longs;t punctum G. Nam <lb/>quia M e&longs;t H, & in linea F H: præterea I e&longs;t in linea<emph.end type="italics"/> <foreign lang="greek">a</foreign> <emph type="italics"/>M, <lb/>erit etiam in linea F H. E&longs;t etiam in circulo<emph.end type="italics"/> <foreign lang="greek">h</foreign> <emph type="italics"/>F<emph.end type="italics"/> <foreign lang="greek">e.</foreign> <emph type="italics"/>Ergo in puncto <lb/>communi vtrique. Nullum autem e&longs;t præter G. Igitur I peruenit<emph.end type="italics"/>

<pb pagenum="175"/><emph type="italics"/>in G. Sicque M retroceßit per angulum M G H. Contrà I an<lb/>teceßit per angulum I G F, qui &longs;unt anguli æquales prop. 15. lib. 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. Hæc ex <lb/>Cardan. prop. 196. lib. 5. de proport.<emph.end type="italics"/></s>

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

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<s>Sit lectus <foreign lang="greek">a z h i.</foreign>] <emph type="italics"/>In tertia ratione &longs;ecundæ quæ&longs;tionis expli<lb/>canda reliquus Ari&longs;totelis contextus totus e&longs;t: &longs;ed adeo mendo&longs;us <lb/>& in verbis, & in diagrammatis, & in diagrammatum characte<lb/>ribus, vt &longs;i Iuppiter cum Æ&longs;culapio mederi, & mendas eluere ve<lb/>lit, non poßit tamen: ideò &longs;atius e&longs;t cum &longs;it nota philo&longs;ophi &longs;enten<lb/>tia, totum adimere, & alium &longs;upplere. Ob&longs;curitas ex tam corru<lb/>pto contextumanans fecit, vt nonnulli interpretes Cardano non &longs;a<lb/>tisfecerint, qui negotium numeris ab&longs;oluunt, cum tamen demon&longs;tra<lb/>tionem geometricam in&longs;tituerint, neque in figuris lectorum a&longs;&longs;um<lb/>ptis, & in contextu ne&longs;cio à quibus po&longs;itis, eundem numerum linea<lb/>rum retineant. Sed in vna octo, in altera decem, non debuerit<emph.end type="italics"/>

<pb pagenum="180"/><emph type="italics"/>idem numerus vbique e&longs;&longs;e: &longs;i quidem magnum quid &longs;it & demon<lb/>&longs;tratu dignum, minus lororum in vna exten&longs;ione expendi: quam in <lb/>altera: qui <expan abbr="deniq;">denique</expan> in vtraque figura obliquas <expan abbr="hab&etilde;t">habent</expan> lineas, quanquam <lb/>alias alÿs obliquiores: & tamen duæ antehac rationes videntur in <lb/>vna figura po&longs;tulare obliquas, in altera rectas. Nos igitur aliter Car<lb/>dani ve&longs;tigia ob&longs;cura, & ni fallor imperfecta, vt &longs;unt <expan abbr="pleraq;">pleraque</expan> huius <lb/>hominis ferè omnia vt arbitror, <expan abbr="quanquã">quanquam</expan> &longs;emper ingeniosè &longs;criben<lb/>tis, &longs;ecuti, apertius & perfectius totum hoc <expan abbr="negoti&utilde;">negotium</expan> euoluemus. At<lb/>que in primis dicimus extendi lora &longs;ecundum diametrum, non e&longs;&longs;e <lb/>ab angulo ad angulum oppo&longs;itum: &longs;ed &longs;ecundum rectas, quæ à latere <lb/>ad latus oppo&longs;itum extenduntur, vt &longs;int aliæ &longs;ecundum longitudi<lb/>nem, aliæ &longs;ecundum latitudinem. Sic enim diameter non<emph.end type="italics"/> <foreign lang="greek"><gap/> gw/nios</foreign><lb/><emph type="italics"/>&longs;umi videtur: qua&longs;i dimetiens, vt quæ dimetiatur longitudinem vel <lb/>latitudinem, æqualis videlicet facta, quo modo licet hîc ab Ari&longs;to<lb/>tele reiecto, hodie adhuc vtuntur. Atque hoc modo &longs;i non intelliga<lb/>tur diameter: &longs;ed<emph.end type="italics"/> <foreign lang="greek"><gap/>a gw/nios,</foreign> <emph type="italics"/>tam obliquæ erunt in vna forma li<lb/>neæ: quam in altera: &longs;icque quæ de ruptione vel fißione & opportu<lb/>nitate dicta &longs;unt, hîc non conuenient, quod e&longs;&longs;et ab&longs;urdum. His igi<lb/>tur ita po&longs;itis de&longs;cribantur duæ formæ lecti, in quibus &longs;int lineæ nu<lb/>mero pares, &longs;itu diuer&longs;æ. Sit igitur prima A B C D, cuius la-<emph.end type="italics"/><lb/>

<arrow.to.target n="fig66"></arrow.to.target><lb/><emph type="italics"/>tus A B duplum &longs;it lateris A C, & quidem illud 4. pe<lb/>dum, hoc duorum. In hac lora &longs;ecundum diametrum &longs;int quidem <lb/>&longs;ecundum longitudinem tria K N. L O, M P, & &longs;ic inter &longs;e<emph.end type="italics"/>

<figure id="fig66"></figure><lb/><emph type="italics"/>tus A B duplum &longs;it lateris A C, & quidem illud 4. pe<lb/>dum, hoc duorum. In hac lora &longs;ecundum diametrum &longs;int quidem <lb/>&longs;ecundum longitudinem tria K N. 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. 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/>

<arrow.to.target n="fig67"></arrow.to.target><lb/><emph type="italics"/>rallelæ &longs;unt, & aduer&longs;æ in &longs;uis parallelogrammis, omnes inter &longs;e <lb/>æquales &longs;unt prop. 34. lib. 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. 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. 47. lib. 1.<emph.end type="italics"/></s>

<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. 34. lib. 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. 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. 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>

