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version 1.4, 2004/08/19 13:56:18

version 1.6, 2004/08/19 16:52:33

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<s id="N1112F">Accedit, quod &longs;æpe vtilitas refunditur in dignitatem obie<lb/>cti; vtilitas enim attenditur ex fine, ad quem ordinatur &longs;cien<lb/>tia; qui profectò in &longs;cientijs practicis coincidit cum obiecto <lb/>formali. </s>

<s id="N11138">Eadem namque &longs;anitas anima&longs;is, e&longs;t finis medicinæ, <lb/>& ratio, &longs;ub qua Medicina agit de &longs;uis &longs;ubiectis. </s>

<s id="N11138">Eadem namque &longs;anitas animalis, e&longs;t finis medicinæ, <lb/>& ratio, &longs;ub qua Medicina agit de &longs;uis &longs;ubiectis. </s>

<s id="N1113D">Eademque <lb/>directio operationum intellectus, e&longs;t finis Logicæ &longs;cientiæ, & <lb/>ratio &longs;ub qua de ip&longs;is operationibus agitur in illa. </s>

<s id="N11144">Cum igi<lb/>tur talis, ac tanta &longs;it vtilitas Mechanicæ &longs;cientiæ ad fines præ<lb/>&longs;tanti&longs;&longs;imos admirabili cum artificio con&longs;equendos, vt ad le<lb/>uanda ingentia pondera, parua, & exigua virtute, ad commo<lb/>ditates tam plurimas, <expan abbr="vrbiumq.">vrbiumque</expan> ornatum tam varium: ad &longs;ub<lb/>mini&longs;trandas tot machinas, & in&longs;trumenta in bello, vt belli<lb/>gerare potius Mechanica, quam armis ip&longs;is, homines videan<lb/>tur: ad aptius mouenda Nauigia; ingentes paruo momento <lb/>excitandas moles, <expan abbr="immaniaq.">immaniaque</expan> euertenda ædificia: ad aquas ar<lb/>tifi cio&longs;i&longs;&longs;i<gap/>nè <expan abbr="&longs;ublimãdas">&longs;ublimandas</expan>, <expan abbr="aeremq.">aeremque</expan> perpetuis follibus emitten<lb/>dum; voces tàm varias effingendas, concentum æquabiliter <lb/>efformandum, motum qua&longs;i animalem in&longs;en&longs;ibilibus imper<lb/>tiendum, & &longs;imilia; ingenue fatendum e&longs;t nec e&longs;&longs;e artem, <lb/>quæ &longs;e Mechanicæ arti in dignitate valeat comparari, nec <lb/>e&longs;&longs;e &longs;cientiam practicam, quam ip&longs;a ex certitudine, & euiden<lb/>tia, qua procedit, & ex dignitate, ac præ&longs;tantia finis, non an<lb/>tecellat; ita vt in quo &longs;uperatur ex parte &longs;ubiecti nobilioris à <lb/>Medicina, vel Logica, comoen&longs;etur, aut vincatur ex parte <lb/>digni&longs;&longs;imi finis, & obiecti formalis, dum admirabili artificio <lb/>intendit ip&longs;os naturæ fines Naturam emulando &longs;uperare. </s>

<s id="N11144">Cum igi<lb/>tur talis, ac tanta &longs;it vtilitas Mechanicæ &longs;cientiæ ad fines præ<lb/>&longs;tanti&longs;&longs;imos admirabili cum artificio con&longs;equendos, vt ad le<lb/>uanda ingentia pondera, parua, & exigua virtute, ad commo<lb/>ditates tam plurimas, <expan abbr="vrbiumq.">vrbiumque</expan> ornatum tam varium: ad &longs;ub<lb/>mini&longs;trandas tot machinas, & in&longs;trumenta in bello, vt belli<lb/>gerare potius Mechanica, quam armis ip&longs;is, homines videan<lb/>tur: ad aptius mouenda Nauigia; ingentes paruo momento <lb/>excitandas moles, <expan abbr="immaniaq.">immaniaque</expan> euertenda ædificia: ad aquas ar<lb/>tificio&longs;i&longs;&longs;imè <expan abbr="&longs;ublimãdas">&longs;ublimandas</expan>, <expan abbr="aeremq.">aeremque</expan> perpetuis follibus emitten<lb/>dum; voces tàm varias effingendas, concentum æquabiliter <lb/>efformandum, motum qua&longs;i animalem in&longs;en&longs;ibilibus imper<lb/>tiendum, & &longs;imilia; ingenue fatendum e&longs;t nec e&longs;&longs;e artem, <lb/>quæ &longs;e Mechanicæ arti in dignitate valeat comparari, nec <lb/>e&longs;&longs;e &longs;cientiam practicam, quam ip&longs;a ex certitudine, & euiden<lb/>tia, qua procedit, & ex dignitate, ac præ&longs;tantia finis, non an<lb/>tecellat; ita vt in quo &longs;uperatur ex parte &longs;ubiecti nobilioris à <lb/>Medicina, vel Logica, compen&longs;etur, aut vincatur ex parte <lb/>digni&longs;&longs;imi finis, & obiecti formalis, dum admirabili artificio <lb/>intendit ip&longs;os naturæ fines Naturam emulando &longs;uperare. </s>

Line 581

<s id="N111DF">Præmittit autem exemplum de magno pondere quod ab exi<lb/>gua virtute admirandum in modum, ip&longs;ius vectis adminiculo <lb/>con&longs;tat moueri. </s>

<s id="N111E6"><expan abbr="Rationemq.">Rationemque</expan> admirationis ac dubitationis <lb/>annectit: Quia &longs;cilicet potius oppo&longs;itum ex eo &longs;equi deberet, <lb/>cum vectis adminiculo, pondus ponderi adiungatur, <expan abbr="inqui&etilde;s">inquiens</expan>. <lb/></s>

<s id="N111F5">Quod enim &longs;ine vecte qui&longs;piam mouere non pote&longs;t, idip&longs;um <lb/>citius mouet, vectis ad illud pondus adiungens. </s>

<s id="N111FA">Verumenim<lb/>uero huius ac &longs;imilium miraculorum omnium cau&longs;as refert <lb/>ad naturam circuli. </s>

<s id="N111FA">Verum enim <lb/>uero huius ac &longs;imilium miraculorum omnium cau&longs;as refert <lb/>ad naturam circuli. </s>

<s id="N11201">Nam vt inferius docet, quæ circa libram <lb/>fiunt, ad circulum rediguntur; quæ vero circa vectem, ad ip<lb/>&longs;am libram; alia autem fere omnia quæ circa Mechanicas <pb pagenum="34" xlink:href="005/01/042.jpg"/>&longs;unt motiones, ad vectem. </s>

<s id="N1120D">Interim ex admiralibi (inquiens) <lb/>mirandum accidere quippiam non e&longs;&longs;e ab&longs;urdum. </s>

<s id="N1120D">Interim ex admirabili (inquiens) <lb/>mirandum accidere quippiam non e&longs;&longs;e ab&longs;urdum. </s>

<s id="N11212">Subin<lb/>telligendo, admirabilem profecto e&longs;&longs;e ip&longs;am naturam circuli <lb/>ex qua tot admiranda procedunt, vt &longs;tatim probare aggredi<lb/>tur in &longs;equentibus. </s>

Line 593

<s id="N11227">Textus Tertius.</s>

<s id="N1122C">M<emph type="italics"/>axime autem e&longs;t admirandum &longs;imul <lb/>contraria fieri; Circulus verò ex buiu&longs;mo<lb/>di e&longs;t con&longs;titutus: &longs;tatim enim ex commoto <lb/>effectus e&longs;t & manente, quorum natura ad <lb/>&longs;e inuicem est contraria. </s>

<s id="N1122C">M<emph type="italics"/>axime autem e&longs;t admirandum &longs;imul <lb/>contraria fieri; Circulus verò ex huiu&longs;mo<lb/>di e&longs;t con&longs;titutus: &longs;tatim enim ex commoto <lb/>effectus e&longs;t & manente, quorum natura ad <lb/>&longs;e inuicem est contraria. </s>

<s id="N1123A">Quamobrem i&longs;thæc <lb/>cernentes minùs admirari conuenit contingentes in illo con<lb/>trarietates.<emph.end type="italics"/></s>

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<s id="N11272">Cum igitur admirandum valde &longs;it, &longs;i<lb/>mul contraria fieri, aut aliquid effici ex contrarijs, & hoc con<lb/>tingat in ip&longs;a con&longs;titutione circuli; minus admirandum e&longs;&longs;e <pb pagenum="35" xlink:href="005/01/043.jpg"/>relinquitur (concludit Ari&longs;toteles) &longs;i ex ip&longs;o circulo con&longs;ti<lb/>tuto, aliæ po&longs;tea oriantur contrarietates, vel alia contraria in <lb/>ip&longs;o con&longs;iderentur, vt mox ex dicendis patebit. </s>

<s id="N11284"><emph type="italics"/>De &longs;ecunda circuli proprieiate.<emph.end type="italics"/></s>

<s id="N11284"><emph type="italics"/>De &longs;ecunda circuli proprietate.<emph.end type="italics"/></s>

<s id="N1128D">Textus Quartus.</s>

<s id="N11292">I<emph type="italics"/>n primis enim lincæ illi, quæ circuti orbem am<lb/>plectitur, nullam habanti latitudinem contraria <lb/>quodammodo ine&longs;&longs;e apparans, concauum &longs;cilices, <lb/>& curuum. </s>

<s id="N11292">I<emph type="italics"/>n primis enim lineæ illi, quæ circuli orbem am<lb/>plectitur, nullam habenti latitudinem contraria <lb/>quodammodo ine&longs;&longs;e apparans, concauum &longs;cilicet, <lb/>& curuum. </s>

<s id="N1129E">Hæc autemeo à &longs;e inuioem di&longs;tant <lb/>modo, quo magnum, & paricum, illorum etenim <lb/>medium e&longs;t æquale: horum verò rectum; quapropter cum ad <lb/>&longs;e inuicem commutantur, illa <expan abbr="quid&etilde;">quidem</expan> prius æqualia &longs;ieri nece&longs;&longs;e <lb/>est, quam extremorum vtrumlibet: lineam vero rectam, <lb/>quando e&longs;t curua, concaua, aut ex buiu&longs;modi rur &longs;um curua &longs;it, <lb/>& circularis. </s>

<s id="N1129E">Hæc autem eo à &longs;e inuicem di&longs;tant <lb/>modo, quo magnum, & paricum, illorum etenim <lb/>medium e&longs;t æquale: horum verò rectum; quapropter cum ad <lb/>&longs;e inuicem commutantur, illa <expan abbr="quid&etilde;">quidem</expan> prius æqualia fieri nece&longs;&longs;e <lb/>est, quam extremorum vtrumlibet: lineam vero rectam, <lb/>quando e&longs;t curua, concaua, aut ex huiu&longs;modi rur&longs;um curua &longs;it, <lb/>& circularis. </s>

<s id="N112B1">V num quidem igitur i&longs;tuc ab&longs;urdum ine&longs;t circulo.<emph.end type="italics"/></s>

Line 625

<s id="N112BE">Secundò admirabilem &longs;e natura circuli o&longs;tendit, &longs;i &longs;u<lb/>matur infacto e&longs;&longs;e, quod cum in primis (inquit Ari&longs;to<lb/>teles) linea, quæ ip&longs;ius circuli orbem complectitur, ac <lb/>peripheria, &longs;eu <expan abbr="circunfer&etilde;tia">circunferentia</expan> nuncupatur, &longs;it per &longs;e quoad la<lb/>titudinem, & profunditatem indiui&longs;ibilis, &longs;imul tamen tan<lb/>quam ex duobus contrarijs inter &longs;e coniunctis con&longs;tituatur <lb/>concaua, & curua, &longs;iuè conuexa. </s>

<s id="N112D1">Etenim e&longs;t verè terminus <lb/>extimus, & conuexum ip&longs;ius circuli, ac &longs;imul ambiens, & <lb/>complectens in &longs;ua concauitate ip&longs;am &longs;uper&longs;iclem circuli: <lb/>Concauum autem, & conuexum &longs;e habent &longs;icut magnum, <lb/>& paruum. </s>

<s id="N112D1">Etenim e&longs;t verè terminus <lb/>extimus, & conuexum ip&longs;ius circuli, ac &longs;imul ambiens, & <lb/>complectens in &longs;ua concauitate ip&longs;am &longs;uperficilem circuli: <lb/>Concauum autem, & conuexum &longs;e habent &longs;icut magnum, <lb/>& paruum. </s>

<s id="N112DC">Horum enim medium e&longs;t æquale, illorum verò <lb/>rectum. </s>

<s id="N112E1">Quarè &longs;icut cum magnum, & paruum inuicem, <lb/>commutantur, prius perueniunt ad æquale, quàm ad hoc vt <lb/>magnum con&longs;tituatur paruum, & paruum con&longs;tituatur ma<pb pagenum="36" xlink:href="005/01/044.jpg"/>gnum: ita quælibet linea curua, &longs;eu conuexa antequam &longs;iat <lb/>concaua, prius debet fieri recta: ab&longs;urdum igitur apparet, ean<lb/>dem omnino circuli periferiam, &longs;imul con&longs;titui concauam, <lb/>& conuexam. </s>

