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Colored diff for /texts/archimedes/xml/Attic/fabri_tract_01_la_1646.xml between version 1.23 and 1.24

version 1.23, 2002/08/14 23:55:25 version 1.24, 2002/08/15 00:42:36
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 <s><lb/>Quia &longs;ub&longs;tantia mobilis non e&longs;t cau&longs;a exigens motum per Th. 5. Impe&shy;<lb/>tus e&longs;t cau&longs;a exigens per Def. </s> <s><lb/>Quia &longs;ub&longs;tantia mobilis non e&longs;t cau&longs;a exigens motum per Th. 5. Impe&shy;<lb/>tus e&longs;t cau&longs;a exigens per Def. </s>
  
 <s>3. &amp; Th. </s> <s>3. &amp; Th. 6. de codem contradictoria dici <lb/>non po&longs;&longs;unt per Ax. </s>
  
 <s>6. de codem contradictoria dici <lb/>non po&longs;&longs;unt per Ax. </s> 
  
 <s>1. n. </s> <s>1. n. </s>
  
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 <s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 14.<emph.end type="center"/></s></p><p type="main"> <s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 14.<emph.end type="center"/></s></p><p type="main">
  
 <s><emph type="italics"/>Impetus exigit motum, id est fluxum mobilis in loco<emph.end type="italics"/>; quia cau&longs;a imme&shy;<lb/>diata motus e&longs;t tantum exigens, per Th. 4. &longs;ed impetus e&longs;t cau&longs;a motus <lb/>immediata per Th. </s> <s><emph type="italics"/>Impetus exigit motum, id est fluxum mobilis in loco<emph.end type="italics"/>; quia cau&longs;a imme&shy;<lb/>diata motus e&longs;t tantum exigens, per Th. 4. &longs;ed impetus e&longs;t cau&longs;a motus <lb/>immediata per Th. 5. &amp; 6. igitur e&longs;t cau&longs;a exigens, adde quod id tant&ugrave;m <lb/>accidens &longs;en&longs;ibile pr&aelig;&longs;tare pote&longs;t in &longs;uo &longs;ubiecto, vt aliquam illius mu&shy;<lb/>tationem pr&aelig;&longs;tet, vel exigat; qu&aelig; vel e&longs;t localis, hoc e&longs;t fluxus quidam: <pb pagenum="19"/>per &longs;patium loci; vel alteratiua, vt vulg&ograve; vocatur; qu&agrave; &longs;cilicet vel re&shy;<lb/>&longs;oluuntur partes, vel rare&longs;iunt, vel lique&longs;cunt, vel concre&longs;cunt &amp;c. </s>
  
 <s>5. &amp; 6. igitur e&longs;t cau&longs;a exigens, adde quod id tant&ugrave;m <lb/>accidens &longs;en&longs;ibile pr&aelig;&longs;tare pote&longs;t in &longs;uo &longs;ubiecto, vt aliquam illius mu&shy;<lb/>tationem pr&aelig;&longs;tet, vel exigat; qu&aelig; vel e&longs;t localis, hoc e&longs;t fluxus quidam: <pb pagenum="19"/>per &longs;patium loci; vel alteratiua, vt vulg&ograve; vocatur; qu&agrave; &longs;cilicet vel re&shy;<lb/>&longs;oluuntur partes, vel rare&longs;iunt, vel lique&longs;cunt, vel concre&longs;cunt &amp;c. </s> 
  
 <s>vel <lb/>dem&ugrave;m mutant &longs;en&longs;ibilem &longs;tatum; vel e&longs;t perfectiua aliquo modo, qua&shy;<lb/>tenus &longs;ubiectum nouam aliquam habitudinem acquirit ad &longs;en&longs;us; &longs;ic <lb/>lumen illuminando obiectum reddit illud vi&longs;ibile. </s> <s>vel <lb/>dem&ugrave;m mutant &longs;en&longs;ibilem &longs;tatum; vel e&longs;t perfectiua aliquo modo, qua&shy;<lb/>tenus &longs;ubiectum nouam aliquam habitudinem acquirit ad &longs;en&longs;us; &longs;ic <lb/>lumen illuminando obiectum reddit illud vi&longs;ibile. </s>
  
