| version 1.10, 2004/09/08 13:11:42 |
version 1.11, 2004/09/08 15:36:20 |
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| <p id="N15B14" type="main"> | <p id="N15B14" type="main"> |
| <s id="N15B16">C<emph type="italics"/>vr nuces ab&longs;que ictu facilè confringuntur in­<lb/>strumentis, qua ad eum fiunt v&longs;um. </s> | <s id="N15B16">C<emph type="italics"/>vr nuces ab&longs;que ictu facilè confringuntur in­<lb/>strumentis, qua ad eum fiunt v&longs;um. </s> |
| <s id="N15B1E">Multum <lb/>enim aufertur virium, motionis &longs;cilicet & vio­<lb/>lentia. </s> | <s id="N15B1E">Multum <lb/>enim aufertur virium, motionis &longs;cilicet & vio­<lb/>lentia. </s> |
| <s id="N15B25">Praterea duro & graui comprimens in­<lb/>&longs;trumento citiùs confringet, quàm ligneo & <lb/>leui. </s> | <s id="N15B25">Praeterea duro & graui comprimens in­<lb/>&longs;trumento citiùs confringet, quàm ligneo & <lb/>leui. </s> |
| <s id="N15B2C">An quia &longs;ic vtrunque à duobus compri­<lb/>mitur vectibus ip&longs;a nux, à vecte autem facilè <lb/>diuelluntur onera? </s> | <s id="N15B2C">An quia &longs;ic vtrunque à duobus compri­<lb/>mitur vectibus ip&longs;a nux, à vecte autem facilè <lb/>diuelluntur onera? </s> |
| <s id="N15B33">Id enim instrumentum ex duobus com­<lb/>ponitur vectibus, idem habentibus bypomochlion, connexio­<lb/>nem videlicet ip&longs;am, vbi est A, quemadmodum igitur fue­<lb/>ro diducta &longs;ecundum extrema molis CD, ip&longs;æ FE &longs;ic à par­<lb/>ua faciliter potentia conducuntur, quod igitur cum percu&longs;sio­<lb/>ne feci&longs;&longs;et pondus id valentiores illæ EC, & FD vectes effi­<lb/>eiunt. </s> | <s id="N15B33">Id enim instrumentum ex duobus com­<lb/>ponitur vectibus, idem habentibus hypomochlion, connexio­<lb/>nem videlicet ip&longs;am, vbi est A, quemadmodum igitur fue­<lb/>ro diducta &longs;ecundum extrema molis CD, ip&longs;æ FE &longs;ic à par­<lb/>ua faciliter potentia conducuntur, quod igitur cum percu&longs;sio­<lb/>ne feci&longs;&longs;et pondus id valentiores illæ EC, & FD vectes effi­<lb/>ciunt. </s> |
| <s id="N15B42">Eleuatione enim in contrarium elati, & comprimentes <lb/>frangunt vbi e&longs;t K. <!-- KEEP S--></s> | <s id="N15B42">Eleuatione enim in contrarium elati, & comprimentes <lb/>frangunt vbi e&longs;t K. <!-- KEEP S--></s> |
| <s id="N15B48">Hanc etiam ob cau&longs;am quanto vicinius <lb/>fuerit K ip&longs;um A, confringitur celerius. </s> | <s id="N15B48">Hanc etiam ob cau&longs;am quanto vicinius <lb/>fuerit K ip&longs;um A, confringitur celerius. </s> |
| <s id="N15B4D">Quantò enim ab bipo­<lb/>mochlio plus di&longs;tat vectis, facilius & plus mouet ab codem <lb/>potentia. </s> | <s id="N15B4D">Quantò enim ab hipo­<lb/>mochlio plus di&longs;tat vectis, facilius & plus mouet ab codem <lb/>potentia. </s> |
| <s id="N15B54">E&longs;t igitur A quidem bipomochlion: ip&longs;a autem DAF <lb/>vectis, & item ip&longs;a CAE. </s> | <s id="N15B54">E&longs;t igitur A quidem hipomochlion: ip&longs;a autem DAF <lb/>vectis, & item ip&longs;a CAE. </s> |
| <s id="N15B59">Quantò igitur ip&longs;um K vicinius <lb/>fuerit angulo ip&longs;ius A, tantò vicinius fit connexioni, vbi est <lb/>A, hoc autem tpomochlion, ab eadem igitur potentia appli­<lb/>cante FE plus extolli nece&longs;&longs;e e&longs;t. </s> | <s id="N15B59">Quantò igitur ip&longs;um K vicinius <lb/>fuerit angulo ip&longs;ius A, tantò vicinius fit connexioni, vbi est <lb/>A, hoc autem hypomochlion, ab eadem igitur potentia appli­<lb/>cante FE plus extolli nece&longs;&longs;e e&longs;t. </s> |
| <s id="N15B62">Quamobrem quoniam ex <lb/>contario e&longs;t eleuatio, nece&longs;&longs;e e&longs;t magis comprimi, quod autem <lb/>comprimitur magis, citius frangitur.<emph.end type="italics"/></s> | <s id="N15B62">Quamobrem quoniam ex <lb/>contario e&longs;t eleuatio, nece&longs;&longs;e e&longs;t magis comprimi, quod autem <lb/>comprimitur magis, citius frangitur.<emph.end type="italics"/></s> |
| </p> | </p> |
| <pb pagenum="194" xlink:href="005/01/202.jpg"/> | <pb pagenum="194" xlink:href="005/01/202.jpg"/> |
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| <s id="N15BAD">Attamen ip&longs;e Philo&longs;ophus huiu&longs;modi difficultatem ac <lb/>dubitationem exeodem principio, quo præcedentem quæ­<lb/>&longs;tionem &longs;oluerat, apti&longs;&longs;imè ac breui&longs;&longs;imè diluit, inquiens, <lb/>explicatum in&longs;trumentum duobus brachijs tanquam duo­<lb/>bus vectibus contrarijs, ad &longs;e&longs;e inuicem conuer&longs;is con&longs;tare, <lb/>vnico fulcimento innixis, quod e&longs;t vtriu&longs;que connexio ac <lb/>veluti axis: duorum autem vectium compre&longs;&longs;ione, vt potè <lb/>qui magnam vim habeant comprimendi, æquè facile nuces <lb/>amygdalas, vel id genus alia confringi, ac ictu vel percu&longs;&longs;io­<lb/>ne cum impetu. </s> | <s id="N15BAD">Attamen ip&longs;e Philo&longs;ophus huiu&longs;modi difficultatem ac <lb/>dubitationem exeodem principio, quo præcedentem quæ­<lb/>&longs;tionem &longs;oluerat, apti&longs;&longs;imè ac breui&longs;&longs;imè diluit, inquiens, <lb/>explicatum in&longs;trumentum duobus brachijs tanquam duo­<lb/>bus vectibus contrarijs, ad &longs;e&longs;e inuicem conuer&longs;is con&longs;tare, <lb/>vnico fulcimento innixis, quod e&longs;t vtriu&longs;que connexio ac <lb/>veluti axis: duorum autem vectium compre&longs;&longs;ione, vt potè <lb/>qui magnam vim habeant comprimendi, æquè facile nuces <lb/>amygdalas, vel id genus alia confringi, ac ictu vel percu&longs;&longs;io­<lb/>ne cum impetu. </s> |
| <s id="N15BC2">Quod vt ad oculos etiam pateat, con&longs;ti­<lb/>tuatur primo in&longs;trumentum ABCD, cuius brachia &longs;int AD <lb/>& CB &longs;uffulta in connexione vtriu&longs;que vbi E. <!-- KEEP S--></s> | <s id="N15BC2">Quod vt ad oculos etiam pateat, con&longs;ti­<lb/>tuatur primo in&longs;trumentum ABCD, cuius brachia &longs;int AD <lb/>& CB &longs;uffulta in connexione vtriu&longs;que vbi E. <!-- KEEP S--></s> |
| <s id="N15BCA">Nux verò <lb/><expan abbr="confring&etilde;da">confringenda</expan> locetur inter A & C vbi F, nempe inter extre­<lb/>ma brachiorum ea parte qua minus di&longs;tant à fulcimento. <lb/></s> | <s id="N15BCA">Nux verò <lb/><expan abbr="confring&etilde;da">confringenda</expan> locetur inter A & C vbi F, nempe inter extre­<lb/>ma brachiorum ea parte qua minus di&longs;tant à fulcimento. <lb/></s> |