<s id="N112E1">Quarè &longs;icut cum magnum, & paruum inuicem, <lb/>commutantur, prius perueniunt ad æquale, quàm ad hoc vt <lb/>magnum con&longs;tituatur paruum, & paruum con&longs;tituatur ma<pb pagenum="36" xlink:href="005/01/044.jpg"/>gnum: ita quælibet linea curua, &longs;eu conuexa antequam fiat <lb/>concaua, prius debet fieri recta: ab&longs;urdum igitur apparet, ean<lb/>dem omnino circuli periferiam, &longs;imul con&longs;titui concauam, <lb/>& conuexam. </s>

<s id="N112F5">Nec difficultatem euadunt, qui dicunt, concauum, & con<lb/>uexum realiter non e&longs;&longs;e idem in circulo, &longs;eu curuitatem, & <lb/>concauitatem non reperiri in eadem linea, &longs;ed in diuer&longs;is, ità <lb/>vt in circunferentia &longs;it tantum curuitas, &longs;eù conuexum, con<lb/>cauitas verò &longs;it potius in corpore extrin&longs;eco ambiente per li<lb/>neam illi corre&longs;pondentem. </s>

<s id="N11302">Etenim cum linea corporis con<lb/>tinentis ambiens circulum, penetretur in eodem &longs;pacio cum <lb/>cir cunferentia ip&longs;ius circuli, <expan abbr="con&longs;idereturq.">con&longs;idereturque</expan> &longs;ola quantitas <lb/>ab&longs;tracta, & figura vtriu&longs;que lineæ coincidentis, eadem &longs;em<lb/>per difficultas ob&longs;tabit; nempè quo pacto fieri po&longs;&longs;it, vt <expan abbr="ead&etilde;">eadem</expan> <lb/>longitudo latitudinis expers, circulum terminans, &longs;eù circu<lb/>lariter exten&longs;a, &longs;imul &longs;it concaua, & conuexa. </s>

<s id="N11319">Sed nihil pro<lb/>hibet eandem circumferentiam indiuifibilem quoad latitudi<lb/>nem, & profunditatem, &longs;imul e&longs;&longs;e concauam, & conuexam <lb/>re&longs;pectu diuer&longs;orum, vt in alijs etiam lineatum figuris, ac &longs;u<lb/>per&longs;iciebus poterit exemplificari: & vt eadem via dicitur <lb/>acliuis, & decliuis; idemque magnum, & paruum reipectu di<lb/>uer&longs;orum, quæ cum illo comparantur. </s>

<s id="N11319">Sed nihil pro<lb/>hibet eandem circumferentiam indiuisibilem quoad latitudi<lb/>nem, & profunditatem, &longs;imul e&longs;&longs;e concauam, & conuexam <lb/>re&longs;pectu diuer&longs;orum, vt in alijs etiam linearum figuris, ac &longs;u<lb/>perficiebus poterit exemplificari: & vt eadem via dicitur <lb/>acliuis, & decliuis; idemque magnum, & paruum rei pectu di<lb/>uer&longs;orum, quæ cum illo comparantur. </s>

<s id="N11328">Quo fit, vt admiran<lb/>dam quidem e&longs;&longs;e huiu&longs;modi proprietatem circuli iure dica<lb/>mus, nullam tamen in &longs;e <expan abbr="repugnantiã">repugnantiam</expan> inuoluere admittamus. </s>

Line 642

<s id="N1133E">Textus Quintus.</s>

<s id="N11343">A<emph type="italics"/>ltervm autem, quod &longs;imul contrarÿi <lb/>mouetur motionibus: &longs;imul enim ad anterio<lb/>rem mouetur locum, & ad po&longs;teriorem. </s>

<s id="N11343">A<emph type="italics"/>ltervm autem, quod &longs;imul contrarijs <lb/>mouetur motionibus: &longs;imul enim ad anterio<lb/>rem mouetur locum, & ad po&longs;teriorem. </s>

<s id="N1134D">Et <lb/>ea, quæ circulum de&longs;cribit, linea eodem &longs;e <lb/>babet modo: Ex que enim incipit loco, illius <lb/>extremum, ad eundem rur&longs;us redit: Illa <lb/>enim continuò commota, extremum rur&longs;us efficitur primum.<emph.end type="italics"/><pb pagenum="37" xlink:href="005/01/045.jpg"/><emph type="italics"/>Quamobrem manife&longs;tum, quod inde muiatum e&longs;t. </s>

<s id="N1134D">Et <lb/>ea, quæ circulum de&longs;cribit, linea eodem &longs;e <lb/>habet modo: Ex que enim incipit loco, illius <lb/>extremum, ad eundem rur&longs;us redit: Illa <lb/>enim continuò commota, extremum rur&longs;us efficitur primum.<emph.end type="italics"/><pb pagenum="37" xlink:href="005/01/045.jpg"/><emph type="italics"/>Quamobrem manife&longs;tum, quod inde mutatum e&longs;t. </s>

<s id="N11361">Quaprop<lb/>ter (vt dictum e&longs;t prius) non e&longs;t inconueniens, ip&longs;um miracutc<lb/>rum omnium e&longs;&longs;e principium.<emph.end type="italics"/></s>

<s id="N11361">Quaprop<lb/>ter (vt dictum e&longs;t prius) non e&longs;t inconueniens, ip&longs;um miraculo<lb/>rum omnium e&longs;&longs;e principium.<emph.end type="italics"/></s>

<s id="N1136C"><emph type="italics"/>Ea igitur, quæ circa libram fiunt, ad virculum referuntur: <lb/>“quæ verocirca vectem, ad ip&longs;am libram; alia autem ferè om-<emph.end type="italics"/><arrow.to.target n="marg13"/><lb/><emph type="italics"/>nia, quæ circa Menbanicas &longs;unt motiones, ad vectem. </s>

<s id="N1136C"><emph type="italics"/>Ea igitur, quæ circa libram fiunt, ad circulum referuntur: <lb/>“quæ vero circa vectem, ad ip&longs;am libram; alia autem ferè om-<emph.end type="italics"/><arrow.to.target n="marg13"/><lb/><emph type="italics"/>nia, quæ circa Menbanicas &longs;unt motiones, ad vectem. </s>

<s id="N1137C">Pra<lb/>tereà etiam quoniam vnica exi&longs;tente, quæ ex centro e&longs;t linea, <lb/>nullum aliud alij, quæ in illa &longs;unt, punctorum æqua velocitate <lb/>feratur; &longs;ed citius &longs;emper, quod à manente termino e&longs;t remo<lb/>tius, <expan abbr="pleraq.">pleraque</expan> miratulorum accidunt in circuli motionibus: de <lb/>quibus in ÿs, quæ po&longs;thac adducentur, quæ&longs;tionibus erit ma<lb/>nife&longs;tam.”<emph.end type="italics"/></s>

<s id="N1137C">Prae<lb/>tereà etiam quoniam vnica exi&longs;tente, quæ ex centro e&longs;t linea, <lb/>nullum aliud alij, quæ in illa &longs;unt, punctorum æqua velocitate <lb/>feratur; &longs;ed citius &longs;emper, quod à manente termino e&longs;t remo<lb/>tius, <expan abbr="pleraq.">pleraque</expan> miraculorum accidunt in circuli motionibus: de <lb/>quibus in ijs, quæ po&longs;thac adducentur, quæ&longs;tionibus erit ma<lb/>nife&longs;tam.”<emph.end type="italics"/></s>

<s id="N11393"><margin.target id="marg13"/>Verba re<lb/>&longs;ecanda.</s>

<s id="N1139C"><emph type="italics"/>Quoniam autem fecundum contrarias &longs;imul motiones mo<lb/>uetur circulus; & alierum quidem diametri ex tremum, vbi A, <lb/>in ante mouctur, alserum verò vbi B, ad retro; efficiunt non<lb/>nulli, vt ab vnica motione multi contrario &longs;imul moueantur <lb/>circuli; que madmodum &longs;unt illi, quos in locis proponunt &longs;acris, <lb/>æneos, & ferreos fabricantes orbiculos. </s>

<s id="N1139C"><emph type="italics"/>Quoniam autem secundum contrarias &longs;imul motiones mo<lb/>uetur circulus; & alienum quidem diametri extremum, vbi A, <lb/>in ante mouetur, alterum verò vbi B, ad retro; efficiunt non<lb/>nulli, vt ab vnica motione multi contrario &longs;imul moueantur <lb/>circuli; quemadmodum &longs;unt illi, quos in locis proponunt &longs;acris, <lb/>æneos, & ferreos fabricantes orbiculos. </s>

<s id="N113AB">Si enim AB, circu<lb/>lum alier contingerit, circulus in quo CD, mota circuli, in quo <lb/>AB, diametro in ante, mouebitur CD, ad retro diametro cir<lb/>culi, vbi e&longs;t A, circà idem mota, In contrarium igitur moue<lb/>bitur circulus vbi CD, ad illum, vbi AB, El rur&longs;us ip&longs;e con<lb/>tiguum vbi EF, in contrarium &longs;ibi ip&longs;i mouebitur propter ean<lb/>dem cau&longs;am. </s>

<s id="N113BA">Eodem etiam modo &longs;i plures fuerint, idem <lb/>facient, vno &longs;olo commoto. </s>

<s id="N113BF">Hanc lgitur in circulo exi&longs;tentem <lb/>animaduertens naturam Arcbitecti, in&longs;trumentum fabricant, <lb/>celantes principium, vt macbinæ &longs;olum mani&longs;e&longs;tum &longs;it illud, <lb/>quod admirationem præ&longs;tat, cau&longs;a verò lateat.<emph.end type="italics"/></s>

<s id="N113BF">Hanc lgitur in circulo exi&longs;tentem <lb/>animaduertens naturam Architecti, in&longs;trumentum fabricant, <lb/>celantes principium, vt machinæ &longs;olum manife&longs;tum &longs;it illud, <lb/>quod admirationem præ&longs;tat, cau&longs;a verò lateat.<emph.end type="italics"/></s>

<s id="N113CC">COMMENTARIVS.</s>

<s id="N113D2">Tertio illud quoque admiratione dignum &longs;e&longs;e o&longs;&longs;ert in <lb/>circulo, quod, inquit Ari&longs;toteles, contrarijs &longs;imul fe<lb/>ratur motionibus, antror&longs;um videlicet, ac retror&longs;um, <lb/>&longs;ur&longs;um, ac deor&longs;um. </s>

<s id="N113D2">Tertio illud quoque admiratione dignum &longs;e&longs;e offert in <lb/>circulo, quod, inquit Ari&longs;toteles, contrarijs &longs;imul fe<lb/>ratur motionibus, antror&longs;um videlicet, ac retror&longs;um, <lb/>&longs;ur&longs;um, ac deor&longs;um. </s>

<s id="N113DB">Dum enim pars circuli &longs;uperior de&longs;cen<lb/>dit, ac mouetur antror&longs;um, v. g. ad dexteram, altera pars illi <pb pagenum="38" xlink:href="005/01/046.jpg"/>oppo&longs;ita, quæ e&longs;t inferior, a&longs;cendit, ac mouetur retror&longs;um ad <lb/>leuam. </s>

<s id="N113EB">Quod &longs;i huiu&longs;modi po&longs;itiones formaliter non con<lb/>&longs;tituantur ni&longs;i in quadam relatione, ac re&longs;pectu vnius partis ad <lb/>alteram, hoc parumrefert, cum fundamentaliter &longs;emper im<lb/>portent realem oppo&longs;itionem, ac diuer&longs;itatem loci, in quo <lb/>ip&longs;e partes relatæ con&longs;tituuntur, vel ad quem tendunt <expan abbr="tanquã">tanquam</expan> <lb/>ad terminum &longs;ui motus. </s>

<s id="N113FC">Quapropter idem Philo&longs;ophus &longs;u<lb/><figure id="id.005.01.046.1.jpg" xlink:href="005/01/046/1.jpg"/><lb/>biungit ex hac contra<lb/>rietate fieri, vt vnius <lb/>circuli motione, alij cir<lb/>culi in contrarium mo<lb/>ueantur. </s>

<s id="N1140F">Vt &longs;i con&longs;ti<lb/>tuatur circulus, qui pri<lb/>mò moueri debeat in<lb/>ter alios quaruor, <expan abbr="&longs;intq.">&longs;intque</expan> <lb/>omnes denticulati, <lb/>quem admodum videre <lb/>e&longs;t in horologijs, <expan abbr="alijsq.">alijsque</expan> <lb/>&longs;imilibus machinis, vt <lb/>in hac &longs;igura: Nam pars <lb/>&longs;uperor medij circuli, <lb/>quæ de&longs;cendit, impellit partem inferiorem &longs;uperioris circuli, <lb/>facitque eam a&longs;cendere. </s>

<s id="N1140F">Vt &longs;i con&longs;ti<lb/>tuatur circulus, qui pri<lb/>mò moueri debeat in<lb/>ter alios quaruor, <expan abbr="&longs;intq.">&longs;intque</expan> <lb/>omnes denticulati, <lb/>quem admodum videre <lb/>e&longs;t in horologijs, <expan abbr="alijsq.">alijsque</expan> <lb/>&longs;imilibus machinis, vt <lb/>in hac figura: Nam pars <lb/>&longs;uperor medij circuli, <lb/>quæ de&longs;cendit, impellit partem inferiorem &longs;uperioris circuli, <lb/>facitque eam a&longs;cendere. </s>

