| version 1.43, 2003/08/17 21:38:42 |
version 1.52, 2003/08/19 13:41:40 |
| |
| <s id="id.2.1.13.1.2.6.0.a"><lb/>Quare ex ip&longs;orum &longs;uppo&longs;itionibus non &longs;olum pondus in D gra­<lb/>uius erit pondere in E; verùm è conuer&longs;o, pondus in E ip&longs;o D <lb/>grauius exi&longs;tet. </s></p><pb xlink:href="036/01/030.jpg"/> | <s id="id.2.1.13.1.2.6.0.a"><lb/>Quare ex ip&longs;orum &longs;uppo&longs;itionibus non &longs;olum pondus in D gra­<lb/>uius erit pondere in E; verùm è conuer&longs;o, pondus in E ip&longs;o D <lb/>grauius exi&longs;tet. </s></p><pb xlink:href="036/01/030.jpg"/> |
| <p id="id.2.1.13.3.0.0.0" type="main"> | <p id="id.2.1.13.3.0.0.0" type="main"> |
| <s id="id.2.1.13.3.1.1.0">Rationes tamen af<lb/>ferunt, quibus demon<lb/>&longs;trare nituntur, libram <lb/>DE in AB horizon­<lb/>ti æquidi&longs;tantem ex <lb/>nece&longs;sitate redire. </s> | <s id="id.2.1.13.3.1.1.0">Rationes tamen af<lb/>ferunt, quibus demon<lb/>&longs;trare nituntur, libram <lb/>DE in AB horizon­<lb/>ti æquidi&longs;tantem ex <lb/>nece&longs;sitate redire. </s> |
| <s id="id.2.1.13.3.1.2.0"> | <s id="id.2.1.13.3.1.2.0"><expan abbr="Pri­mùm">Pri­<lb/>mum</expan> quidem o&longs;ten­<lb/>dunt, idem pondus <lb/>grauius e&longs;&longs;e in A, <lb/>quàm in alio &longs;itu, &que;m <lb/>æqualitatis &longs;itum no­<lb/>minant, cum linea <lb/>AB &longs;it horizonti æ­<lb/><figure id="id.036.01.030.1.jpg" place="text" xlink:href="036/01/030/1.jpg"/><lb/>quidi&longs;tans. </s> |
| <expan abbr="Pri­mùm">Pri­<lb/>mum</expan> quidem o&longs;ten­<lb/>dunt, idem pondus <lb/>grauius e&longs;&longs;e in A, <lb/>quàm in alio &longs;itu, &que;m <lb/>æqualitatis &longs;itum no­<lb/>minant, cum linea <lb/>AB &longs;it horizonti æ­<lb/><figure id="id.036.01.030.1.jpg" place="text" xlink:href="036/01/030/1.jpg"/><lb/>quidi&longs;tans. </s> | |
| <s id="id.2.1.13.3.1.3.0">deinde quò propius e&longs;t ip&longs;i A, quouis alio remotiori <lb/>grauius e&longs;&longs;e. </s> | <s id="id.2.1.13.3.1.3.0">deinde quò propius e&longs;t ip&longs;i A, quouis alio remotiori <lb/>grauius e&longs;&longs;e. </s> |
| <s id="id.2.1.13.3.1.4.0">Vt pondus in A grauius e&longs;&longs;e, quàm in D; & in D, <lb/>quàm in L. &longs;imiliter in A grauius, quam in N; & in N grauius, <lb/>quàm in M. </s> | <s id="id.2.1.13.3.1.4.0">Vt pondus in A grauius e&longs;&longs;e, quàm in D; & in D, <lb/>quàm in L. &longs;imiliter in A grauius, quam in N; & in N grauius, <lb/>quàm in M. </s> |
| <s id="id.2.1.13.3.1.4.0.a">Vnum tantùm con&longs;iderando pondus in altero libræ <lb/><arrow.to.target n="note22"/>brachio &longs;ur&longs;um deor&longs;umq; moto. </s> | <s id="id.2.1.13.3.1.4.0.a">Vnum tantùm con&longs;iderando pondus in altero libræ <lb/><arrow.to.target n="note22"/>brachio &longs;ur&longs;um deor&longs;umq; moto. </s> |
| |
| <s id="id.2.1.17.5.1.26.0"><lb/>pondus deor&longs;um per rectam k S moueretur, non autem per cir<lb/>cumferentiam k H. </s> | <s id="id.2.1.17.5.1.26.0"><lb/>pondus deor&longs;um per rectam k S moueretur, non autem per cir<lb/>cumferentiam k H. </s> |
| <s id="N10E6E">&longs;imiliter CH pondus retinet, cùm per circum<lb/> | <s id="N10E6E">&longs;imiliter CH pondus retinet, cùm per circum<lb/> |
| <expan abbr="ferentiã">ferentiam</expan> HG moueri compellat. </s> | <expan abbr="ferentiã">ferentiam</expan> HG moueri compellat. </s> |
| <s id="id.2.1.17.5.1.27.0"> | <s id="id.2.1.17.5.1.27.0"><expan abbr="Quoniã">Quoniam</expan> autem angulus CHS ma­<lb/>ior e&longs;t angulo CKS, <expan abbr="d&etilde;ptis">demptis</expan> æqualibus angulis CHG CkH; erit <lb/>reliquus SHG reliquo SKH maior. </s> |
| <expan abbr="Quoniã">Quoniam</expan> autem angulus CHS ma­<lb/>ior e&longs;t angulo CKS, <expan abbr="d&etilde;ptis">demptis</expan> æqualibus angulis CHG CkH; erit <lb/>reliquus SHG reliquo SKH maior. </s> | |
| <s id="id.2.1.17.5.1.28.0">circumferentia igitur k H, hoc <lb/>e&longs;t de&longs;cen&longs;us ponderis in k, propior erit motui naturali ponderis in <lb/>k &longs;oluti, hoc e&longs;t lineæ k S, quàm circumferentia HG lineæ HS. </s> | <s id="id.2.1.17.5.1.28.0">circumferentia igitur k H, hoc <lb/>e&longs;t de&longs;cen&longs;us ponderis in k, propior erit motui naturali ponderis in <lb/>k &longs;oluti, hoc e&longs;t lineæ k S, quàm circumferentia HG lineæ HS. </s> |
| <s id="N10E8A">mi<lb/>nus idcirco detinet linea Ck, quàm CH: cùm pondus naturali­<lb/>ter magis moueatur per k H, quàm per HG. </s> | <s id="N10E8A">mi<lb/>nus idcirco detinet linea Ck, quàm CH: cùm pondus naturali­<lb/>ter magis moueatur per k H, quàm per HG. </s> |
| <s id="id.2.1.17.5.1.28.0.a">&longs;imili ratione o&longs;ten­<lb/>detur, quò minor erit angulus SkH, lineam Ck minus &longs;u&longs;tinere. </s> | <s id="id.2.1.17.5.1.28.0.a">&longs;imili ratione o&longs;ten­<lb/>detur, quò minor erit angulus SkH, lineam Ck minus &longs;u&longs;tinere. </s> |
| <s id="id.2.1.17.5.1.29.0"> | <s id="id.2.1.17.5.1.29.0"><pb xlink:href="036/01/036.jpg"/>exi&longs;tente igitur pondere in O, quia angu<lb/>lus SOC non &longs;olum minor e&longs;t angulo <lb/>CKS, verùm etiam omnium angulorum <lb/>à punctis CS prodeuntium, verticemq; <lb/>in circumferuntia OkG habentium mi­<lb/>nimus; erit <expan abbr="anglus">angulus</expan> SOK, & angulo SkH, <lb/>& eiu&longs;modi omnium minimus. </s> |
| <pb xlink:href="036/01/036.jpg"/>exi&longs;tente igitur pondere in O, quia angu<lb/>lus SOC non &longs;olum minor e&longs;t angulo <lb/>CKS, verùm etiam omnium angulorum <lb/>à punctis CS prodeuntium, verticemq; <lb/>in circumferuntia OkG habentium mi­<lb/>nimus; erit <expan abbr="anglus">angulus</expan> SOK, & angulo SkH, <lb/>& eiu&longs;modi omnium minimus. </s> | |
| <s id="id.2.1.17.5.1.30.0">ergo de­<lb/>&longs;cen&longs;us ponderis in O propior erit motui <lb/>naturali ip&longs;ius in O &longs;oluti, quàm in alio <lb/>&longs;itu circumferentiæ OkG. </s> | <s id="id.2.1.17.5.1.30.0">ergo de­<lb/>&longs;cen&longs;us ponderis in O propior erit motui <lb/>naturali ip&longs;ius in O &longs;oluti, quàm in alio <lb/>&longs;itu circumferentiæ OkG. </s> |
| <s id="N10EB4">lineaq; CO <lb/>minus pondus &longs;u&longs;tinebit, quàm &longs;i pon­<lb/>dus in quouis alio fuerit &longs;itu eiu&longs;dem cir<lb/>cumferentiæ OG. </s> | <s id="N10EB4">lineaq; CO <lb/>minus pondus &longs;u&longs;tinebit, quàm &longs;i pon­<lb/>dus in quouis alio fuerit &longs;itu eiu&longs;dem cir<lb/>cumferentiæ OG. </s> |
| <s id="id.2.1.17.5.1.30.0.a">&longs;imiliter quoniam con<lb/>tingentiæ angulus SOk, & angulo SDA, <lb/>& SAO, ac quibu&longs;cunq; &longs;imilibus e&longs;t mi <lb/>nor; erit de&longs;cen&longs;us ponderis in O motui <lb/>naturali ip&longs;ius ponderis in O &longs;oluti pro­<lb/>pior, quàm in alio &longs;itu circumferentiæ <lb/>ODF. </s> | <s id="id.2.1.17.5.1.30.0.a">&longs;imiliter quoniam con<lb/>tingentiæ angulus SOk, & angulo SDA, <lb/>& SAO, ac quibu&longs;cunq; &longs;imilibus e&longs;t mi <lb/>nor; erit de&longs;cen&longs;us ponderis in O motui <lb/>naturali ip&longs;ius ponderis in O &longs;oluti pro­<lb/>pior, quàm in alio &longs;itu circumferentiæ <lb/>ODF. </s> |
| |
| <s id="id.2.1.21.2.1.4.0.a">Quoniam enim <lb/><arrow.to.target n="note42"/>LE DM &longs;e inuicem &longs;ecant in S; erit rectangulum LSE rectan­<lb/><arrow.to.target n="note43"/>gulo DSM æquale. </s> | <s id="id.2.1.21.2.1.4.0.a">Quoniam enim <lb/><arrow.to.target n="note42"/>LE DM &longs;e inuicem &longs;ecant in S; erit rectangulum LSE rectan­<lb/><arrow.to.target n="note43"/>gulo DSM æquale. </s> |
| <s id="id.2.1.21.2.1.5.0">quare vt LS ad DS ita erit SM <lb/><arrow.to.target n="note44"/>ad SE. </s> | <s id="id.2.1.21.2.1.5.0">quare vt LS ad DS ita erit SM <lb/><arrow.to.target n="note44"/>ad SE. </s> |
| <s id="id.2.1.21.2.1.5.0.a">maior autem e&longs;t LS, quàm DS; & SM ip&longs;a SE. </s> | <s id="id.2.1.21.2.1.5.0.a">maior autem e&longs;t LS, quàm DS; & SM ip&longs;a SE. </s> |
| <s id="id.2.1.21.2.1.5.0.b"> | <s id="id.2.1.21.2.1.5.0.b"><pb n="14" xlink:href="036/01/041.jpg"/>ergo LS SE &longs;imul &longs;umptæ ip&longs;is DS SM maiores erunt. </s> |
| <pb n="14" xlink:href="036/01/041.jpg"/>ergo LS SE &longs;imul &longs;umptæ ip&longs;is DS SM maiores erunt. </s> | |
| <s id="id.2.1.21.2.1.6.0">eademq; <arrow.to.target n="note45"/><lb/>ratione kN minorem e&longs;&longs;e DM o&longs;tendetur. </s> | <s id="id.2.1.21.2.1.6.0">eademq; <arrow.to.target n="note45"/><lb/>ratione kN minorem e&longs;&longs;e DM o&longs;tendetur. </s> |
| <s id="id.2.1.21.2.1.7.0">rur&longs;us quoniam re<lb/>ctangulum OSH æquale e&longs;t rectangulo kSN; ob eandem cau&longs;am <lb/>HO maior erit kN. </s> | <s id="id.2.1.21.2.1.7.0">rur&longs;us quoniam re<lb/>ctangulum OSH æquale e&longs;t rectangulo kSN; ob eandem cau&longs;am <lb/>HO maior erit kN. </s> |
| <s id="N1113F">eodemq; pror&longs;us modo kN omnibus a­<lb/>liis per punctum S tran&longs;euntibus minorem e&longs;&longs;e demon&longs;trabitur. </s> | <s id="N1113F">eodemq; pror&longs;us modo kN omnibus a­<lb/>liis per punctum S tran&longs;euntibus minorem e&longs;&longs;e demon&longs;trabitur. </s> |
| |