| <s id="N15BD5">Potentia verò confringentis applicetur in extremis ecrun­<lb/>dem brachiorum ea parte, qua magis di&longs;tant a fulcimento, <pb pagenum="195" xlink:href="005/01/203.jpg"/><figure id="id.005.01.203.1.jpg" xlink:href="005/01/203/1.jpg"/><lb/>tanquam in manubrijs, <expan abbr="nimirũ">nimirum</expan> in BD. <!-- KEEP S--></s> | <s id="N15BD5">Potentia verò confringentis applicetur in extremis eorun­<lb/>dem brachiorum ea parte, qua magis di&longs;tant a fulcimento, <pb pagenum="195" xlink:href="005/01/203.jpg"/><figure id="id.005.01.203.1.jpg" xlink:href="005/01/203/1.jpg"/><lb/>tanquam in manubrijs, <expan abbr="nimirũ">nimirum</expan> in BD. <!-- KEEP S--></s> |
| <s id="N15BEA">Con&longs;ideretur dein­<lb/>de vtrum que brachium tanquam duplicem vectem moueri <lb/>circa immotum fulcimentum E; ita vt ad motum B ver&longs;us <lb/>D, alterum extremum nempe C appropinquetur ad A; & è <lb/>conuer&longs;o, ad motum D ver&longs;us B, ip&longs;um A appropinquetur <lb/>ad C. <!-- KEEP S--></s> | <s id="N15BEA">Con&longs;ideretur dein­<lb/>de vtrum que brachium tanquam duplicem vectem moueri <lb/>circa immotum fulcimentum E; ita vt ad motum B ver&longs;us <lb/>D, alterum extremum nempe C appropinquetur ad A; & è <lb/>conuer&longs;o, ad motum D ver&longs;us B, ip&longs;um A appropinquetur <lb/>ad C. <!-- KEEP S--></s> |
| <s id="N15BF8">Tunc dicimus nucem, qu&etail; quidem tanquam pondus <lb/>ab vtroque extremo duplicis vectis AC pellitur ac repelli­<lb/>tur, facilè comprimi, ac tandem nimia compre&longs;&longs;ione con­<lb/>fringi, &longs;iquidem dum magis ac magis ip&longs;a extrema AC ad <lb/>inuicem appropinquantur, nece&longs;&longs;ariò quæ inter ip&longs;a interci­<lb/>pitur, nucem comprimunt, & comprimendo confringunt. </s> | <s id="N15BF8">Tunc dicimus nucem, qu&etail; quidem tanquam pondus <lb/>ab vtroque extremo duplicis vectis AC pellitur ac repelli­<lb/>tur, facilè comprimi, ac tandem nimia compre&longs;&longs;ione con­<lb/>fringi, &longs;iquidem dum magis ac magis ip&longs;a extrema AC ad <lb/>inuicem appropinquantur, nece&longs;&longs;ariò quæ inter ip&longs;a interci­<lb/>pitur, nucem comprimunt, & comprimendo confringunt. </s> |
| </p> | </p> |
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| <s id="N15D20">Quando igitur corpus <expan abbr="confringendũ">confringendum</expan> col­<lb/>locatur inter extrema <expan abbr="brachiorũ">brachiorum</expan> præfati in&longs;trumenti longi&longs;­<lb/>&longs;ime a centro, <expan abbr="tantũ">tantum</expan> &longs;patium in fractione percurrunt ip&longs;a ex­<lb/>trema, <expan abbr="quantũ">quantum</expan> alia oppo&longs;ita in quibus applicatur potentia. </s> | <s id="N15D20">Quando igitur corpus <expan abbr="confringendũ">confringendum</expan> col­<lb/>locatur inter extrema <expan abbr="brachiorũ">brachiorum</expan> præfati in&longs;trumenti longi&longs;­<lb/>&longs;ime a centro, <expan abbr="tantũ">tantum</expan> &longs;patium in fractione percurrunt ip&longs;a ex­<lb/>trema, <expan abbr="quantũ">quantum</expan> alia oppo&longs;ita in quibus applicatur potentia. </s> |
| </p> | </p> |
| <p id="N15D39" type="main"> | <p id="N15D39" type="main"> |
| <s id="N15D3B">Quod fi corpus confringendum collocetur propinquius <lb/>centro, &longs;eu connexioni brachiorum E, ita vt exten&longs;io eius <lb/>AF, quæ per confractionem deperditur, con&longs;tituatur exem­<lb/>pli gratia in HI, A tran&longs;lato in H &longs;uper eandem lineam, <lb/>AD, & F in I ver&longs;us lineam CB; & per ip&longs;um punctum <lb/>I, & centrum E excitetur alia diagonalis KL, quæ pa­<lb/>riter de&longs;ignet locum, ac fitum quo transferri debet idem <lb/>brachium AD po&longs;t confractionem: Tunc maiorem ar­<lb/>cum inueniemus de&longs;cribitura in ip&longs;a compre&longs;&longs;ione extrema <lb/>DA, quam &longs;it &longs;patium HI, quod deperditur per illam. <lb/></s> | <s id="N15D3B">Quod fi corpus confringendum collocetur propinquius <lb/>centro, &longs;eu connexioni brachiorum E, ita vt exten&longs;io eius <lb/>AF, quæ per confractionem deperditur, con&longs;tituatur exem­<lb/>pli gratia in HI, A tran&longs;lato in H &longs;uper eandem lineam, <lb/>AD, & F in I ver&longs;us lineam CB; & per ip&longs;um punctum <lb/>I, & centrum E excitetur alia diagonalis KL, quæ pa­<lb/>riter de&longs;ignet locum, ac situm quo transferri debet idem <lb/>brachium AD po&longs;t confractionem: Tunc maiorem ar­<lb/>cum inueniemus de&longs;cribitura in ip&longs;a compre&longs;&longs;ione extrema <lb/>DA, quam &longs;it &longs;patium HI, quod deperditur per illam. <lb/></s> |
| <s id="N15D51">Quandoquidem A transferetur in K, & D in L: Spatium <lb/>autem DL continet &longs;patium DG, &longs;icut &longs;patium AK con­<lb/>tinet &longs;patium AF æquale ip&longs;i HI, quo propterea maius e&longs;t <lb/>ip&longs;um AK, & DL, quæ per rationem &longs;uprafactam &longs;unt <lb/>æqualia. </s> | <s id="N15D51">Quandoquidem A transferetur in K, & D in L: Spatium <lb/>autem DL continet &longs;patium DG, &longs;icut &longs;patium AK con­<lb/>tinet &longs;patium AF æquale ip&longs;i HI, quo propterea maius e&longs;t <lb/>ip&longs;um AK, & DL, quæ per rationem &longs;uprafactam &longs;unt <lb/>æqualia. </s> |
| <s id="N15D5C">Rur&longs;us verò &longs;i excitetur linea recta à puncto A <lb/>ad punctum K, & con&longs;iderentur i&longs;ta duo triangula, nempe <lb/>HEI, & AEK, inuenientur habere latera proportionalia <lb/>circa eundem angulum E; ba&longs;esq &longs;imilis rationis per quar­<lb/>tam propo&longs;. </s> | <s id="N15D5C">Rur&longs;us verò &longs;i excitetur linea recta à puncto A <lb/>ad punctum K, & con&longs;iderentur i&longs;ta duo triangula, nempe <lb/>HEI, & AEK, inuenientur habere latera proportionalia <lb/>circa eundem angulum E; ba&longs;esque &longs;imilis rationis per quar­<lb/>tam propo&longs;. </s> |
| <s id="N15D67">&longs;exti. </s> | <s id="N15D67">&longs;exti. </s> |
| <s id="N15D6A">Cumque ba&longs;is AK longioribus lineis <lb/>&longs;ubtendatur ip&longs;i angulo E, maior erit, quàm ba&longs;is HI ei­<lb/>dem angulo &longs;ubten&longs;a breuioribus lineis EH, & EI. </s> | <s id="N15D6A">Cumque ba&longs;is AK longioribus lineis <lb/>&longs;ubtendatur ip&longs;i angulo E, maior erit, quàm ba&longs;is HI ei­<lb/>dem angulo &longs;ubten&longs;a breuioribus lineis EH, & EI. </s> |