<s id="N11430">Et pars inferior eiu&longs;dem medij cir<lb/>culi, a&longs;cendendo facit de&longs;cendere partem &longs;uperiorem circuli <lb/>inferioris. </s>

<s id="N11437">Deinde &longs;imiliter idem circulus medius dum dex<lb/>tror&longs;um mouetur, mouet circulum dexterum &longs;ini&longs;tror&longs;um, & <lb/>&longs;ini&longs;trum dextror&longs;um. </s>

Line 681

<s id="N1147D">Quæ autem de libra ac vatia punctorum &longs;emidiametri ve<lb/>locitate hìc docet Ari&longs;toteles, fru&longs;tra interpo&longs;ita &longs;unt ac præ<lb/>ter Auctoris intentum, cum ad rem de qua agitur non perti<lb/>neant, ac alibi proprijs in locis repetantur. </s>

<s id="N11486">Quare ex hoc <lb/>textu re&longs;ecanda e&longs;&longs;ent, incipiendo à particula (Ea igitur) <lb/>v&longs;que ad (erit manife&longs;tum) inclu&longs;iue, prout lineis confi<lb/>gnauimus. </s>

<s id="N11491"><emph type="italics"/>De Quarta Circuli Proprietate.<emph.end type="italics"/></s>

Line 691

<s id="N114A0">I<emph type="italics"/>n primis igitur quæ accidunt circa libram du<lb/>bitare faciunt, quam nam obcau&longs;am exactio<lb/>res minoribus maiores &longs;unt libræ. </s>

<s id="N114AA">IIuius au<lb/>tem rei principium est quamobrem in ip&longs;o cir<lb/>culo, quæ plus à centro di&longs;tat linea eadem vi <lb/>commota, citius fertur, quàm illa quæ minus distat. </s>

<s id="N114AA">Huius au<lb/>tem rei principium est quamobrem in ip&longs;o cir<lb/>culo, quæ plus à centro di&longs;tat linea eadem vi <lb/>commota, citius fertur, quàm illa quæ minus distat. </s>

<s id="N114B3">Citius <lb/>enim bifariam dicitur: &longs;iue enim in minori tempore æqualem <lb/>pertran&longs;it locum, citius feci&longs;&longs;e dicimus: &longs;eu in æquali maio<lb/>rem. </s>

<s id="N114BC">Maior autem in æquali tempore, maiorem de&longs;cribit cir<lb/>culum: qui enim extra e&longs;t, maior eo qui intus e&longs;t. </s>

<s id="N114C1">Horum <lb/>autem cau&longs;a, quoniam duas fertur lationes ea quæ circulum <lb/>de&longs;cribit linea. </s>

<s id="N114C8">Quandoquidem igitur in proportione fertur <lb/>aliqua id quod fertur, &longs;uper rectam ferri nece&longs;&longs;e: Et bæc dia<lb/>meter efficitur &longs;iguræ quam faciunt illæ quæ in buiu&longs;modi pro<lb/>portione coaptantur lineæ. </s>

<s id="N114C8">Quandoquidem igitur in proportione fertur <lb/>aliqua id quod fertur, &longs;uper rectam ferri nece&longs;&longs;e: Et hæc dia<lb/>meter efficitur figuræ quam faciunt illæ quæ in huiu&longs;modi pro<lb/>portione coaptantur lineæ. </s>

<s id="N114D1">Sit enim proportio &longs;eoundum quam <lb/>latum fertur, quam habet AB ad AC. & A quidem fertur <lb/>ver&longs;us B: A B vero &longs;ubter&longs;eratur ver&longs;us MC: latum au<lb/>tem &longs;it A quidem ad D. </s>

<s id="N114D1">Sit enim proportio &longs;ecundum quam <lb/>latum fertur, quam habet AB ad AC. & A quidem fertur <lb/>ver&longs;us B: A B vero &longs;ubter&longs;eratur ver&longs;us MC: latum au<lb/>tem &longs;it A quidem ad D. </s>

<s id="N114DB">Vbi autem est A B ver&longs;us E: quo<lb/>niam igitur lationis erat proportio, quam A B habet ad A C, <lb/>nece&longs;&longs;e e&longs;t & A D ad A E hanc habere proportionem. </s>

<s id="N114E2">Simile <lb/>igitur est proportione paruum quadrilaterum maiori: quam<lb/>obrem & eadem illorum e&longs;t diameter, & A erit ad F. </s>

<s id="N114EA">Eodem <lb/>etiam o&longs;tendetur modo, vbicunque latio deprabendatur; &longs;em-<emph.end type="italics"/><pb pagenum="40" xlink:href="005/01/048.jpg"/><emph type="italics"/>per enim &longs;upra diametrum erit. </s>

<s id="N114EA">Eodem <lb/>etiam o&longs;tendetur modo, vbicunque latio deprahendatur; &longs;em-<emph.end type="italics"/><pb pagenum="40" xlink:href="005/01/048.jpg"/><emph type="italics"/>per enim &longs;upra diametrum erit. </s>

<s id="N114F8">Manife&longs;tum igitur, quod id <lb/>quod &longs;ecundum diametrum duabus fertur lationibus, nece&longs;&longs;a<lb/>riò &longs;ecundum laterum proportionem fertur. </s>

<s id="N114FF">Si enim &longs;ecun<lb/>dum aliam quampiam, non fertur &longs;ecundam diametrum. <lb/></s>

<s id="N11505">Si autem in nulla fertur proportione &longs;ecundum duas lationes <lb/>nullo in tempore, rectam e&longs;&longs;e lationem, e&longs;t impo&longs;&longs;ibile. </s>

<s id="N1150A">Sit enim <lb/>recta. </s>

<s id="N1150F">Po&longs;ita igitur bac pro diametro, & circumrepletis late<lb/>ribus, illud quod fertur, &longs;ecundum laterum proportionem fer<lb/>ri nece&longs;&longs;e e&longs;t: hoc enim demon&longs;tratum e&longs;t prius. </s>

<s id="N1150F">Po&longs;ita igitur hac pro diametro, & circumrepletis late<lb/>ribus, illud quod fertur, &longs;ecundum laterum proportionem fer<lb/>ri nece&longs;&longs;e e&longs;t: hoc enim demon&longs;tratum e&longs;t prius. </s>

<s id="N11516">Non igitur <lb/>restam efficiet id quod &longs;ecundum nullam proportionem, in nul<lb/>lo &longs;ertur tempore. </s>

<s id="N11516">Non igitur <lb/>rectam efficiet id quod &longs;ecundum nullam proportionem, in nul<lb/>lo fertur tempore. </s>

<s id="N1151D">Si autem &longs;ecundum quampiam feratur <lb/>proportionem, & in tempore quopiam, hoc nece&longs;&longs;e est tempus <lb/>rectam e<32>e lationem, per ea quæ retro &longs;unt dicta. </s>

<s id="N11524">Quamob<lb/>remcirculare e&longs;t id, quod &longs;ecundum nullam proportionem nul<lb/>lo in tempore duas fertur lationes.<emph.end type="italics"/></s>

Line 718

<s id="N11555">Quod ita &longs;e habere <lb/>o&longs;tendit ex eo, quia dupliciter aliquid intelligimus velocius <lb/>alio moueri; nempe, vel quia in minori tempore, æquale <lb/>&longs;patium pertran&longs;it; vel quia eodem tempore, maius interual<lb/>lum percurrit. </s>

<s id="N11560">Et hoc pacto inquit in de&longs;criptione circuli <lb/>contingere vt puncta quæ magis à centro di&longs;tant, velocius <lb/>moueantur. </s>

<s id="N11567">Siquidem eodem tempore maiorem de&longs;cribunt <pb pagenum="41" xlink:href="005/01/049.jpg"/>ambitum. </s>

<s id="N1156F">Maior enim e&longs;t circum &longs;erentia cireuli continentis, <lb/>quàm contenti. </s>

<s id="N1156F">Maior enim e&longs;t circum &longs;erentia circuli continentis, <lb/>quàm contenti. </s>

<s id="N11574">Si autem circaidem centrum plures cir culi <lb/>ducantur, &longs;emper ille qui coeteros continet, à remotiori pun<lb/>cto &longs;emidiametri de&longs;cribetur, <expan abbr="proindeq.">proindeque</expan> quò remotiora erunt <lb/>ip&longs;a puncta &longs;emidiametri à centro, eò velocius mouebuntur. </s>

<s id="N11583">Horum autem cau&longs;am e&longs;&longs;e inquit Ari&longs;toteles, quoniam &longs;e<lb/>midiameter circulum de&longs;cribens mouetur motu quodam <lb/>mixto ex duabus lationibus, nempe naturali, ac præternatu<lb/>rali, vt infra &longs;equenti textu probabitur; quam duplicem la<lb/>tionem partes &longs;emidiametri non æquè participant, hoc e&longs;t <lb/>non participant &longs;ecundum eandem proportionem. </s>

<s id="N11590">Quando<lb/>quidem, vt infra pariter ip&longs;e Philo&longs;ophus o&longs;tendit, partes quæ <lb/>remotiores &longs;unt à centro, magis participant de latione natu<lb/>rali: contra verò quæ centro &longs;unt viciniores, magis partici<lb/>pant de motione præternaturali. </s>

<s id="N1159B">Si enim &longs;ecundum eandem <lb/>aliquam proportionem, duplicem illam lationem omnes ip<lb/>fæ participarent, non vtique mouerentur motu circulari, &longs;ed <lb/>recto, vt &longs;tatim ip&longs;e demon&longs;trat. </s>

<s id="N1159B">Si enim &longs;ecundum eandem <lb/>aliquam proportionem, duplicem illam lationem omnes ip<lb/>sæ participarent, non vtique mouerentur motu circulari, &longs;ed <lb/>recto, vt &longs;tatim ip&longs;e demon&longs;trat. </s>

<s id="N115A4">Quare &longs;uppo&longs;ito quòd mo<lb/>bile tanto velocius monetur, quanto magis participat de mo<lb/>tu naturali, vt ex dicendis etiam tex. 8. con&longs;tabit, a primo ad <lb/>vltimum conuincitur, puncta vel partes &longs;emidiametri quò <lb/>plus à centro di&longs;tauerint in de&longs;criptione circuli, eò c&oelig;lerius <lb/>moueri, quò vero minus, co tardius. </s>

<s id="N115B5">Et confirmari pote&longs;t argumento quod idem Philo&longs;ophus, <lb/>alijs interpo&longs;itis, &longs;equenti textu adiecit; niminum, quia &longs;i <lb/>duobus (inquit) ab eadem potentia latis, hoc quidem plus <lb/>repellatur vel impediatur ab aliquo, illud verò minus; ratio<lb/>ni con&longs;entancum e&longs;t, tardius moueri id quod plus præpedi<lb/>tur, aut repellit ur: Sed lineæ circumductæ in circulo, vel pun<lb/>cta quæ &longs;unt in eius diametro, quò magis appropinquantur <lb/>centro, eò magis repelluntur in motu circulari ac impediun<lb/>tur ab ip&longs;o centro; ergo tardius mouentur. </s>

<s id="N115B5">Et confirmari pote&longs;t argumento quod idem Philo&longs;ophus, <lb/>alijs interpo&longs;itis, &longs;equenti textu adiecit; nimirum, quia &longs;i <lb/>duobus (inquit) ab eadem potentia latis, hoc quidem plus <lb/>repellatur vel impediatur ab aliquo, illud verò minus; ratio<lb/>ni con&longs;entaneum e&longs;t, tardius moueri id quod plus præpedi<lb/>tur, aut repellitur: Sed lineæ circumductæ in circulo, vel pun<lb/>cta quæ &longs;unt in eius diametro, quò magis appropinquantur <lb/>centro, eò magis repelluntur in motu circulari ac impediun<lb/>tur ab ip&longs;o centro; ergo tardius mouentur. </s>

<s id="N115C8">Minor propo&longs;itio <lb/>huius argumenti probatur; quia cum centrum &longs;it fixum & <lb/>immotum, <expan abbr="eiq.">eique</expan> colligatæ &longs;int omnes partes diametri per lon<lb/>gitudinem exten&longs;æ, illæ quæ magis ei appropinquantur, ma<lb/>gis vinciuntur ac detinentur nè moueantur: quæ verò magis <pb pagenum="42" xlink:href="005/01/050.jpg"/>ab eo di&longs;tant, magis relaxantur, <expan abbr="magisq.">magisque</expan> &longs;oluuntur à princi<lb/>pio detinente, ac propterea minus impediuntur nè ad im<lb/>pul&longs;um vel motum alterius moueantur, & &longs;ic velocius fe<lb/>runtur. </s>

Line 743

<s id="N11631">Rur&longs;us antequam ad exactam eius probationem ex Geo<lb/>metricis principijs accedamus, idem prælibare licebit exem<lb/>plo huius figuræ, quod non parum ad dilucidationem textus, <lb/><expan abbr="doctrinæq.">doctrinæque</expan> Ari&longs;totelis conducet. </s>

<s id="N1163D">Sit enim corpus &longs;eu pon<lb/>dus quod moueri debeat con&longs;titutum &longs;uper planum vbi A, <lb/>mouentia verò vbi B, C. </s>