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<s>Cau&longs;a vero e&longs;t, quod ex <lb/>medio &longs;ubleuato &longs;emper <lb/>extrema &longs;e inuicem &longs;uble<lb/>uant: & altera pars alteram <lb/>promptè attollit. Medium <lb/>enim quod habet <expan abbr="&longs;ubleuãs">&longs;ubleuans</expan> <lb/>vel <expan abbr="fer&etilde;s">ferens</expan> efficitur tanquam <lb/>centrum. Itaque <expan abbr="vtrumq;">vtrumque</expan> <lb/>extremorum deor&longs;um ver<lb/>gens &longs;ur&longs;um &longs;u&longs;penditur. <lb/>At ab extremo <expan abbr="eleuat&utilde;">eleuatum</expan> vel <lb/>ge&longs;tatum non idem facit: <lb/>quin totum onus vergit ad <lb/>medium vnum quò eleua<lb/>tur vel fertur. Hoc &longs;it <foreign lang="greek">a,</foreign><lb/>extrema <foreign lang="greek">b, g.</foreign> Igitur eleuato <lb/>vel ge&longs;tato qua parte e&longs;t <foreign lang="greek">a</foreign>:

<arrow.to.target n="fig68"></arrow.to.target><lb/><foreign lang="greek">b</foreign> quidem deor&longs;um ver<lb/>gens attollit <foreign lang="greek">g:g</foreign> vero deor<lb/>&longs;um repens attollit <foreign lang="greek">b.</foreign> Si<lb/>mul autem eleuata idem præ&longs;tant.</s>

<figure id="fig68"></figure><lb/><foreign lang="greek">b</foreign> quidem deor&longs;um ver<lb/>gens attollit <foreign lang="greek">g:g</foreign> vero deor<lb/>&longs;um repens attollit <foreign lang="greek">b.</foreign> Si<lb/>mul autem eleuata idem præ&longs;tant.</s>

<s>COMMENTARIVS.</s>

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<s>Cau&longs;a vero.] <emph type="italics"/>Confirmatio e&longs;t a&longs;&longs;umptionis ex æquis extremo<lb/>rum ponderibus vicißim ob id &longs;e &longs;ubleuantibus: &longs;i enim vnius <lb/>propen &longs;io vergit deor&longs;um: alterius re&longs;i&longs;tentia ad motum &longs;ur&longs;um im<lb/>pediet. Et &longs;ic &longs;e&longs;e mutuò librantia pondera, mutuò etiam &longs;e &longs;ubleuant. <lb/>E&longs;t enim medium quod fertur, tanquam centrum, à quo extrema vt <lb/>æquæ lances in iu&longs;ta libra, &longs;u&longs;penduntur. Non ita e&longs;t vbi lignum per <lb/>extremum fertur: &longs;ed totum ad partem vnam vergit ab co per quod<emph.end type="italics"/><lb/>

<arrow.to.target n="fig69"></arrow.to.target><lb/><emph type="italics"/>ge&longs;tatur deflectens. Ex deflexione autem <lb/>&longs;eu depreßione extremi, tanquam ponderis <lb/>prementis, labor augetur in ferente. Ergo <lb/>vbi depreßio nulla e&longs;t, vt in priori modo, <lb/>ibi labor minor erit. Et &longs;ic lignum lon<lb/>gum ab extremo difficilius fertur quam <lb/>à medio. Sed hîc etiam quæri pote&longs;t cur <lb/>lignum longum puta lancea ab extremo <lb/>vno ge&longs;tata facilius feratur, &longs;i perpendi<lb/>cularis &longs;it plano horizontis: <expan abbr="quã">quam</expan> ad ip&longs;um <lb/>inclinata. Hoc fit quia in perpendiculari <lb/>partes inferiores &longs;u&longs;tinent &longs;uperiores: in <lb/>inclinata non item, omnes enim &longs;ine ful<lb/>cimento tendunt pro natura &longs;ua deor&longs;um. <lb/>Præterea in perpendiculari ip&longs;a lancea to<lb/>ta pondus e&longs;t. Huic &longs;u&longs;tinendæ quæ vis<emph.end type="italics"/>

<figure id="fig69"></figure><lb/><emph type="italics"/>ge&longs;tatur deflectens. Ex deflexione autem <lb/>&longs;eu depreßione extremi, tanquam ponderis <lb/>prementis, labor augetur in ferente. Ergo <lb/>vbi depreßio nulla e&longs;t, vt in priori modo, <lb/>ibi labor minor erit. Et &longs;ic lignum lon<lb/>gum ab extremo difficilius fertur quam <lb/>à medio. Sed hîc etiam quæri pote&longs;t cur <lb/>lignum longum puta lancea ab extremo <lb/>vno ge&longs;tata facilius feratur, &longs;i perpendi<lb/>cularis &longs;it plano horizontis: <expan abbr="quã">quam</expan> ad ip&longs;um <lb/>inclinata. Hoc fit quia in perpendiculari <lb/>partes inferiores &longs;u&longs;tinent &longs;uperiores: in <lb/>inclinata non item, omnes enim &longs;ine ful<lb/>cimento tendunt pro natura &longs;ua deor&longs;um. <lb/>Præterea in perpendiculari ip&longs;a lancea to<lb/>ta pondus e&longs;t. Huic &longs;u&longs;tinendæ quæ vis<emph.end type="italics"/>

<pb pagenum="186"/><emph type="italics"/>&longs;ufficiet, &longs;ufficiet &<emph.end type="italics"/><lb/>

<arrow.to.target n="fig70"></arrow.to.target><lb/><emph type="italics"/>ferendæ, inque &longs;u&longs;ti<lb/>nenda tantum labo<lb/>rat: in inclinata ex<lb/>tremum e&longs;t hypomoch<lb/>lium, à quo non longè <lb/>abe&longs;t vis mouens: pon<lb/>dus verò quod e&longs;t reli<lb/>qua pars, ab hoc extre<lb/>mo alterum extremum <lb/>quantò longius: tantò <lb/>maiorem rationem ad <lb/>vim mouentem habe<lb/>bit, & &longs;ic difficilius <lb/>feretur.<emph.end type="italics"/></s>

<figure id="fig70"></figure><lb/><emph type="italics"/>ferendæ, inque &longs;u&longs;ti<lb/>nenda tantum labo<lb/>rat: in inclinata ex<lb/>tremum e&longs;t hypomoch<lb/>lium, à quo non longè <lb/>abe&longs;t vis mouens: pon<lb/>dus verò quod e&longs;t reli<lb/>qua pars, ab hoc extre<lb/>mo alterum extremum <lb/>quantò longius: tantò <lb/>maiorem rationem ad <lb/>vim mouentem habe<lb/>bit, & &longs;ic difficilius <lb/>feretur.<emph.end type="italics"/></s>

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<s><emph type="italics"/>Sit igitur lignum <lb/>longius A B è me-<emph.end type="italics"/><lb/>