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 <s><emph type="italics"/>Ni&longs;i e&longs;&longs;et impetus, non e&longs;&longs;et naturaliter motus.<emph.end type="italics"/></s><s> Quia ni&longs;i e&longs;&longs;etcau&longs;a, non <lb/>e&longs;&longs;et naturaliter effectus per Ax. </s> <s><emph type="italics"/>Ni&longs;i e&longs;&longs;et impetus, non e&longs;&longs;et naturaliter motus.<emph.end type="italics"/></s><s> Quia ni&longs;i e&longs;&longs;etcau&longs;a, non <lb/>e&longs;&longs;et naturaliter effectus per Ax. </s>
  
 <s>8. Impetus enim e&longs;t cau&longs;a motus per <lb/>Th.15. Deinde omnis motus e&longs;t ab aliqua potentia motrice, vt patet ex <lb/>omni hypothe&longs;i; &longs;iue &longs;it naturalis in grauibus, &amp; leuibus, &longs;iue &longs;evitalis <lb/>in viuentibus; &longs;iue &longs;it media in compre&longs;&longs;is, &amp; dilatatis; &longs;iue alia qu&aelig;li&shy;<lb/>bet: &longs;ed omnis potentia motrix e&longs;t actiua, quia mouet; ergo agit, &longs;ed <lb/>motum non producit per Th. 2. Igitur impetum, qui deinde exigit mo&shy;<lb/>tum per Th. </s> <s>8. Impetus enim e&longs;t cau&longs;a motus per <lb/>Th.15. Deinde omnis motus e&longs;t ab aliqua potentia motrice, vt patet ex <lb/>omni hypothe&longs;i; &longs;iue &longs;it naturalis in grauibus, &amp; leuibus, &longs;iue &longs;evitalis <lb/>in viuentibus; &longs;iue &longs;it media in compre&longs;&longs;is, &amp; dilatatis; &longs;iue alia qu&aelig;li&shy;<lb/>bet: &longs;ed omnis potentia motrix e&longs;t actiua, quia mouet; ergo agit, &longs;ed <lb/>motum non producit per Th. 2. Igitur impetum, qui deinde exigit mo&shy;<lb/>tum per Th. 14. Dixi naturaliter; quia non e&longs;t dubium, quin Deus &longs;ine <lb/>impetu aliquo modo mouere po&longs;&longs;it; ide&longs;t, facere &longs;ine impetu, vt corpus <lb/>mutet locum: nec dicas Deum non po&longs;&longs;e &longs;upplere vices cau&longs;&aelig; formalis; <lb/>nam concedo id quidem pro effectu formali primario; nec enim Deus <lb/>pote&longs;t facere, vt aliquid &longs;it calidum &longs;ine calore; cum e&longs;&longs;e calidum &longs;it <lb/>idem, ac e&longs;&longs;e habens calorem; id tamen nego pro effectu &longs;ecundario, <lb/>quem &longs;cilicet cau&longs;a formalis exigit: Etenim &longs;icut pote&longs;t &longs;ummo iure non <lb/>&longs;atisfacere exigenti&aelig;; ita pote&longs;t id <expan abbr="c&otilde;ferre">conferre</expan> &longs;ine exigenti&acirc;, qu&ograve;d cum exi&shy;<lb/>gentia conferre pote&longs;t; &longs;ic pote&longs;t corpus re&longs;oluere &longs;ine calore, mouere <lb/>fine impetu &amp;c. </s>
  
 <s>14. Dixi naturaliter; quia non e&longs;t dubium, quin Deus &longs;ine <lb/>impetu aliquo modo mouere po&longs;&longs;it; ide&longs;t, facere &longs;ine impetu, vt corpus <lb/>mutet locum: nec dicas Deum non po&longs;&longs;e &longs;upplere vices cau&longs;&aelig; formalis; <lb/>nam concedo id quidem pro effectu formali primario; nec enim Deus <lb/>pote&longs;t facere, vt aliquid &longs;it calidum &longs;ine calore; cum e&longs;&longs;e calidum &longs;it <lb/>idem, ac e&longs;&longs;e habens calorem; id tamen nego pro effectu &longs;ecundario, <lb/>quem &longs;cilicet cau&longs;a formalis exigit: Etenim &longs;icut pote&longs;t &longs;ummo iure non <lb/>&longs;atisfacere exigenti&aelig;; ita pote&longs;t id <expan abbr="c&otilde;ferre">conferre</expan> &longs;ine exigenti&acirc;, qu&ograve;d cum exi&shy;<lb/>gentia conferre pote&longs;t; &longs;ic pote&longs;t corpus re&longs;oluere &longs;ine calore, mouere <lb/>fine impetu &amp;c. </s> 
  