| <s id="id.2.1.33.3.1.14.0">ponderis ve­<lb/>rò in E liberi, ac &longs;oluti, naturalis propen&longs;io erit per ES: ponderis <lb/>autem in D &longs;imiliter &longs;oluti erit per DS. ac propterea non e&longs;t incon­<lb/>ueniens idem pondus modò in E, modò in D, grauius e&longs;&longs;e in E, <lb/>quàm in D. </s> | <s id="id.2.1.33.3.1.14.0">ponderis ve­<lb/>rò in E liberi, ac &longs;oluti, naturalis propen&longs;io erit per ES: ponderis <lb/>autem in D &longs;imiliter &longs;oluti erit per DS. ac propterea non e&longs;t incon­<lb/>ueniens idem pondus modò in E, modò in D, grauius e&longs;&longs;e in E, <lb/>quàm in D. </s> |
| <s id="id.2.1.33.3.1.14.0.a">&longs;i verò pondera in ED &longs;ibi inuicem connexa, quate­<lb/>nusq; &longs;unt connexa con&longs;iderauerimus; erit ponderis in E natura­<lb/>lis propen&longs;io per lineam MEK: grauitas enim alterius ponde­<lb/>ris in D efficit, nè pondus in E per lineam ES grauitet, &longs;ed per <lb/>Ek. </s> | <s id="id.2.1.33.3.1.14.0.a">&longs;i verò pondera in ED &longs;ibi inuicem connexa, quate­<lb/>nusq; &longs;unt connexa con&longs;iderauerimus; erit ponderis in E natura­<lb/>lis propen&longs;io per lineam MEK: grauitas enim alterius ponde­<lb/>ris in D efficit, nè pondus in E per lineam ES grauitet, &longs;ed per <lb/>Ek. </s> |
| <s id="id.2.1.33.3.1.15.0">quod ip&longs;um quoq; grauitas ponderis in E efficit, nè &longs;cilicet <lb/>pondus in D per rectam DS degrauet; &longs;ed &longs;ecundùm DH: vtra­<lb/>&que; enim &longs;e impediunt, nè ad propria loca <expan abbr="permeent">permeant</expan>. </s> | <s id="id.2.1.33.3.1.15.0">quod ip&longs;um quoq; grauitas ponderis in E efficit, nè &longs;cilicet <lb/>pondus in D per rectam DS degrauet; &longs;ed &longs;ecundùm DH: vtra­<lb/>&que; enim &longs;e impediunt, nè ad propria loca <expan abbr="permeent">permeant</expan>. </s> |
| <s id="id.2.1.33.3.1.16.0">Cùm igi<lb/>tur naturalis de&longs;cen&longs;us rectus ponderum in DE &longs;it &longs;ecundùm <lb/>LDH MEK: erit <expan abbr="&longs;imliter">similiter</expan> rectus eorum a&longs;cen&longs;us &longs;ecundùm ea&longs;<lb/>dem lineas HDL KEM. atq; a&longs;cen&longs;us ponderis in E magis, mi<lb/>nu&longs;uè obliquus dicetur; quantò &longs;ecundùm &longs;patium magis, mi­<lb/>nu&longs;uè iuxta lineam Mk mouebitur. </s> | <s id="id.2.1.33.3.1.16.0">Cùm igi<lb/>tur naturalis de&longs;cen&longs;us rectus ponderum in DE &longs;it &longs;ecundùm <lb/>LDH MEK: erit <expan abbr="&longs;imliter">similiter</expan> rectus eorum a&longs;cen&longs;us &longs;ecundùm ea&longs;<lb/>dem lineas HDL KEM. </s> |
| | <s id="id.2.1.33.3.1.16.0.a">atq; a&longs;cen&longs;us ponderis in E magis, mi<lb/>nu&longs;uè obliquus dicetur; quantò &longs;ecundùm &longs;patium magis, mi­<lb/>nu&longs;uè iuxta lineam Mk mouebitur. </s> |
| <s id="id.2.1.33.3.1.17.0">hocq; pror&longs;us modo iuxta li<lb/>neam LH &longs;ummendus e&longs;t, tùm de&longs;cen&longs;us, tùm a&longs;cen&longs;us ponde­<lb/>ris in D. </s> | <s id="id.2.1.33.3.1.17.0">hocq; pror&longs;us modo iuxta li<lb/>neam LH &longs;ummendus e&longs;t, tùm de&longs;cen&longs;us, tùm a&longs;cen&longs;us ponde­<lb/>ris in D. </s> |
| <s id="N117DE">&longs;i itaq; pondus in E deor&longs;um per EG moueretur; pon<lb/>dus in D &longs;ur&longs;um per DF moueret. </s> | <s id="N117DE">&longs;i itaq; pondus in E deor&longs;um per EG moueretur; pon<lb/>dus in D &longs;ur&longs;um per DF moueret. </s> |
| <s id="id.2.1.33.3.1.18.0">& quoniam angulus CEK <arrow.to.target n="note60"/><lb/>æqualis e&longs;t angulo CDL, & angulus CEG angulo CDF æqua­<lb/>lis; erit reliquus GEK reliquo LDF æqualis. </s> | <s id="id.2.1.33.3.1.18.0">& quoniam angulus CEK <arrow.to.target n="note60"/><lb/>æqualis e&longs;t angulo CDL, & angulus CEG angulo CDF æqua­<lb/>lis; erit reliquus GEK reliquo LDF æqualis. </s> |
| |
| <s id="id.2.1.33.3.1.20.0">cùm non minus manife&longs;ta, <pb xlink:href="036/01/054.jpg"/>rationiq; &longs;it con&longs;entanea. </s> | <s id="id.2.1.33.3.1.20.0">cùm non minus manife&longs;ta, <pb xlink:href="036/01/054.jpg"/>rationiq; &longs;it con&longs;entanea. </s> |
| <s id="id.2.1.33.3.1.21.0">æqualis <lb/>igitur erit de&longs;cen&longs;us ponderis in E <lb/>a&longs;cen&longs;ui ponderis in D. </s> | <s id="id.2.1.33.3.1.21.0">æqualis <lb/>igitur erit de&longs;cen&longs;us ponderis in E <lb/>a&longs;cen&longs;ui ponderis in D. </s> |
| <s id="N11807">eandem <lb/>enim obliquitatem habet de&longs;cen&longs;us <lb/>ponderis in E, quam habet a&longs;cen­<lb/>&longs;us ponderis in D; & qualis erit <lb/>propen&longs;io vnius ad motum deor&longs;um, <lb/>talis quoq; erit re&longs;i&longs;tentia alterius ad <lb/>motum &longs;ur&longs;um. </s> | <s id="N11807">eandem <lb/>enim obliquitatem habet de&longs;cen&longs;us <lb/>ponderis in E, quam habet a&longs;cen­<lb/>&longs;us ponderis in D; & qualis erit <lb/>propen&longs;io vnius ad motum deor&longs;um, <lb/>talis quoq; erit re&longs;i&longs;tentia alterius ad <lb/>motum &longs;ur&longs;um. </s> |
| <s id="id.2.1.33.3.1.22.0"> | <s id="id.2.1.33.3.1.22.0"><expan abbr="nõ">non</expan> ergo pondus in E <lb/>pondus in D &longs;ur&longs;um mouebit. </s> |
| <expan abbr="nõ">non</expan> ergo pondus in E <lb/>pondus in D &longs;ur&longs;um mouebit. </s> | |
| <s id="id.2.1.33.3.1.23.0">neq; <lb/>pondus in D deor&longs;um mouebitur, ita <lb/>vt &longs;ur&longs;um moueat pondus in E. nam <lb/> | <s id="id.2.1.33.3.1.23.0">neq; <lb/>pondus in D deor&longs;um mouebitur, ita <lb/>vt &longs;ur&longs;um moueat pondus in E. nam <lb/> |
| <expan abbr="cũ">cum</expan> angulus CEB &longs;it ip&longs;i CDA æqua­<lb/><arrow.to.target n="note61"/>lis, & Angulus CEM &longs;it angulo <lb/>CDH æqualis; erit reliquus MEB <lb/>reliquo HDA æqualis. </s> | <expan abbr="cũ">cum</expan> angulus CEB &longs;it ip&longs;i CDA æqua­<lb/><arrow.to.target n="note61"/>lis, & Angulus CEM &longs;it angulo <lb/>CDH æqualis; erit reliquus MEB <lb/>reliquo HDA æqualis. </s> |
| <s id="id.2.1.33.3.1.24.0">de&longs;cen&longs;us <lb/>igitur ponderis in D a&longs;cen&longs;ui ponde<lb/>ris in E æqualis erit. </s> | <s id="id.2.1.33.3.1.24.0">de&longs;cen&longs;us <lb/>igitur ponderis in D a&longs;cen&longs;ui ponde<lb/>ris in E æqualis erit. </s> |
| |
| <s id="id.2.1.39.3.1.2.0">Produ<lb/>catur primùm CD v&longs;q; ad <lb/>mundi <expan abbr="centrũ">centrum</expan>, quod &longs;it S. de <lb/>inde AC CB EC CF HS <lb/> | <s id="id.2.1.39.3.1.2.0">Produ<lb/>catur primùm CD v&longs;q; ad <lb/>mundi <expan abbr="centrũ">centrum</expan>, quod &longs;it S. de <lb/>inde AC CB EC CF HS <lb/> |
| <expan abbr="cõnectantur">connectantur</expan>, à puncti&longs;q; EF <lb/>ip&longs;i HS æquidi&longs;tantes du<lb/>cantur Ek GFL. </s> | <expan abbr="cõnectantur">connectantur</expan>, à puncti&longs;q; EF <lb/>ip&longs;i HS æquidi&longs;tantes du<lb/>cantur Ek GFL. </s> |
| <s id="id.2.1.39.3.1.2.0.a">Quoniam <lb/>igitur naturalis de&longs;cen&longs;us re<lb/>ctus totius magnitudinis, <lb/>libræ &longs;cilicet EF &longs;ic con&longs;ti­<lb/>tutæ vná cum ponderibus, <lb/>e&longs;t <expan abbr="&longs;cundùm">secundum</expan> grauitatis cen<lb/>trum H per rectam HS; erit <lb/><figure id="id.036.01.059.1.jpg" place="text" xlink:href="036/01/059/1.jpg"/><lb/>quoq; ponderum in EF ita po&longs;sitorum de&longs;cen&longs;us &longs;ecundùm re­<lb/>ctas Ek FL ip&longs;i HS parallelas; &longs;icuti &longs;upra demon&longs;trauimus. </s> | <s id="id.2.1.39.3.1.2.0.a">Quoniam <lb/>igitur naturalis de&longs;cen&longs;us re<lb/>ctus totius magnitudinis, <lb/>libræ &longs;cilicet EF &longs;ic con&longs;ti­<lb/>tutæ vná cum ponderibus, <lb/>e&longs;t <expan abbr="&longs;cundùm">secundum</expan> grauitatis cen<lb/>trum H per rectam HS; erit <lb/><figure id="id.036.01.059.1.jpg" place="text" xlink:href="036/01/059/1.jpg"/><lb/>quoq; ponderum in EF ita po&longs;sitorum de&longs;cen&longs;us &longs;ecundùm re­<lb/>ctas Ek FL ip&longs;i HS parallelas; &longs;icuti &longs;upra demon&longs;trauimus. </s> |
| <s id="id.2.1.39.3.1.3.0"> | <s id="id.2.1.39.3.1.3.0"><pb xlink:href="036/01/060.jpg"/>De&longs;cen&longs;us igitur, & a&longs;cen­<lb/>&longs;us ponderum in EF ma­<lb/>gis, minu&longs;uè obliquus di­<lb/>cetur &longs;ecundùm acce&longs;&longs;um, <lb/>& rece&longs;&longs;um iuxta lineas Ek <lb/>FL de&longs;ignatum. </s> |
| <pb xlink:href="036/01/060.jpg"/>De&longs;cen&longs;us igitur, & a&longs;cen­<lb/>&longs;us ponderum in EF ma­<lb/>gis, minu&longs;uè obliquus di­<lb/>cetur &longs;ecundùm acce&longs;&longs;um, <lb/>& rece&longs;&longs;um iuxta lineas Ek <lb/>FL de&longs;ignatum. </s> | <s id="id.2.1.39.3.1.4.0"><expan abbr="Quoniã">Quoniam</expan> |
| <s id="id.2.1.39.3.1.4.0"> | |
| <expan abbr="Quoniã">Quoniam</expan> | |
| <expan abbr="au­t&etilde;">au­<lb/>tem</expan> duo latera AD DC duo<lb/>bus lateribus BD DE &longs;unt <lb/>æqualia; anguliq; ad D &longs;unt <lb/><arrow.to.target n="note65"/>recti; erit latus AC lateri <lb/>CB æquale. </s> | <expan abbr="au­t&etilde;">au­<lb/>tem</expan> duo latera AD DC duo<lb/>bus lateribus BD DE &longs;unt <lb/>æqualia; anguliq; ad D &longs;unt <lb/><arrow.to.target n="note65"/>recti; erit latus AC lateri <lb/>CB æquale. </s> |