| </p> | </p> |
| <pb pagenum="198" xlink:href="005/01/206.jpg"/> | <pb pagenum="198" xlink:href="005/01/206.jpg"/> |
| <p id="N15D75" type="main"> | <p id="N15D75" type="main"> |
| <s id="N15D77">Quod autem exempli&longs;icauimus in brachio, &longs;eu vecte AD, <lb/>idem etiam procedit de brachio CB. <!-- KEEP S--></s> | <s id="N15D77">Quod autem exempli&longs;icauimus in brachio, &longs;eu vecte AD, <lb/>idem etiam procedit de brachio CB. <!-- KEEP S--></s> |
| <s id="N15D7D">Et quod de brachijs <lb/>in m dio ad inuicem connexis, ac bifariam &longs;e&longs;e inter&longs;ecan­<lb/>tibus dictum e&longs;t, accommodari pote&longs;t in alijs nonita &longs;e ha­<lb/>bentibus &longs;eu alibi connexis. </s> | <s id="N15D7D">Et quod de brachijs <lb/>in medio ad inuicem connexis, ac bifariam &longs;e&longs;e inter&longs;ecan­<lb/>tibus dictum e&longs;t, accommodari pote&longs;t in alijs non ita &longs;e ha­<lb/>bentibus &longs;eu alibi connexis. </s> |
| <s id="N15D86">Nam &longs;emper verificabitur ad <lb/>maiorem approximationem corporis confringendi ad cen­<lb/>trum connexionis eorum, &longs;eu fulcimentum, magis ip&longs;a bra­<lb/>chia dilatari, maiu&longs;que deinde &longs;patium eodem tempore, <lb/>comprimendo percurrere, quod e&longs;t velocius agere, vnde & <lb/>validius colligitur fiangere, vt dicebamus ex Ari&longs;totele. <!-- KEEP S--></s> | <s id="N15D86">Nam &longs;emper verificabitur ad <lb/>maiorem approximationem corporis confringendi ad cen­<lb/>trum connexionis eorum, &longs;eu fulcimentum, magis ip&longs;a bra­<lb/>chia dilatari, maiu&longs;que deinde &longs;patium eodem tempore, <lb/>comprimendo percurrere, quod e&longs;t velocius agere, vnde & <lb/>validius colligitur frangere, vt dicebamus ex Ari&longs;totele. <!-- KEEP S--></s> |
| </p> | </p> |
| <p id="N15D94" type="main"> | <p id="N15D94" type="main"> |
| <s id="N15D96">Alio verò ex capite eadem con&longs;equentia probatur, quia <lb/>cum vectis beneficio eandem proportionem habeat po­<lb/>tentia ad pondus leuandum, aut deprimendum, quam habet <lb/>eius di&longs;tantia à fulcimento ad di&longs;tantiam ponderis ab eo­<lb/>dem fulcimento, vt quæ&longs;t. </s> | <s id="N15D96">Alio verò ex capite eadem con&longs;equentia probatur, quia <lb/>cum vectis beneficio eandem proportionem habeat po­<lb/>tentia ad pondus leuandum, aut deprimendum, quam habet <lb/>eius di&longs;tantia à fulcimento ad di&longs;tantiam ponderis ab eo­<lb/>dem fulcimento, vt quæ&longs;t. </s> |
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| <s id="N15DBE">Quæ&longs;tio Vige&longs;imatertia.</s> | <s id="N15DBE">Quæ&longs;tio Vige&longs;imatertia.</s> |
| </p> | </p> |
| <p id="N15DC1" type="main"> | <p id="N15DC1" type="main"> |
| <s id="N15DC3">C<emph type="italics"/>vr &longs;i duo extrema in rhombo puncta duabus <lb/>ferantur lat onibus, baudquaquam æquale <lb/>vtrumque eorum pertran&longs;it rectam, &longs;ed multò <lb/>plus alterum? </s> | <s id="N15DC3">C<emph type="italics"/>vr &longs;i duo extrema in rhombo puncta duabus <lb/>ferantur latonibus, haudquaquam æquale <lb/>vtrumque eorum pertran&longs;it rectam, &longs;ed multò <lb/>plus alterum? </s> |
| <s id="N15DCF">Idem autem e&longs;t &longs;ermo, cur quod <lb/>&longs;uper latus fertur, minus pertran&longs;it quam <lb/>ip&longs;um latus? </s> | <s id="N15DCF">Idem autem e&longs;t &longs;ermo, cur quod <lb/>&longs;uper latus fertur, minus pertran&longs;it quam <lb/>ip&longs;um latus? </s> |
| <s id="N15DD6">Illud enim diametrum minorem <lb/>boc vero maius latus. </s> | <s id="N15DD6">Illud enim diametrum minorem <lb/>hoc vero maius latus. </s> |
| <s id="N15DDB">Et hoc quidem vnica. </s> | <s id="N15DDB">Et hoc quidem vnica. </s> |
| <s id="N15DDE">Il­<lb/>lud verò duabus fertur lationibus. </s> | <s id="N15DDE">Il­<lb/>lud verò duabus fertur lationibus. </s> |
| <s id="N15DE3">Feratur enim ex ip&longs;a AB, A<emph.end type="italics"/><pb pagenum="199" xlink:href="005/01/207.jpg"/><emph type="italics"/>quidem ad <expan abbr="ipsũ">ipsum</expan> B, B verò ad <expan abbr="ipsũ">ipsum</expan> D eadem celeritate. </s> | <s id="N15DE3">Feratur enim ex ip&longs;a AB, A<emph.end type="italics"/><pb pagenum="199" xlink:href="005/01/207.jpg"/><emph type="italics"/>quidem ad <expan abbr="ipsũ">ipsum</expan> B, B verò ad <expan abbr="ipsũ">ipsum</expan> D eadem celeritate. </s> |
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| <s id="N15E33">Repleto igitur ab ip&longs;o G quod in­<lb/>tus e&longs;t, toti e&longs;t &longs;imile, & ip&longs;um B in ip&longs;a diametro erit &longs;ecun­<lb/>dum laterum connexionem. </s> | <s id="N15E33">Repleto igitur ab ip&longs;o G quod in­<lb/>tus e&longs;t, toti e&longs;t &longs;imile, & ip&longs;um B in ip&longs;a diametro erit &longs;ecun­<lb/>dum laterum connexionem. </s> |
| <s id="N15E3A">Et &longs;imul latus pertran&longs;it latus, & <lb/>B ip&longs;um BC diametrum. </s> | <s id="N15E3A">Et &longs;imul latus pertran&longs;it latus, & <lb/>B ip&longs;um BC diametrum. </s> |
| <s id="N15E3F">Simul igitur Amultò plus ip&longs;a AB <lb/>pertran&longs;it, & ip&longs;um latus minus latus eadem lata teleritate: <lb/>& ip&longs;um latus maiorem quàm B pertran&longs;iuit vna <expan abbr="latũ">latum</expan> latio­<lb/>ne. </s> | <s id="N15E3F">Simul igitur Amultò plus ip&longs;a AB <lb/>pertran&longs;it, & ip&longs;um latus minus latus eadem lata teleritate: <lb/>& ip&longs;um latus maiorem quàm B pertran&longs;iuit vna <expan abbr="latũ">latum</expan> latio­<lb/>ne. </s> |
| <s id="N15E4C">Quantò enim acutior fuerit rbombus, diameter quidem <lb/>minor fit, AC autem maior; latus verò ip&longs;ius BC minus. </s> | <s id="N15E4C">Quantò enim acutior fuerit rhombus, diameter quidem <lb/>minor fit, AC autem maior; latus verò ip&longs;ius BC minus. </s> |
| <s id="N15E51">Ab­<lb/>&longs;urdum e&longs;t enim (vt dictum e&longs;t) id quod duabus fertur latio­<lb/>nibus, aliquando ferri tardius illo, quo fertur vnica, & vtri&longs;­<lb/>que po&longs;itis æquali velocitate punctis, alterum pertran&longs;ire ma­<lb/>iorem Cau&longs;a autem e&longs;t quoniam ei, quod ab obtu&longs;o fertur an­<lb/>gulo, ambæ ferè contrariæ fiunt lationes, & illa &longs;ecundum <lb/>quam ip&longs;um fertur, & illa &longs;ecundum quam ip&longs;um à latere de­<lb/>fertur. </s> | <s id="N15E51">Ab­<lb/>&longs;urdum e&longs;t enim (vt dictum e&longs;t) id quod duabus fertur latio­<lb/>nibus, aliquando ferri tardius illo, quo fertur vnica, & vtri&longs;­<lb/>que po&longs;itis æquali velocitate punctis, alterum pertran&longs;ire ma­<lb/>iorem Cau&longs;a autem e&longs;t quoniam ei, quod ab obtu&longs;o fertur an­<lb/>gulo, ambæ ferè contrariæ fiunt lationes, & illa &longs;ecundum <lb/>quam ip&longs;um fertur, & illa &longs;ecundum quam ip&longs;um à latere de­<lb/>fertur. </s> |