 <s>quanquam vt verum fatear non e&longs;&longs;et propri&egrave; motus, &longs;ed <lb/>qua&longs;i continu&aelig; reproductionis modus; nam motus dicit aliquam pa&longs;&shy;<lb/>&longs;ionem; &longs;cilicet actum entis in potenti&acirc;, vt aiunt. </s></p><p type="main"> <s>quanquam vt verum fatear non e&longs;&longs;et propri&egrave; motus, &longs;ed <lb/>qua&longs;i continu&aelig; reproductionis modus; nam motus dicit aliquam pa&longs;&shy;<lb/>&longs;ionem; &longs;cilicet actum entis in potenti&acirc;, vt aiunt. </s></p><p type="main">
  
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 <s><lb/>2. &longs;icut vna pars caloris non re&longs;oluit alias partes &longs;ubiecti; ita nec im&shy;<lb/>petus. </s> <s><lb/>2. &longs;icut vna pars caloris non re&longs;oluit alias partes &longs;ubiecti; ita nec im&shy;<lb/>petus. </s>
  
 <s>3. Ratio &agrave; priori e&longs;t; quia impetus non e&longs;t cau&longs;a efficiens motus <lb/>per Th. 13. &longs;ed tant&ugrave;m cau&longs;a formalis per Th. </s> <s>3. Ratio &agrave; priori e&longs;t; quia impetus non e&longs;t cau&longs;a efficiens motus <lb/>per Th. 13. &longs;ed tant&ugrave;m cau&longs;a formalis per Th. 15. Igitur pr&aelig;&longs;tat tant&ugrave;m <lb/>&longs;uum effectum formalem in eo &longs;ubiecto, in quo e&longs;t. </s></p><p type="main">
  
 <s>15. Igitur pr&aelig;&longs;tat tant&ugrave;m <lb/>&longs;uum effectum formalem in eo &longs;ubiecto, in quo e&longs;t. </s></p><p type="main"> 
  
 <s><emph type="center"/><emph type="italics"/>Corollarium<emph.end type="italics"/> 1.<emph.end type="center"/></s></p><p type="main"> <s><emph type="center"/><emph type="italics"/>Corollarium<emph.end type="italics"/> 1.<emph.end type="center"/></s></p><p type="main">
  
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 <s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 52.<emph.end type="center"/></s></p><p type="main"> <s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 52.<emph.end type="center"/></s></p><p type="main">
  
 <s><emph type="italics"/>Si linea motus &longs;it inter vtramque; est minus impedimentum.<emph.end type="italics"/> &longs;it globus <lb/>immobilis BA; &longs;it linea motus GC cum impedimento, de qua in Th. 50. <lb/>&longs;it alia KB cum nullo impedimento, de qua in Th. </s> <s><emph type="italics"/>Si linea motus &longs;it inter vtramque; est minus impedimentum.<emph.end type="italics"/> &longs;it globus <lb/>immobilis BA; &longs;it linea motus GC cum impedimento, de qua in Th. 50. <lb/>&longs;it alia KB cum nullo impedimento, de qua in Th. 51. &longs;int ali&aelig; HD, <lb/>IE; cert&egrave; minus e&longs;t impedimentum in contactu D, qu&agrave;m in C; quia ca&shy;<lb/>dit obliqu&egrave; in D, perinde atque &longs;i caderet in tangentem NO; Igitur <lb/>minus impeditur; in qua vero proportione, dicemus ali&agrave;s, cum de re&shy;<lb/>flexione, &amp; de motu mixto. </s></p><p type="main">
  
 <s>51. &longs;int ali&aelig; HD, <lb/>IE; cert&egrave; minus e&longs;t impedimentum in contactu D, qu&agrave;m in C; quia ca&shy;<lb/>dit obliqu&egrave; in D, perinde atque &longs;i caderet in tangentem NO; Igitur <lb/>minus impeditur; in qua vero proportione, dicemus ali&agrave;s, cum de re&shy;<lb/>flexione, &amp; de motu mixto. </s></p><p type="main"> 
  