| <s id="id.2.1.39.3.1.5.0">& cùm pun­<lb/>ctum C &longs;it immobile; dum <lb/>puncta AB mouentur, cir<lb/>culi circumferentiam de&longs;cri<lb/>bent, cuius &longs;emidiameter <lb/>erit AC. quare centro C, <lb/>circulus de&longs;cribatur AEBF. <lb/>puncta AB EF in circuli <lb/>circumferentia erunt. </s> | <s id="id.2.1.39.3.1.5.0">& cùm pun­<lb/>ctum C &longs;it immobile; dum <lb/>puncta AB mouentur, cir<lb/>culi circumferentiam de&longs;cri<lb/>bent, cuius &longs;emidiameter <lb/>erit AC. quare centro C, <lb/>circulus de&longs;cribatur AEBF. <lb/>puncta AB EF in circuli <lb/>circumferentia erunt. </s> |
| <s id="id.2.1.39.3.1.6.0">&longs;ed <lb/>cùm EF &longs;it ip&longs;i AB æqua <lb/><arrow.to.target n="note66"/>lis; erit circumferentia <lb/>EAF circumferentiæ AFB <lb/>æqualis. </s> | <s id="id.2.1.39.3.1.6.0">&longs;ed <lb/>cùm EF &longs;it ip&longs;i AB æqua <lb/><arrow.to.target n="note66"/>lis; erit circumferentia <lb/>EAF circumferentiæ AFB <lb/>æqualis. </s> |
| |
| <figure id="id.036.01.077.1.jpg" place="text" xlink:href="036/01/077/1.jpg"/></s></p><p id="id.2.1.53.12.0.0.0" type="main"> | <figure id="id.036.01.077.1.jpg" place="text" xlink:href="036/01/077/1.jpg"/></s></p><p id="id.2.1.53.12.0.0.0" type="main"> |
| <s id="id.2.1.53.12.1.1.0">Sit deniq; libra AB, & ex punctis AB &longs;u&longs;pen&longs;a &longs;int pondera <lb/>EF; &longs;itq; centrum libræ C intra pondera; diuidaturq; AB in <lb/>D, ita vt AD ad DB &longs;it, vt pondus F ad pondus E. </s> | <s id="id.2.1.53.12.1.1.0">Sit deniq; libra AB, & ex punctis AB &longs;u&longs;pen&longs;a &longs;int pondera <lb/>EF; &longs;itq; centrum libræ C intra pondera; diuidaturq; AB in <lb/>D, ita vt AD ad DB &longs;it, vt pondus F ad pondus E. </s> |
| <s id="id.2.1.53.12.1.1.0.a">Dico pon<lb/>dera EF tàm in AB ponderare, quám &longs;i vtraq; ex puncto D &longs;u&longs;pen<lb/>dantur. </s> | <s id="id.2.1.53.12.1.1.0.a">Dico pon<lb/>dera EF tàm in AB ponderare, quám &longs;i vtraq; ex puncto D &longs;u&longs;pen<lb/>dantur. </s> |
| <s id="id.2.1.53.12.1.2.0">fiat CG æqualis ip&longs;i CD; & vt DC ad CA, ita fiat <lb/>pondus E ad aliud H; quod appendatur in D. vt autem GC ad <lb/>CB, ita fiat pondus F ad aliud K; appendaturq; k in G. </s> | <s id="id.2.1.53.12.1.2.0">fiat CG æqualis ip&longs;i CD; & vt DC ad CA, ita fiat <lb/>pondus E ad aliud H; quod appendatur in D. </s> |
| <s id="id.2.1.53.12.1.2.0.a"> | <s id="id.2.1.53.12.1.2.0.a">vt autem GC ad <lb/>CB, ita fiat pondus F ad aliud K; appendaturq; k in G. </s> |
| <expan abbr="Quoniã">Quoniam</expan> enim <lb/>e&longs;t, vt BC ad CG, hoc e&longs;t ad CD, ita pondus k ad F; erit K ma <lb/>ius pondere F. </s> | <s id="id.2.1.53.12.1.2.0.b"><expan abbr="Quoniã">Quoniam</expan> enim <lb/>e&longs;t, vt BC ad CG, hoc e&longs;t ad CD, ita pondus k ad F; erit K ma <lb/>ius pondere F. </s> |
| <s id="N12329">quare diuidatur pondus k in L, & MN; fiatq; <lb/>pars L ip&longs;i F æqualis; erit vt BC ad CD, vt totum LMN ad <lb/>L; & diuidendo, vt BD ad DC, ita pars MN ad partem L. </s> | <s id="N12329">quare diuidatur pondus k in L, & MN; fiatq; <lb/>pars L ip&longs;i F æqualis; erit vt BC ad CD, vt totum LMN ad <lb/>L; & diuidendo, vt BD ad DC, ita pars MN ad partem L. </s> |
| <s id="N1232F">vt <arrow.to.target n="note95"/><lb/>igitur BD ad DC, ita pars MN ad F. </s> | <s id="N1232F">vt <arrow.to.target n="note95"/><lb/>igitur BD ad DC, ita pars MN ad F. </s> |
| <s id="N12336">vt autem AD ad DB, <lb/>ita F ad E: quare ex æquali, vt AD ad DC, ita MN ad E. </s> | <s id="N12336">vt autem AD ad DB, <lb/>ita F ad E: quare ex æquali, vt AD ad DC, ita MN ad E. </s> |
| |
| <s id="id.2.1.57.3.1.1.0.c">Dico pri<lb/>múm pondera GF ex puncto C &longs;u&longs;pen&longs;a tantùm ponderare, quan<lb/>tùm pondera EF ex punctis DC. </s> | <s id="id.2.1.57.3.1.1.0.c">Dico pri<lb/>múm pondera GF ex puncto C &longs;u&longs;pen&longs;a tantùm ponderare, quan<lb/>tùm pondera EF ex punctis DC. </s> |
| <s id="id.2.1.57.3.1.1.0.d">Secetur DC bifariam in H, & <lb/>ex H appendantur vtraq; pondera EF. </s> | <s id="id.2.1.57.3.1.1.0.d">Secetur DC bifariam in H, & <lb/>ex H appendantur vtraq; pondera EF. </s> |
| <s id="N125BE">ponderabunt EF &longs;imul <lb/>&longs;umpta in eo &longs;itu, quantùm ponderant in DC. ponatur BA <arrow.to.target n="note108"/><lb/>æqualis AH, &longs;eceturq; BA in K, ita vt &longs;it KA æqualis AD: <lb/>deinde ex puncto B appendatur pondus L duplum ponderis F, <lb/>hoc e&longs;t æquale duobus ponderibus EF, quod quidem æ&que;ponde<lb/>rabit ponderibus EF in H appen&longs;is, hoc e&longs;t appen&longs;is in DC. </s> | <s id="N125BE">ponderabunt EF &longs;imul <lb/>&longs;umpta in eo &longs;itu, quantùm ponderant in DC. ponatur BA <arrow.to.target n="note108"/><lb/>æqualis AH, &longs;eceturq; BA in K, ita vt &longs;it KA æqualis AD: <lb/>deinde ex puncto B appendatur pondus L duplum ponderis F, <lb/>hoc e&longs;t æquale duobus ponderibus EF, quod quidem æ&que;ponde<lb/>rabit ponderibus EF in H appen&longs;is, hoc e&longs;t appen&longs;is in DC. </s> |
| <s id="id.2.1.57.3.1.1.0.e"> | <s id="id.2.1.57.3.1.1.0.e"><expan abbr="Quoniã">Quoniam</expan><lb/>igitur, vt CA ad AD, ita e&longs;t pondus F ad pondus G; erit compo<lb/>nendo vt CA AD ad AD, hoc e&longs;t vt Ck ad AD, ita ponde­<lb/>ra <arrow.to.target n="note109"/>FG ad pondus G. </s> |
| <expan abbr="Quoniã">Quoniam</expan><lb/>igitur, vt CA ad AD, ita e&longs;t pondus F ad pondus G; erit compo<lb/>nendo vt CA AD ad AD, hoc e&longs;t vt Ck ad AD, ita ponde­<lb/>ra <arrow.to.target n="note109"/>FG ad pondus G. </s> | |
| <s id="N125DC">&longs;ed cùm &longs;it, vt CA ad AD, ita F pon­<lb/>dus ad pondus G; erit conuertendo, vt DA ad AC, ita pondus <arrow.to.target n="note110"/><lb/>G ad pondus F; & con&longs;e&que;ntium dupla, vt DA ad duplam ip&longs;ius <lb/>AC, ita pondus G ad duplum ponderis F, hoc e&longs;t ad pondus <lb/>L. </s> | <s id="N125DC">&longs;ed cùm &longs;it, vt CA ad AD, ita F pon­<lb/>dus ad pondus G; erit conuertendo, vt DA ad AC, ita pondus <arrow.to.target n="note110"/><lb/>G ad pondus F; & con&longs;e&que;ntium dupla, vt DA ad duplam ip&longs;ius <lb/>AC, ita pondus G ad duplum ponderis F, hoc e&longs;t ad pondus <lb/>L. </s> |
| <s id="id.2.1.57.3.1.1.0.f">Quare vt Ck ad DA, ita pondera EF ad pondus G; & vt <pb xlink:href="036/01/082.jpg"/> | <s id="id.2.1.57.3.1.1.0.f">Quare vt Ck ad DA, ita pondera EF ad pondus G; & vt <pb xlink:href="036/01/082.jpg"/> |
| <figure id="id.036.01.082.1.jpg" place="text" xlink:href="036/01/082/1.jpg"/><lb/><arrow.to.target n="note111"/>AD ad <expan abbr="duplã">duplam</expan> ip&longs;ius AC, ita pondus G ad pondus L; ergo ex æquali, <lb/>vt Ck ad <expan abbr="duplã">duplam</expan> ip&longs;ius AC, ita pondera FG ad pondus L. </s> | <figure id="id.036.01.082.1.jpg" place="text" xlink:href="036/01/082/1.jpg"/><lb/><arrow.to.target n="note111"/>AD ad <expan abbr="duplã">duplam</expan> ip&longs;ius AC, ita pondus G ad pondus L; ergo ex æquali, <lb/>vt Ck ad <expan abbr="duplã">duplam</expan> ip&longs;ius AC, ita pondera FG ad pondus L. </s> |
| |
| <s id="N12773">appendatur in A <lb/>pondus D, quod <lb/>æ&que;ponderet ap<lb/>pendiculo E in F <lb/><figure id="id.036.01.084.1.jpg" place="text" xlink:href="036/01/084/1.jpg"/><lb/>appen&longs;o. </s> | <s id="N12773">appendatur in A <lb/>pondus D, quod <lb/>æ&que;ponderet ap<lb/>pendiculo E in F <lb/><figure id="id.036.01.084.1.jpg" place="text" xlink:href="036/01/084/1.jpg"/><lb/>appen&longs;o. </s> |
| <s id="id.2.1.63.1.1.2.0">aliud quoq; appendatur pondus G in A, quod etiam <lb/>appendiculo E in B appen&longs;o æ&que;ponderet. </s> | <s id="id.2.1.63.1.1.2.0">aliud quoq; appendatur pondus G in A, quod etiam <lb/>appendiculo E in B appen&longs;o æ&que;ponderet. </s> |
| <s id="id.2.1.63.1.1.3.0">Dico grauitatem <lb/>ponderis D ad grauitatem ponderis G ita e&longs;&longs;e, vt CF ad CB. </s> | <s id="id.2.1.63.1.1.3.0">Dico grauitatem <lb/>ponderis D ad grauitatem ponderis G ita e&longs;&longs;e, vt CF ad CB. </s> |
| <s id="id.2.1.63.1.1.3.0.a"><lb/>Quoniam enim grauitas ponderis D e&longs;t æqualis grauitati ponde­<lb/>ris E in F appen&longs;i, & grauitas ponderis G e&longs;t æqualis grauitati pon<lb/>deris E in B; erit grauitas ponderis D ad grauitatem ponderis E in <lb/>F, vt grauitas ponderis G ad grauitatem ponderis E in B: & permu<lb/><arrow.to.target n="note116"/>tando, vt grauitas ponderis D ad grauitatem ponderis G, ita graui<lb/>tas ip&longs;ius E in F, ad grauitatem ip&longs;ius E in B; grauitas autem pon<lb/><arrow.to.target n="note117"/>deris E in F ad grauitatem ponderis E in B e&longs;t, vt CF ad CB; vt <lb/>igitur grauitas ponderis D ad grauitatem ponderis G, ita e&longs;t CF <lb/>ad CB &longs;i ergo pars &longs;capi CB in partes diuidatur æquales, &longs;olo <lb/>pondere E, & propius, & longius à puncto C po&longs;ito; ponderum <lb/>grauitates, quæ ex puncto A &longs;u&longs;penduntur inter &longs;e &longs;e notæ erunt. </s> | <s id="id.2.1.63.1.1.3.0.a"><lb/>Quoniam enim grauitas ponderis D e&longs;t æqualis grauitati ponde­<lb/>ris E in F appen&longs;i, & grauitas ponderis G e&longs;t æqualis grauitati pon<lb/>deris E in B; erit grauitas ponderis D ad grauitatem ponderis E in <lb/>F, vt grauitas ponderis G ad grauitatem ponderis E in B: & permu<lb/><arrow.to.target n="note116"/>tando, vt grauitas ponderis D ad grauitatem ponderis G, ita graui<lb/>tas ip&longs;ius E in F, ad grauitatem ip&longs;ius E in B; grauitas autem pon<lb/><arrow.to.target n="note117"/>deris E in F ad grauitatem ponderis E in B e&longs;t, vt CF ad CB; vt <lb/>igitur grauitas ponderis D ad grauitatem ponderis G, ita e&longs;t CF <lb/>ad CB. </s> |