| <s id="N15E62">Ei autem quod ab acuto fertur, accidit vt ad idem fe­<lb/>ratur. </s> | <s id="N15E62">Ei autem quod ab acuto fertur, accidit vt ad idem fe­<lb/>ratur. </s> |
| <s id="N15E67">Coadiuuat enim quæ ip&longs;ius e&longs;t lateris,, illam quæ e&longs;t &longs;u­<lb/>per diametrum. </s> | <s id="N15E67">Coadiuuat enim quæ ip&longs;ius e&longs;t lateris,, illam quæ e&longs;t &longs;u­<lb/>per diametrum. </s> |
| <s id="N15E6C">Et quantò bunc quidem acutiorem feceris, <lb/>illum verò obtu&longs;um magis: bæc quidem tardior erit, illa verò <lb/>celerior. </s> | <s id="N15E6C">Et quantò hunc quidem acutiorem feceris, <lb/>illum verò obtu&longs;um magis: hæc quidem tardior erit, illa verò <lb/>celerior. </s> |
| <s id="N15E73">Hæ quidem igitur magis contrariæ fiunt, quoniam <lb/>obtu&longs;ior fit angulus: illæ verò ad idem magis, quoniam lineæ <lb/>coarctantur. </s> | <s id="N15E73">Hæ quidem igitur magis contrariæ fiunt, quoniam <lb/>obtu&longs;ior fit angulus: illæ verò ad idem magis, quoniam lineæ <lb/>coarctantur. </s> |
| <s id="N15E7A">Ip&longs;um enim A ferè ad idem fertur &longs;ecundum <lb/>ambas lationes. </s> | <s id="N15E7A">Ip&longs;um enim A ferè ad idem fertur &longs;ecundum <lb/>ambas lationes. </s> |
| <s id="N15E7F">Coadiuuatur igitur altera & quantò &longs;anè <lb/>acutior fuerit angulus, tantò magis ip&longs;um A ad contrarium, <lb/>ip&longs;um enim ad B fertur, latus autem defert ip&longs;um ad D. <!-- KEEP S--></s> | <s id="N15E7F">Coadiuuatur igitur altera & quantò &longs;anè <lb/>acutior fuerit angulus, tantò magis ip&longs;um A ad contrarium, <lb/>ip&longs;um enim ad B fertur, latus autem defert ip&longs;um ad D. <!-- KEEP S--></s> |
| <s id="N15E87">Et <lb/>quantò &longs;anè obtu&longs;ior fuerit angulus, magis contrartæ fiunt <lb/>lationes, rectior enim efficitur linea. </s> | <s id="N15E87">Et <lb/>quantò &longs;anè obtu&longs;ior fuerit angulus, magis contrariæ fiunt <lb/>lationes, rectior enim efficitur linea. </s> |
| <s id="N15E8E">Si autem omnino recta <lb/>fieret penitus vtique e&longs;sent contrariæ. </s> | <s id="N15E8E">Si autem omnino recta <lb/>fieret penitus vtique e&longs;sent contrariæ. </s> |
| <s id="N15E93">Latus verò &longs;ecundum <lb/>vnicam latam lationem à nullo præpeditur, rationabiliter igi­<lb/>tur maiorem pertran&longs;it.<emph.end type="italics"/></s> | <s id="N15E93">Latus verò &longs;ecundum <lb/>vnicam latam lationem à nullo præpeditur, rationabiliter igi­<lb/>tur maiorem pertran&longs;it.<emph.end type="italics"/></s> |
| </p> | </p> |
| |
| </p> | </p> |
| <p id="N15EC1" type="main"> | <p id="N15EC1" type="main"> |
| <s id="N15EC3">Prima difficultas e&longs;t, cur &longs;i duo puncta extrema vnius la­<lb/>teris in rhombo duabus &longs;imul ferantur lationibus cum ea­<lb/>dem velocitate, vnum maius, alterum minus &longs;patium per­<lb/>currit. </s> | <s id="N15EC3">Prima difficultas e&longs;t, cur &longs;i duo puncta extrema vnius la­<lb/>teris in rhombo duabus &longs;imul ferantur lationibus cum ea­<lb/>dem velocitate, vnum maius, alterum minus &longs;patium per­<lb/>currit. </s> |
| <s id="N15ECC">Ad cuius rei explieationem &longs;upponimus ex. </s> | <s id="N15ECC">Ad cuius rei explicationem &longs;upponimus ex. </s> |
| <s id="N15ECF">31. de­<lb/>finitione primi Euclidis Rhombum e&longs;&longs;e figuram quadrila­<lb/>teram quidem, & æquilateram, &longs;ed non rectangulam; quip­<lb/>pe quæ duos angulos habet acutos, duos verò obtu&longs;os. </s> | <s id="N15ECF">31. de­<lb/>finitione primi Euclidis Rhombum e&longs;&longs;e figuram quadrila­<lb/>teram quidem, & æquilateram, &longs;ed non rectangulam; quip­<lb/>pe quæ duos angulos habet acutos, duos verò obtu&longs;os. </s> |
| <s id="N15ED8">Si <lb/><figure id="id.005.01.208.1.jpg" xlink:href="005/01/208/1.jpg"/><lb/>igitur in Rhombo ABCD, cuius <lb/>acuti anguli &longs;int A & D, obtu&longs;i <lb/>verò B & C, duo extrema pun­<lb/>cta lateris AB, nempe ip&longs;um A, & <lb/>ip&longs;um B, æqua velocitate duabus <lb/>ferantur lationibus, vna qua pun­<lb/>ctum A &longs;uper idem latus feratur <lb/>ver&longs;us B, & B feratur ver&longs;us A: <lb/>altera verò qua <expan abbr="dũ">dum</expan> ip&longs;a duo pun­<lb/>cta &longs;ibi obuiam procedunt, &longs;imul <lb/>cum toto latere AB, moueantur <lb/>ver&longs;us latus CD, ita vt &longs;emper la­<lb/>tus, &longs;eu linea AB, ip&longs;i CD &longs;it pa­<lb/>ralella, de&longs;cendatque per latera <lb/>AC, & BD quou&longs;que coincidat <lb/>cum eadem CD: Cum ex duabus lationibus, eadem &longs;em­<lb/>per laterum proportione &longs;eruata, recta quædam linea pro­<lb/>ducatur, vt &longs;upra demon&longs;tratum e&longs;t ex eodem Ari&longs;totele <lb/>1. par. </s> | <s id="N15ED8">Si <lb/><figure id="id.005.01.208.1.jpg" xlink:href="005/01/208/1.jpg"/><lb/>igitur in Rhombo ABCD, cuius <lb/>acuti anguli &longs;int A & D, obtu&longs;i <lb/>verò B & C, duo extrema pun­<lb/>cta lateris AB, nempe ip&longs;um A, & <lb/>ip&longs;um B, æqua velocitate duabus <lb/>ferantur lationibus, vna qua pun­<lb/>ctum A &longs;uper idem latus feratur <lb/>ver&longs;us B, & B feratur ver&longs;us A: <lb/>altera verò qua <expan abbr="dũ">dum</expan> ip&longs;a duo pun­<lb/>cta &longs;ibi obuiam procedunt, &longs;imul <lb/>cum toto latere AB, moueantur <lb/>ver&longs;us latus CD, ita vt &longs;emper la­<lb/>tus, &longs;eu linea AB, ip&longs;i CD &longs;it pa­<lb/>ralella, de&longs;cendatque per latera <lb/>AC, & BD quou&longs;que coincidat <lb/>cum eadem CD: Cum ex duabus lationibus, eadem &longs;em­<lb/>per laterum proportione &longs;eruata, recta quædam linea pro­<lb/>ducatur, vt &longs;upra demon&longs;tratum e&longs;t ex eodem Ari&longs;totele <lb/>1. par. </s> |