 <s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 53.<emph.end type="center"/></s></p><p type="main"> <s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 53.<emph.end type="center"/></s></p><p type="main">
  
 <s><emph type="italics"/>Hinc producitur in contactu<emph.end type="italics"/> C, <emph type="italics"/>totus impetus; in contactu<emph.end type="italics"/> D, <emph type="italics"/>min&ugrave;s; <gap/><lb/>contactu<emph.end type="italics"/> E <emph type="italics"/>adhuc min&ugrave;s; in<emph.end type="italics"/> B <emph type="italics"/>nihil<emph.end type="italics"/>; quia in ca proportione producitui <lb/>pl&ugrave;s vel min&ugrave;s impetus, quo pl&ugrave;s e&longs;t, vel min&ugrave;s impedimenti per <lb/>Th. 49. &longs;ed min&ugrave;s e&longs;t impedimentum in E, qu&agrave;m in C; &amp; in E, qu&agrave;m <lb/>in D, per Th. </s> <s><emph type="italics"/>Hinc producitur in contactu<emph.end type="italics"/> C, <emph type="italics"/>totus impetus; in contactu<emph.end type="italics"/> D, <emph type="italics"/>min&ugrave;s; <gap/><lb/>contactu<emph.end type="italics"/> E <emph type="italics"/>adhuc min&ugrave;s; in<emph.end type="italics"/> B <emph type="italics"/>nihil<emph.end type="italics"/>; quia in ca proportione producitui <lb/>pl&ugrave;s vel min&ugrave;s impetus, quo pl&ugrave;s e&longs;t, vel min&ugrave;s impedimenti per <lb/>Th. 49. &longs;ed min&ugrave;s e&longs;t impedimentum in E, qu&agrave;m in C; &amp; in E, qu&agrave;m <lb/>in D, per Th. 52; Igitur in D producitur min&ugrave;s impetus, qu&agrave;m in C, <lb/>&amp; min&ugrave;s in E, qu&agrave;m in D. </s></p><p type="main">
  
 <s>52; Igitur in D producitur min&ugrave;s impetus, qu&agrave;m in C, <lb/>&amp; min&ugrave;s in E, qu&agrave;m in D. </s></p><p type="main"> 
  
 <s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 54.<emph.end type="center"/></s></p><p type="main"> <s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 54.<emph.end type="center"/></s></p><p type="main">
  
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 <s><emph type="italics"/>Si linea directionis ducatur per centrum vtriu&longs;que globi, mobilis &longs;cilicet <lb/>&amp; immobilis, impetus producit totum impetum quem pote&longs;t producere &longs;iue in <lb/>maiori globo, &longs;iue in minori, &longs;iue in &aelig;quali<emph.end type="italics"/>; patet experientia; cuius ratio <lb/>e&longs;t; quia impetus e&longs;t cau&longs;a nece&longs;&longs;aria; Igitur idem impetus codem mo&shy;<lb/>do applicatus &aelig;quali tempore, &aelig;qualem &longs;emper effectum producit, per <lb/>Ax. </s> <s><emph type="italics"/>Si linea directionis ducatur per centrum vtriu&longs;que globi, mobilis &longs;cilicet <lb/>&amp; immobilis, impetus producit totum impetum quem pote&longs;t producere &longs;iue in <lb/>maiori globo, &longs;iue in minori, &longs;iue in &aelig;quali<emph.end type="italics"/>; patet experientia; cuius ratio <lb/>e&longs;t; quia impetus e&longs;t cau&longs;a nece&longs;&longs;aria; Igitur idem impetus codem mo&shy;<lb/>do applicatus &aelig;quali tempore, &aelig;qualem &longs;emper effectum producit, per <lb/>Ax. </s>
  
 <s>12. igitur cum impetus agat tant&ugrave;m, vt tollat impedimentum per <lb/>Th. 44. &amp; cum in pr&aelig;dicta linea agat quantum pote&longs;t per Th. </s> <s>12. igitur cum impetus agat tant&ugrave;m, vt tollat impedimentum per <lb/>Th. 44. &amp; cum in pr&aelig;dicta linea agat quantum pote&longs;t per Th. 50. cer&shy;<lb/>t&egrave; &aelig;qualem effectum producat nece&longs;&longs;e e&longs;t; &longs;iue in maiori &longs;iue in mino&shy;<lb/>ri, &longs;iue in &aelig;quali globo immobili. </s></p><p type="main">
  