| <s id="id.2.1.63.1.1.4.0"> | <s id="id.2.1.63.1.1.3.0.b">&longs;i ergo pars &longs;capi CB in partes diuidatur æquales, &longs;olo <lb/>pondere E, & propius, & longius à puncto C po&longs;ito; ponderum <lb/>grauitates, quæ ex puncto A &longs;u&longs;penduntur inter &longs;e &longs;e notæ erunt. </s> |
| <pb n="36" xlink:href="036/01/085.jpg"/>Vt &longs;i di&longs;tantia CB tripla &longs;it di&longs;tantiæ CF, erit quoq; grauitas ip­<lb/>&longs;ius G grauitatis ip&longs;ius D tripla, quod demon&longs;trare oportebat. </s></p><p id="id.2.1.64.1.0.0.0" type="margin"> | <s id="id.2.1.63.1.1.4.0"><pb n="36" xlink:href="036/01/085.jpg"/>Vt &longs;i di&longs;tantia CB tripla &longs;it di&longs;tantiæ CF, erit quoq; grauitas ip­<lb/>&longs;ius G grauitatis ip&longs;ius D tripla, quod demon&longs;trare oportebat. </s></p><p id="id.2.1.64.1.0.0.0" type="margin"> |
| <s id="id.2.1.64.1.1.1.0"><margin.target id="note116"/>16 <emph type="italics"/>Quinti.<emph.end type="italics"/></s> | <s id="id.2.1.64.1.1.1.0"><margin.target id="note116"/>16 <emph type="italics"/>Quinti.<emph.end type="italics"/></s> |
| <s id="id.2.1.64.1.1.2.0"><margin.target id="note117"/>6 <emph type="italics"/>Huius.<emph.end type="italics"/></s></p><p id="id.2.1.65.1.0.0.0" type="main"> | <s id="id.2.1.64.1.1.2.0"><margin.target id="note117"/>6 <emph type="italics"/>Huius.<emph.end type="italics"/></s></p><p id="id.2.1.65.1.0.0.0" type="main"> |
| <s id="id.2.1.65.1.1.1.0">Alio quoq; modo &longs;tatera vti po&longs;&longs;umus, vt <lb/>ponderum grauitates notæ reddantur. </s></p><p id="id.2.1.65.2.0.0.0" type="main"> | <s id="id.2.1.65.1.1.1.0">Alio quoq; modo &longs;tatera vti po&longs;&longs;umus, vt <lb/>ponderum grauitates notæ reddantur. </s></p><p id="id.2.1.65.2.0.0.0" type="main"> |
| |
| <s id="id.2.1.75.4.1.1.0">Alio modo vecte vti po&longs;sumus. </s></p><p id="id.2.1.75.5.0.0.0" type="main"> | <s id="id.2.1.75.4.1.1.0">Alio modo vecte vti po&longs;sumus. </s></p><p id="id.2.1.75.5.0.0.0" type="main"> |
| <s id="id.2.1.75.5.1.1.0">Sit vectis AB, cuius <lb/>fulcimentum &longs;it B, & <lb/>pondus C vtcunq; in <lb/>D inter AB appen­<lb/>&longs;um; &longs;itq; potentia in <lb/>A &longs;u&longs;tinens pondus C. </s> | <s id="id.2.1.75.5.1.1.0">Sit vectis AB, cuius <lb/>fulcimentum &longs;it B, & <lb/>pondus C vtcunq; in <lb/>D inter AB appen­<lb/>&longs;um; &longs;itq; potentia in <lb/>A &longs;u&longs;tinens pondus C. </s> |
| <s id="id.2.1.75.5.1.1.0.a"><lb/>Dico vt BD ad BA, <lb/><figure id="id.036.01.091.1.jpg" place="text" xlink:href="036/01/091/1.jpg"/><lb/>ita e&longs;&longs;e potentiam in A ad pondus C. </s> | <s id="id.2.1.75.5.1.1.0.a"><lb/>Dico vt BD ad BA, <lb/><figure id="id.036.01.091.1.jpg" place="text" xlink:href="036/01/091/1.jpg"/><lb/>ita e&longs;&longs;e potentiam in A ad pondus C. </s> |
| <s id="N12A22">appendatur in A pondus <lb/>E æquale ip&longs;i C; & vt AB ad BD, ita fiat pondus E ad aliud F. <lb/>& quoniam pondera CE &longs;unt inter &longs;e &longs;e æqualia, erit pondus C <lb/>ad pondus F, vt AB ad BD. </s> | <s id="N12A22">appendatur in A pondus <lb/>E æquale ip&longs;i C; & vt AB ad BD, ita fiat pondus E ad aliud F. <lb/></s> |
| | <s id="N12A23">& quoniam pondera CE &longs;unt inter &longs;e &longs;e æqualia, erit pondus C <lb/>ad pondus F, vt AB ad BD. </s> |
| <s id="N12A2A">appendatur quoq; pondus F in A. <lb/></s> | <s id="N12A2A">appendatur quoq; pondus F in A. <lb/></s> |
| <s id="N12A2D">& quoniam pondus E ad pondus F e&longs;t, vt grauitas ip&longs;ius E ad gra­<lb/>uitatem <arrow.to.target n="note127"/>ip&longs;ius F; & pondus E ad F e&longs;t, vt AB ad BD; vt igitur <lb/>grauitas ponderis E ad grauitatem ponderis F, ita e&longs;t AB ab BD. <lb/></s> | <s id="N12A2D">& quoniam pondus E ad pondus F e&longs;t, vt grauitas ip&longs;ius E ad gra­<lb/>uitatem <arrow.to.target n="note127"/>ip&longs;ius F; & pondus E ad F e&longs;t, vt AB ad BD; vt igitur <lb/>grauitas ponderis E ad grauitatem ponderis F, ita e&longs;t AB ab BD. <lb/></s> |
| <s id="N12A38">vt autem AB ad BD, ita e&longs;t grauitas ponderis E ad grauitatem <arrow.to.target n="note128"/> | <s id="N12A38">vt autem AB ad BD, ita e&longs;t grauitas ponderis E ad grauitatem <arrow.to.target n="note128"/> |
| |
| <s id="id.2.1.75.5.1.2.0">Ponatur itaq; potentia in A &longs;u&longs;tinens <lb/>pondus F; erit potentia in A æqualis ip&longs;i ponderi F. </s> | <s id="id.2.1.75.5.1.2.0">Ponatur itaq; potentia in A &longs;u&longs;tinens <lb/>pondus F; erit potentia in A æqualis ip&longs;i ponderi F. </s> |
| <s id="id.2.1.75.5.1.2.0.a">& quoniam <lb/>pondus F in A appen&longs;um æquè graue e&longs;t, vt pondus C in D ap­<lb/>pen&longs;um; eandem proportionem habebit potentia in A ad grauita­<lb/><arrow.to.target n="note130"/>tem ponderis F in A appen&longs;i, quam habet ad grauitatem ponde­<lb/>ris C in D appen&longs;i. </s> | <s id="id.2.1.75.5.1.2.0.a">& quoniam <lb/>pondus F in A appen&longs;um æquè graue e&longs;t, vt pondus C in D ap­<lb/>pen&longs;um; eandem proportionem habebit potentia in A ad grauita­<lb/><arrow.to.target n="note130"/>tem ponderis F in A appen&longs;i, quam habet ad grauitatem ponde­<lb/>ris C in D appen&longs;i. </s> |
| <s id="id.2.1.75.5.1.3.0">Potentia verò in A ip&longs;i F æqualis &longs;u&longs;tinet <lb/>pondus F, ergo potentia in A pondus quoq; C &longs;u&longs;tinebit. </s> | <s id="id.2.1.75.5.1.3.0">Potentia verò in A ip&longs;i F æqualis &longs;u&longs;tinet <lb/>pondus F, ergo potentia in A pondus quoq; C &longs;u&longs;tinebit. </s> |
| <s id="id.2.1.75.5.1.4.0">Itaq; <lb/>cùm potentia in A &longs;it æqualis ponderi F, & pondus C ad pon­<lb/>dus F &longs;it, vt AB ad BD; erit pondus C ad potentiam in A, vt <lb/><arrow.to.target n="note131"/>AB ad BD. & è conuer&longs;o, vt BD ad BA, ita potentia in A ad <lb/>pondus C. potentia ergo ad pondus ita erit, vt di&longs;tantia fulci­<lb/>mento, ac ponderis &longs;u&longs;pen&longs;ioni intercepta ad di&longs;tantiam à fulci <lb/>mento ad potentiam. </s> | <s id="id.2.1.75.5.1.4.0">Itaq; <lb/>cùm potentia in A &longs;it æqualis ponderi F, & pondus C ad pon­<lb/>dus F &longs;it, vt AB ad BD; erit pondus C ad potentiam in A, vt <lb/><arrow.to.target n="note131"/>AB ad BD. </s> |
| | <s id="id.2.1.75.5.1.4.0.a">& è conuer&longs;o, vt BD ad BA, ita potentia in A ad <lb/>pondus C. </s> |
| | <s id="id.2.1.75.5.1.4.0.b">potentia ergo ad pondus ita erit, vt di&longs;tantia fulci­<lb/>mento, ac ponderis &longs;u&longs;pen&longs;ioni intercepta ad di&longs;tantiam à fulci <lb/>mento ad potentiam. </s> |
| <s id="id.2.1.75.5.1.5.0">quod oportebat demon&longs;trare. </s></p><p id="id.2.1.76.1.0.0.0" type="margin"> | <s id="id.2.1.75.5.1.5.0">quod oportebat demon&longs;trare. </s></p><p id="id.2.1.76.1.0.0.0" type="margin"> |
| <s id="id.2.1.76.1.1.1.0"><margin.target id="note127"/><emph type="italics"/>In &longs;exta huius de libra Ex<emph.end type="italics"/> 11 <emph type="italics"/>quinti.<emph.end type="italics"/></s> | <s id="id.2.1.76.1.1.1.0"><margin.target id="note127"/><emph type="italics"/>In &longs;exta huius de libra Ex<emph.end type="italics"/> 11 <emph type="italics"/>quinti.<emph.end type="italics"/></s> |
| <s id="id.2.1.76.1.1.2.0"><margin.target id="note128"/>6 <emph type="italics"/>Huius. de libra.<emph.end type="italics"/></s> | <s id="id.2.1.76.1.1.2.0"><margin.target id="note128"/>6 <emph type="italics"/>Huius. de libra.<emph.end type="italics"/></s> |
| |
| <s id="N12C1D">& cùm pondera CE &longs;int inter &longs;e &longs;e æqualia; erit <lb/>pondus C ad pondus F, vt BD ad BA. </s> | <s id="N12C1D">& cùm pondera CE &longs;int inter &longs;e &longs;e æqualia; erit <lb/>pondus C ad pondus F, vt BD ad BA. </s> |
| <s id="id.2.1.81.7.1.1.0.c">appendatur pondus <lb/>F quoq; in D. </s> | <s id="id.2.1.81.7.1.1.0.c">appendatur pondus <lb/>F quoq; in D. </s> |
| <s id="id.2.1.81.7.1.1.0.d">& quoniam pondus E ad ip&longs;um F e&longs;t, vt grauitas <lb/>ponderis E ad grauitatem ponderis F; & pondus E ad pondus F <arrow.to.target n="note134"/><lb/>e&longs;t, vt BD ad BA: vt igitur grauitas ponderis E ad grauitatem <lb/>ponderis F, ita e&longs;t BD ad BA. </s> | <s id="id.2.1.81.7.1.1.0.d">& quoniam pondus E ad ip&longs;um F e&longs;t, vt grauitas <lb/>ponderis E ad grauitatem ponderis F; & pondus E ad pondus F <arrow.to.target n="note134"/><lb/>e&longs;t, vt BD ad BA: vt igitur grauitas ponderis E ad grauitatem <lb/>ponderis F, ita e&longs;t BD ad BA. </s> |
| <s id="N12C32">vt autem BD ad BA, ita e&longs;t gra<arrow.to.target n="note135"/><lb/>uitas ponderis E ad grauitatem ponderis C; quare grauitas ponde­<lb/>ris E ad grauitatem ponderis F eandem habet proportionem, <lb/>quam habet ad grauitatem ponderis C. pondera ergo CF eandem <arrow.to.target n="note136"/><lb/>habent grauitatem. </s> | <s id="N12C32">vt autem BD ad BA, ita e&longs;t gra<arrow.to.target n="note135"/><lb/>uitas ponderis E ad grauitatem ponderis C; quare grauitas ponde­<lb/>ris E ad grauitatem ponderis F eandem habet proportionem, <lb/>quam habet ad grauitatem ponderis C. </s> |