| <s id="N15F0B">tex. <!-- REMOVE S-->6. vtraque puncta prædicta eandem laterum ip­<lb/>&longs;ius rhombi proportionem in &longs;uo motu &longs;eruando, propriam <pb pagenum="201" xlink:href="005/01/209.jpg"/>rectam lineam de&longs;cribent: A quidem lineam AD, B verò <lb/>BC: quæ nimirum erunt diametri eiu&longs;dem rhombi. </s> | <s id="N15F0B">tex. <!-- REMOVE S-->6. vtraque puncta prædicta eandem laterum ip­<lb/>&longs;ius rhombi proportionem in &longs;uo motu &longs;eruando, propriam <pb pagenum="201" xlink:href="005/01/209.jpg"/>rectam lineam de&longs;cribent: A quidem lineam AD, B verò <lb/>BC: quæ nimirum erunt diametri eiu&longs;dem rhombi. </s> |
| |
| <s id="N15F33">Quod mirum proculdubio omnibus cau&longs;am igno­<lb/>rantibus videri &longs;olet. </s> | <s id="N15F33">Quod mirum proculdubio omnibus cau&longs;am igno­<lb/>rantibus videri &longs;olet. </s> |
| </p> | </p> |
| <p id="N15F38" type="main"> | <p id="N15F38" type="main"> |
| <s id="N15F3A">Verùm quod linea recta, quam de&longs;cribere diximus pun­<lb/>ctum A, &longs;it ipfa diameter AD; quam verò punctum B, <lb/>&longs;it diameter BC, facilè demon&longs;tratur ex eo. </s> | <s id="N15F3A">Verùm quod linea recta, quam de&longs;cribere diximus pun­<lb/>ctum A, &longs;it ipsa diameter AD; quam verò punctum B, <lb/>&longs;it diameter BC, facilè demon&longs;tratur ex eo. </s> |
| <s id="N15F41">Nam &longs;i pun­<lb/>ctum A, proprio motu delatum fuerit exempli gratia v&longs;que <lb/>ad punctum E medium ip&longs;ius lineæ AB, & linea tota <lb/>AB eodem tempore, æquale &longs;patium pertran&longs;ierit ver&longs;us <lb/>CD, ita vt alterum eius extremum peruenerit ad punctum <lb/>F, medium lateris AC; alterum verò ad punctum G, me­<lb/>dium lateris BD: quoniam AF æqualis e&longs;t ip&longs;i AE, &longs;i com­<lb/>pleatur figura &longs;imilis toti, productis lineis EH, & FG per <lb/>punctum medium K, nempe rhombus AEKF, &longs;imilis <lb/>rhombo maiori ABCD per 24. &longs;exti elementorum; erit <lb/>recta FK æqualis oppo&longs;itæ AE, & AF ip&longs;i EK; proin­<lb/>deque punctum A cum duabus tran&longs;latum &longs;it lationibus <lb/>&longs;emper proportionalibus iuxta rationem æqualitatis; quam <lb/>latera rhomborum habent inter &longs;e, vtique tran&longs;latum erit <lb/>&longs;uper rectam AK in ip&longs;um K, quod e&longs;t punctum medium <lb/>diametri AD; Cuius reliquum dimidium conficiet, tum <lb/>ex motu &longs;uo ab E v&longs;que ad B, tum ex alieno ab F v&longs;que <lb/>ad C, ita vt tandem perueniat ad punctum D. <!-- KEEP S--></s> | <s id="N15F41">Nam &longs;i pun­<lb/>ctum A, proprio motu delatum fuerit exempli gratia v&longs;que <lb/>ad punctum E medium ip&longs;ius lineæ AB, & linea tota <lb/>AB eodem tempore, æquale &longs;patium pertran&longs;ierit ver&longs;us <lb/>CD, ita vt alterum eius extremum peruenerit ad punctum <lb/>F, medium lateris AC; alterum verò ad punctum G, me­<lb/>dium lateris BD: quoniam AF æqualis e&longs;t ip&longs;i AE, &longs;i com­<lb/>pleatur figura &longs;imilis toti, productis lineis EH, & FG per <lb/>punctum medium K, nempe rhombus AEKF, &longs;imilis <lb/>rhombo maiori ABCD per 24. &longs;exti elementorum; erit <lb/>recta FK æqualis oppo&longs;itæ AE, & AF ip&longs;i EK; proin­<lb/>deque punctum A cum duabus tran&longs;latum &longs;it lationibus <lb/>&longs;emper proportionalibus iuxta rationem æqualitatis; quam <lb/>latera rhomborum habent inter &longs;e, vtique tran&longs;latum erit <lb/>&longs;uper rectam AK in ip&longs;um K, quod e&longs;t punctum medium <lb/>diametri AD; Cuius reliquum dimidium conficiet, tum <lb/>ex motu &longs;uo ab E v&longs;que ad B, tum ex alieno ab F v&longs;que <lb/>ad C, ita vt tandem perueniat ad punctum D. <!-- KEEP S--></s> |
| </p> | </p> |
| <p id="N15F67" type="main"> | <p id="N15F67" type="main"> |
| <s id="N15F69">Eodem pacto, quod dictum e&longs;t de puncto A, applica­<lb/>ri pote&longs;t in puncto B. </s> | <s id="N15F69">Eodem pacto, quod dictum e&longs;t de puncto A, applica­<lb/>ri pote&longs;t in puncto B. </s> |
| <s id="N15F6E">Nam &longs;i hoc cum eadem velocitate <lb/>moueatur ver&longs;us A, &longs;icut linea AB ver&longs;us CD, quo tem­<lb/>pore per proprium motum percurri&longs;&longs;er v&longs;que ad E, alieno <lb/>motu perueni&longs;&longs;et v&longs;que ad G; <expan abbr="æqualesq.">æqualesque</expan> forent lineæ BE, <pb pagenum="202" xlink:href="005/01/210.jpg"/>& BG; producti&longs;que lateribus, EH, & GF, rhombus <lb/>EBGK per illa con&longs;titutus, &longs;imilis e&longs;&longs;et rhombo continen­<lb/>ti ABCD: Ideoque GK æqualis oppo&longs;itæ BE, & BG <lb/>æqualis EK. </s> | <s id="N15F6E">Nam &longs;i hoc cum eadem velocitate <lb/>moueatur ver&longs;us A, &longs;icut linea AB ver&longs;us CD, quo tem­<lb/>pore per proprium motum percurri&longs;&longs;et v&longs;que ad E, alieno <lb/>motu perueni&longs;&longs;et v&longs;que ad G; <expan abbr="æqualesq.">æqualesque</expan> forent lineæ BE, <pb pagenum="202" xlink:href="005/01/210.jpg"/>& BG; producti&longs;que lateribus, EH, & GF, rhombus <lb/>EBGK per illa con&longs;titutus, &longs;imilis e&longs;&longs;et rhombo continen­<lb/>ti ABCD: Ideoque GK æqualis oppo&longs;itæ BE, & BG <lb/>æqualis EK. </s> |
| <s id="N15F86">Quare punctum B vtroque motu<gap/> tran&longs;la­<lb/>tum cum eadem proportione æqualitatis, mouebitur motu <lb/>mixto &longs;uper diametrum ip&longs;ius rhombi, & quo tempore <lb/>transferri deberet in E & in G, transfertur in K, quod e&longs;t <lb/>punctum medium diametri BC; cuius reliquum dimidium <lb/>conficiet per motum proprium ab E v&longs;que ad A, & alie­<lb/>no à G v&longs;que ad D; ita vt tandem reperiatur in C. <!-- KEEP S--></s> | <s id="N15F86">Quare punctum B vtroque motum tran&longs;la­<lb/>tum cum eadem proportione æqualitatis, mouebitur motu <lb/>mixto &longs;uper diametrum ip&longs;ius rhombi, & quo tempore <lb/>transferri deberet in E & in G, transfertur in K, quod e&longs;t <lb/>punctum medium diametri BC; cuius reliquum dimidium <lb/>conficiet per motum proprium ab E v&longs;que ad A, & alie­<lb/>no à G v&longs;que ad D; ita vt tandem reperiatur in C. <!-- KEEP S--></s> |
| <s id="N15F98">Cum <lb/>igitur &longs;patium BC, vt dicebamus, minus &longs;it quam &longs;patium <lb/>AD eodem tempore peragratum à puncto A, difficile vi­<lb/>detur qua ratione id po&longs;&longs;it contingere, po&longs;tquam ita rem <lb/>&longs;e habere con&longs;titerit. </s> | <s id="N15F98">Cum <lb/>igitur &longs;patium BC, vt dicebamus, minus &longs;it quam &longs;patium <lb/>AD eodem tempore peragratum à puncto A, difficile vi­<lb/>detur qua ratione id po&longs;&longs;it contingere, po&longs;tquam ita rem <lb/>&longs;e habere con&longs;titerit. </s> |