<arrow.to.target n="fig71"></arrow.to.target><lb/><emph type="italics"/>dio C ge&longs;tatum.<emph.end type="italics"/></s>

<figure id="fig71"></figure><lb/><emph type="italics"/>dio C ge&longs;tatum.<emph.end type="italics"/></s>

<s><emph type="italics"/>Sit & breuius<emph.end type="italics"/><lb/>

<arrow.to.target n="fig72"></arrow.to.target><lb/><emph type="italics"/>D E eiu&longs;dem pon<lb/>deris puta decem librarum è medio F ge&longs;tatum etiam. Quia partes <lb/>cum pariter multiplicibus &longs;unt in eadem ratione prop. 15. lib. 5. & <lb/>e&longs;t A B maior ip&longs;o D E, erit dimidium A C maius dimidio D F. <lb/>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. Item B. Ergotum A tum B <lb/>plus impediunt ferentem ex C: quam D & E ex F. Quæri hic <lb/>po&longs;&longs;et cur pondera &longs;ini&longs;tro humero facilius ferantur, quam dextro. <lb/>Hoc fit, quia dextrum <expan abbr="cumnat&utilde;">cumnatum</expan> &longs;it ad mouere: &longs;ini&longs;trum ad moueri: <lb/>illud &longs;i liberum &longs;it ab onere impo&longs;ito (quod premit ideoque impedit) <lb/>facilius & maiori vi mouebit. Impeditum enim omne minus probe <lb/>fungitur officio. Præterea cum progreßio fiat impul&longs;ione vnius cru<lb/>ris, & tractione, tum impul&longs;ione alterius, melius e&longs;t aliud, quod plus <lb/>impul&longs;ione & tractionevalet ab onere liberari. E&longs;t <expan abbr="aut&etilde;">autem</expan> <expan abbr="dextr&utilde;">dextrum</expan> crus.<emph.end type="italics"/></s>

<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. Quia partes <lb/>cum pariter multiplicibus &longs;unt in eadem ratione prop. 15. lib. 5. & <lb/>e&longs;t A B maior ip&longs;o D E, erit dimidium A C maius dimidio D F. <lb/>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. Item B. Ergotum A tum B <lb/>plus impediunt ferentem ex C: quam D & E ex F. Quæri hic <lb/>po&longs;&longs;et cur pondera &longs;ini&longs;tro humero facilius ferantur, quam dextro. <lb/>Hoc fit, quia dextrum <expan abbr="cumnat&utilde;">cumnatum</expan> &longs;it ad mouere: &longs;ini&longs;trum ad moueri: <lb/>illud &longs;i liberum &longs;it ab onere impo&longs;ito (quod premit ideoque impedit) <lb/>facilius & maiori vi mouebit. Impeditum enim omne minus probe <lb/>fungitur officio. Præterea cum progreßio fiat impul&longs;ione vnius cru<lb/>ris, & tractione, tum impul&longs;ione alterius, melius e&longs;t aliud, quod plus <lb/>impul&longs;ione & tractionevalet ab onere liberari. E&longs;t <expan abbr="aut&etilde;">autem</expan> <expan abbr="dextr&utilde;">dextrum</expan> crus.<emph.end type="italics"/></s>

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<s><emph type="italics"/>Machina hæc quæ ab officio tollendi tolleno dicitur, con&longs;tat trabe <lb/>erecta, vt D C, & tigno tran&longs;uer&longs;o circa axiculum in alto trabis<emph.end type="italics"/><lb/>

<arrow.to.target n="fig73"></arrow.to.target><lb/><emph type="italics"/>ver&longs;atili, vt A B, à cuius extremo B cum cathena B E pendet <lb/>vas E, in altero A pondus plumbeum, vel lapideum G adÿcitur ad <lb/>commodiorem, vt vult hîc Ari&longs;tottles, à puteo F exhau&longs;tum. Quæ<lb/>rit igitur cur in altero tollenonis extremo pondus adÿciatur. Huius <lb/>quæ&longs;tionis difficultas arguitur, quod &longs;itula &longs;eu vacua, &longs;eu plena, &longs;it <lb/>pondus. Pondus autem ponderi adiectum difficilius moueri deberet.<emph.end type="italics"/></s>

<figure id="fig73"></figure><lb/><emph type="italics"/>ver&longs;atili, vt A B, à cuius extremo B cum cathena B E pendet <lb/>vas E, in altero A pondus plumbeum, vel lapideum G adÿcitur ad <lb/>commodiorem, vt vult hîc Ari&longs;tottles, à puteo F exhau&longs;tum. Quæ<lb/>rit igitur cur in altero tollenonis extremo pondus adÿciatur. Huius <lb/>quæ&longs;tionis difficultas arguitur, quod &longs;itula &longs;eu vacua, &longs;eu plena, &longs;it <lb/>pondus. Pondus autem ponderi adiectum difficilius moueri deberet.<emph.end type="italics"/></s>

<s>An quod in duo.] <emph type="italics"/>Re&longs;pon&longs;io e&longs;tex di&longs;tinctione duplicis mo<lb/>tus exhau&longs;tioni per tollenonem nece&longs;&longs;arÿ. Alter e&longs;t immer&longs;ionis: al<lb/>ter eleuationis. Et illum quidem fatetur Ari&longs;toteles ex adiecto pon<lb/>dere reddi difficiliorem: at hunc contra multo effici faciliorem. Ad<lb/>mittendum autem in vna totius operis parte leue incommodum, pro<lb/>pter &longs;ub&longs;ecuturam in altera opero&longs;iori parte longè maiorem commo<lb/>ditatem. Vnde autem tum hæc, tum illud pendeat non dicit Ari&longs;tote<lb/>les, quia ex antecedentibus facile intellectum. Tignus enim tran&longs;<lb/>uer&longs;us e&longs;t vectis, cuius <expan abbr="fulciment&utilde;">fulcimentum</expan> e&longs;t in axiculo trabis, <expan abbr="atq;">atque</expan> in motu <lb/>immer&longs;ionis pondus <expan abbr="mouend&utilde;">mouendum</expan> e&longs;t in A: mouens vero e&longs;t in B, vel in <lb/>&longs;itula E. Quò igitur pondus in A erit grauius, eò difficilius attol<lb/>letur, &longs;ic natura grauitatis ferente: & &longs;ic maiore vi opus erit: contrà <lb/>in motu eleuationis, pondus mouendum e&longs;t &longs;itula, mouens e&longs;t in A, <lb/>hic adiutus pondere adiecto natura &longs;ua deor&longs;um vergente, facilius <lb/>tantò deprimet ip&longs;um A: quantò grauius erit G. Et &longs;ic facilius B <lb/>attolletur cum annexa &longs;itula. Po&longs;&longs;et etiam hæc quæ&longs;tio ad libram <lb/>commodißimè referri.<emph.end type="italics"/></s>