| | <s id="N12C33">pondera ergo CF eandem <arrow.to.target n="note136"/><lb/>habent grauitatem. </s> |
| <s id="id.2.1.81.7.1.2.0">&longs;it igitur potentia in D &longs;u&longs;tinens pondus F, <lb/>erit potentia in D ip&longs;i ponderi F æqualis. </s> | <s id="id.2.1.81.7.1.2.0">&longs;it igitur potentia in D &longs;u&longs;tinens pondus F, <lb/>erit potentia in D ip&longs;i ponderi F æqualis. </s> |
| <s id="id.2.1.81.7.1.3.0">& quoniam pondus F <lb/>in D æquè graue e&longs;t, vt pondus C in A; habebit potentia in D <lb/>eandem proportionem ad grauitatem ponderis F, quam habet ad <arrow.to.target n="note137"/><lb/>grauitatem ponderis C. </s> | <s id="id.2.1.81.7.1.3.0">& quoniam pondus F <lb/>in D æquè graue e&longs;t, vt pondus C in A; habebit potentia in D <lb/>eandem proportionem ad grauitatem ponderis F, quam habet ad <arrow.to.target n="note137"/><lb/>grauitatem ponderis C. </s> |
| <s id="id.2.1.81.7.1.3.0.a">&longs;ed potentia in D pondus F &longs;u&longs;tinet; po­<lb/>tentia igitur in D pondus quoq; C &longs;u&longs;tinebit: & pondus C ad po­<lb/>tentiam in D ita erit, vt pondus C ad pondus F; & C ad F e&longs;t, vt <lb/>BD ad BA; erit igitur pondus C ad potentiam in D, vt BD ad <lb/>BA: & conuertendo, vt AB ad BD, ita potentia in D ad pondus <lb/>C. </s> | <s id="id.2.1.81.7.1.3.0.a">&longs;ed potentia in D pondus F &longs;u&longs;tinet; po­<lb/>tentia igitur in D pondus quoq; C &longs;u&longs;tinebit: & pondus C ad po­<lb/>tentiam in D ita erit, vt pondus C ad pondus F; & C ad F e&longs;t, vt <lb/>BD ad BA; erit igitur pondus C ad potentiam in D, vt BD ad <lb/>BA: & conuertendo, vt AB ad BD, ita potentia in D ad pondus <lb/>C. </s> |
| |
| <s id="id.2.1.83.2.1.5.0">Ponatur igi<lb/>tur in D tanta vis, vt pondera FGC æ&que;ponderent; erit po­<lb/>tentia in D æqualis ponderi G: pondera enim FC æ&que;ponde­<lb/>rant, & potentia in D nil aliud efficere debet, ni&longs;i &longs;u&longs;tinere pon­<lb/>dus G ne de&longs;cendat. </s> | <s id="id.2.1.83.2.1.5.0">Ponatur igi<lb/>tur in D tanta vis, vt pondera FGC æ&que;ponderent; erit po­<lb/>tentia in D æqualis ponderi G: pondera enim FC æ&que;ponde­<lb/>rant, & potentia in D nil aliud efficere debet, ni&longs;i &longs;u&longs;tinere pon­<lb/>dus G ne de&longs;cendat. </s> |
| <s id="id.2.1.83.2.1.6.0">& quoniam pondera FGC, & potentia in <lb/>D æ&que;ponderant, demptis igitur FG ponderibus, quæ æ&que;pon<lb/>derant; reliqua æ&que;ponderabunt, &longs;cilicet potentia in D ponderi C. <lb/></s> | <s id="id.2.1.83.2.1.6.0">& quoniam pondera FGC, & potentia in <lb/>D æ&que;ponderant, demptis igitur FG ponderibus, quæ æ&que;pon<lb/>derant; reliqua æ&que;ponderabunt, &longs;cilicet potentia in D ponderi C. <lb/></s> |
| <s id="N12CDC">hoc e&longs;t potentia in D pondus C &longs;u&longs;tinebit, ita vt vectis AB ma­<lb/>neat, vt prius. </s> | <s id="N12CDC">hoc e&longs;t potentia in D pondus C &longs;u&longs;tinebit, ita vt vectis AB ma­<lb/>neat, vt prius. </s> |
| <s id="id.2.1.83.2.1.7.0">& cùm potentia in D &longs;it æqualis ponderi G, & pon­<lb/>dus C æquale ponderi F; habebit potentia in D ad pondus C ean<lb/>dem proportionem, quam EB, hoc e&longs;t AB ad BD. quod de­<lb/>mon&longs;trare oportebat. </s></p><p id="id.2.1.83.3.0.0.0" type="head"> | <s id="id.2.1.83.2.1.7.0">& cùm potentia in D &longs;it æqualis ponderi G, & pon­<lb/>dus C æquale ponderi F; habebit potentia in D ad pondus C ean<lb/>dem proportionem, quam EB, hoc e&longs;t AB ad BD. </s> |
| | <s id="id.2.1.83.2.1.7.0.a">quod de­<lb/>mon&longs;trare oportebat. </s></p><p id="id.2.1.83.3.0.0.0" type="head"> |
| <s id="id.2.1.83.3.1.1.0">COROLLARIVM I. </s></p><p id="id.2.1.83.4.0.0.0" type="main"> | <s id="id.2.1.83.3.1.1.0">COROLLARIVM I. </s></p><p id="id.2.1.83.4.0.0.0" type="main"> |
| <s id="id.2.1.83.4.1.1.0">Ex hoc etiam pàtet, vt prius, &longs;i coftituatur pon<lb/>dus fulcimento B propius, vt in H; à minori po­<lb/>tentia pondus ip&longs;um &longs;ub&longs;tineri debere. </s></p><pb n="42" xlink:href="036/01/097.jpg"/> | <s id="id.2.1.83.4.1.1.0">Ex hoc etiam pàtet, vt prius, &longs;i coftituatur pon<lb/>dus fulcimento B propius, vt in H; à minori po­<lb/>tentia pondus ip&longs;um &longs;ub&longs;tineri debere. </s></p><pb n="42" xlink:href="036/01/097.jpg"/> |
| <p id="id.2.1.83.6.0.0.0" type="main"> | <p id="id.2.1.83.6.0.0.0" type="main"> |
| |
| <s id="id.2.1.85.8.1.3.0">Moueatur igi­<lb/>tur AB in EF; erunt AE <lb/><figure id="id.036.01.098.1.jpg" place="text" xlink:href="036/01/098/1.jpg"/><lb/>BF circulorum circumferentiæ, quorum &longs;emidiametri &longs;unt CA <lb/>CB. </s> | <s id="id.2.1.85.8.1.3.0">Moueatur igi­<lb/>tur AB in EF; erunt AE <lb/><figure id="id.036.01.098.1.jpg" place="text" xlink:href="036/01/098/1.jpg"/><lb/>BF circulorum circumferentiæ, quorum &longs;emidiametri &longs;unt CA <lb/>CB. </s> |
| <s id="N12D91">tota compleatur circumferentia AGE, & tota BHF; &longs;intq; <lb/>KH puncta, vbi AB, & EF circulum BHF &longs;ecant. </s> | <s id="N12D91">tota compleatur circumferentia AGE, & tota BHF; &longs;intq; <lb/>KH puncta, vbi AB, & EF circulum BHF &longs;ecant. </s> |
| <s id="id.2.1.85.8.1.4.0">Quoniam e­<lb/><arrow.to.target n="note139"/>nim angulus BCF e&longs;t æqualis angulo HCk; erit circumferentia <lb/><arrow.to.target n="note140"/>kH circumferentiæ BF æqualis. </s> | <s id="id.2.1.85.8.1.4.0">Quoniam e­<lb/><arrow.to.target n="note139"/>nim angulus BCF e&longs;t æqualis angulo HCk; erit circumferentia <lb/><arrow.to.target n="note140"/>kH circumferentiæ BF æqualis. </s> |
| <s id="id.2.1.85.8.1.5.0">cùm autem circumferentiæ AE <lb/>kH &longs;int &longs;ub eodem angulo ACE, & circumferentia AE ad to­<lb/>tam circumferentiam AGE &longs;it, vt angulus ACE ad quatuor re­<lb/>ctos; vt autem idem angulus HCk ad quatuor rectos, ita quoq; <lb/>e&longs;t circumferentia HK ad totam circumferentiam HBK; erit cir<lb/>cumferentia AE ad totam circumferentiam AGE, vt circumfe­<lb/><arrow.to.target n="note141"/>rentia kH ad totam kFH. & permutando, vt circumferentia <lb/>AE ad circumferentiam kH, hoc e&longs;t BF, ita tota circumferen­<lb/>tia AGE ad totam circumferentiam BHF. </s> | <s id="id.2.1.85.8.1.5.0">cùm autem circumferentiæ AE <lb/>kH &longs;int &longs;ub eodem angulo ACE, & circumferentia AE ad to­<lb/>tam circumferentiam AGE &longs;it, vt angulus ACE ad quatuor re­<lb/>ctos; vt autem idem angulus HCk ad quatuor rectos, ita quoq; <lb/>e&longs;t circumferentia HK ad totam circumferentiam HBK; erit cir<lb/>cumferentia AE ad totam circumferentiam AGE, vt circumfe­<lb/><arrow.to.target n="note141"/>rentia kH ad totam kFH. </s> |
| <s id="id.2.1.85.8.1.5.0.a">tota verò circumfe<lb/>rentia AGE ita &longs;e habet ad totam BHF, vt diameter circuli AEG <lb/><arrow.to.target n="note142"/>ad diametrum circuli BHF. </s> | <s id="id.2.1.85.8.1.5.0.a">& permutando, vt circumferentia <lb/>AE ad circumferentiam kH, hoc e&longs;t BF, ita tota circumferen­<lb/>tia AGE ad totam circumferentiam BHF. </s> |
| <s id="id.2.1.85.8.1.5.0.b">Vt igitur circumferentia AE ad cir<lb/><arrow.to.target n="note143"/>cumferentiam BF, ita diameter circuli AGE ad diametrum cir<lb/>culi BHF: vt autem diameter ad diametrum, ita &longs;emidiameter <lb/>ad &longs;emidiametrum, hoc e&longs;t CA ad CB: quare vt circumferen­<lb/>tia AE ad circumferentiam BF, ita CA ad CF. </s> | <s id="id.2.1.85.8.1.5.0.b">tota verò circumfe<lb/>rentia AGE ita &longs;e habet ad totam BHF, vt diameter circuli AEG <lb/><arrow.to.target n="note142"/>ad diametrum circuli BHF. </s> |
| | <s id="id.2.1.85.8.1.5.0.c">Vt igitur circumferentia AE ad cir<lb/><arrow.to.target n="note143"/>cumferentiam BF, ita diameter circuli AGE ad diametrum cir<lb/>culi BHF: vt autem diameter ad diametrum, ita &longs;emidiameter <lb/>ad &longs;emidiametrum, hoc e&longs;t CA ad CB: quare vt circumferen­<lb/>tia AE ad circumferentiam BF, ita CA ad CF. </s> |
| <s id="N12DD0">circumferentia <lb/>verò AE &longs;patium e&longs;t potentiæ motæ, & circumferentia BF e&longs;t <pb n="43" xlink:href="036/01/099.jpg"/>æqualis &longs;patio ponderis D moti. </s> | <s id="N12DD0">circumferentia <lb/>verò AE &longs;patium e&longs;t potentiæ motæ, & circumferentia BF e&longs;t <pb n="43" xlink:href="036/01/099.jpg"/>æqualis &longs;patio ponderis D moti. </s> |
| <s id="id.2.1.85.8.1.6.0">&longs;patium enim motus ponderis <lb/>D &longs;emper æquale e&longs;t &longs;patio motus puncti B, cùm in B &longs;it appen<lb/>&longs;um: &longs;patium ergo potentiæ motæ ad &longs;patium moti ponderis e&longs;t, <lb/>vt CA ad CB; hoc e&longs;t vt di&longs;tantia à fulcimento ad potentiam <lb/>ad di&longs;tantiam ab eodem ad ponderis &longs;u&longs;pen&longs;ionem. </s> | <s id="id.2.1.85.8.1.6.0">&longs;patium enim motus ponderis <lb/>D &longs;emper æquale e&longs;t &longs;patio motus puncti B, cùm in B &longs;it appen<lb/>&longs;um: &longs;patium ergo potentiæ motæ ad &longs;patium moti ponderis e&longs;t, <lb/>vt CA ad CB; hoc e&longs;t vt di&longs;tantia à fulcimento ad potentiam <lb/>ad di&longs;tantiam ab eodem ad ponderis &longs;u&longs;pen&longs;ionem. </s> |