| </p> | </p> |
| <p id="N15FA3" type="main"> | <p id="N15FA3" type="main"> |
| <s id="N15FA5">Huius tamen euentus cau&longs;am &longs;oluendo primam partem <lb/>quæ&longs;tionis, <expan abbr="primamq.">primamque</expan> difficultatem, eam e&longs;&longs;e inquit Ari&longs;to­<lb/>teles, quia cum in rhombo duo &longs;int obtu&longs;i anguli, duo verò <lb/>acuti, lationes illæ, quibus fertur punctum, quod ab obtu&longs;o <lb/>angulo di&longs;cedit, vt in propo&longs;ita figura e&longs;t punctum B, &longs;unt <lb/>inter &longs;e omnino ferè contrariæ, cum vna, verbi gratia &longs;ur­<lb/>&longs;um penè tendat ver&longs;us A, altera verò deor&longs;um ver&longs;us D: <lb/>Quo fit vt mutuo præpediantur, ac retardentur. </s> | <s id="N15FA5">Huius tamen euentus cau&longs;am &longs;oluendo primam partem <lb/>quæ&longs;tionis, <expan abbr="primamq.">primamque</expan> difficultatem, eam e&longs;&longs;e inquit Ari&longs;to­<lb/>teles, quia cum in rhombo duo &longs;int obtu&longs;i anguli, duo verò <lb/>acuti, lationes illæ, quibus fertur punctum, quod ab obtu&longs;o <lb/>angulo di&longs;cedit, vt in propo&longs;ita figura e&longs;t punctum B, &longs;unt <lb/>inter &longs;e omnino ferè contrariæ, cum vna, verbi gratia &longs;ur­<lb/>&longs;um penè tendat ver&longs;us A, altera verò deor&longs;um ver&longs;us D: <lb/>Quo fit vt mutuo præpediantur, ac retardentur. </s> |
| <s id="N15FBA">Lationes <lb/>verò quibus fertur punctum, quod ab acuto angulo di&longs;cedit <lb/>vt A; quamuis diuer&longs;æ in &longs;e &longs;int, nullo tamen modo con­<lb/>&longs;tituuntur contrariæ, cum ad eandem ferè partem pergere <lb/>teneantur, <expan abbr="parumq.">parumque</expan> aut minus &longs;emper di&longs;tent inter &longs;e termi­<lb/>ni ad quos tendunt. </s> | <s id="N15FBA">Lationes <lb/>verò quibus fertur punctum, quod ab acuto angulo di&longs;cedit <lb/>vt A; quamuis diuer&longs;æ in &longs;e &longs;int, nullo tamen modo con­<lb/>&longs;tituuntur contrariæ, cum ad eandem ferè partem pergere <lb/>teneantur, <expan abbr="parumq.">parumque</expan> aut minus &longs;emper di&longs;tent inter &longs;e termi­<lb/>ni ad quos tendunt. </s> |
| <s id="N15FCB">Quare potius ip&longs;æ ad inuicem iuuan­<lb/>tur, quàm aliquo modo impediantur. </s> | <s id="N15FCB">Quare potius ip&longs;æ ad inuicem iuuan­<lb/>tur, quàm aliquo modo impediantur. </s> |
| <s id="N15FD0">Rationi autem con­<lb/>&longs;entaneum e&longs;t, vt punctum contrarijs ferè lationibus &longs;e&longs;e <lb/>impedientibus latum, minori interuallo in eodem tempore <lb/>feratur, quàm punctum, quod duabus lationibus &longs;e&longs;e mutuo <lb/>adiuuantibus a&longs;portatur; mitumque propterea non e&longs;&longs;e &longs;i <lb/>hoc maiorem diametrum, illud verò minorem eodem tem­<lb/>pore percurrat. </s> | <s id="N15FD0">Rationi autem con­<lb/>&longs;entaneum e&longs;t, vt punctum contrarijs ferè lationibus &longs;e&longs;e <lb/>impedientibus latum, minori interuallo in eodem tempore <lb/>feratur, quàm punctum, quod duabus lationibus &longs;e&longs;e mutuo <lb/>adiuuantibus a&longs;portatur; mirumque propterea non e&longs;&longs;e &longs;i <lb/>hoc maiorem diametrum, illud verò minorem eodem tem­<lb/>pore percurrat. </s> |
| <s id="N15FDF">Vnde etia n &longs;equitur, vt quò acutiores <lb/>con&longs;tituantur anguli A, & D, <expan abbr="proindeq.">proindeque</expan> obtu&longs;iores B, <lb/>& C; tardius ac minori interuallo feratur ip&longs;um B; cele-<pb pagenum="203" xlink:href="005/01/211.jpg"/>rius verò ac maiori &longs;patio ip&longs;um A. <!-- KEEP S--></s> | <s id="N15FDF">Vnde etiam &longs;equitur, vt quò acutiores <lb/>con&longs;tituantur anguli A, & D, <expan abbr="proindeq.">proindeque</expan> obtu&longs;iores B, <lb/>& C; tardius ac minori interuallo feratur ip&longs;um B; cele-<pb pagenum="203" xlink:href="005/01/211.jpg"/>rius verò ac maiori &longs;patio ip&longs;um A. <!-- KEEP S--></s> |
| <s id="N15FF0">Quandoquidem ex ma­<lb/>iori angu&longs;tia angulorum magis. </s> | <s id="N15FF0">Quandoquidem ex ma­<lb/>iori angu&longs;tia angulorum magis. </s> |
| <s id="N15FF5">vniuntur latera, magis <expan abbr="q.">que</expan> ad <lb/>vnum, & idem terminum appropinquantur. </s> | <s id="N15FF5">vniuntur latera, magis <expan abbr="q.">que</expan> ad <lb/>vnum, & idem terminum appropinquantur. </s> |
| </p> | </p> |
| <p id="N15FFE" type="main"> | <p id="N15FFE" type="main"> |
| <s id="N16000">Quam Ari&longs;totelis &longs;olutionem pluribus euerrere conatur <lb/>Baldus, quæ &longs;ummatim in hoc tantum redigi po&longs;&longs;unt, quòd <lb/>ex ea &longs;equeretur, idem &longs;imiliter dicendum e&longs;&longs;e de duo­<lb/>bus punctis v<gap/> ius lateris in quadrato, &longs;i duabus &longs;imul latio­<lb/>nibus mouerentur eo pacto quo in rhombo Philo&longs;ophus <lb/>de&longs;crip&longs;it; vt &longs;cilicet punctum, quod duabus lationibus fer­<lb/>tur, ambabus deor&longs;um tendentibus &longs;uper de&longs;cendentem <lb/>diametrum ip&longs;ius quadrati, velocius feratur, quàm punctum, <lb/>quod duabus lationibus fertur, vna deor&longs;um tendente, alte­<lb/>ra verò &longs;ur&longs;um &longs;uper diametrum tran&longs;uer&longs;am. </s> | <s id="N16000">Quam Ari&longs;totelis &longs;olutionem pluribus euerrere conatur <lb/>Baldus, quæ &longs;ummatim in hoc tantum redigi po&longs;&longs;unt, quòd <lb/>ex ea &longs;equeretur, idem &longs;imiliter dicendum e&longs;&longs;e de duo­<lb/>bus punctis vnius lateris in quadrato, &longs;i duabus &longs;imul latio­<lb/>nibus mouerentur eo pacto quo in rhombo Philo&longs;ophus <lb/>de&longs;crip&longs;it; vt &longs;cilicet punctum, quod duabus lationibus fer­<lb/>tur, ambabus deor&longs;um tendentibus &longs;uper de&longs;cendentem <lb/>diametrum ip&longs;ius quadrati, velocius feratur, quàm punctum, <lb/>quod duabus lationibus fertur, vna deor&longs;um tendente, alte­<lb/>ra verò &longs;ur&longs;um &longs;uper diametrum tran&longs;uer&longs;am. </s> |