 <s>50. cer&shy;<lb/>t&egrave; &aelig;qualem effectum producat nece&longs;&longs;e e&longs;t; &longs;iue in maiori &longs;iue in mino&shy;<lb/>ri, &longs;iue in &aelig;quali globo immobili. </s></p><p type="main"> 
  
 <s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 58.<emph.end type="center"/></s></p><p type="main"> <s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 58.<emph.end type="center"/></s></p><p type="main">
  
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 <s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 5.<emph.end type="center"/></s></p><p type="main"> <s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 5.<emph.end type="center"/></s></p><p type="main">
  
 <s><emph type="italics"/>Hinc motus naturalis e&longs;t ab impetu.<emph.end type="italics"/></s><s> Probatur; e&longs;t ab aliqua cau&longs;a per <lb/>Ax.8. lib.1. ab aliqua intrin&longs;eca per Th. 1. non &agrave; &longs;ub&longs;tantia corporis <lb/>grauis per Th. </s> <s><emph type="italics"/>Hinc motus naturalis e&longs;t ab impetu.<emph.end type="italics"/></s><s> Probatur; e&longs;t ab aliqua cau&longs;a per <lb/>Ax.8. lib.1. ab aliqua intrin&longs;eca per Th. 1. non &agrave; &longs;ub&longs;tantia corporis <lb/>grauis per Th. 3. non &agrave; grauitace per Th. 4. igitur ab impetu, quia <lb/>nihil aliud e&longs;&longs;e pote&longs;t intrin&longs;ecum, &agrave; quo &longs;it motus pet definitionem <lb/>3. lib.
  
 <s>3. non &agrave; grauitace per Th. </s> 
  
 <s>4. igitur ab impetu, quia <lb/>nihil aliud e&longs;&longs;e pote&longs;t intrin&longs;ecum, &agrave; quo &longs;it motus pet definitionem <lb/>3. lib.  
  
 1. </s></p><pb pagenum="81"/><p type="main"> 1. </s></p><pb pagenum="81"/><p type="main">
  
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 <s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 132.<emph.end type="center"/></s></p><p type="main"> <s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 132.<emph.end type="center"/></s></p><p type="main">
  
 <s><emph type="italics"/>Hinc cert&egrave; concludo contra Galileum, &amp; alios quo&longs;dam motum grauium <lb/>po&longs;t aliquod &longs;patium decur&longs;um ex naturaliter accelerato non fieri &aelig;quabilem,<emph.end type="italics"/><lb/>quia in tantum fieret &aelig;quabilis in quantum tanta e&longs;&longs;et re&longs;i&longs;tentia, vt no&shy;<lb/>uam accelerationem impediret; &longs;ed h&aelig;c ratio nulla e&longs;t; quia in eadem <lb/>ratione cre&longs;cit re&longs;i&longs;tentia, in qua cre&longs;cunt vires per Th. 129. igitur non <lb/>mutatur progre&longs;&longs;io motuum per Th. </s> <s><emph type="italics"/>Hinc cert&egrave; concludo contra Galileum, &amp; alios quo&longs;dam motum grauium <lb/>po&longs;t aliquod &longs;patium decur&longs;um ex naturaliter accelerato non fieri &aelig;quabilem,<emph.end type="italics"/><lb/>quia in tantum fieret &aelig;quabilis in quantum tanta e&longs;&longs;et re&longs;i&longs;tentia, vt no&shy;<lb/>uam accelerationem impediret; &longs;ed h&aelig;c ratio nulla e&longs;t; quia in eadem <lb/>ratione cre&longs;cit re&longs;i&longs;tentia, in qua cre&longs;cunt vires per Th. 129. igitur non <lb/>mutatur progre&longs;&longs;io motuum per Th. 130. igitur nec acceleratio; igitur <lb/>motus naturalis ex accelerato non fit &aelig;quabilis: Equidem, vt iam &longs;upr&agrave; <lb/>dictum e&longs;t, in minori &longs;emper ratione cre&longs;cit velocitas, it&eacute;mque ip&longs;a re&longs;i&shy;<lb/>&longs;tentia quod in omni progre&longs;&longs;ione arithmetica iuxta numeros 1.2.3.4.5. </s></p><p type="main">
  