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<s>Cvr cum duo.] <emph type="italics"/>Fu&longs;tes teretes nodis carentes ad onera go&longs;tan<lb/>da apti palangæ à Nonio & Varrone dicuntur, vel phalangæ <lb/>à Plinio vnde phalangarÿ Baiuli ÿs <expan abbr="vt&etilde;tes">vtentes</expan>, qui ex numero tetrapho<lb/>ri, & hexaphori dicti &longs;unt. Quærit igitur hîc Ari&longs;toteles. cur è duo<lb/>bus pondus aliquod phalanga ferentibus, quò ponderi propinquior e&longs;t <lb/>alter, eò magis remotiori prematur. Cuius quæ&longs;tionis <expan abbr="causã">causam</expan> refert ad <lb/><expan abbr="vect&etilde;">vectem</expan>, cuius <expan abbr="hypomochli&utilde;">hypomochlium</expan> &longs;it in <expan abbr="põdere">pondere</expan> ge&longs;tato, vel <expan abbr="&longs;u&longs;t&etilde;to">&longs;u&longs;tento</expan>. Siue enim <lb/>homines <expan abbr="ambul&etilde;t">ambulent</expan>: &longs;iue &longs;tent, nihil intere&longs;t, vtpotè quod grauitate &longs;ua <lb/>ne attollatur, ob &longs;i&longs;tat. <expan abbr="Mouend&utilde;">Mouendum</expan> e&longs;t in &longs;u&longs;tinente propinquiore: <expan abbr="mou&etilde;s">mouens</expan> <lb/>e&longs;t in remotiore. Et cur ita potius, cau&longs;am adfert, quia vectis pars ma<lb/>ior facilius mouetur, id e&longs;t vt interpretor &longs;u&longs;tinetur, vel eleuatur: &longs;ic<lb/>que pars minor magis deprimetur, depre&longs;&longs;a <expan abbr="ferent&etilde;">ferentem</expan> vel <expan abbr="&longs;u&longs;tinent&etilde;">&longs;u&longs;tinentem</expan> ma<lb/>gis premet, vt hîc moueri <expan abbr="nõ">non</expan> &longs;it aliud: <expan abbr="quã">quam</expan> deor&longs;um premi: & mouere <lb/>&longs;u&longs;tinere, vel attollere. Alioqui &longs;i mouere aliter &longs;umatur, ratio qua <lb/>vectis longior facilius mouet, e&longs;t in motione circa <expan abbr="hypomochli&utilde;">hypomochlium</expan> am<lb/>bitus magnitudo, ob <expan abbr="quã">quam</expan> quia motio redditur tardior, & ideò leuior <lb/><expan abbr="etiã">etiam</expan> e&longs;t, hîc conuenire <expan abbr="nõ">non</expan> pote&longs;t. Neque enim in hac vectis <expan abbr="circ&utilde;duci-tur">circunduci<lb/>tur</expan>: &longs;ed premit <expan abbr="tant&utilde;">tantum</expan> &longs;u&longs;tinentes, vt quid graue. Sed & aliter quam <lb/>Ari&longs;toteles re&longs;ponderi pote&longs;t, ita accepto motu, &longs;i dicamus <expan abbr="alterutr&utilde;">alterutrum</expan> <lb/>e &longs;u&longs;tinentibus e&longs;&longs;e <expan abbr="fulciment&utilde;">fulcimentum</expan>, & alterum e&longs;&longs;e <expan abbr="potentiã">potentiam</expan>: mobile <expan abbr="aut&etilde;">autem</expan> <lb/>e&longs;&longs;e id, quod inter <expan abbr="vtrumq;">vtrumque</expan> appendet. Nam <expan abbr="ver&utilde;">verum</expan> e&longs;t quod è tertio co<lb/>roll. prop. 2. tractatus de vecte apud <expan abbr="Gvid&utilde;">Gvidum</expan> Vbaldum demon&longs;trate <lb/>deducitur. Nempe &longs;i in extremis vectis duæ &longs;int potentiæ, inter quas <lb/>pondus &longs;it &longs;u&longs;pen&longs;um. Erit vna ad alteram vt interualla inter po<lb/>tentias, & pondus reciprocè. Vt &longs;i &longs;it vectis A B, poten<lb/>tiæ A & B, pondus &longs;u&longs;tentum C E, erit A ad B. vt B C <lb/>ad A C. Sit igitur vt B C &longs;it minor: quam A C. Ergo A.<emph.end type="italics"/>

<pb pagenum="192"/><emph type="italics"/>potentia<emph.end type="italics"/><lb/>

<arrow.to.target n="fig74"></arrow.to.target><lb/><emph type="italics"/>erit mi<lb/>nor: <expan abbr="quã">quam</expan> <lb/>B, id e&longs;t <lb/>potentia <lb/>minorin <lb/>A &longs;ic di <lb/>&longs;tante à <lb/>C &longs;ufficiet &longs;u&longs;tinendo ponderi. Po&longs;itis igitur A & B potentÿs <lb/>æqualibus, A facilius &longs;u&longs;tinebit, & quidem tantò: quantò A <gap/><lb/>&longs;tabit magis ab C. Sit præterea vt C &longs;it in medio vectis A B. <lb/>quia B C erit æqualis ip&longs;i A C potentiæ æquales A & B e&longs;&longs;e <lb/>debent, vt æquè pondus idem &longs;u&longs;tineant. Ob id rectè dictum e&longs;t illud <lb/>ab Ouidio,<emph.end type="italics"/></s>

<figure id="fig74"></figure><lb/><emph type="italics"/>erit mi<lb/>nor: <expan abbr="quã">quam</expan> <lb/>B, id e&longs;t <lb/>potentia <lb/>minorin <lb/>A &longs;ic di <lb/>&longs;tante à <lb/>C &longs;ufficiet &longs;u&longs;tinendo ponderi. Po&longs;itis igitur A & B potentÿs <lb/>æqualibus, A facilius &longs;u&longs;tinebit, & quidem tantò: quantò A <gap/><lb/>&longs;tabit magis ab C. Sit præterea vt C &longs;it in medio vectis A B. <lb/>quia B C erit æqualis ip&longs;i A C potentiæ æquales A & B e&longs;&longs;e <lb/>debent, vt æquè pondus idem &longs;u&longs;tineant. Ob id rectè dictum e&longs;t illud <lb/>ab Ouidio,<emph.end type="italics"/></s>