| <s id="N16017">Id quod per <lb/>&longs;e fal&longs;um e&longs;&longs;e con&longs;tat; cum æquali tempore; æquale &longs;patium <lb/>vtrumque punctum conficeret Siquidem in quadrato vtra­<lb/>que diameter alteri ad inuicem &longs;emper e&longs;t æqualis. </s> | <s id="N16017">Id quod per <lb/>&longs;e fal&longs;um e&longs;&longs;e con&longs;tat; cum æquali tempore; æquale &longs;patium <lb/>vtrumque punctum conficeret Siquidem in quadrato vtra­<lb/>que diameter alteri ad inuicem &longs;emper e&longs;t æqualis. </s> |
| <s id="N16020"><expan abbr="Idemq.">Idemque</expan> <lb/>confirmat: in rhombo inuer&longs;o. </s> | <s id="N16020"><expan abbr="Idemq.">Idemque</expan> <lb/>confirmat: in rhombo inuer&longs;o. </s> |
| <s id="N16028">Nam &longs;equeretur, punctum <lb/>duabus lationibus latum deor&longs;um per minorem diametrum, <lb/>citius ferri, quàm punctum, quod duabus lationibus, vna <lb/>&longs;ur&longs;um: altera deor&longs;um tendente: pertran&longs;iret diametrum <lb/>tran&longs;uer&longs;am, nempe maiorem, Quod quippe ab&longs;urdum e&longs;­<lb/>&longs;e liquet. </s> | <s id="N16028">Nam &longs;equeretur, punctum <lb/>duabus lationibus latum deor&longs;um per minorem diametrum, <lb/>citius ferri, quàm punctum, quod duabus lationibus, vna <lb/>&longs;ur&longs;um: altera deor&longs;um tendente: pertran&longs;iret diametrum <lb/>tran&longs;uer&longs;am, nempe maiorem, Quod quippe ab&longs;urdum e&longs;­<lb/>&longs;e liquet. </s> |
| </p> | </p> |
| <p id="N16035" type="main"> | <p id="N16035" type="main"> |
| <s id="N16037">Verumenimuerò Baldus in his propriam potius appre­<lb/>hen&longs;ionem, quam Ari&longs;totelis &longs;olutionem euertit. </s> | <s id="N16037">Verumenimuerò Baldus in his propriam potius appre­<lb/>hen&longs;ionem, quam Ari&longs;totelis &longs;olutionem euertit. </s> |
| <s id="N1603C">Porrò <lb/>hæc non fundatur in eo, quod e&longs;t &longs;ur&longs;um, aut deor&longs;um pun­<lb/>cta ip&longs;a duabus lationibus ferri, vt ip&longs;e &longs;upponit, quamuis ad <lb/>explicationem præ dicti motus, <expan abbr="doctrinæq.">doctrinæque</expan> Ari&longs;totelis, om­<lb/>nes vtamur exemplo diuer&longs;arum po&longs;itionum, vt &longs;ur&longs;um, aut <lb/>deor&longs;um: &longs;ed ab&longs;trahendo à quacumque po&longs;itione, tota <lb/>&longs;olutionis ratio ab Ari&longs;totele con&longs;tituitur in maiori vnione, <lb/>&longs;eu propinquitate laterum acutranguli, & in maiori &longs;epara­<lb/>none, &longs;eu di&longs;tantia laterum anguli obtu&longs;i. </s> | <s id="N1603C">Porrò <lb/>hæc non fundatur in eo, quod e&longs;t &longs;ur&longs;um, aut deor&longs;um pun­<lb/>cta ip&longs;a duabus lationibus ferri, vt ip&longs;e &longs;upponit, quamuis ad <lb/>explicationem præ dicti motus, <expan abbr="doctrinæq.">doctrinæque</expan> Ari&longs;totelis, om­<lb/>nes vtamur exemplo diuer&longs;arum po&longs;itionum, vt &longs;ur&longs;um, aut <lb/>deor&longs;um: &longs;ed ab&longs;trahendo à quacumque po&longs;itione, tota <lb/>&longs;olutionis ratio ab Ari&longs;totele con&longs;tituitur in maiori vnione, <lb/>&longs;eu propinquitate laterum acuti anguli, & in maiori &longs;epara­<lb/>tione, &longs;eu di&longs;tantia laterum anguli obtu&longs;i. </s> |
| <s id="N16053">Nam per ip&longs;a <lb/>latera anguli obtu&longs;i; punctum in diuer&longs;as longè partesra­<lb/>pitur, qua&longs;i omnino contrario motu: per latera verò anguli <lb/>acuti, in vnam ferè partem, qua&longs;i per eundem motum, qui <lb/>propterea velocior con&longs;tituitur, vt dictum e&longs;t. </s> | <s id="N16053">Nam per ip&longs;a <lb/>latera anguli obtu&longs;i; punctum in diuer&longs;as longè partesra­<lb/>pitur, qua&longs;i omnino contrario motu: per latera verò anguli <lb/>acuti, in vnam ferè partem, qua&longs;i per eundem motum, qui <lb/>propterea velocior con&longs;tituitur, vt dictum e&longs;t. </s> |
| </p> | </p> |
| <pb pagenum="204" xlink:href="005/01/212.jpg"/> | <pb pagenum="204" xlink:href="005/01/212.jpg"/> |
| <p id="N16062" type="main"> | <p id="N16062" type="main"> |
| <s id="N16064">Deinde propria Baldi &longs;olutio, quam ex proprijs cau&longs;is <lb/>ip&longs;e ait e&longs;&longs;e de&longs;umptam, nullam cau&longs;am affert propo&longs;iti effe­<lb/>ctus ad diluendam difficultatem, &longs;eu rationem dubitandi, <lb/>&longs;ed rur&longs;us noua cluntaxat via idip&longs;um demon&longs;trat, quod Ari­<lb/>&longs;totelis argumento demon&longs;tratum e&longs;t de veritate ip&longs;ius ef­<lb/>fectus, nempe punctum A per longiorem diametrum AD, <lb/>illis duabus lationibus ferri eodem tempore, quo punctum <lb/>B fertur &longs;uper minorem diametrum BC; quod e&longs;t citius <lb/>moueri: nihil attingens de cau&longs;a cur id contingat, &longs;eu ob <lb/>quam punctum A, eodem tempore maiorem valeat li­<lb/>neam pertran&longs;ire, <expan abbr="proindeq.">proindeque</expan> velocius moueri; id quod opti­<lb/>mè fecit Ari&longs;toteles vt vidimus. </s> | <s id="N16064">Deinde propria Baldi &longs;olutio, quam ex proprijs cau&longs;is <lb/>ip&longs;e ait e&longs;&longs;e de&longs;umptam, nullam cau&longs;am affert propo&longs;iti effe­<lb/>ctus ad diluendam difficultatem, &longs;eu rationem dubitandi, <lb/>&longs;ed rur&longs;us noua duntaxat via idip&longs;um demon&longs;trat, quod Ari­<lb/>&longs;totelis argumento demon&longs;tratum e&longs;t de veritate ip&longs;ius ef­<lb/>fectus, nempe punctum A per longiorem diametrum AD, <lb/>illis duabus lationibus ferri eodem tempore, quo punctum <lb/>B fertur &longs;uper minorem diametrum BC; quod e&longs;t citius <lb/>moueri: nihil attingens de cau&longs;a cur id contingat, &longs;eu ob <lb/>quam punctum A, eodem tempore maiorem valeat li­<lb/>neam pertran&longs;ire, <expan abbr="proindeq.">proindeque</expan> velocius moueri; id quod opti­<lb/>mè fecit Ari&longs;toteles vt vidimus. </s> |
| </p> | </p> |
| <p id="N16081" type="main"> | <p id="N16081" type="main"> |
| <s id="N16083">Secunda autem difficultas, quam Philo&longs;ophus hac in <lb/>quæ&longs;tione proponit, e&longs;t, cur in eodem rhombo punctum B, <lb/>quod vt diximus &longs;ua &longs;ponte fertur &longs;uper latus BA, <expan abbr="totamq.">totamque</expan> <lb/>eius longitudinem percurrit; minus quippe pertran&longs;eat &longs;pa­<lb/>tium, quàm totum ip&longs;ummet latus BA, in quo fertur ver&longs;us <lb/>CD; imò quàm &longs;it ip&longs;ummet latus BA, quod percurrit. <lb/></s> | <s id="N16083">Secunda autem difficultas, quam Philo&longs;ophus hac in <lb/>quæ&longs;tione proponit, e&longs;t, cur in eodem rhombo punctum B, <lb/>quod vt diximus &longs;ua &longs;ponte fertur &longs;uper latus BA, <expan abbr="totamq.">totamque</expan> <lb/>eius longitudinem percurrit; minus quippe pertran&longs;eat &longs;pa­<lb/>tium, quàm totum ip&longs;ummet latus BA, in quo fertur ver&longs;us <lb/>CD; imò quàm &longs;it ip&longs;ummet latus BA, quod percurrit. <lb/></s> |