<s id="N11645">Deinde &longs;upponamus æquali virtu<lb/>te & æquali &longs;imul tempore vtrumque mouens ad &longs;e pondus <pb pagenum="43" xlink:href="005/01/051.jpg"/><figure id="id.005.01.051.1.jpg" xlink:href="005/01/051/1.jpg"/><lb/>ip&longs;um trahere; quod e&longs;t, eandem &longs;emper proportionem ad <lb/>inuicem &longs;eruare, vt bene&longs;icio trochlearum vel alterius in&longs;tru<lb/>menti. </s>

<s id="N11645">Deinde &longs;upponamus æquali virtu<lb/>te & æquali &longs;imul tempore vtrumque mouens ad &longs;e pondus <pb pagenum="43" xlink:href="005/01/051.jpg"/><figure id="id.005.01.051.1.jpg" xlink:href="005/01/051/1.jpg"/><lb/>ip&longs;um trahere; quod e&longs;t, eandem &longs;emper proportionem ad <lb/>inuicem &longs;eruare, vt beneficio trochlearum vel alterius in&longs;tru<lb/>menti. </s>

<s id="N11659">Tunc enim dicimus primo, corpus ip&longs;um mobile A <lb/>moueri motu quodam mixto ex duabus lationibus, nempe <lb/>qua appropinquatur ad B, & qua appropinquantur ad C. <lb/></s>

<s id="N11662">Quia durante huiu&longs;modi motu, non datur in&longs;tans in quo non <lb/>magis ip&longs;um pondus A appropinquetur ad B, ac &longs;imul ad C. <lb/></s>

<s id="N11669">Præterea dicimus, huiu&longs;modi motum nece&longs;&longs;ariò e&longs;&longs;e rectum, <lb/>non verò circularem, &longs;eu pondus non ni&longs;i &longs;uper rectam tunc <lb/>&longs;emper moueri. </s>

<s id="N11670">Ftenim &longs;eruata eadem proportione, pon<lb/>dus ip&longs;um, & quælibet eius pars æqualiter vtrique mouenti in <lb/>æquali tempore deberet appropinquari: quia non e&longs;&longs;et maiot <lb/>ratio cur magis aut citius appropinquaretur ad B, quàm ad C. <lb/></s>

<s id="N11670">Etenim &longs;eruata eadem proportione, pon<lb/>dus ip&longs;um, & quælibet eius pars æqualiter vtrique mouenti in <lb/>æquali tempore deberet appropinquari: quia non e&longs;&longs;et maior <lb/>ratio cur magis aut citius appropinquaretur ad B, quàm ad C. <lb/></s>

<s id="N1167B">At non po&longs;&longs;et æqualiter vtrique appropinquari, ni&longs;i feratur <pb pagenum="44" xlink:href="005/01/052.jpg"/>per diamctrom quadranguli A B C D, quæ e&longs;t recta A D; <lb/>&longs;iquidem in nulla alia parte interiecti &longs;pacij, di&longs;tantia e&longs;&longs;et <lb/>æqualis, vt &longs;en&longs;u con&longs;tat: Ergo &longs;eruata eadem proportione in <lb/>ip&longs;a duplici latione re&longs;pectu mobilis & cuiu&longs;que partis ip&longs;ius, <lb/>motus nece&longs;&longs;ariò erit rectus, &longs;eu <expan abbr="põdus">pondus</expan> & quælibet eius pars, <lb/>nonni&longs;i per rectam lineam poterit moueri. </s>

<s id="N1167B">At non po&longs;&longs;et æqualiter vtrique appropinquari, ni&longs;i feratur <pb pagenum="44" xlink:href="005/01/052.jpg"/>per diametrem quadranguli A B C D, quæ e&longs;t recta A D; <lb/>&longs;iquidem in nulla alia parte interiecti &longs;patij, di&longs;tantia e&longs;&longs;et <lb/>æqualis, vt &longs;en&longs;u con&longs;tat: Ergo &longs;eruata eadem proportione in <lb/>ip&longs;a duplici latione re&longs;pectu mobilis & cuiu&longs;que partis ip&longs;ius, <lb/>motus nece&longs;&longs;ariò erit rectus, &longs;eu <expan abbr="põdus">pondus</expan> & quælibet eius pars, <lb/>non ni&longs;i per rectam lineam poterit moueri. </s>

<s id="N11693">Deinde quod infert Ari&longs;toteles, circulare e&longs;&longs;e id quod &longs;e<lb/>cundum nullam proportionem, nullo in tempore duas pati<lb/>tur lationes, fal&longs;um e&longs;&longs;et etiam iuxta præfatam explicationé <lb/>proportionis; ni&longs;i per circulare intelligeremus lato modo, id <lb/>quod e&longs;t curuum. </s>

Line 760

<s id="N116C1">Sit inquit proportio ip&longs;arum lationum <lb/><figure id="id.005.01.052.1.jpg" xlink:href="005/01/052/1.jpg"/><lb/>quam habent inter <lb/>&longs;e latera A B & AC <lb/>in dato rectangulo <lb/>A B C D. </s>

<s id="N116D3">Et A <lb/><expan abbr="quid&etilde;">quidem</expan> duplici motu <lb/>feratur, vno quo <lb/><expan abbr="t&etilde;dat">tendat</expan> ver&longs;us B, qua<lb/>&longs;i ex &longs;e incedendo <lb/>&longs;uper lineam A B: <lb/>altero verò, quo &longs;imul cum ip&longs;a linea A B &longs;ubterferatur ver<lb/>&longs;us C, &longs;eu ver&longs;us lineam C D cum eadem &longs;emper proportio<lb/>ne. </s>

<s id="N116EC">Tunc dicimus punctum A motu ip&longs;o mixto, nece&longs;&longs;ariò <lb/>ferriper rectam A D, quæ e&longs;t diameter eiu&longs;dem quadrilateri <lb/>A B C D. </s>

<s id="N116F4">Etcnim &longs;i <expan abbr="cõ&longs;tituatur">con&longs;tituatur</expan> rectangulus minor A E F G <pb pagenum="45" xlink:href="005/01/053.jpg"/>proportionalis maiori A B C D, ac per motum proprium <lb/>ver&longs;us B, ip&longs;um punctum A peragrauerit quantum e&longs;t v&longs;que <lb/>ad E; & per motum totius lineæ A B, ver&longs;us lineam C D, <lb/>peragrauerit quantum e&longs;t ab A, v&longs;que ad F, &longs;eruata eadem <lb/>proportione ip&longs;orum laterum; certe punctum A reperiri non <lb/>po&longs;&longs;et in E, neque in F; &longs;iquidem non fui&longs;&longs;et latum duabus <lb/>lationibus, nec peragra&longs;&longs;et &longs;pacium &longs;ecundum vtramque po<lb/>&longs;itionem, &longs;imul accedendo quantum &longs;ieri pote&longs;t ad B & ad <lb/>C; &longs;ed vna tantùm latione, alterum &longs;olum &longs;pacium percur<lb/>ri&longs;&longs;et. </s>

<s id="N116F4">Etenim &longs;i <expan abbr="cõ&longs;tituatur">con&longs;tituatur</expan> rectangulus minor A E F G <pb pagenum="45" xlink:href="005/01/053.jpg"/>proportionalis maiori A B C D, ac per motum proprium <lb/>ver&longs;us B, ip&longs;um punctum A peragrauerit quantum e&longs;t v&longs;que <lb/>ad E; & per motum totius lineæ A B, ver&longs;us lineam C D, <lb/>peragrauerit quantum e&longs;t ab A, v&longs;que ad F, &longs;eruata eadem <lb/>proportione ip&longs;orum laterum; certe punctum A reperiri non <lb/>po&longs;&longs;et in E, neque in F; &longs;iquidem non fui&longs;&longs;et latum duabus <lb/>lationibus, nec peragra&longs;&longs;et &longs;pacium &longs;ecundum vtramque po<lb/>&longs;itionem, &longs;imul accedendo quantum fieri pote&longs;t ad B & ad <lb/>C; &longs;ed vna tantùm latione, alterum &longs;olum &longs;pacium percur<lb/>ri&longs;&longs;et. </s>

<s id="N11712">Reperietur ergo ip&longs;um. </s>

<s id="N11715">punctum A vbi vtraque pro<lb/>gre&longs;&longs;io pote&longs;t verificari, vt in puncto G. </s>

<s id="N1171B">Quia nimirum F G <lb/>e&longs;t æqualis ip&longs;i A E, & E G æqualis ip&longs;i A F, cum &longs;int latera <lb/>oppo&longs;ita eiu&longs;dem rectanguli, vt patet per 34. primi Elemen<lb/>torum Euclidis. </s>

Line 782

<s id="N11793">Q<emph type="italics"/>vod quidem igitur ea quæ circulum de&longs;cri<lb/>bit, duas &longs;imul feratur lationes, manifestum <lb/>e&longs;t cùm ex istis, tùm quia &longs;ecundum rectum <lb/>lata ad perpendiculum peruenit, vt &longs;it rur&longs;us <lb/>ip&longs;a à centro <expan abbr="perpendicul&utilde;">perpendiculum</expan>. </s>

<s id="N117A5">Sit circulus ABCD, <lb/>extremum autem vbi e&longs;t B. feratur ad ip&longs;um <lb/>D, peruenit &longs;ane aliquando ad ip&longs;um C. </s>

<s id="N117AD">Siquidem igitur in <lb/>propurtione feratur, quam babet BE, EC, fertur vtique &longs;ecun<lb/>dum diametrum BC. </s>

<s id="N117AD">Siquidem igitur in <lb/>proportione feratur, quam habet BE, EC, fertur vtique &longs;ecun<lb/>dum diametrum BC. </s>

<s id="N117B5">N unc autem, <expan abbr="quoniã">quoniam</expan> in nulla proportione, <lb/>in circunferentia certè fertur vbi BEC. </s>

<s id="N117BE">Si autem duobus ab <lb/><expan abbr="ead&etilde;">eadem</expan> potentia latis, hoc <expan abbr="quid&etilde;">quidem</expan> plus repellatur, illud vero minus, <lb/>rationi <expan abbr="con&longs;entane&utilde;">con&longs;entaneum</expan> e&longs;t, tardius moueri id quod plus repellitur <lb/>eo quod repellitur minus. </s>

<s id="N117D2">Quod videtur acctdere maiori & mi<lb/>nori illarum quæ ex centro circulos de&longs;cribunt. </s>

<s id="N117D2">Quod videtur accidere maiori & mi<lb/>nori illarum quæ ex centro circulos de&longs;cribunt. </s>

<s id="N117D7"><expan abbr="Quoniã">Quoniam</expan> enim <lb/>propius e&longs;t manenti, eius quæ minor e&longs;t, <expan abbr="extrem&utilde;">extremum</expan>, quam id quod <lb/>e&longs;t maioris, veluti rectum in contrarium, ad medium, tardius <lb/>fertur minoris extremum. </s>

<s id="N117E7">Omne quidem igitur circulum de<lb/>&longs;cribenti i&longs;tud accidi<gap/>: <expan abbr="ferturq.">ferturque</expan> eam quæ &longs;ecundum naturam <lb/>e&longs;t lationem, &longs;ecundum circumferentiam: illam vero quæ præ<lb/>ter naturam, in tran&longs;uer&longs;um & &longs;ecundum centrum. </s>

<s id="N117F6">Maio-<emph.end type="italics"/><pb pagenum="47" xlink:href="005/01/055.jpg"/><emph type="italics"/>tem autem &longs;emper eam quæ præter naturam e&longs;t ip&longs;a minor <lb/>fertur: quia enim centro e&longs;t vicinior quod trahit, vincitur <lb/>magis.<emph.end type="italics"/></s>

<s id="N117F6">Maio-<emph.end type="italics"/><pb pagenum="47" xlink:href="005/01/055.jpg"/><emph type="italics"/>rem autem &longs;emper eam quæ præter naturam e&longs;t ip&longs;a minor <lb/>fertur: quia enim centro e&longs;t vicinior quod trahit, vincitur <lb/>magis.<emph.end type="italics"/></s>

<s id="N1180A">COMMENTARIVS.</s>

<s id="N11810">Qvamuis Philo&longs;ophus &longs;uperiori textu &longs;emel atque <lb/>iterum a&longs;&longs;ump&longs;erit, &longs;ernidiametrum, &longs;eu lineam <lb/>circulum de&longs;cribentem, duabus ferri lationibus, <lb/>prout explicuimus; huc tamen illud probandum <lb/>reliquit, & ex dictis etiam de motu antror&longs;um & retror&longs;um <lb/>manife&longs;tum e&longs;&longs;e docet. </s>

<s id="N11810">Qvamuis Philo&longs;ophus &longs;uperiori textu &longs;emel atque <lb/>iterum a&longs;&longs;ump&longs;erit, &longs;emidiametrum, &longs;eu lineam <lb/>circulum de&longs;cribentem, duabus ferri lationibus, <lb/>prout explicuimus; huc tamen illud probandum <lb/>reliquit, & ex dictis etiam de motu antror&longs;um & retror&longs;um <lb/>manife&longs;tum e&longs;&longs;e docet. </s>

<s id="N1181D">Id igitur hic probat ex eo. </s>

<s id="N11820">Nam &longs;i <lb/>in de&longs;criptione circuli, &longs;emidiameter vnam tantum lationem <lb/>pateretur, vt verbi gratia naturalem, qua rectà tenderet ver<lb/>&longs;us, vnam aliquam differentiam &longs;itus, nunquam ad ip&longs;ius dia<lb/>metri perpendiculum perueniret. </s>