<s>Non benè inæquales veniunt ad aratra Iuuenci:</s>

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<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. 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/>

<arrow.to.target n="fig75"></arrow.to.target><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. 46. <lb/>& 47. lib. 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. 18. lib. 1. Et &longs;ic E plus <lb/>de&longs;cendit re&longs;pectu B: quam re&longs;pectu A. 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>

<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. 46. <lb/>& 47. lib. 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. 18. lib. 1. Et &longs;ic E plus <lb/>de&longs;cendit re&longs;pectu B: quam re&longs;pectu A. 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>

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<s>Cur omnes qui &longs;urgunt.] <emph type="italics"/>Quærit hîc Ari&longs;toteles, cur &longs;ur<lb/>gens de &longs;eßione nece&longs;&longs;ario con&longs;tituat angu<lb/>lum acutum ex tibia cum femore, vel ex <lb/>thorace, &longs;eu &longs;pina cum femore, vt in &longs;e&longs;-<emph.end type="italics"/><lb/>

<arrow.to.target n="fig76"></arrow.to.target><lb/><emph type="italics"/>&longs;ione &longs;it thorax A B, femur B C, tibia C <lb/>D, anguli A B C & B C D recti. Ex hoc <lb/>&longs;ituad &longs;urgendum innitens nece&longs;&longs;e habet addu<lb/>cere C D ad C E, vel A B ad B F, vt è <lb/>rectis A B C, B C D angulis, fiant acuti <lb/>F B C, B C E.<emph.end type="italics"/></s>

<figure id="fig76"></figure><lb/><emph type="italics"/>&longs;ione &longs;it thorax A B, femur B C, tibia C <lb/>D, anguli A B C & B C D recti. Ex hoc <lb/>&longs;ituad &longs;urgendum innitens nece&longs;&longs;e habet addu<lb/>cere C D ad C E, vel A B ad B F, vt è <lb/>rectis A B C, B C D angulis, fiant acuti <lb/>F B C, B C E.<emph.end type="italics"/></s>

<s>An quia quod æquale.] <emph type="italics"/>Quæ&longs;tionem propo&longs;itam &longs;oluit du<lb/>pliciter. Primo modo è cau&longs;a quietis in &longs;e&longs;sione <expan abbr="per&longs;euerãte">per&longs;euerante</expan>, quandiu <lb/>recti anguli con&longs;eruantur. hic erit &longs;yllogi&longs;mus.<emph.end type="italics"/></s>

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<s>Vel quod &longs;urgens.] <emph type="italics"/>Secundus modus e&longs;t &longs;olutionis quæ&longs;tionis <lb/>propo&longs;itæ per modum mutationis, quæ fit dum quis è <expan abbr="&longs;ed&etilde;te">&longs;edente</expan> fit &longs;tans, <lb/>quæ &longs;urrectio dicitur. Hæc igitur, &longs;i quis &longs;tare debeat facere debet, <lb/>vt &longs;it particeps di&longs;po&longs;itionis, quæ in &longs;tante e&longs;t. At di&longs;po&longs;itio quæ in <lb/>&longs;tante e&longs;t, e&longs;t &longs;itus pedum & capitis, &longs;pinæque in eadem recta. Huius <lb/>&longs;eßio non e&longs;t particeps. quia pedes & &longs;pina &longs;unt in Lineis parallelis: <lb/>contra adductio tibiæ, ita vt angulum acutum cum femore con&longs;ti-<emph.end type="italics"/>

<pb pagenum="197"/><emph type="italics"/>tuat: vel thoracis vt cum <lb/>femore, quia pedes rectà<emph.end type="italics"/><lb/>

<arrow.to.target n="fig77"></arrow.to.target><lb/><emph type="italics"/>&longs;ub capite, aut &longs;altem re<lb/>ctius: quam ante collocat, <lb/>&longs;tationis magis e&longs;t parti<lb/>ceps. Ad &longs;urrectionem igi<lb/>tur nece&longs;&longs;arij &longs;unt anguli <lb/>acuti facti vel à thorace <lb/>cum femoribus, vel à fe<lb/>moribus cum tibijs, vt diagrammate<emph.end type="italics"/> <foreign lang="greek">a b g d</foreign> <emph type="italics"/>pro &longs;edente, &<emph.end type="italics"/> <foreign lang="greek">e b <lb/>g z</foreign> <emph type="italics"/>pro &longs;urgente declaratur.<emph.end type="italics"/></s>

<figure id="fig77"></figure><lb/><emph type="italics"/>&longs;ub capite, aut &longs;altem re<lb/>ctius: quam ante collocat, <lb/>&longs;tationis magis e&longs;t parti<lb/>ceps. Ad &longs;urrectionem igi<lb/>tur nece&longs;&longs;arij &longs;unt anguli <lb/>acuti facti vel à thorace <lb/>cum femoribus, vel à fe<lb/>moribus cum tibijs, vt diagrammate<emph.end type="italics"/> <foreign lang="greek">a b g d</foreign> <emph type="italics"/>pro &longs;edente, &<emph.end type="italics"/> <foreign lang="greek">e b <lb/>g z</foreign> <emph type="italics"/>pro &longs;urgente declaratur.<emph.end type="italics"/></s>

<s><emph type="italics"/>Et hinc patet quod &longs;i thorace cum femore, & femore cum tibia <lb/>&longs;imul anguli acuti fiant, facilius &longs;urgetur: & rur&longs;us quantò an<lb/>guli illi erunt acutiores: tantò facilius &longs;urgetur: &longs;icque &longs;urgunt <lb/>imbecilli, & conuale&longs;centes. Porrò &longs;urrectio è &longs;edente ad &longs;tandum <lb/>declarata e&longs;t angulis acutis indigere: &longs;urrectionem è iacente etiam <lb/>indigere clarum e&longs;t. Is enim qui iace<gap/>, vt &longs;urgat, & &longs;tet, quatuor <lb/>acutos efficit, utroque brachio & latere: thorace & cruribus: fe<lb/>moribus & tibiis, vt ia<lb/>ceat A B G D. vt &longs;ur-<emph.end type="italics"/><lb/>