| <s id="N16095">Quandoquidem punctum B non conficit ni&longs;i&longs;patium BC: <lb/>totum autem latus BA conficit &longs;patium BD, &longs;eu AC, <lb/>quod maius e&longs;t quàm BC. <!-- KEEP S--></s> | <s id="N16095">Quandoquidem punctum B non conficit ni&longs;i&longs;patium BC: <lb/>totum autem latus BA conficit &longs;patium BD, &longs;eu AC, <lb/>quod maius e&longs;t quàm BC. <!-- KEEP S--></s> |
| <s id="N1609D">Sicut ip&longs;um latus BA maius <lb/>con&longs;tituitur, quàm diameter BC in rhombo propo&longs;ito. <lb/></s> | <s id="N1609D">Sicut ip&longs;um latus BA maius <lb/>con&longs;tituitur, quàm diameter BC in rhombo propo&longs;ito. <lb/></s> |
| <s id="N160A3"><expan abbr="Totaq.">Totaque</expan> ratio difficultatis in eo &longs;ita e&longs;t, quoniam punctum <lb/>B, duplici fertur latione, latus verò AB, vnica, & <lb/>vtrunque pari velocitate: Quamobrem potius punctum <lb/>B, quàm latus BA, &longs;equeretur maius &longs;patium pertran&longs;i­<lb/>re. </s> | <s id="N160A3"><expan abbr="Totaq.">Totaque</expan> ratio difficultatis in eo &longs;ita e&longs;t, quoniam punctum <lb/>B, duplici fertur latione, latus verò AB, vnica, & <lb/>vtrunque pari velocitate: Quamobrem potius punctum <lb/>B, quàm latus BA, &longs;equeretur maius &longs;patium pertran&longs;i­<lb/>re. </s> |
| <s id="N160B1">Accedit quia punctum B verè totum latus BA, in <lb/>quo fertur percurrit eodem tempore, quo vehitur cum ip­<lb/>&longs;omet latere ve<gap/>&longs;us CD; ideoque &longs;atis arduum videtur, <lb/>minus ip&longs;um B &longs;patium pertran&longs;ire quàm &longs;it latus BA, in <lb/>quo fertur. </s> | <s id="N160B1">Accedit quia punctum B verè totum latus BA, in <lb/>quo fertur percurrit eodem tempore, quo vehitur cum ip­<lb/>&longs;omet latere ver&longs;us CD; ideoque &longs;atis arduum videtur, <lb/>minus ip&longs;um B &longs;patium pertran&longs;ire quàm &longs;it latus BA, in <lb/>quo fertur. </s> |
| </p> | </p> |
| <p id="N160BE" type="main"> | <p id="N160BE" type="main"> |
| <s id="N160C0">Sed vnde hæc dubitandi ratio de&longs;umpta e&longs;t, inde pariter <lb/>ade&longs;t ratio difficultatem &longs;oluendi. </s> | <s id="N160C0">Sed vnde hæc dubitandi ratio de&longs;umpta e&longs;t, inde pariter <lb/>ade&longs;t ratio difficultatem &longs;oluendi. </s> |
| |
| <s id="N16138">Si autem quarta pars æqualem conuol­<lb/>uitur, manife&longs;tum e&longs;t, quod totus circulus toti circulo æqualem <lb/>conuoluetur. </s> | <s id="N16138">Si autem quarta pars æqualem conuol­<lb/>uitur, manife&longs;tum e&longs;t, quod totus circulus toti circulo æqualem <lb/>conuoluetur. </s> |
| <s id="N1613F">Quare quando BG linea ad ip&longs;um peruenerit <lb/>K, & ip&longs;a FC circumferentia erit in ip&longs;a CL & vniuer&longs;us <lb/>erit conuolutus circulus. </s> | <s id="N1613F">Quare quando BG linea ad ip&longs;um peruenerit <lb/>K, & ip&longs;a FC circumferentia erit in ip&longs;a CL & vniuer&longs;us <lb/>erit conuolutus circulus. </s> |
| <s id="N16146"><expan abbr="Similiq.">Similique</expan> modo &longs;i magnum mouero, <lb/>illi paruum annectens, eodem existente centro, &longs;imul cum AC <lb/>ip&longs;a AB perpendiculum & recta erit: hac quidem ad ip&longs;am<emph.end type="italics"/><pb pagenum="206" xlink:href="005/01/214.jpg"/><emph type="italics"/>FI, illæ verò ad GM. </s> | <s id="N16146"><expan abbr="Similiq.">Similique</expan> modo &longs;i magnum mouero, <lb/>illi paruum annectens, eodem existente centro, &longs;imul cum AC <lb/>ip&longs;a AB perpendiculum & recta erit: hac quidem ad ip&longs;am<emph.end type="italics"/><pb pagenum="206" xlink:href="005/01/214.jpg"/><emph type="italics"/>FI, illæ verò ad GM. </s> |
| <s id="N16159">Quamobrem quando bæc quidam <lb/>ip&longs;i GM pertran&longs;iuerit, illa verò ip&longs;i FI, & rur&longs;um facta <lb/>fuerit recta ip&longs;a FA ad ip&longs;am FL, & ip&longs;a AG rur&longs;um re­<lb/>cta, velut à principio erant in ip&longs;is MI. </s> | <s id="N16159">Quamobrem quando hæc quidam <lb/>ip&longs;i GM pertran&longs;iuerit, illa verò ip&longs;i FI, & rur&longs;um facta <lb/>fuerit recta ip&longs;a FA ad ip&longs;am FL, & ip&longs;a AG rur&longs;um re­<lb/>cta, velut à principio erant in ip&longs;is MI. </s> |
| <s id="N16162">Hoc autem neque <lb/>alia intercedente mora maioris ad minorem, vbi &longs;eilicet per <lb/>aliquod temporis &longs;patium &longs;taret in eodem puncto, neque tran&longs;i­<lb/>liente minore aliquod punctum, maiorem quidem æqualem mi­<lb/>nori p<gap/>rtran&longs;ire, bunc autem maiori, ab&longs;urdum e&longs;t. </s> | <s id="N16162">Hoc autem neque <lb/>alia intercedente mora maioris ad minorem, vbi &longs;cilicet per <lb/>aliquod temporis &longs;patium &longs;taret in eodem puncto, neque tran&longs;i­<lb/>liente minore aliquod punctum, maiorem quidem æqualem mi­<lb/>nori pertran&longs;ire, hunc autem maiori, ab&longs;urdum e&longs;t. </s> |
| <s id="N1616F">Præterea <lb/>vnica etiam &longs;emper existente motione, centrorum motum inter­<lb/>dum quidem magnam, nonnunquam verò minorem conuerti, <lb/>admirandum est. </s> | <s id="N1616F">Præterea <lb/>vnica etiam &longs;emper existente motione, centrorum motum inter­<lb/>dum quidem magnam, nonnunquam verò minorem conuerti, <lb/>admirandum est. </s> |
| <s id="N16178">I dem enim celeritate eadem latum æqualem <lb/>natum boc e&longs;t pertran&longs;ire: eadem autem celeritate vtroque <lb/>modo æqualem licet mouere. </s> | <s id="N16178">I dem enim celeritate eadem latum æqualem <lb/>natum boc e&longs;t pertran&longs;ire: eadem autem celeritate vtroque <lb/>modo æqualem licet mouere. </s> |
| <s id="N1617F">Principium autem &longs;umendum <lb/>est circa i&longs;torum cau&longs;am, quod eadem potentia, & æqualit <lb/>bans quidem tardius mouet magnitudinem, illam verò cel<gap/>­<lb/>rius. </s> | <s id="N1617F">Principium autem &longs;umendum <lb/>est circa i&longs;torum cau&longs;am, quod eadem potentia, & æqualit <lb/>bans quidem tardius mouet magnitudinem, illam verò cel<gap/>­<lb/>rius. </s> |
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