<s id="N1182B">Implicat enim vnica la<lb/>tione, aliquid &longs;imul rectà tendere, ac in tran&longs;uer&longs;um, quem<lb/>admodum &longs;e habet perpendiculum ad diametrum à qua pro<lb/>pendit: At &longs;emidiameter circulum de&longs;cribendo, aliquando <lb/>peruenit ad &longs;uum perpendiculum, ita vt coincidat cum illo: <lb/>Ergo non vnica, &longs;ed duplici latione conuincitur ferri. </s>

Line 806

<s id="N11851">Si igitur ip&longs;a recta <lb/>A E, altero eius extremo <lb/>manente in centro E, al<lb/>tero vero nempè A, cir<lb/>cumferatur, aliquando <lb/>ab&longs;que dubio erit in ED, <lb/>quæ e&longs;t perpendicularis <lb/>diametro AC. </s>

<s id="N11863">Per <expan abbr="mot&utilde;">motum</expan> <lb/>autem naturalem ip&longs;a AE, de&longs;cendi&longs;&longs;et in FD, vel aliò rectè <lb/>tran&longs;lata fui&longs;&longs;et. </s>

<s id="N1186E">Non ergo linea circulum de&longs;cribens fertur, <pb pagenum="48" xlink:href="005/01/056.jpg"/>vnico tantummodo motu ver&longs;us vnicam differentiam &longs;itus, <lb/>&longs;ed duplici motu, nempe mixto ex naturali & præternaturali; <lb/>ver&longs;us duplicem differentiam &longs;itus. </s>

<s id="N1187A">Naturali quippe, quo in <lb/>propo&longs;ita figura fertur ver&longs;us latus F D, præternaturali verò, <lb/>quo retrahitur in tran&longs;uer&longs;um ver&longs;us latus E D, co quòd alte<lb/>rum eius extremum detineatur in centro E, vt clarius infra <lb/>patebit. </s>

<s id="N1187A">Naturali quippe, quo in <lb/>propo&longs;ita figura fertur ver&longs;us latus F D, præternaturali verò, <lb/>quo retrahitur in tran&longs;uer&longs;um ver&longs;us latus E D, eo quòd alte<lb/>rum eius extremum detineatur in centro E, vt clarius infra <lb/>patebit. </s>

<s id="N11887">Quibus ita con&longs;titutis, reuertitur Ari&longs;toteles ad <expan abbr="proband&utilde;">probandum</expan>, <lb/>partes vel puncta &longs;emidiamet<gap/>i, eò velocius moueri, quò plus <lb/>à centro di&longs;tauerint; cò verò tardius, quò magis ad centrum <lb/>acce&longs;&longs;erint. </s>

<s id="N11887">Quibus ita con&longs;titutis, reuertitur Ari&longs;toteles ad <expan abbr="proband&utilde;">probandum</expan>, <lb/>partes vel puncta &longs;emidiametri, eò velocius moueri, quò plus <lb/>à centro di&longs;tauerint; eò verò tardius, quò magis ad centrum <lb/>acce&longs;&longs;erint. </s>

<s id="N11896">Quod cum ad doctrinam in &longs;uperiori textu tra<lb/>ditam &longs;pectet, <expan abbr="illucq.">illucque</expan> propterea à nobis tran&longs;lat um &longs;it, ac &longs;a<lb/>tis expo&longs;itum, non e&longs;t cur hic rur&longs;us idem repetatur ac denuo <lb/>exponatur. </s>

<s id="N118A3">Acceptionem autem & explicationem motus <lb/>naturalis ac præternaturalis, qua v&longs;i &longs;umus, &longs;ump&longs;imus ex co<lb/>dem Philo&longs;opho textu &longs;equenti, & lib.

Line 819

<s id="N118DC"><emph type="italics"/>Qua ratione partes diametri a oentro remotio<lb/>res magis participent de motu naturali, <lb/>propinquiores verò magis de præ<lb/>ternaturali.<emph.end type="italics"/></s>

<s id="N118DC"><emph type="italics"/>Qua ratione partes diametri a centro remotio<lb/>res magis participent de motu naturali, <lb/>propinquiores verò magis de præ<lb/>ternaturali.<emph.end type="italics"/></s>

<s id="N118EB">Textus Octauus</s>

<s id="N118F0">Q<emph type="italics"/>vod autem magis quod præter naturam <lb/>e&longs;t mouetur ip&longs;a minor, quam maior illarum, <lb/>quæ ex centro circulos de&longs;cribunt, ex ÿs est <lb/>manifestum. </s>

<s id="N118FC">Sit circulus vbi B C D E, & <lb/>alter in hoc minor, vbi M N O P, circà <lb/>idem centrum A, & proÿciantur diametri <lb/>in magno quidem, in quibus C D, B E, in minori verò ip&longs;æ <lb/>M O, N P: & altera parte longius quadratum &longs;uppleatur <lb/>D K R C: &longs;iquidem A B circulum de&longs;cribens ad id perue<lb/>niet, vnde e&longs;t egre&longs;&longs;a; manife&longs;tum e&longs;t, quod ad ip&longs;am fertur <lb/>AB. </s>

<s id="N118FC">Sit circulus vbi B C D E, & <lb/>alter in hoc minor, vbi M N O P, circà <lb/>idem centrum A, & projiciantur diametri <lb/>in magno quidem, in quibus C D, B E, in minori verò ip&longs;æ <lb/>M O, N P: & altera parte longius quadratum &longs;uppleatur <lb/>D K R C: &longs;iquidem A B circulum de&longs;cribens ad id perue<lb/>niet, vnde e&longs;t egre&longs;&longs;a; manife&longs;tum e&longs;t, quod ad ip&longs;am fertur <lb/>AB. </s>

<s id="N1190E">Similiter etiam A M adip&longs;am A M perueniet. </s>

<s id="N11911">T ardiùs <lb/>autem fertur A M, quam A B quemadmodum dictum <lb/>e&longs;t: quia maior fit repul&longs;io, & magis retrabitur A M. </s>

<s id="N11918">Du<lb/>catur igitur ip&longs;a A L F, & abip&longs;o L perpendiculum ad ip<lb/>&longs;am AB, ip&longs;a LQ in minore circulo: & rur&longs;um ab L du<lb/>casur iuxtà A B L S, & S T adip&longs;am A B perpendicu<lb/>lum, & ip&longs;a FX: ip&longs;æ igitur vbi &longs;unt ST, & LQ, æqua<lb/>les: ip&longs;a ergò B T minor est, quam M <expan abbr="q.">que</expan> Aequales enim <lb/>rectæ lineæ in &etail;qualibus coniecta circulis perpendiculares à <lb/>diametro, minorem diametri re&longs;ecant &longs;ectionem in maioribus <lb/>circulis. </s>

<s id="N11918">Du<lb/>catur igitur ip&longs;a A L F, & ab ip&longs;o L perpendiculum ad ip<lb/>&longs;am AB, ip&longs;a LQ in minore circulo: & rur&longs;um ab L du<lb/>catur iuxtà A B L S, & S T ad ip&longs;am A B perpendicu<lb/>lum, & ip&longs;a FX: ip&longs;æ igitur vbi &longs;unt ST, & LQ, æqua<lb/>les: ip&longs;a ergò B T minor est, quam M <expan abbr="q.">que</expan> Aequales enim <lb/>rectæ lineæ in &etail;qualibus coniecta circulis perpendiculares à <lb/>diametro, minorem diametri re&longs;ecant &longs;ectionem in maioribus <lb/>circulis. </s>

<s id="N1192F">Est autem ip&longs;a S T æqualis ip&longs;i L <expan abbr="q.">que</expan> In quan<lb/>to autem tempore ip&longs;a AL ip&longs;am ML lata e&longs;t, in tanto tem<lb/>poris &longs;patio in maiori circulo, maiorem, quam &longs;it B S, latum <lb/>erit extremum ip&longs;is AB. </s>

<s id="N1193D">Latio quidem igit ur &longs;ecundum na<lb/>turam æqualis: Ea autem, quæ præter naturam e&longs;t minor, <lb/>videlicet B T, quam M <expan abbr="q.">que</expan> Oportet autem proportiona-<emph.end type="italics"/><pb pagenum="50" xlink:href="005/01/058.jpg"/><emph type="italics"/>biliter e&longs;&longs;e, &longs;icut quod est fecundum naturam, ita quod est <lb/>præter naturam, ad id, quod est præter naturan; maiorem <lb/>igitur circumferentiam pertran&longs;iuit, quam &longs;it ip&longs;a S B. </s>

<s id="N11955">Ne<lb/>ce&longs;&longs;e autem e&longs;t ip&longs;am F B. in hoc tempore pertran&longs;i<32>e: bic <lb/>enim erit, quando proportion abiliter vtrinque accidis, quod e&longs;t <lb/>præter naturam, ad id quod e&longs;t &longs;ecundum naturam. </s>

<s id="N11955">Ne<lb/>ce&longs;&longs;e autem e&longs;t ip&longs;am F B. in hoc tempore pertran&longs;i<32>e: hic <lb/>enim erit, quando proportionabiliter vtrinque accidis, quod e&longs;t <lb/>præter naturam, ad id quod e&longs;t &longs;ecundum naturam. </s>

<s id="N1195E">Si igi<lb/>tur maius e&longs;t, quod &longs;ecundum naturam in maiori, & quod e&longs;t <lb/>præter naturam, magis vtique bic coincidit vno modo: ita <lb/>quod B &longs;it latum per ip&longs;am B F in tanto tempore, in quo <lb/>M punctum per ip&longs;am M L. </s>

<s id="N1195E">Si igi<lb/>tur maius e&longs;t, quod &longs;ecundum naturam in maiori, & quod e&longs;t <lb/>præter naturam, magis vtique hic coincidit vno modo: ita <lb/>quod B &longs;it latum per ip&longs;am B F in tanto tempore, in quo <lb/>M punctum per ip&longs;am M L. </s>

<s id="N1196A">Hic enim &longs;eeundum naturam <lb/>quidem &longs;igno B fit X F: e&longs;t enim ab ip&longs;o F perpendiculum: <lb/>præter naturam verò ad ip&longs;am X B. </s>

<s id="N11971">E&longs;t autem quem ad<lb/>modum FX ad X B, &longs;ic L Q ad M <expan abbr="q.">que</expan> Manife&longs;tum <lb/>autem &longs;i coniunguntur ab ip&longs;a B M ad FL. </s>

<s id="N1197C">Si autem mi<lb/>nor, aut mator, quam &longs;it FB erit illa, quam latum e&longs;t B, <lb/>non &longs;imiliter erit, neque proportionale in vtri&longs;que quod e&longs;t &longs;e<lb/>cundum naturam ad id quod e&longs;t præter naturam. </s>

<s id="N1197C">Si autem mi<lb/>nor, aut maior, quam &longs;it FB erit illa, quam latum e&longs;t B, <lb/>non &longs;imiliter erit, neque proportionale in vtri&longs;que quod e&longs;t &longs;e<lb/>cundum naturam ad id quod e&longs;t præter naturam. </s>

<s id="N11985">Quam igi<lb/>tur ob cau&longs;am ab eadem potentia celerius fertur id quod plus <lb/>à centro di&longs;tat punctum ex ÿs, quæ dicta &longs;unt e&longs;t mani<lb/>fe&longs;tum.<emph.end type="italics"/></s>

<s id="N11985">Quam igi<lb/>tur ob cau&longs;am ab eadem potentia celerius fertur id quod plus <lb/>à centro di&longs;tat punctum ex ijs, quæ dicta &longs;unt e&longs;t mani<lb/>fe&longs;tum.<emph.end type="italics"/></s>

<s id="N11992">COMMENTARIVS.</s>

<s id="N11998">Ex a&longs;&longs;umptis ab Ari&longs;totele in illo priori argumento <lb/>iam &longs;upra textu 6. à nobis expo&longs;ito ad o&longs;tenden<lb/>dum in ip&longs;o circulo, quæ plus à centro di&longs;tat linea <lb/>eadem vi commota citius ferri quàm illa, quæ minus di&longs;tat; <lb/>illud du<gap/>taxat ci probandum reman&longs;erat, videlicet partes <lb/>lineæ circulum de&longs;cribentis, quò viciniores centro &longs;unt, eò <lb/>magis detrahi à motu naturali, <expan abbr="magisq.">magisque</expan> participare de motu <lb/>præternaturali; E contrà verò quo remotiores &longs;unt à cen<lb/>tro, magis participare de motu naturali, vt inde inferatur ve<lb/>locius moueri. </s>

<s id="N11998">Ex a&longs;&longs;umptis ab Ari&longs;totele in illo priori argumento <lb/>iam &longs;upra textu 6. à nobis expo&longs;ito ad o&longs;tenden<lb/>dum in ip&longs;o circulo, quæ plus à centro di&longs;tat linea <lb/>eadem vi commota citius ferri quàm illa, quæ minus di&longs;tat; <lb/>illud dumtaxat ci probandum reman&longs;erat, videlicet partes <lb/>lineæ circulum de&longs;cribentis, quò viciniores centro &longs;unt, eò <lb/>magis detrahi à motu naturali, <expan abbr="magisq.">magisque</expan> participare de motu <lb/>præternaturali; E contrà verò quo remotiores &longs;unt à cen<lb/>tro, magis participare de motu naturali, vt inde inferatur ve<lb/>locius moueri. </s>