<arrow.to.target n="fig78"></arrow.to.target><lb/><emph type="italics"/>gat A B thorax bra<lb/>chiorum in acutos con<lb/>formatorum adminiculo <lb/>adducetur ad E B: &longs;ic<lb/>que E B G erit acutus <lb/>ex thorace & femoribus, <lb/>& G D tibia adducetur in G F: &longs;icque erit acutus B G F.<emph.end type="italics"/></s>

<figure id="fig78"></figure><lb/><emph type="italics"/>gat A B thorax bra<lb/>chiorum in acutos con<lb/>formatorum adminiculo <lb/>adducetur ad E B: &longs;ic<lb/>que E B G erit acutus <lb/>ex thorace & femoribus, <lb/>& G D tibia adducetur in G F: &longs;icque erit acutus B G F.<emph.end type="italics"/></s>

<s><emph type="italics"/>Cæterum &longs;eßio, de qua hîc Aristoteles, e&longs;t propriè dicta, & hanc <lb/>Galenus cum &longs;ecuritate e&longs;&longs;e dixit. Et ea maximè vtuntur, qui &longs;e<lb/>dentarias artes exercent. At tamen &longs;eßio latè &longs;umpta, fit ad angu<lb/>los acutos, vt cum &longs;ella humilior e&longs;t tibÿs &longs;edentis, & ad obtu&longs;os <lb/>cum altior e&longs;t. Vnde experientia notum e&longs;t hominem quantò altius <lb/>&longs;edet, tantò facilius &longs;urgere, quod tamen videtur repugnare prædi<lb/>ctis, cum obtu&longs;i anguli longius ab &longs;int, etiam quam recti, ab acutis.<emph.end type="italics"/>

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<arrow.to.target n="fig79"></arrow.to.target><lb/><emph type="italics"/>K facilius &longs;ur<lb/>get: quam ex L: <lb/>quamque ex M. <lb/>Ratio e&longs;t, quia <lb/>A B &longs;uper K <lb/>magis e&longs;t parti<lb/>ceps &longs;tationis: <lb/>quam &longs;uper L. <lb/>Et &longs;uper L quam <lb/>quam &longs;uper M. <lb/>Vt enim &longs;urrectionis initium fiat per angulos acutos: Me<lb/>dium tamen perducens ad terminum ad quem, qui e&longs;t &longs;itum <lb/>e&longs;&longs;e in vna recta vt A B G D, tran&longs;it per minus acutos <lb/>ad rectum, & tandem ad obtu&longs;os, & obtu&longs;is obtu&longs;iores: quou&longs;que <lb/>ad vnam rectam peruentum &longs;it, in qua e&longs;t &longs;tatio vt e&longs;t A B G D <lb/>relicta &longs;ella K, vel L, vel M. Sed præter hæc ob&longs;eruatione di<lb/>gnum e&longs;t, quod in ambulatione progre&longs;&longs;uque no&longs;tro femora cum ti<lb/>bijs, & thoracem cum femoribus non omnino in rectam: &longs;ed in an<lb/>gulos obtu&longs;ißimos: tum crura inter &longs;e in acutum angulum, qui e&longs;t <lb/>vertex trianguli I&longs;o&longs;celis conformamus. Altero &longs;cilicet pedum fir<lb/>mato in &longs;olum, altero celeriter circumlato. vt cum P Ramo aduer<lb/>&longs;us philo&longs;ophos illos, &longs;i diis placet, qui Platonicis alis de&longs;tituti, philo<lb/>&longs;ophari aggrediuntur, concludamus, quod quie&longs;cimus, quod &longs;edemus, <lb/>quod &longs;urgimus, quod &longs;tamus, quod ambulamus, quod currimus, geo<lb/>metriæ v&longs;um e&longs;&longs;e. Sed & addemus ex nostro Galeno, id quoque ve<lb/>rum e&longs;&longs;e de brutis omnibus, quorum pedes in&longs;i&longs;tunt terræ ad rectos <lb/>angulos, <expan abbr="&longs;pinã">&longs;pinam</expan> pedibus tanquam columnis ad rectos etiam &longs;uperemi<lb/>nere. Hinc cau&longs;am collige, cur &longs;int nonnulla ex his tam apta ferendis <lb/>&longs;arcinis & oneribus. Hinc quoque, &longs;i vis, collige cau&longs;am, cur baiuli <lb/>Pari&longs;ien&longs;es onera tanta &longs;uis harpagonibus: alÿ &longs;portulis ferant, nimi<lb/>rum cum ita componant &longs;pinam, vt antror&longs;um reclinata moles &longs;u-<emph.end type="italics"/>

<figure id="fig79"></figure><lb/><emph type="italics"/>K facilius &longs;ur<lb/>get: quam ex L: <lb/>quamque ex M. <lb/>Ratio e&longs;t, quia <lb/>A B &longs;uper K <lb/>magis e&longs;t parti<lb/>ceps &longs;tationis: <lb/>quam &longs;uper L. <lb/>Et &longs;uper L quam <lb/>quam &longs;uper M. <lb/>Vt enim &longs;urrectionis initium fiat per angulos acutos: Me<lb/>dium tamen perducens ad terminum ad quem, qui e&longs;t &longs;itum <lb/>e&longs;&longs;e in vna recta vt A B G D, tran&longs;it per minus acutos <lb/>ad rectum, & tandem ad obtu&longs;os, & obtu&longs;is obtu&longs;iores: quou&longs;que <lb/>ad vnam rectam peruentum &longs;it, in qua e&longs;t &longs;tatio vt e&longs;t A B G D <lb/>relicta &longs;ella K, vel L, vel M. Sed præter hæc ob&longs;eruatione di<lb/>gnum e&longs;t, quod in ambulatione progre&longs;&longs;uque no&longs;tro femora cum ti<lb/>bijs, & thoracem cum femoribus non omnino in rectam: &longs;ed in an<lb/>gulos obtu&longs;ißimos: tum crura inter &longs;e in acutum angulum, qui e&longs;t <lb/>vertex trianguli I&longs;o&longs;celis conformamus. Altero &longs;cilicet pedum fir<lb/>mato in &longs;olum, altero celeriter circumlato. vt cum P Ramo aduer<lb/>&longs;us philo&longs;ophos illos, &longs;i diis placet, qui Platonicis alis de&longs;tituti, philo<lb/>&longs;ophari aggrediuntur, concludamus, quod quie&longs;cimus, quod &longs;edemus, <lb/>quod &longs;urgimus, quod &longs;tamus, quod ambulamus, quod currimus, geo<lb/>metriæ v&longs;um e&longs;&longs;e. Sed & addemus ex nostro Galeno, id quoque ve<lb/>rum e&longs;&longs;e de brutis omnibus, quorum pedes in&longs;i&longs;tunt terræ ad rectos <lb/>angulos, <expan abbr="&longs;pinã">&longs;pinam</expan> pedibus tanquam columnis ad rectos etiam &longs;uperemi<lb/>nere. Hinc cau&longs;am collige, cur &longs;int nonnulla ex his tam apta ferendis <lb/>&longs;arcinis & oneribus. Hinc quoque, &longs;i vis, collige cau&longs;am, cur baiuli <lb/>Pari&longs;ien&longs;es onera tanta &longs;uis harpagonibus: alÿ &longs;portulis ferant, nimi<lb/>rum cum ita componant &longs;pinam, vt antror&longs;um reclinata moles &longs;u-<emph.end type="italics"/>