| <s id="id.2.1.85.8.1.7.0">quod demon<lb/>&longs;trare oportebat. </s></p><p id="id.2.1.86.1.0.0.0" type="margin"> | <s id="id.2.1.85.8.1.7.0">quod demon<lb/>&longs;trare oportebat. </s></p><p id="id.2.1.86.1.0.0.0" type="margin"> |
| |
| <s id="id.2.1.87.1.1.1.0">Sit autem vectis AB, cu­<lb/>ius fulcimentum B; potentia­<lb/>&queacute; mouens in A; & pondus <lb/>in C. </s> | <s id="id.2.1.87.1.1.1.0">Sit autem vectis AB, cu­<lb/>ius fulcimentum B; potentia­<lb/>&queacute; mouens in A; & pondus <lb/>in C. </s> |
| <s id="id.2.1.87.1.1.1.0.a">dico &longs;patium potentiæ <lb/>translatæ ad &longs;patium transla<lb/>ti ponderis ita e&longs;&longs;e, vt BA ad <lb/>BC. </s> | <s id="id.2.1.87.1.1.1.0.a">dico &longs;patium potentiæ <lb/>translatæ ad &longs;patium transla<lb/>ti ponderis ita e&longs;&longs;e, vt BA ad <lb/>BC. </s> |
| <s id="id.2.1.87.1.1.1.0.b">Moueatur vectis, & vt <lb/>pondus sursum attollatur, ne­<lb/>ce&longs;&longs;e e&longs;t puncta C A &longs;ur&longs;um <lb/>moueri. </s> | <s id="id.2.1.87.1.1.1.0.b">Moueatur vectis, & vt <lb/>pondus sursum attollatur, ne­<lb/>ce&longs;&longs;e e&longs;t puncta C A &longs;ur&longs;um <lb/>moueri. </s> |
| <s id="id.2.1.87.1.1.2.0">Moueatur igitur A <lb/>&longs;ur&longs;um v&longs;q; ad D; &longs;itq; ve­<lb/>ctis motus BD. eodemq; <lb/>modo (vt prius dictum e&longs;t) <lb/>o&longs;tendemus puncta CA cir­<lb/>culorum circumferentias de­<lb/><figure id="id.036.01.099.1.jpg" place="text" xlink:href="036/01/099/1.jpg"/><lb/>&longs;cribere, <expan abbr="quorũ">quorum</expan> &longs;emidiametri &longs;unt BA BC. &longs;imiliterq; o&longs;tendemus <lb/>ita e&longs;&longs;e AD ad CE, vt &longs;emidiameter AB ad &longs;emidiametrum BC. </s></p><p id="id.2.1.87.2.0.0.0" type="main"> | <s id="id.2.1.87.1.1.2.0">Moueatur igitur A <lb/>&longs;ur&longs;um v&longs;q; ad D; &longs;itq; ve­<lb/>ctis motus BD. </s> |
| | <s id="id.2.1.87.1.1.2.0.a">eodemq; <lb/>modo (vt prius dictum e&longs;t) <lb/>o&longs;tendemus puncta CA cir­<lb/>culorum circumferentias de­<lb/><figure id="id.036.01.099.1.jpg" place="text" xlink:href="036/01/099/1.jpg"/><lb/>&longs;cribere, <expan abbr="quorũ">quorum</expan> &longs;emidiametri &longs;unt BA BC. </s> |
| | <s id="id.2.1.87.1.1.2.0.b">&longs;imiliterq; o&longs;tendemus <lb/>ita e&longs;&longs;e AD ad CE, vt &longs;emidiameter AB ad &longs;emidiametrum BC. </s></p><p id="id.2.1.87.2.0.0.0" type="main"> |
| <s id="id.2.1.87.2.1.1.0">Eademq; ratione, &longs;i potentia e&longs;&longs;et in C, & pondus in A, <lb/>o&longs;tendetur ita e&longs;&longs;e CE ad AD, vt BC ad BA; hoc e&longs;t di&longs;tan<lb/>tia à fulcimento ad potentiam ad di&longs;tantiam ab eodem ad ponde<lb/>ris &longs;u&longs;pen&longs;ionem. </s> | <s id="id.2.1.87.2.1.1.0">Eademq; ratione, &longs;i potentia e&longs;&longs;et in C, & pondus in A, <lb/>o&longs;tendetur ita e&longs;&longs;e CE ad AD, vt BC ad BA; hoc e&longs;t di&longs;tan<lb/>tia à fulcimento ad potentiam ad di&longs;tantiam ab eodem ad ponde<lb/>ris &longs;u&longs;pen&longs;ionem. </s> |
| <s id="id.2.1.87.2.1.2.0">quod oportebat demon&longs;trare. </s></p><p id="id.2.1.87.3.0.0.0" type="head"> | <s id="id.2.1.87.2.1.2.0">quod oportebat demon&longs;trare. </s></p><p id="id.2.1.87.3.0.0.0" type="head"> |
| <s id="id.2.1.87.3.1.1.0">COROLLARIVM. </s></p><p id="id.2.1.87.4.0.0.0" type="main"> | <s id="id.2.1.87.3.1.1.0">COROLLARIVM. </s></p><p id="id.2.1.87.4.0.0.0" type="main"> |
| |
| <s id="id.2.1.91.4.1.4.0">quare in vecte AB graue&longs;cet <lb/>in H, & ad vectem eandem habebit con&longs;titutionem, quam prius; <lb/>idcirco erit, ac &longs;i in H e&longs;&longs;et appen&longs;um. </s> | <s id="id.2.1.91.4.1.4.0">quare in vecte AB graue&longs;cet <lb/>in H, & ad vectem eandem habebit con&longs;titutionem, quam prius; <lb/>idcirco erit, ac &longs;i in H e&longs;&longs;et appen&longs;um. </s> |
| <s id="id.2.1.91.4.1.5.0">eadem igitur potentia ìdem <lb/>pondus BE, &longs;iue in H, &longs;iue in B, & Q &longs;uffultum, &longs;u&longs;tinebit. </s> | <s id="id.2.1.91.4.1.5.0">eadem igitur potentia ìdem <lb/>pondus BE, &longs;iue in H, &longs;iue in B, & Q &longs;uffultum, &longs;u&longs;tinebit. </s> |
| <s id="id.2.1.91.4.1.6.0">Potentia ve<arrow.to.target n="note147"/><lb/>rò in A &longs;u&longs;tinens pondus BE vecte AB in H appen&longs;um ad ip&longs;um <lb/>pondus eandem habet proportionem, quam DH ad DA; eadem <lb/>ergo potentia in A &longs;u&longs;tinens pondus BE in punctis BQ &longs;u&longs;tenta <lb/>tum ad ip&longs;um pondus erit, vt DH ad DA. </s> | <s id="id.2.1.91.4.1.6.0">Potentia ve<arrow.to.target n="note147"/><lb/>rò in A &longs;u&longs;tinens pondus BE vecte AB in H appen&longs;um ad ip&longs;um <lb/>pondus eandem habet proportionem, quam DH ad DA; eadem <lb/>ergo potentia in A &longs;u&longs;tinens pondus BE in punctis BQ &longs;u&longs;tenta <lb/>tum ad ip&longs;um pondus erit, vt DH ad DA. </s> |
| <s id="id.2.1.91.4.1.6.0.a">Similiter o&longs;tende­<lb/>tur pondus BE &longs;i in G &longs;u&longs;tineatur, manere; &longs;icuti à punctis BP <lb/>&longs;u&longs;tinebatur: </s> | <s id="id.2.1.91.4.1.6.0.a">Similiter o&longs;tende­<lb/>tur pondus BE &longs;i in G &longs;u&longs;tineatur, manere; &longs;icuti à punctis BP <lb/>&longs;u&longs;tinebatur: & in puncto k, vt à punctis BR. </s> |
| <s id="N12FFD">& in puncto k, vt à punctis BR. </s> | |
| <s id="N12FFF">quare potentia in <lb/>L &longs;u&longs;tinens pondus BE ad ip&longs;um pondus ita erit, vt NG ad NL. <lb/></s> | <s id="N12FFF">quare potentia in <lb/>L &longs;u&longs;tinens pondus BE ad ip&longs;um pondus ita erit, vt NG ad NL. <lb/></s> |
| <s id="N13004">potentia verò in M ad pondus, vt OK ad OM; hoc e&longs;t vt di&longs;tan<lb/>tia à fulcimento ad punctum, vbi à centro grauitatis ponderis ho<lb/>rizonti ducta perpendicularis vectem &longs;ecat, ad di&longs;tantiam à fulci­<lb/>mento ad potentiam. </s> | <s id="N13004">potentia verò in M ad pondus, vt OK ad OM; hoc e&longs;t vt di&longs;tan<lb/>tia à fulcimento ad punctum, vbi à centro grauitatis ponderis ho<lb/>rizonti ducta perpendicularis vectem &longs;ecat, ad di&longs;tantiam à fulci­<lb/>mento ad potentiam. </s> |
| <s id="id.2.1.91.4.1.7.0">quod demon&longs;trare quoq; oportebat. </s></p><p id="id.2.1.92.1.0.0.0" type="margin"> | <s id="id.2.1.91.4.1.7.0">quod demon&longs;trare quoq; oportebat. </s></p><p id="id.2.1.92.1.0.0.0" type="margin"> |
| |
| <s id="id.2.1.95.4.1.2.0">&longs;i it aq; con&longs;tituatur angu<lb/>lus GkQ ip&longs;i FHM æqua <lb/>lis, linea KQ ip&longs;am GN ita <lb/>&longs;ecabit, vt GQ ip&longs;i FM æqua <lb/>lis euadat: quare maior. </s> | <s id="id.2.1.95.4.1.2.0">&longs;i it aq; con&longs;tituatur angu<lb/>lus GkQ ip&longs;i FHM æqua <lb/>lis, linea KQ ip&longs;am GN ita <lb/>&longs;ecabit, vt GQ ip&longs;i FM æqua <lb/>lis euadat: quare maior. </s> |
| <s id="id.2.1.95.4.1.3.0">erit <lb/>GN, quàm FM; quibus &longs;i <lb/>æquales adiiciantur BF BG, <lb/>erit BN ip&longs;a BM maior. </s> | <s id="id.2.1.95.4.1.3.0">erit <lb/>GN, quàm FM; quibus &longs;i <lb/>æquales adiiciantur BF BG, <lb/>erit BN ip&longs;a BM maior. </s> |
| <s id="id.2.1.95.4.1.4.0">& <lb/>cùm BM &longs;it ip&longs;a FB maior, <lb/>erit quoq; ip&longs;a BA maior. </s> | <s id="id.2.1.95.4.1.4.0">& <lb/>cùm BM &longs;it ip&longs;a FB maior, <lb/>erit quoq; ip&longs;a BA maior. </s> |
| <s id="id.2.1.95.4.1.5.0">&longs;i <lb/>militer o&longs;tendetur, quò pro <lb/>pius fuerit BG ip&longs;i BC, li­<lb/>neam BN &longs;emper maiorem <lb/>e&longs;&longs;e. <figure id="id.036.01.108.1.jpg" place="text" xlink:href="036/01/108/1.jpg"/></s> | <s id="id.2.1.95.4.1.5.0">&longs;i <lb/>militer o&longs;tendetur, quò pro <lb/>pius fuerit BG ip&longs;i BC, li­<lb/>neam BN &longs;emper maiorem <lb/>e&longs;&longs;e. <figure id="id.036.01.108.1.jpg" place="text" xlink:href="036/01/108/1.jpg"/></s></p> |
| <pb n="48" xlink:href="036/01/109.jpg"/> | <pb n="48" xlink:href="036/01/109.jpg"/> |
| <s id="id.2.1.95.4.3.1.0">PROPOSITIO VII. </s></p><p id="id.2.1.95.5.0.0.0" type="main"> | <p id="id.2.1.95.5.0.0.0" type="head"> |
| | <s id="id.2.1.95.4.3.1.0">PROPOSITIO VII. </s></p><p id="id.2.1.95.5.0.0.0.a" type="main"> |
| <s id="id.2.1.95.5.1.1.0">Sit recta linea AB, cuì perpendicularis exi­<lb/>&longs;tat AD, quæ ex parte D producatur vtcunq; v&longs;q; <lb/>ad C; connectaturq; CB, quæ producatur e­<lb/>tiam v&longs;q; ad E; & inter AB BE lineæ &longs;imiliter <lb/>vtcunq; ducantur BF BG ip&longs;i AB æquales; à <lb/>punctisq; FG lineæ FH GK ip&longs;i AB æquales, <lb/>ip&longs;is verò BF BG <expan abbr="per­p&etilde;diculares">per­<lb/>pendiculares</expan> ducantur; <lb/>ac &longs;i BA AD motæ <lb/>&longs;int in BF FH BG <lb/>GK: Connectanturq; <lb/>CH CK, quæ lineas <lb/>BF BG productas &longs;e­<lb/>cent in punctis MN. </s> | <s id="id.2.1.95.5.1.1.0">Sit recta linea AB, cuì perpendicularis exi­<lb/>&longs;tat AD, quæ ex parte D producatur vtcunq; v&longs;q; <lb/>ad C; connectaturq; CB, quæ producatur e­<lb/>tiam v&longs;q; ad E; & inter AB BE lineæ &longs;imiliter <lb/>vtcunq; ducantur BF BG ip&longs;i AB æquales; à <lb/>punctisq; FG lineæ FH GK ip&longs;i AB æquales, <lb/>ip&longs;is verò BF BG <expan abbr="per­p&etilde;diculares">per­<lb/>pendiculares</expan> ducantur; <lb/>ac &longs;i BA AD motæ <lb/>&longs;int in BF FH BG <lb/>GK: Connectanturq; <lb/>CH CK, quæ lineas <lb/>BF BG productas &longs;e­<lb/>cent in punctis MN. </s> |