<s id="N119B3">Probat autem hoc modo; &longs;it enim, inquit, <lb/>Circulus B C D E; & alter in hoc minor vbi M N O P <lb/>circà idem centrum A. <expan abbr="Sintq.">Sintque</expan> Diametri maioris quidem C. <lb/>D, & B E; minoris verò M O, & N P. </s>

<s id="N119C1">Deinde complea-<pb pagenum="51" xlink:href="005/01/059.jpg"/><figure id="id.005.01.059.1.jpg" xlink:href="005/01/059/1.jpg"/><lb/>tur quadrangu'um rectangulum D K R C nempe ducen<lb/>do lineam K R. paralellam, & æqualem ip&longs;i D C. per pun<lb/>ctum B, & claudendo ip&longs;as K R & D C per lineas D K <lb/>& C R. </s>

<s id="N119C1">Deinde complea-<pb pagenum="51" xlink:href="005/01/059.jpg"/><figure id="id.005.01.059.1.jpg" xlink:href="005/01/059/1.jpg"/><lb/>tur quadrangulum rectangulum D K R C nempe ducen<lb/>do lineam K R. paralellam, & æqualem ip&longs;i D C. per pun<lb/>ctum B, & claudendo ip&longs;as K R & D C per lineas D K <lb/>& C R. </s>

<s id="N119D6">Cum igitur motus naturalis cuiu&longs;libet lineæ dica<lb/>tur ille, quo recta fertur ver&longs;us eam partem in quam tendit, <lb/>&longs;i linea A B &longs;tantis circuli de&longs;cripti deo<gap/>&longs;um tenderet &longs;im<lb/>plici motu naturali, ab&longs;que dubio rectè, ac perpendiculari<lb/>ter tota &longs;imul caderet, & coincid et cum C R. </s>

<s id="N119D6">Cum igitur motus naturalis cuiu&longs;libet lineæ dica<lb/>tur ille, quo recta fertur ver&longs;us eam partem in quam tendit, <lb/>&longs;i linea A B &longs;tantis circuli de&longs;cripti deor&longs;um tenderet &longs;im<lb/>plici motu naturali, ab&longs;que dubio rectè, ac perpendiculari<lb/>ter tota &longs;imul caderet, & coincid<gap/>et cum C R. </s>

<s id="N119E4">Quoniam <lb/>vero non pote&longs;t ita ferri &longs;implici motu naturali, eò quod al<lb/>terum eius extremum detineatur in centro, illæ partes ip<lb/>&longs;ius dicentur magis participare de motu naturali, quæ re<lb/>ctius tendunt in ip&longs;am C R; hoc e&longs;t per lineam magis appro<lb/>pinquantem ad perpendiculum; &longs;icut è contrà illæ dicentur <lb/>magis detrahi à motu naturali, quæ magis incuruantur ten<lb/>dendo ver&longs;us lineam C D. </s>

<s id="N119F6">Itaque progre&longs;&longs;as perpendicu<lb/>laris ver&longs;us C R erit motus naturalis, ver&longs;us autem C D erit <lb/>præternaturalis Quod certè videtur &longs;upponere Ari&longs;toteles. <lb/></s>

<s id="N119FF">Nunc autem &longs;ic procedit ad o&longs;tenden lum propo&longs;itum, <lb/>nempè partem dia necri propinquiorem centro, vt A M <pb pagenum="52" xlink:href="005/01/060.jpg"/>magis detrahi à motu naturali, ac tardiùs moueri, quàm <lb/>M B quæ magis di&longs;tat ab illo. </s>

<s id="N119FF">Nunc autem &longs;ic procedit ad o&longs;tenden lum propo&longs;itum, <lb/>nempè partem diametri propinquiorem centro, vt A M <pb pagenum="52" xlink:href="005/01/060.jpg"/>magis detrahi à motu naturali, ac tardiùs moueri, quàm <lb/>M B quæ magis di&longs;tat ab illo. </s>

<s id="N11A0B">Ducatur inquit à centro li<lb/>nea A L F; & à puncto L perpendicularis ip&longs;i A B quæ <lb/>&longs;it L Q, & rur&longs;us ab eodem L ducatur L S paralella ei<lb/>dem A B. </s>

<s id="N11A14">Deinde à puncto S excitetur alia perpendicu<lb/>laris eidem AB. <expan abbr="Sitq.">Sitque</expan> ST; & ab F item eidem perpendicu<lb/>laris F X. </s>

<s id="N11A20">His po&longs;itis linea QL erit æqualis lineæ T S, vt <lb/>patet ex 34. primi Euclidis, cum &longs;int latera oppo&longs;ita rectan<lb/>guli T L. </s>

Line 863

<s id="N11A6A">Id quod <lb/>primo loco erat probandum. </s>

<s id="N11A71">Vlterius verò quod punctum B magis moueatur motu <lb/>&longs;ecundum naturam, quam ip&longs;um punctum M probatur ex <lb/>co; Nam quo tempore punctum M latum fuerit v&longs;que ad <lb/>L; punctum B eodem tempore perueniet v&longs;que ad F. </s>

<s id="N11A71">Vlterius verò quod punctum B magis moueatur motu <lb/>&longs;ecundum naturam, quam ip&longs;um punctum M probatur ex <lb/>eo; Nam quo tempore punctum M latum fuerit v&longs;que ad <lb/>L; punctum B eodem tempore perueniet v&longs;que ad F. </s>

<s id="N11A7B">Ete<lb/>nim cum ita &longs;e habere debeat motus naturalis ip&longs;ius B ad <lb/>motum præter naturam eiu&longs;dem B quemadmodum &longs;e ha<lb/>bet motus naturalis ip&longs;ius M ad motum præter naturam <pb pagenum="53" xlink:href="005/01/061.jpg"/>eiu&longs;dem M talis proportio &longs;olum verificari pote&longs;t in F, <lb/>nam proportio, quam habet linea F X referens &longs;pacium <lb/>tran&longs;actum &longs;ecundum naturam ad B X, quod ab eodem <lb/>puncto B tran&longs;actum e&longs;t præter naturam in maiori circulo, <lb/>eadem e&longs;t, ac proportio lineæ QL tran&longs;actæ &longs;ecundum <lb/>naturam ad lineam M Q tran&longs;actam præter naturam in mi<lb/>nori circulo. </s>

<s id="N11A95">Quod inde patere pote&longs;t, nam &longs;i ducantur re<lb/>ctæ B F, & M L efficientur duo triangula æquiangula <lb/>B X F, & M Q L quæ per 4. &longs;exti habebunt latera pro<lb/>portionalia circà æquales angulos: Vnde &longs;icut &longs;e habet F X <lb/>ad X B circa angulum. </s>

<s id="N11AA0">rectum X, ita &longs;e habet L Q ad <lb/>QM circà angulum rectum <expan abbr="q.">que</expan> Et permutando, &longs;icut &longs;e <lb/>habet F X ad L Q, ità X B ad QM per 16. Quinti. </s>

Line 879

<s id="N11ADB">Attenta natura circuli cum &longs;uis proprietatibus modò <lb/>explicatis ad hoc acumen humani ingenij iam pridem <lb/>peruenit, vt machinas qua&longs;dam excogitaret, quæ naturam <lb/>ip&longs;ius circuli participantes, motricem potentiam in motu <lb/>grauium ac leuium iuuarent. </s>

<s id="N11AE6">Huiu&longs;modi autem machinas <lb/>in&longs;trumenta mechanica communiter appellamus, vtpotè <lb/>quæ mechanica &longs;peculatione adinuenta &longs;unt, <expan abbr="eademq.">eademque</expan> arte <pb pagenum="54" xlink:href="005/01/062.jpg"/>adhibentur tanquam in&longs;trumenta ad leuanda pondera, vel <lb/>quomodolibet mouenda grauia, quæ re&longs;pectiuè dicuntur <lb/>etiam leuia. </s>

<s id="N11AFA">Sunt autem hæc in&longs;trumenta præcipua &longs;ex, ad <lb/>quæ cætera omniareducuntur: nempè Libra. </s>

<s id="N11B00">Vectis, Tro<lb/>chlea, Axis in Peritrochio, Cuneus, & Cochlea Et licet Ari<lb/>&longs;toteles di&longs;tinciam eorum tractationem prætermi&longs;erit, ac <lb/>nonni&longs;i quatuor ex ip&longs;is hic, vel in &longs;equentibus quæ&longs;tionibus <lb/>pro opportunitate meminerit, &longs;upponit nihilominus <expan abbr="tanquã">tanquam</expan> <lb/>certum, illa omnia ac &longs;imilia participare naturam circuli, <lb/>eorumque vim qua motricem augent potentiam in hoc ip<lb/>&longs;o con&longs;i&longs;tere, vt circuli proprietatem &longs;apiendo, faciliùs & <lb/>mouerentur, & motum præ&longs;tarent oneribus ac ponderibus <lb/>mouendis, cum circularis &longs;ine orbicularis figura &longs;it omnium <lb/>mouenti&longs;&longs;ima. </s>

<s id="N11B00">Vectis, Tro<lb/>chlea, Axis in Peritrochio, Cuneus, & Cochlea Et licet Ari<lb/>&longs;toteles di&longs;tinctam eorum tractationem prætermi&longs;erit, ac <lb/>non ni&longs;i quatuor ex ip&longs;is hic, vel in &longs;equentibus quæ&longs;tionibus <lb/>pro opportunitate meminerit, &longs;upponit nihilominus <expan abbr="tanquã">tanquam</expan> <lb/>certum, illa omnia ac &longs;imilia participare naturam circuli, <lb/>eorumque vim qua motricem augent potentiam in hoc ip<lb/>&longs;o con&longs;i&longs;tere, vt circuli proprietatem &longs;apiendo, faciliùs & <lb/>mouerentur, & motum præ&longs;tarent oneribus ac ponderibus <lb/>mouendis, cum circularis &longs;ine orbicularis figura &longs;it omnium <lb/>mouenti&longs;&longs;ima. </s>

<s id="N11B1B">Ait enim &longs;upra tex. 5. Ea igitur quæ circa <lb/>libram fiunt, ad circulum referuntur: quæ verò circa vectem, <lb/>ad ip&longs;am libram: alia autem ferè omnia, quæ circamecha<lb/>nicas &longs;unt motiones, ad vectem. </s>

<s id="N11B26">Ex quibus infertur &longs;iue im<lb/>mediate, &longs;iue mediante, alia quadam ab&longs;tracta ratione quam <lb/>ip&longs;a participent, mechanica penè omnia in&longs;trumenta in &longs;uis <lb/>motionibus ad circuli naturam referri. </s>

<s id="N11B2F">Quod vt clarius te<lb/>neatur, pauca &longs;altem de &longs;ingulis ip&longs;is in&longs;trumentis hic adij<lb/>cere operepretium putauimus, ea &longs;cilicet tantummo<lb/>do, quæ ad in&longs;titutam textus dilucidationem no<lb/>uerimus pertinere, Cum exacta huiu&longs;modi <lb/>in&longs;trumentum tractatio habeatur apud <lb/>Heronem, Pappum, & alios ve<lb/>teres, noui&longs;simè verò & <lb/>accurati&longs;simè apud <lb/>Guidum Vbal<lb/>dum <lb/><gap/> Marchionibus Montis, qui &longs;i<lb/>gillatim de illis præcla <lb/>rum librum in<lb/>&longs;tituit. </s>

<s id="N11B2F">Quod vt clarius te<lb/>neatur, pauca &longs;altem de &longs;ingulis ip&longs;is in&longs;trumentis hic adij<lb/>cere opere pretium putauimus, ea &longs;cilicet tantum mo<lb/>do, quæ ad in&longs;titutam textus dilucidationem no<lb/>uerimus pertinere, Cum exacta huiu&longs;modi <lb/>in&longs;trumentum tractatio habeatur apud <lb/>Heronem, Pappum, & alios ve<lb/>teres, noui&longs;simè verò & <lb/>accurati&longs;simè apud <lb/>Guidum Vbal-<lb/>dum <lb/><gap/> Marchionibus Montis, qui &longs;i<lb/>gillatim de illis præcla<lb/>rum librum in<lb/>&longs;tituit. </s>

<s id="N11B55">DE LIBRA.</s>

<s id="N11B5A">Libra, quæ inter mechanica in&longs;trumenta iure <lb/>primum &longs;ibi vendicat locum, co quod imme<lb/>diatius, ac magis participet <expan abbr="naturã">naturam</expan> circuli in <lb/>&longs;uis motionibus, e&longs;t <expan abbr="iug&utilde;">iugum</expan> <expan abbr="quoddã">quoddam</expan> ex medio <lb/>liberè &longs;u&longs;pen&longs;um, <expan abbr="axeq.">axeque</expan> <expan abbr="&longs;uffult&utilde;">&longs;uffultum</expan>, ac plano ho<lb/>rizontis <expan abbr="parallel&utilde;">parallelum</expan>, ex cuius <expan abbr="vtraq;">vtraque</expan> extremitate gemina lanx <lb/>pendet, <expan abbr="cuiusq.">cuiusque</expan> conuer&longs;ione circa ip&longs;um axem, dum altera <lb/>eleuatur, altera deprimitur, pódus vel exce&longs;&longs;us <expan abbr="põderis">ponderis</expan> cu <lb/>iu&longs;libet, deprehenditur, ac men&longs;uratur. </s>