<pb pagenum="199"/><emph type="italics"/>perna corporis æquiponderet onere & viribus oneri impo&longs;ito hu<lb/>meris, & ita tamen vt ambo cum femoribus & tibiis, tali&longs;que recta <lb/>in&longs;istant ad terram ad angulos rectos, adiectis ad ea firmitatis &longs;ta<lb/>tionis gratia, tanquam ba&longs;is & fundamenti, tar&longs;o, pedio, & digitis <lb/>pedum. Sic enim moles &longs;uperni corporis, & onus habent aliquid ad <lb/>perpendiculum inferiorum partium, quod &longs;e &longs;uffulciat. Totu&longs;que ba<lb/>iulus cum onere, quod gestat instar turbinis, aut coni vertice terræ <lb/>incumbit, ba&longs;i &longs;upereminente. Hinc etiam collige cur baiulis cum <lb/>onere a&longs;cen&longs;us graduum facilior e&longs;t: quam de&longs;cen&longs;us. In a&longs;cen&longs;u enim <lb/>quantum antror&longs;um &longs;e incuruent, nullum inde illis ca&longs;us periculum: <lb/>at in de&longs;cen&longs;iu vel exigua illis curuatura periculum adfert, ex quo <lb/><expan abbr="etiãrarò">etiarrarò</expan> videas, ni&longs;i ebiberint plus paulò, baiulos <expan abbr="c&utilde;">cum</expan> onere de&longs;cendere, <lb/>a&longs;cendere autem, quoties opus e&longs;t.<emph.end type="italics"/></s>

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<s><emph type="italics"/>Quod autem quie&longs;cens vim motoris diminuat, patet. quia &longs;i &longs;ineretur <lb/>nec impelleretur, exempli gratia, &longs;ur&longs;um, vel lateraliter, natura &longs;ua <lb/>&longs;ublato impedimento rectà deor&longs;um ferretur. Ergò qua vieò moue<lb/>retur, eadem re&longs;i&longs;tit, ne &longs;ur&longs;um vellateraliter impellatur. Re&longs;istere <lb/>autem motori, diminuere e&longs;t eius vim in mouendo. Imò vera e&longs;t illa <lb/>propo&longs;itio. Ab æquali aut minore vi quam &longs;it impedimentum non <lb/>fit motus. Sit enim A B C D <lb/>quod re&longs;istat per decem ne &longs;ur&longs;um<emph.end type="italics"/><lb/>

<arrow.to.target n="fig80"></arrow.to.target><lb/><emph type="italics"/>trahatur. Dico quod &longs;ur&longs;um non <lb/>trahetur, neque per 10. neque per 9. <lb/>&c. Nam &longs;ub&longs;tracto impedimento, <lb/>quod impedit ne A deor&longs;um fera<lb/>tur, eo ferretur vt 10. Quod &longs;i eo<lb/>dem tempore &longs;ur&longs;um trahatur à vi <lb/>quæ &longs;it etiam vt 10. tunc tantum <lb/>mouebitur deor&longs;um: quantum &longs;ur<lb/>&longs;um, quie&longs;cet igitur. Si verò &longs;ur&longs;um trahatur à vi minore, vt nouem, <lb/>quia à maiore vi deor&longs;um fertur, non &longs;ur&longs;um: &longs;ed deor&longs;um &longs;impliciter<emph.end type="italics"/>

<figure id="fig80"></figure><lb/><emph type="italics"/>trahatur. Dico quod &longs;ur&longs;um non <lb/>trahetur, neque per 10. neque per 9. <lb/>&c. Nam &longs;ub&longs;tracto impedimento, <lb/>quod impedit ne A deor&longs;um fera<lb/>tur, eo ferretur vt 10. Quod &longs;i eo<lb/>dem tempore &longs;ur&longs;um trahatur à vi <lb/>quæ &longs;it etiam vt 10. tunc tantum <lb/>mouebitur deor&longs;um: quantum &longs;ur<lb/>&longs;um, quie&longs;cet igitur. Si verò &longs;ur&longs;um trahatur à vi minore, vt nouem, <lb/>quia à maiore vi deor&longs;um fertur, non &longs;ur&longs;um: &longs;ed deor&longs;um &longs;impliciter<emph.end type="italics"/>

<pb pagenum="201"/><emph type="italics"/>feretur. Præterea alia etiam demon&longs;tratione quæ&longs;tio ab Aristotele <lb/>propo&longs;ita concludi pote&longs;t. &longs;ic,<emph.end type="italics"/></s>

<s><emph type="italics"/>Omne duobus motibus ad diuer&longs;a tendentibus commotum, tan<lb/>tò minus vno mouetur: quantò magis altero. quia vis quæ <lb/>aliquò mouet plus: plus etiam ob&longs;i&longs;tit, & &longs;ic retardat & in<lb/>fringit vim, quæ aliò mouet.<emph.end type="italics"/></s>