| <s id="id.2.1.95.5.1.1.0.a"><lb/>Dico BN maiorem e&longs; <lb/>&longs;e BM, & BM ip&longs;a BA. <lb/><figure id="id.036.01.109.1.jpg" place="text" xlink:href="036/01/109/1.jpg"/></s></p><p id="id.2.1.95.6.0.0.0" type="main"> | <s id="id.2.1.95.5.1.1.0.a"><lb/>Dico BN maiorem e&longs; <lb/>&longs;e BM, & BM ip&longs;a BA. <lb/><figure id="id.036.01.109.1.jpg" place="text" xlink:href="036/01/109/1.jpg"/></s></p><p id="id.2.1.95.6.0.0.0" type="main"> |
| <s id="id.2.1.95.6.1.1.0">Connectantur BD BH Bk, <lb/>& centro B, interuallo quidem <lb/>BD, circulus de&longs;cribatur. </s> | <s id="id.2.1.95.6.1.1.0">Connectantur BD BH Bk, <lb/>& centro B, interuallo quidem <lb/>BD, circulus de&longs;cribatur. </s> |
| |
| <s id="id.2.1.95.12.1.2.0">ducatur deinde kN ip&longs;i EF perpen­<lb/>dicularis, quæ ip&longs;i HL æqualis erit, & CN ip&longs;i CL æqualis. </s> | <s id="id.2.1.95.12.1.2.0">ducatur deinde kN ip&longs;i EF perpen­<lb/>dicularis, quæ ip&longs;i HL æqualis erit, & CN ip&longs;i CL æqualis. </s> |
| <s id="id.2.1.95.12.1.3.0">Quo­<lb/><arrow.to.target n="note153"/>niam enim HL horizonti e&longs;t perpendicularis, potentia in A &longs;u<lb/>&longs;tinens pondus BD ad ip&longs;um pondus eam habebit proportionem, <lb/>quam CL ad CA. </s> | <s id="id.2.1.95.12.1.3.0">Quo­<lb/><arrow.to.target n="note153"/>niam enim HL horizonti e&longs;t perpendicularis, potentia in A &longs;u<lb/>&longs;tinens pondus BD ad ip&longs;um pondus eam habebit proportionem, <lb/>quam CL ad CA. </s> |
| <s id="id.2.1.95.12.1.3.0.a">rur&longs;us quoniam kM horizonti e&longs;t perpendicu<lb/>laris, potentia in E pondus FG &longs;u&longs;tinens ita erit ad pondus, vt <lb/>CM ad CE. </s> | <s id="id.2.1.95.12.1.3.0.a">rur&longs;us quoniam kM horizonti e&longs;t perpendicu<lb/>laris, potentia in E pondus FG &longs;u&longs;tinens ita erit ad pondus, vt <lb/>CM ad CE. </s> |
| <s id="id.2.1.95.12.1.3.0.b">Cùm autem CN NK ip&longs;is CL LH &longs;int æquales, <lb/><arrow.to.target n="note154"/>angulosq; rectos contineant; erit CM minor ip&longs;a CL; ergo CM <lb/><arrow.to.target n="note155"/>ad CA minorem habebit proportionem, quam CL ad CA; & <pb n="45" xlink:href="036/01/113.jpg"/>CA ip&longs;i CE e&longs;t æqualis, minorem igitur proportionem habebit <lb/>CM ad CE. </s> | <s id="id.2.1.95.12.1.3.0.b">Cùm autem CN NK ip&longs;is CL LH &longs;int æquales, <lb/><arrow.to.target n="note154"/>angulosq; rectos contineant; erit CM minor ip&longs;a CL; ergo CM <lb/><arrow.to.target n="note155"/>ad CA minorem habebit proportionem, quam CL ad CA; & <pb n="45" xlink:href="036/01/113.jpg"/>CA ip&longs;i CE e&longs;t æqualis, minorem igitur proportionem habebit <lb/>CM ad CE. quàm CL ad CA: & cùm pondera BD FG &longs;int <lb/>æqualia, e&longs;t enim idem pondus; ergo minor erit proportio po<lb/>tentiæ in E pondus FG &longs;u&longs;tinentis ad ip&longs;um pondus, quàm po<lb/>tentiæ in A pondus BD &longs;u&longs;tinentis ad ip&longs;um pondus. </s> |
| <s id="N1338C">quàm CL ad CA: & cùm pondera BD FG &longs;int <lb/>æqualia, e&longs;t enim idem pondus; ergo minor erit proportio po<lb/>tentiæ in E pondus FG &longs;u&longs;tinentis ad ip&longs;um pondus, quàm po<lb/>tentiæ in A pondus BD &longs;u&longs;tinentis ad ip&longs;um pondus. </s> | |
| <s id="id.2.1.95.12.1.4.0">Quare <arrow.to.target n="note156"/><lb/>minor potentia in E &longs;u&longs;tinebit pondus FG, quàm potentia in A <lb/>pondus BD. </s> | <s id="id.2.1.95.12.1.4.0">Quare <arrow.to.target n="note156"/><lb/>minor potentia in E &longs;u&longs;tinebit pondus FG, quàm potentia in A <lb/>pondus BD. </s> |
| <s id="N1339E">& quò pondus magis eleuabitur; &longs;emper o&longs;tendetur <lb/>minorem adhuc potentiam pondus &longs;u&longs;tinere; cùm linea PC mi <arrow.to.target n="note157"/><lb/>nor &longs;it linea CM. </s> | <s id="N1339E">& quò pondus magis eleuabitur; &longs;emper o&longs;tendetur <lb/>minorem adhuc potentiam pondus &longs;u&longs;tinere; cùm linea PC mi <arrow.to.target n="note157"/><lb/>nor &longs;it linea CM. </s> |
| <s id="id.2.1.95.12.1.4.0.a">&longs;it deinde vectis in QR, & pondus in QS, <lb/>cuius <expan abbr="centrũ">centrum</expan> grauitatis &longs;it O. </s> | <s id="id.2.1.95.12.1.4.0.a">&longs;it deinde vectis in QR, & pondus in QS, <lb/>cuius <expan abbr="centrũ">centrum</expan> grauitatis &longs;it O. </s> |
| |
| <s id="id.2.1.139.4.1.2.0">Sit FG <lb/>æquidi&longs;tans CB. </s> | <s id="id.2.1.139.4.1.2.0">Sit FG <lb/>æquidi&longs;tans CB. </s> |
| <s id="id.2.1.139.4.1.2.0.a"><lb/>Quoniam igitur pon<lb/><arrow.to.target n="note217"/>dus A manet; erit <lb/><figure id="id.036.01.140.1.jpg" place="text" xlink:href="036/01/140/1.jpg"/><lb/>CB horizonti plano perpendicularis <*> quare FG eidem plano per­<lb/><arrow.to.target n="note218"/>pendicularis erit. </s> | <s id="id.2.1.139.4.1.2.0.a"><lb/>Quoniam igitur pon<lb/><arrow.to.target n="note217"/>dus A manet; erit <lb/><figure id="id.036.01.140.1.jpg" place="text" xlink:href="036/01/140/1.jpg"/><lb/>CB horizonti plano perpendicularis <*> quare FG eidem plano per­<lb/><arrow.to.target n="note218"/>pendicularis erit. </s> |
| <s id="id.2.1.139.4.1.3.0">Sint CF <expan abbr="pũcta">puncta</expan> in orbiculo, à quibus funes CB FG <lb/>in horizontis <expan abbr="planũ">planum</expan> ad rectos angulos de&longs;cendunt; tangent BC FG <lb/></s> | <s id="id.2.1.139.4.1.3.0">Sint CF <expan abbr="pũcta">puncta</expan> in orbiculo, à quibus funes CB FG <lb/>in horizontis <expan abbr="planũ">planum</expan> ad rectos angulos de&longs;cendunt; tangent BC FG <lb/></s> |
| <s id="N140A0"> | <s id="N140A0"><expan abbr="orbiculũ">orbiculum</expan> CEF in punctis CF. <expan abbr="orbiculũ">orbiculum</expan> enim &longs;ecare <expan abbr="nõ">non</expan> po&longs;&longs;unt. </s> |
| <expan abbr="orbiculũ">orbiculum</expan> CEF in punctis CF. <expan abbr="orbiculũ">orbiculum</expan> enim &longs;ecare <expan abbr="nõ">non</expan> po&longs;&longs;unt. </s> | |
| <s id="id.2.1.139.4.1.4.0">con<lb/>nectantur DC DF; erit CF recta linea, & anguli DCB DFG recti. </s> | <s id="id.2.1.139.4.1.4.0">con<lb/>nectantur DC DF; erit CF recta linea, & anguli DCB DFG recti. </s> |
| <s id="id.2.1.139.4.1.5.0"><lb/><arrow.to.target n="note219"/> | <s id="id.2.1.139.4.1.5.0"><lb/><arrow.to.target n="note219"/> |
| <expan abbr="Quoniã">Quoniam</expan> | <expan abbr="Quoniã">Quoniam</expan> |
| |
| <s id="id.2.1.167.11.1.1.0">Sit trochlea habens orbiculum, cuius <lb/>centrum A; & &longs;it pondus B alligatum fu<lb/>ni CDEFG, qui circa orbiculum &longs;it re­<lb/>uolutus, ac tandem religatus in G: &longs;itq; <lb/>potentia in H &longs;u&longs;tinens pondus. </s> | <s id="id.2.1.167.11.1.1.0">Sit trochlea habens orbiculum, cuius <lb/>centrum A; & &longs;it pondus B alligatum fu<lb/>ni CDEFG, qui circa orbiculum &longs;it re­<lb/>uolutus, ac tandem religatus in G: &longs;itq; <lb/>potentia in H &longs;u&longs;tinens pondus. </s> |
| <s id="id.2.1.167.11.1.2.0">dico po<lb/>tentiam in H duplam e&longs;&longs;e ponderis B. </s> | <s id="id.2.1.167.11.1.2.0">dico po<lb/>tentiam in H duplam e&longs;&longs;e ponderis B. </s> |
| <s id="N150B6">du<lb/>catur DF per <expan abbr="centrũ">centrum</expan> A horizonti æquidi<lb/>&longs;tans. </s> | <s id="N150B6">du<lb/>catur DF per <expan abbr="centrũ">centrum</expan> A horizonti æquidi<lb/>&longs;tans. </s> |
| <s id="id.2.1.167.11.1.3.0"> | <s id="id.2.1.167.11.1.3.0"><expan abbr="quoniã">quoniam</expan> igitur potentia in H &longs;u&longs;tinet <lb/> |
| <expan abbr="quoniã">quoniam</expan> igitur potentia in H &longs;u&longs;tinet <lb/> | |
| <expan abbr="trochleã">trochleam</expan>, quæ &longs;u&longs;tinet <expan abbr="orbiculũ">orbiculum</expan> in eius <expan abbr="c&etilde;tro">centro</expan><lb/>A, qui pondus &longs;u&longs;tinet; erit potentia &longs;u&longs;ti<lb/>nens <expan abbr="orbiculũ">orbiculum</expan>, ac &longs;i in A <expan abbr="cõ&longs;tituta">con&longs;tituta</expan> e&longs;&longs;et; ip&longs;a <lb/>ergo in A exi&longs;tente, pondere verò in D <lb/>appen&longs;o, funiq; CD religato; erit DF <lb/>tanquam vectis, cuius fulcimentum erit <lb/>F, pondus in D, & potentia in A. </s> | <expan abbr="trochleã">trochleam</expan>, quæ &longs;u&longs;tinet <expan abbr="orbiculũ">orbiculum</expan> in eius <expan abbr="c&etilde;tro">centro</expan><lb/>A, qui pondus &longs;u&longs;tinet; erit potentia &longs;u&longs;ti<lb/>nens <expan abbr="orbiculũ">orbiculum</expan>, ac &longs;i in A <expan abbr="cõ&longs;tituta">con&longs;tituta</expan> e&longs;&longs;et; ip&longs;a <lb/>ergo in A exi&longs;tente, pondere verò in D <lb/>appen&longs;o, funiq; CD religato; erit DF <lb/>tanquam vectis, cuius fulcimentum erit <lb/>F, pondus in D, & potentia in A. </s> |