<s id="N11B5A">Libra, quæ inter mechanica in&longs;trumenta iure <lb/>primum &longs;ibi vendicat locum, eo quod imme<lb/>diatius, ac magis participet <expan abbr="naturã">naturam</expan> circuli in <lb/>&longs;uis motionibus, e&longs;t <expan abbr="iug&utilde;">iugum</expan> <expan abbr="quoddã">quoddam</expan> ex medio <lb/>liberè &longs;u&longs;pen&longs;um, <expan abbr="axeq.">axeque</expan> <expan abbr="&longs;uffult&utilde;">&longs;uffultum</expan>, ac plano ho<lb/>rizontis <expan abbr="parallel&utilde;">parallelum</expan>, ex cuius <expan abbr="vtraq;">vtraque</expan> extremitate gemina lanx <lb/>pendet, <expan abbr="cuiusq.">cuiusque</expan> conuer&longs;ione circa ip&longs;um axem, dum altera <lb/>eleuatur, altera deprimitur, póndus vel exce&longs;&longs;us <expan abbr="põderis">ponderis</expan> cu<lb/>iu&longs;libet, deprehenditur, ac men&longs;uratur. </s>

<s id="N11B91">Qua in de&longs;criptione <lb/>&longs;upponitur <expan abbr="iug&utilde;">iugum</expan> ex medio, trutina, &longs;eu axe &longs;u&longs;pen&longs;um, con&longs;ti<lb/>tui, ac manere parallelum plano horizontis propter <expan abbr="æqui-ponderantiã">æqui<lb/>ponderantiam</expan> vtriu&longs;que medietatis: <expan abbr="motumq.">motumque</expan> circularem, &longs;eu <lb/><expan abbr="conuer&longs;ion&etilde;">conuer&longs;ionem</expan> circa fulcimentum tanquam circa <expan abbr="centr&utilde;">centrum</expan> im<lb/>motum, nonni&longs;i ratione <expan abbr="inæquali&utilde;">inæqualium</expan> <expan abbr="ponder&utilde;">ponderum</expan> in gemina lance <lb/>vtrinque pendentium illi competere: vnde &longs;i pondera &longs;int <lb/>æqualia, libra &longs;emper maneat, & in æquilibrio con&longs;tituatur, <lb/>&longs;eu æquidi&longs;tans à plano horizontis. </s>

<s id="N11BBF">Deinde ita &longs;upponitur, <lb/>pondera in lancibus impo&longs;ita, ex vtraque iugi extremitate <lb/><expan abbr="p&etilde;dere">pendere</expan>, vt hoc non &longs;it <expan abbr="nece&longs;&longs;ari&utilde;">nece&longs;&longs;arium</expan>, <expan abbr="neq;">neque</expan> e&longs;&longs;entialiter pertineat <lb/>ad <expan abbr="con&longs;titution&etilde;">con&longs;titutionem</expan> libræ, &longs;ed potius ad <expan abbr="commoditat&etilde;">commoditatem</expan> ponde<lb/>randi, cum &longs;atis intelligatur libra e&longs;&longs;entialiter con&longs;tituta <lb/>etiam ab&longs;que lancibus, ponderibus in ip&longs;is iugi extremita<lb/>tibus, adiacentibus, vt cernere e&longs;t in &longs;equentibus figuris. </s>

<s id="N11BE3">Quo autem pacto libra in &longs;ui motione participet natu<lb/>ram circuli per &longs;e con&longs;tat con&longs;ideranti, iugum, diametri vi<lb/>cem gerere, axem verò &longs;eu trutinam, aut <expan abbr="fulciment&utilde;">fulcimentum</expan> quod<lb/>libet, centri locum tenere, circa quod immotum, ip&longs;a dia<lb/>meter vertitur dum circulum de&longs;cribit; &longs;iquidem immoto <lb/>axe, &longs;eu fulcimento ip&longs;ius libræ, iugum, alterius extremita<lb/>tis depre&longs;sione ob exuperantiam <expan abbr="põderis">ponderis</expan>, alterius verò ele<lb/>uatione, circumagitur, non &longs;ecus ac diameter circulum <lb/>con&longs;iciendo. </s>

<s id="N11BFE">Quod &longs;i partes iugi vtrinque à centro produ<lb/>ctæ, non &longs;int inter &longs;e <expan abbr="lõgitudine">longitudine</expan> æquales, quamuis æquipon<lb/>derantes; tunc quidem in ip&longs;is iugi conuer&longs;ione, ac circum<pb pagenum="56" xlink:href="005/01/064.jpg"/>latione duo circuli de&longs;cribentur alter altero malor, <expan abbr="tanquã">tanquam</expan> <lb/>à duplici &longs;emidiametro circumlato, vt hic erit in&longs;picere. </s>

<s id="N11BFE">Quod &longs;i partes iugi vtrinque à centro produ<lb/>ctæ, non &longs;int inter &longs;e <expan abbr="lõgitudine">longitudine</expan> æquales, quamuis æquipon<lb/>derantes; tunc quidem in ip&longs;is iugi conuer&longs;ione, ac circum<pb pagenum="56" xlink:href="005/01/064.jpg"/>latione duo circuli de&longs;cribentur alter altero maior, <expan abbr="tanquã">tanquam</expan> <lb/>à duplici &longs;emidiametro circumlato, vt hic erit in&longs;picere. </s>

<s id="N11C1B">DE VECTE.</s>

<s id="N11C20">Vectis &longs;implex <expan abbr="quoddã">quoddam</expan> <expan abbr="in&longs;trument&utilde;">in&longs;trumentum</expan> e&longs;t ligneum, <lb/>vel <expan abbr="ferre&utilde;">ferreum</expan> &longs;atis oblongum veluti palus, aut fu&longs;ti<gap/><lb/>grandior, ad promouenda pondera; cuius vt <expan abbr="plu-rim&utilde;">plu<lb/>rimum</expan> altera extremitas <expan abbr="põderi">ponderi</expan> eleuando &longs;ubijci<lb/>tur, altera verò manu, &longs;eu <expan abbr="pot&etilde;tia">potentia</expan> præmitur, &longs;ub<lb/>&longs;trato inter <expan abbr="vtramq;">vtramque</expan> aliquo fulcimento, cui inni<lb/>tatur, quòd græcè hypomochilion appellatur, quodq <expan abbr="quãto">quanto</expan> pro<lb/>pinquius ponderi locatur, tanto facilius ip&longs;o vecte leuatur. </s>

<s id="N11C20">Vectis &longs;implex <expan abbr="quoddã">quoddam</expan> <expan abbr="in&longs;trument&utilde;">in&longs;trumentum</expan> e&longs;t ligneum, <lb/>vel <expan abbr="ferre&utilde;">ferreum</expan> &longs;atis oblongum veluti palus, aut fu&longs;ti<gap/><lb/>grandior, ad promouenda pondera; cuius vt <expan abbr="plu-rim&utilde;">plu<lb/>rimum</expan> altera extremitas <expan abbr="põderi">ponderi</expan> eleuando &longs;ubijci<lb/>tur, altera verò manu, &longs;eu <expan abbr="pot&etilde;tia">potentia</expan> præmitur, &longs;ub<lb/>&longs;trato inter <expan abbr="vtramq;">vtramque</expan> aliquo fulcimento, cui inni<lb/>tatur, quòd græcè hypomochilion appellatur, <expan abbr="quodq">quoque</expan> <expan abbr="quãto">quanto</expan> pro<lb/>pinquius ponderi locatur, tanto facilius ip&longs;o vecte leuatur. </s>

<s id="N11C52">Ali<lb/>quando verò altera extremitas <expan abbr="nõ">non</expan> ponderi, &longs;ed fulcimento &longs;ubij<lb/>citur, vel ei quoquomodo innititur <expan abbr="tanquã">tanquam</expan> manenti valido, pon-<pb pagenum="57" xlink:href="005/01/065.jpg"/><expan abbr="dusq.">dusque</expan> eleuatur, aut deprimitur per vectis <expan abbr="part&etilde;">partem</expan> mediam, quæ e&longs;t <lb/>inter <expan abbr="vtramq.">vtramque</expan> <expan abbr="extremitat&etilde;">extremitatem</expan> iuxta <expan abbr="eleuation&etilde;">eleuationem</expan>, aut <expan abbr="depre&longs;&longs;ion&etilde;">depre&longs;&longs;ionem</expan> al<lb/>terius extremitatis vbi applicatur <expan abbr="pot&etilde;tia">potentia</expan>: vel certè <expan abbr="põdus">pondus</expan> ele<lb/>uatur per <expan abbr="alterã">alteram</expan> extremitatem, &longs;i in illa locetur, <expan abbr="manusq.">manusque</expan> aut po<lb/>tentia in medio adhibeatur. </s>

<s id="N11C95">Vnde tres nonnulli &longs;pecies <expan abbr="vecti&utilde;">vectium</expan> di<lb/>&longs;tinguunt, quas iuxta prædicta figuris <expan abbr="etiã">etiam</expan> hic &longs;tuduimus expri<lb/>mere; Illud interim admonendo, eas omnes facilè in &longs;uis motio<lb/>nibus ad <expan abbr="circul&utilde;">circulum</expan> referri, cum ip&longs;æ nonni&longs;i <expan abbr="diametr&utilde;">diametrum</expan>, vel <expan abbr="&longs;emidia-metr&utilde;">&longs;emidia<lb/>metrum</expan> <expan abbr="circul&utilde;">circulum</expan> circa <expan abbr="immot&utilde;">immotum</expan> <expan abbr="fulciment&utilde;">fulcimentum</expan> <expan abbr="de&longs;cribent&etilde;">de&longs;cribentem</expan> referant, vt <lb/>per &longs;e patet, ac prima quæ &longs;anè vtilior & frequentius in v&longs;u e&longs;t, <lb/>ad <expan abbr="librã">libram</expan> à <expan abbr="fulcim&etilde;to">fulcimento</expan> inæquales vtrinque partes <expan abbr="habent&etilde;">habentem</expan> eniden<lb/>ti&longs;simè reducatur, vt amplius deinceps <expan abbr="cõ&longs;tabit">con&longs;tabit</expan>. </s>

<s id="N11C95">Vnde tres nonnulli &longs;pecies <expan abbr="vecti&utilde;">vectium</expan> di<lb/>&longs;tinguunt, quas iuxta prædicta figuris <expan abbr="etiã">etiam</expan> hic &longs;tuduimus expri<lb/>mere; Illud interim admonendo, eas omnes facilè in &longs;uis motio<lb/>nibus ad <expan abbr="circul&utilde;">circulum</expan> referri, cum ip&longs;æ non ni&longs;i <expan abbr="diametr&utilde;">diametrum</expan>, vel <expan abbr="&longs;emidia-metr&utilde;">&longs;emidia<lb/>metrum</expan> <expan abbr="circul&utilde;">circulum</expan> circa <expan abbr="immot&utilde;">immotum</expan> <expan abbr="fulciment&utilde;">fulcimentum</expan> <expan abbr="de&longs;cribent&etilde;">de&longs;cribentem</expan> referant, vt <lb/>per &longs;e patet, ac prima quæ &longs;anè vtilior & frequentius in v&longs;u e&longs;t, <lb/>ad <expan abbr="librã">libram</expan> à <expan abbr="fulcim&etilde;to">fulcimento</expan> inæquales vtrinque partes <expan abbr="habent&etilde;">habentem</expan> euiden<lb/>ti&longs;simè reducatur, vt amplius deinceps <expan abbr="cõ&longs;tabit">con&longs;tabit</expan>. </s>

<s id="N11CDA"><expan abbr="Nã">Nam</expan> hoc quod e&longs;t <lb/>fulciri per <expan abbr="&longs;u&longs;pen&longs;ion&etilde;">&longs;u&longs;pen&longs;ionem</expan> beneficio trutinæ, vel per <expan abbr="&longs;ubiection&etilde;">&longs;ubiectionem</expan> al<lb/>terius corporis, quod non minus axis, ac centri <expan abbr="vic&etilde;">vicem</expan> &longs;ubeat, e&longs;t <lb/>differentia valde accidentalis. </s>

Line 920

<s id="N11D30">Reducitur autem Trochlea ad Vectem, & con&longs;equen<lb/>ter ad libram, quia vnu&longs;qui&longs;que orbiculus illius per diame<lb/>trum nititur proprio axiculo tanquam fulcimento, quod in<lb/>ter onus leuandum, aut &longs;u&longs;tinendum, & potentiam eleuan<lb/>tem locatur, ita vt ad depre&longs;sionem vnius extremitatis dia-<pb pagenum="59" xlink:href="005/01/067.jpg"/>metri, vbi mouentis potentia applicatur, altera extremitas, <lb/>quæ onus &longs;u&longs;tinet, eleuetur; licet hoc nonimmediatè fiat; <lb/>&longs;ed mediante fune ductario, vt hic ad oculos &longs;pectandum <lb/>proponetur ac infra fu&longs;iùs explicabitur quæ&longs;t. </s>