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<s>Cvr lata in vortice.] <foreign lang="greek">*dino/m<gap/>uon u(/dw<gap/></foreign> <emph type="italics"/>&longs;eu<emph.end type="italics"/> <foreign lang="greek">di/nh</foreign> <emph type="italics"/>Latinis vor<lb/>texaquæ, & gurges. Locus e&longs;t profundus in flumine in quo <lb/>aqua vertitur, &longs;ic dictus quod gulæ in&longs;tar ad &longs;e trahat, & deuoret. <lb/>Innatantia enim &longs;eu grauia vt nauim: &longs;eu leuia vt plumam, &longs;tatim <lb/>atque ad medium &longs;ui adduxit, tam rapidè &longs;ummergit, vt in momen<lb/>to nu&longs;quam videas. Ari&longs;toteles in hoc loco præ&longs;upponit<emph.end type="italics"/> <foreign lang="greek"><gap/>)n di/nh su/<lb/><gap/>ofas t<gap/> u(da/twn</foreign> <emph type="italics"/>vortices aquo&longs;os e&longs;&longs;e multos circulos concen<lb/>tricos, quorum vt continens maior e&longs;t contento: ita &longs;emper celerius<emph.end type="italics"/>

<pb pagenum="207"/><emph type="italics"/>ferri. quod quam verum &longs;it, postea docebimus, vbi problema cum <lb/>&longs;uis cau&longs;is ex mente Ari&longs;tote<lb/>lis explicuerimus. Quæritigi-<emph.end type="italics"/><lb/>

<arrow.to.target n="fig81"></arrow.to.target><lb/><emph type="italics"/>tur Aristoteles cur quæ fe<lb/>runtur in vortico&longs;a aqua, om<lb/>nia tandem ad medium deuol<lb/>uantur. Sit igitur A medium <lb/>aquæ per circulos B C D, <lb/>E F G, H I K, L M N, <lb/>O P Q volutæ: &longs;it & vt <lb/>nauis R feratur per vorticem <lb/>B C D.<emph.end type="italics"/></s>

<figure id="fig81"></figure><lb/><emph type="italics"/>tur Aristoteles cur quæ fe<lb/>runtur in vortico&longs;a aqua, om<lb/>nia tandem ad medium deuol<lb/>uantur. Sit igitur A medium <lb/>aquæ per circulos B C D, <lb/>E F G, H I K, L M N, <lb/>O P Q volutæ: &longs;it & vt <lb/>nauis R feratur per vorticem <lb/>B C D.<emph.end type="italics"/></s>

<s><emph type="italics"/>Dico quod ad A medium <lb/>deuoluetur.<emph.end type="italics"/></s>

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<s><emph type="italics"/>Sit A inte<lb/>rius extremum, <lb/>

<arrow.to.target n="fig82"></arrow.to.target><lb/>& B exterius <lb/>lineæ &longs;piralis A <lb/>B plurium reuo<lb/>lutionum, in ex<lb/>tremo B &longs;it na<lb/>uis C. Dico quod <lb/>C feretur ad A, <lb/>& in&longs;uper quod <lb/>cum erit in A <lb/>&longs;ummergetur in<lb/>tra aby&longs;&longs;um A <lb/>E.<emph.end type="italics"/></s>

<figure id="fig82"></figure><lb/>& B exterius <lb/>lineæ &longs;piralis A <lb/>B plurium reuo<lb/>lutionum, in ex<lb/>tremo B &longs;it na<lb/>uis C. Dico quod <lb/>C feretur ad A, <lb/>& in&longs;uper quod <lb/>cum erit in A <lb/>&longs;ummergetur in<lb/>tra aby&longs;&longs;um A <lb/>E.<emph.end type="italics"/></s>

<s>Demon&longs;t. <lb/><emph type="italics"/><expan abbr="Innatãs">Innatans</expan> in vor<lb/>tico&longs;a aqua fer<lb/>tur ad motum <lb/>vndæ impul&longs;æ, <lb/>vel tractæ.<emph.end type="italics"/></s>

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<s><emph type="italics"/>6.28. hominum 7.11. engibatis 8.11. vtilitatem 8.22.<emph.end type="italics"/> Hanc &longs;ed <lb/>10.4. <emph type="italics"/><foreign lang="greek">ow)to/ma<gap/></foreign> 11.17. vinum. 11.19. cucurbitulæ 12.5. nullus <lb/>18.19. intrò 19.27. quintupedalis 30.15. dimetientem 30.33. duas <lb/>36.1. radiorum 37.5.<emph.end type="italics"/> <foreign lang="greek">e)f) ou_</foreign> <emph type="italics"/>39. littera<emph.end type="italics"/> <foreign lang="greek">w</foreign> <emph type="italics"/>debet intelligi in angu<lb/>lonon &longs;ignato parallelogrammi<emph.end type="italics"/><lb/>

<arrow.to.target n="fig83"></arrow.to.target><lb/><foreign lang="greek">uzq</foreign> 48.9. <foreign lang="greek"><gap/>i/on</foreign> 77.10. <lb/><emph type="italics"/>quadrupedibus 81. dee&longs;t figura <lb/>96.12.<emph.end type="italics"/> <foreign lang="greek">a)su/sa<gap/></foreign> <emph type="italics"/>142.24. Epi<lb/>grammatis 167.32. per 182. <lb/>tota pagina vbi e&longs;t litera<emph.end type="italics"/> <foreign lang="greek">z</foreign> <emph type="italics"/>re<lb/>ponenda littera<emph.end type="italics"/> <foreign lang="greek"><gap/></foreign> 190.13. <foreign lang="greek">tou_ <lb/>bar/ous.</foreign></s>

<figure id="fig83"></figure><lb/><foreign lang="greek">uzq</foreign> 48.9. <foreign lang="greek"><gap/>i/on</foreign> 77.10. <lb/><emph type="italics"/>quadrupedibus 81. dee&longs;t figura <lb/>96.12.<emph.end type="italics"/> <foreign lang="greek">a)su/sa<gap/></foreign> <emph type="italics"/>142.24. Epi<lb/>grammatis 167.32. per 182. <lb/>tota pagina vbi e&longs;t litera<emph.end type="italics"/> <foreign lang="greek">z</foreign> <emph type="italics"/>re<lb/>ponenda littera<emph.end type="italics"/> <foreign lang="greek"><gap/></foreign> 190.13. <foreign lang="greek">tou_ <lb/>bar/ous.</foreign></s>

<s><emph type="italics"/>In contextu Græco omi&longs;imus de indu&longs;tria diagrammata Vve<lb/>cheli, partim par&longs;imonia &longs;umptuum, partim quod po&longs;ata in commen<lb/>tarÿs eorum vtcumque vicem &longs;upplerent. Si indigeas, ab eo re<lb/>petere licet.<emph.end type="italics"/></s>

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