| <s id="id.2.1.167.11.1.3.0.a">po­<lb/><arrow.to.target n="note253"/>tentia verò ad pondus e&longs;t, vt DF ad <lb/>ad FA, & DF dupla e&longs;t ip&longs;ius FA; Po­<lb/><figure id="id.036.01.180.1.jpg" place="text" xlink:href="036/01/180/1.jpg"/><lb/>tentia igitur in A, &longs;iue in H, quod idem e&longs;t, ponderis B dupla erit. </s><lb/> | <s id="id.2.1.167.11.1.3.0.a">po­<lb/><arrow.to.target n="note253"/>tentia verò ad pondus e&longs;t, vt DF ad <lb/>ad FA, & DF dupla e&longs;t ip&longs;ius FA; Po­<lb/><figure id="id.036.01.180.1.jpg" place="text" xlink:href="036/01/180/1.jpg"/><lb/>tentia igitur in A, &longs;iue in H, quod idem e&longs;t, ponderis B dupla erit. </s><lb/> |
| <s id="id.2.1.167.11.1.4.0">quod demon&longs;trare oportebat. </s></p><p id="id.2.1.168.1.0.0.0" type="margin"> | <s id="id.2.1.167.11.1.4.0">quod demon&longs;trare oportebat. </s></p><p id="id.2.1.168.1.0.0.0" type="margin"> |
| |
| <s id="id.2.1.218.1.1.1.0"><margin.target id="note300"/><emph type="italics"/>Ex<emph.end type="italics"/> 1 <emph type="italics"/>huius<emph.end type="italics"/></s> | <s id="id.2.1.218.1.1.1.0"><margin.target id="note300"/><emph type="italics"/>Ex<emph.end type="italics"/> 1 <emph type="italics"/>huius<emph.end type="italics"/></s> |
| <s id="id.2.1.218.1.1.2.0"><margin.target id="note301"/>2 <emph type="italics"/>Huius.<emph.end type="italics"/></s> | <s id="id.2.1.218.1.1.2.0"><margin.target id="note301"/>2 <emph type="italics"/>Huius.<emph.end type="italics"/></s> |
| <s id="id.2.1.218.1.1.3.0"><margin.target id="note302"/><emph type="italics"/>Ex<emph.end type="italics"/> 9 <emph type="italics"/>huius<emph.end type="italics"/></s></p><p id="id.2.1.219.1.0.0.0" type="main"> | <s id="id.2.1.218.1.1.3.0"><margin.target id="note302"/><emph type="italics"/>Ex<emph.end type="italics"/> 9 <emph type="italics"/>huius<emph.end type="italics"/></s></p><p id="id.2.1.219.1.0.0.0" type="main"> |
| <s id="id.2.1.219.1.1.1.0"> | <s id="id.2.1.219.1.1.1.0"><expan abbr="Animaduertendũ">Animaduertendum</expan> quoq; e&longs;t in mo <lb/>uendis ponderibus, potentiam ali­<lb/>quando for&longs;itan melius mouere mo<lb/>uendo &longs;e deor&longs;um, quàm mouendo <lb/>&longs;e &longs;ur&longs;um. </s> |
| <expan abbr="Animaduertendũ">Animaduertendum</expan> quoq; e&longs;t in mo <lb/>uendis ponderibus, potentiam ali­<lb/>quando for&longs;itan melius mouere mo<lb/>uendo &longs;e deor&longs;um, quàm mouendo <lb/>&longs;e &longs;ur&longs;um. </s> | |
| <s id="id.2.1.219.1.1.2.0">vt circumuoluatur adhuc <lb/>funis per alium trochleæ &longs;uperioris <lb/>orbiculum, cuius centrum C, funi&longs;q; <lb/><arrow.to.target n="note303"/>perueniat in D; erit <expan abbr="pot&etilde;tia">potentia</expan> in D <expan abbr="&longs;u&longs;ti­n&etilde;s">&longs;u&longs;ti­nens</expan> | <s id="id.2.1.219.1.1.2.0">vt circumuoluatur adhuc <lb/>funis per alium trochleæ &longs;uperioris <lb/>orbiculum, cuius centrum C, funi&longs;q; <lb/><arrow.to.target n="note303"/>perueniat in D; erit <expan abbr="pot&etilde;tia">potentia</expan> in D <expan abbr="&longs;u&longs;ti­n&etilde;s">&longs;u&longs;ti­nens</expan> |
| <expan abbr="põdus">pondus</expan> B &longs;imiliter duodecim, <expan abbr="&quetilde;">&que;m</expan><lb/>admodum erat in A. </s> | <expan abbr="põdus">pondus</expan> B &longs;imiliter duodecim, <expan abbr="&quetilde;">&que;m</expan><lb/>admodum erat in A. </s> |
| <s id="id.2.1.219.1.1.2.0.a">Ideo poten­<lb/>tia vt tredecim in D pondus B mo­<lb/>uebit. </s> | <s id="id.2.1.219.1.1.2.0.a">Ideo poten­<lb/>tia vt tredecim in D pondus B mo­<lb/>uebit. </s> |
| |
| <s id="id.2.1.237.16.1.6.0">&longs;imiliter ponatur EF in MP, circum­<lb/>uoluaturq; triangulum EFG circa cylindrum; de&longs;cribaturq; per <lb/>EG helix PRM. </s> | <s id="id.2.1.237.16.1.6.0">&longs;imiliter ponatur EF in MP, circum­<lb/>uoluaturq; triangulum EFG circa cylindrum; de&longs;cribaturq; per <lb/>EG helix PRM. </s> |
| <s id="N16DFD">cùm itaq; PMPN &longs;int æquales EFHI, erit <lb/>MN æqualis ip&longs;i AC, & cùm helices PRM PQN &longs;int æquales <lb/>lineis EGHk; helices igitur ip&longs;is ABBC æquales erunt. </s> | <s id="N16DFD">cùm itaq; PMPN &longs;int æquales EFHI, erit <lb/>MN æqualis ip&longs;i AC, & cùm helices PRM PQN &longs;int æquales <lb/>lineis EGHk; helices igitur ip&longs;is ABBC æquales erunt. </s> |
| <s id="id.2.1.237.16.1.7.0">cu­<lb/>neus ergo ABC totus circumuolutus erit circa cylindrum LMNO. </s> | <s id="id.2.1.237.16.1.7.0">cu­<lb/>neus ergo ABC totus circumuolutus erit circa cylindrum LMNO. </s> |
| <s id="N16E08"> | <s id="N16E08"><pb xlink:href="036/01/256.jpg"/>incidantur deinde helices, <lb/>vt docet Pappus &longs;ecundùm <lb/>latitudinem cunei; & hoc <lb/>modo cuneus vná cum cy<lb/>lindro nihil aliud erit, <lb/>quàm cochlea duas habens <lb/>helices PRMPQN cir<lb/>ca cylindrum LN in vnico <lb/>puncto P inuicem coniun<lb/>ctas. </s> |
| <pb xlink:href="036/01/256.jpg"/>incidantur deinde helices, <lb/>vt docet Pappus &longs;ecundùm <lb/>latitudinem cunei; & hoc <lb/>modo cuneus vná cum cy<lb/>lindro nihil aliud erit, <lb/>quàm cochlea duas habens <lb/>helices PRMPQN cir<lb/>ca cylindrum LN in vnico <lb/>puncto P inuicem coniun<lb/>ctas. </s> | |
| <s id="id.2.1.237.16.1.8.0">quod demon&longs;trare o­<lb/>portebat. </s></p> | <s id="id.2.1.237.16.1.8.0">quod demon&longs;trare o­<lb/>portebat. </s></p> |
| <figure id="id.036.01.256.1.jpg" place="text" xlink:href="036/01/256/1.jpg"/> | <figure id="id.036.01.256.1.jpg" place="text" xlink:href="036/01/256/1.jpg"/> |
| <p id="id.2.1.237.16.3.1.0" type="head"> | <p id="id.2.1.237.16.3.1.0" type="head"> |
| |
| <s id="id.2.1.245.2.1.4.0">e&longs;t autem animaduertendum, quòd dum cochlea mouet <lb/>pondus, &longs;i mente concipiatur, quòd loco trahendi pondus O fune, <lb/>pondus &longs;uper helices ABCD moueat; pondus quoq; in k, quod <lb/>&longs;it R, &longs;uper helices etiam facilius mouebit. </s> | <s id="id.2.1.245.2.1.4.0">e&longs;t autem animaduertendum, quòd dum cochlea mouet <lb/>pondus, &longs;i mente concipiatur, quòd loco trahendi pondus O fune, <lb/>pondus &longs;uper helices ABCD moueat; pondus quoq; in k, quod <lb/>&longs;it R, &longs;uper helices etiam facilius mouebit. </s> |
| <s id="id.2.1.245.2.1.5.0">e&longs;t enim LK vectis, cuius <lb/><arrow.to.target n="note332"/>fulcimentum e&longs;t I: cùm circa axem cochlea circumuertatur; po­<lb/><arrow.to.target n="note333"/>tentia mouens in L; & pondus in k. </s> | <s id="id.2.1.245.2.1.5.0">e&longs;t enim LK vectis, cuius <lb/><arrow.to.target n="note332"/>fulcimentum e&longs;t I: cùm circa axem cochlea circumuertatur; po­<lb/><arrow.to.target n="note333"/>tentia mouens in L; & pondus in k. </s> |
| <s id="id.2.1.245.2.1.6.0">facilius enim mouetur pon<lb/>dus vecte Lk, quàm &longs;ine vecte; quia LI &longs;emper maior e&longs;t Ik. </s> | <s id="id.2.1.245.2.1.6.0">facilius enim mouetur pon<lb/>dus vecte Lk, quàm &longs;ine vecte; quia LI &longs;emper maior e&longs;t Ik. </s> |
| <s id="id.2.1.245.2.1.7.0"> | <s id="id.2.1.245.2.1.7.0"><pb n="128" xlink:href="036/01/269.jpg"/>Intelligatur itaq; manente cochlea pondus R moueri à potentia <lb/>in L vecte Lk &longs;uper helicen Ck: vel quod idem e&longs;t, &longs;icut etiam <lb/>&longs;upra diximus, &longs;i pondus R aptetur ita, vt moueri non po&longs;sit, ni <lb/>&longs;i &longs;uper rectam PQ axi cylindri æquidi&longs;tantem; circumuertaturq; <lb/>cochlea, potentia exi&longs;tente in L; mouebitur pondus R &longs;uper he­<lb/>licen CD eodem modo, ac &longs;i à vecte Lk moueretur. </s> |
| <pb n="128" xlink:href="036/01/269.jpg"/>Intelligatur itaq; manente cochlea pondus R moueri à potentia <lb/>in L vecte Lk &longs;uper helicen Ck: vel quod idem e&longs;t, &longs;icut etiam <lb/>&longs;upra diximus, &longs;i pondus R aptetur ita, vt moueri non po&longs;sit, ni <lb/>&longs;i &longs;uper rectam PQ axi cylindri æquidi&longs;tantem; circumuertaturq; <lb/>cochlea, potentia exi&longs;tente in L; mouebitur pondus R &longs;uper he­<lb/>licen CD eodem modo, ac &longs;i à vecte Lk moueretur. </s> | |
| <s id="id.2.1.245.2.1.8.0">idem enim <lb/>e&longs;t, &longs;iue pondus manente cochlea &longs;uper helicen moueatur; &longs;iue he<lb/>lix circumuertatur, ita vt pondus &longs;uper ip&longs;am moueatur. </s> | <s id="id.2.1.245.2.1.8.0">idem enim <lb/>e&longs;t, &longs;iue pondus manente cochlea &longs;uper helicen moueatur; &longs;iue he<lb/>lix circumuertatur, ita vt pondus &longs;uper ip&longs;am moueatur. </s> |
| <s id="id.2.1.245.2.1.9.0">cùm <lb/>ab eadem potentia in L moueatur. </s> | <s id="id.2.1.245.2.1.9.0">cùm <lb/>ab eadem potentia in L moueatur. </s> |
| <s id="id.2.1.245.2.1.10.0">&longs;imiliter o&longs;tendetur, quò lon<lb/>gior &longs;it LI, adhuc pondus facilius &longs;emper moueri. </s> | <s id="id.2.1.245.2.1.10.0">&longs;imiliter o&longs;tendetur, quò lon<lb/>gior &longs;it LI, adhuc pondus facilius &longs;emper moueri. </s> |
![[BACK]](http://archimedes.mpiwg-berlin.mpg.de/arch/img/icons/back.gif){kind=icon}
Return to monte_mecha_01_la_1577.xml
CVS log ![[TXT]](http://archimedes.mpiwg-berlin.mpg.de/arch/img/icons/text.gif){kind=icon}
![[DIR]](http://archimedes.mpiwg-berlin.mpg.de/arch/img/icons/dir.gif){kind=icon}
Up to [CVSROOT] / texts / archimedes / xml