<s id="N11D46">18. Sit enim <lb/>trochleç orbiculus ABC, dia<lb/><figure id="id.005.01.067.1.jpg" xlink:href="005/01/067/1.jpg"/><lb/>meter verò orbiculi linea ho<lb/>rizonti parallela AB, & axicu<lb/>lus C, tanquam centrum lo<lb/>catum in medio: Deinde per <lb/>funem ductarium ab extremo <lb/>A propendeat onus D, & ab <lb/>extremo B idem funis demit<lb/>tatur, cui applicara &longs;it poten<lb/>tia motiua in E. </s>

<s id="N11D46">18. Sit enim <lb/>trochleae orbiculus ABC, dia<lb/><figure id="id.005.01.067.1.jpg" xlink:href="005/01/067/1.jpg"/><lb/>meter verò orbiculi linea ho<lb/>rizonti parallela AB, & axicu<lb/>lus C, tanquam centrum lo<lb/>catum in medio: Deinde per <lb/>funem ductarium ab extremo <lb/>A propendeat onus D, & ab <lb/>extremo B idem funis demit<lb/>tatur, cui applicata &longs;it poten<lb/>tia motiua in E. </s>

<s id="N11D64">Dicimus er<lb/>go totum orbiculum incum<lb/>bere, ac niti axiculo C tan<lb/>quam fulcimento per diame<lb/>trum eius AB in cuius medio <lb/>axiculus e&longs;t locatus, & in cuius <lb/>extremis AB, vtrinque &longs;it tota <lb/>compre&longs;sio, nempe oneris ac potentiæ; <expan abbr="proindeq.">proindeque</expan> ip&longs;am <lb/>diametrum AB, vectis vicem in motione gerere, qua<lb/>tenus nixa in præfato fulcimento C, ad depre&longs;<lb/>&longs;ionem extremimitatis B per vim trahen<lb/>tem in E, extremitas A nece&longs;&longs;ario <lb/>eleuatur, ac &longs;imul cum illa <lb/>pondus D pendens ex <lb/>ip&longs;a, vt per &longs;e <lb/>patet. </s>

<s id="N11D64">Dicimus er<lb/>go totum orbiculum incum<lb/>bere, ac niti axiculo C tan<lb/>quam fulcimento per diame<lb/>trum eius AB in cuius medio <lb/>axiculus e&longs;t locatus, & in cuius <lb/>extremis AB, vtrinque &longs;it tota <lb/>compre&longs;sio, nempe oneris ac potentiæ; <expan abbr="proindeq.">proindeque</expan> ip&longs;am <lb/>diametrum AB, vectis vicem in motione gerere, qua<lb/>tenus nixa in præfato fulcimento C, ad depre&longs;<lb/>&longs;ionem extreminitatis B per vim trahen<lb/>tem in E, extremitas A nece&longs;&longs;ario <lb/>eleuatur, ac &longs;imul cum illa <lb/>pondus D pendens ex <lb/>ip&longs;a, vt per &longs;e <lb/>patet. </s>

<s id="N11D8F">DE AXE IN PERITROCHIO.</s>

<s id="N11D94">Axis in Peritrochio e&longs;t oblongus quidam <lb/>cylindrus Peritrochio firmiter in&longs;ixus, ac pa<lb/>rallelus horizontis plano locatus, cuius ex<lb/>trema in rotundis foraminibus immoti peg<lb/>matis expeditè vertuntur. </s>

<s id="N11D94">Axis in Peritrochio e&longs;t oblongus quidam <lb/>cylindrus Peritrochio firmiter infixus, ac pa<lb/>rallelus horizontis plano locatus, cuius ex<lb/>trema in rotundis foraminibus immoti peg<lb/>matis expeditè vertuntur. </s>

<s id="N11D9F">Peritrochium ve<lb/>rò, e&longs;t machina rotunda, ad rotæ &longs;eu tympani &longs;imilitudi<lb/>nem efformata, in cuius conuexa peripheria &longs;tipites qui & <lb/>Scytalæ vocantur, tanquam radij infinguntur; quibus admo<lb/>ta manu tota machina &longs;imul cum axe ver&longs;atur, ac funibus <lb/>circa axem conuolutis, trahuntur pondera illis alligata; vt <lb/>hic licebit in&longs;picere. </s>

<s id="N11DB5">Reducitur <expan abbr="aut&etilde;">autem</expan> <lb/>tota huiu&longs;modi ma <lb/>china, &longs;eu in&longs;tru<lb/>mentum ad <expan abbr="vect&etilde;">vectem</expan>; <lb/>Nam &longs;i con&longs;idere<lb/>mus <expan abbr="con&longs;titut&utilde;">con&longs;titutum</expan> ex <lb/>diametro axis, ac <lb/>&longs;emidiametro Pe<lb/>ritrochij <expan abbr="coincid&etilde;-te">coinciden<lb/>te</expan> cum illa non ali<lb/>ter in circumuolu<lb/>tione &longs;e habere <expan abbr="cõ-perimus">con<lb/>perimus</expan>, ac <expan abbr="Vect&etilde;">Vectem</expan>, <lb/>qui circa &longs;uum ful<lb/>cimentum vertitur, <lb/>tanquam circa pro<lb/>prium centrum. <lb/></s>

<s id="N11DB5">Reducitur <expan abbr="aut&etilde;">autem</expan> <lb/>tota huiu&longs;modi ma <lb/>china, &longs;eu in&longs;tru<lb/>mentum ad <expan abbr="vect&etilde;">vectem</expan>; <lb/>Nam &longs;i con&longs;idere<lb/>mus <expan abbr="con&longs;titut&utilde;">con&longs;titutum</expan> ex <lb/>diametro axis, ac <lb/>&longs;emidiametro Pe<lb/>ritrochij <expan abbr="coincid&etilde;-te">coinciden<lb/>te</expan> cum illa non ali<lb/>ter in circumuolu<lb/>tione &longs;e habere <expan abbr="cõ-perimus">com<lb/>perimus</expan>, ac <expan abbr="Vect&etilde;">Vectem</expan>, <lb/>qui circa &longs;uum ful<lb/>cimentum vertitur, <lb/>tanquam circa pro<lb/>prium centrum. <lb/></s>

<s id="N11DF1">E&longs;to enim Axis &longs;imul, ac Peritrochij immobile centrum <lb/>A, circa quod vtriu&longs;que circumferentia de&longs;cripta &longs;it, nem<lb/>pe tàm Axis, quàm Tympani ip&longs;ius Peritrochij cum &longs;cyta<lb/>lis; Diameter verò Axis &longs;it linea BC; ac &longs;emidiameter Pe<lb/>titrochij AD, con&longs;tituentes integram lineam BD. </s>

<s id="N11DFD">Tum <pb pagenum="61" xlink:href="005/01/069.jpg"/>ex Axe per funem BE propendeat onus F; <expan abbr="virtusq.">virtusque</expan> mo<lb/>uentis applicetur in &longs;cytala vbi e&longs;t ip&longs;um D. </s>

<s id="N11E0C">Ad motum <lb/>igitur deor&longs;um ip&longs;ius D, linea BD, non aliter &longs;e pote&longs;t <lb/>habere, ac vectis firmiter innixa immobili centro A, tan<lb/>quam fulcimento, ac dum pars AD deprimitur, altera. <lb/></s>

Line 944

<s id="N11E22">DE CVNEO.</s>

<s id="N11E27">Cvnevs e&longs;t &longs;implex quoddam in&longs;trumen<lb/>tum ad findenda, &longs;eu &longs;cindéda corpora apti&longs;<lb/>&longs;imum accedente percu&longs;&longs;ione. </s>

<s id="N11E27">Cvnevs e&longs;t &longs;implex quoddam in&longs;trumen<lb/>tum ad findenda, &longs;eu &longs;cindénda corpora apti&longs;<lb/>&longs;imum accedente percu&longs;&longs;ione. </s>

<s id="N11E2E">E&longs;t enim &longs;oli<lb/>dum, quod ex quadrangulari ba&longs;e <expan abbr="con&longs;urg&etilde;s">con&longs;urgens</expan>, <lb/>quatuor &longs;uperficiebus in peracutam aciem <lb/>terminantibus, clauditur. </s>

<s id="N11E3B">Duabus videlicet &longs;ibi oppo&longs;itis <lb/>quadrangularibus, ac altera parte longioribus; duabus verò <lb/>&longs;imiliter oppo&longs;itis, &longs;ed triangularibus in prædictam acutam, <lb/>& oblongam aciem terminantibus. </s>

<s id="N11E44">Quæ &longs;anè acies cum in <lb/>timulam quamlibet <expan abbr="&longs;cind&etilde;dæ">&longs;cindendæ</expan> molis &longs;e in&longs;inuare præualeat, <pb pagenum="62" xlink:href="005/01/070.jpg"/>adueniente valida percu&longs;&longs;ione, vt quæ per malleú &longs;uper ba<lb/>&longs;im adactum fieri con&longs;ueuit, facilè totum cuneum cogit ad<lb/>mittere, <expan abbr="proindeq.">proindeque</expan> partes molis ab inuicem &longs;ecedere, quod <lb/>e&longs;t molem<gap/>p&longs;am &longs;cindi, ac diuidi. </s>

<s id="N11E44">Quæ &longs;anè acies cum in <lb/>rimulam quamlibet <expan abbr="&longs;cind&etilde;dæ">&longs;cindendæ</expan> molis &longs;e in&longs;inuare præualeat, <pb pagenum="62" xlink:href="005/01/070.jpg"/>adueniente valida percu&longs;&longs;ione, vt quæ per malleúm &longs;uper ba<lb/>&longs;im adactum fieri con&longs;ueuit, facilè totum cuneum cogit ad<lb/>mittere, <expan abbr="proindeq.">proindeque</expan> partes molis ab inuicem &longs;ecedere, quod <lb/>e&longs;t molem ip&longs;am &longs;cindi, ac diuidi. </s>

<s id="N11E5E">Cunei ergo figura &longs;ic de<lb/>lineanda cen&longs;uimus ex quadrata ba&longs;i ABCD, excitando <lb/>&longs;operficiem quadrangularem DBEF, ac aliam triangula<lb/>rem CDE, quæ &longs;imul cum &longs;uis oppo&longs;itis omnes quatuor <lb/>de&longs;inant, ac terminentur in aciem EF. </s>

<s id="N11E5E">Cunei ergo figura &longs;ic de<lb/>lineanda cen&longs;uimus ex quadrata ba&longs;i ABCD, excitando <lb/>&longs;uperficiem quadrangularem DBEF, ac aliam triangula<lb/>rem CDE, quæ &longs;imul cum &longs;uis oppo&longs;itis omnes quatuor <lb/>de&longs;inant, ac terminentur in aciem EF. </s>

<s id="N11E70">Refertur auté hoc quoque in&longs;tru<lb/>mentum ad vecté, eo quod ex duplici <lb/>vecte videatur con&longs;tare, vt infra qu&etail;&longs;t. <lb/></s>

<s id="N11E78">17. ex Ari&longs;totele magis ex profe&longs;&longs;o <lb/>probabitur. </s>

<s id="N11E7D">Etenim &longs;i con&longs;iderentur <lb/>duo eius latera, quæ ex ba&longs;i in aciem <lb/>terminantur, vt CE, & DE non &longs;e<lb/>cus ac duo vectes &longs;ibi inuicem obuer<lb/>&longs;i, & cótra conantes reperientur, quo<lb/>rum <expan abbr="vtiq;">vtique</expan> fulc menta &longs;unt partes &longs;cin<lb/>dendi corporis vtrinque con&longs;titutæ vt <lb/>GH, quibus intrando cuneus innititur. </s>

<s id="N11E7D">Etenim &longs;i con&longs;iderentur <lb/>duo eius latera, quæ ex ba&longs;i in aciem <lb/>terminantur, vt CE, & DE non &longs;e<lb/>cus ac duo vectes &longs;ibi inuicem obuer<lb/>&longs;i, & cóntra conantes reperientur, quo<lb/>rum <expan abbr="vtiq;">vtique</expan> fulc menta &longs;unt partes &longs;cin<lb/>dendi corporis vtrinque con&longs;titutæ vt <lb/>GH, quibus intrando cuneus innititur. </s>

<s id="N11E92">Onera verò &longs;unt re<lb/><figure id="id.005.01.070.2.jpg" xlink:href="005/01/070/2.jpg"/><lb/>reliquæ eiu&longs;dem corporis partes <lb/>&longs;ucce&longs;siuè dimouend&etail;, & adinui<lb/>cem &longs;eparádæ per aciem intran<lb/>tem vbi E, vt in propo&longs;ita figu <lb/>ra e&longs;t l, & K. </s>

<s id="N11EA6">Nam pars vbi K <lb/>e&longs;t onus re&longs;pectu vectis CE in<lb/>nixæ in G; & pars vbi I, e&longs;t <lb/>onus re&longs;pectu vectis DE innixæ <lb/>in H. </s>

<s id="N11EB2">Et extrema in quibus ap<lb/>plicatur potentia &longs;unt initia ip&longs;o<lb/>rum laterum ex parte ba&longs;is vbi <lb/>fit tota percu&longs;&longs;io, nempe vbi C <lb/>& D, quæ omnia aperti&longs;&longs;imè <lb/>citata quæ&longs;tione amplius con&longs;ta<lb/>bunt. </s>

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