 <s>130. igitur nec acceleratio; igitur <lb/>motus naturalis ex accelerato non fit &aelig;quabilis: Equidem, vt iam &longs;upr&agrave; <lb/>dictum e&longs;t, in minori &longs;emper ratione cre&longs;cit velocitas, it&eacute;mque ip&longs;a re&longs;i&shy;<lb/>&longs;tentia quod in omni progre&longs;&longs;ione arithmetica iuxta numeros 1.2.3.4.5. </s></p><p type="main"> 
  
 <s><emph type="center"/><emph type="italics"/>Scholium.<emph.end type="italics"/><emph.end type="center"/></s></p><p type="main"> <s><emph type="center"/><emph type="italics"/>Scholium.<emph.end type="italics"/><emph.end type="center"/></s></p><p type="main">
  
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 <s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 78.<emph.end type="center"/></s></p><p type="main"> <s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 78.<emph.end type="center"/></s></p><p type="main">
  
 <s><emph type="italics"/>Hinc reiicio omnes alias combinationes recepta &longs;exta; imm&ograve; &longs;extam <lb/>ip&longs;am ex parte<emph.end type="italics"/>; nec enim naturalis acceleratur in hoc motu in ea <lb/>proportione, in qua acceleratur per lineam perpendicularem deor&shy;<lb/>&longs;um per Th. 29.&longs;ed iuxta rationem planorum inclinatorum per Theo&shy;<lb/>rema 31. nec etiam violentus de&longs;truitur vniformiter, &longs;ed pro rata per <lb/>Th. </s> <s><emph type="italics"/>Hinc reiicio omnes alias combinationes recepta &longs;exta; imm&ograve; &longs;extam <lb/>ip&longs;am ex parte<emph.end type="italics"/>; nec enim naturalis acceleratur in hoc motu in ea <lb/>proportione, in qua acceleratur per lineam perpendicularem deor&shy;<lb/>&longs;um per Th. 29.&longs;ed iuxta rationem planorum inclinatorum per Theo&shy;<lb/>rema 31. nec etiam violentus de&longs;truitur vniformiter, &longs;ed pro rata per <lb/>Th. 39. </s></p><p type="main">
  
 <s>39. </s></p><p type="main"> 
  
 <s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 79.<emph.end type="center"/></s></p><p type="main"> <s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 79.<emph.end type="center"/></s></p><p type="main">
  
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 <s>Ob&longs;eruabis, lic&egrave;t i&longs;te motus non fiat per lineam parabolicam, vt &longs;upr&agrave; <lb/>demon&longs;trauimus Th. 54. &amp; reliquis; quia tamen &longs;en&longs;ibiliter proxim&egrave; <lb/>accedit, deinceps vtemur Parabola vt in fig. </s> <s>Ob&longs;eruabis, lic&egrave;t i&longs;te motus non fiat per lineam parabolicam, vt &longs;upr&agrave; <lb/>demon&longs;trauimus Th. 54. &amp; reliquis; quia tamen &longs;en&longs;ibiliter proxim&egrave; <lb/>accedit, deinceps vtemur Parabola vt in fig. </s>
  
 <s>Th. </s> <s>Th. 83. &amp; horizontalem <lb/>motum accipiemus pro &aelig;quabili; lic&egrave;t omnin&ograve; &aelig;quabilis non &longs;it; ni&longs;i <lb/>tant&ugrave;m &aelig;quiualenter; dixi &aelig;quiualenter, quia eodem modo &longs;e habet hic <lb/>motus, ac &longs;i per inclinatam &longs;ur&longs;um LC impetu &longs;cilicet LC mobile pro&shy;<lb/>iiceretur; &longs;ed in hoc ca&longs;u de&longs;trueretur impetus ille per inclinatam &longs;im&shy;<lb/>plex; igitur &amp; mixtus; quia tamen ille qui remanet partim ex LA, par&shy;<lb/>tim ex LF eodem modo fer&egrave; &longs;e habet ac &longs;i totus LF intactus maneret; <lb/>hinc dictum e&longs;t &longs;upr&agrave; &aelig;quiualenter e&longs;&longs;e &aelig;quabilem. </s></p><p type="main">
  
 <s>83. &amp; horizontalem <lb/>motum accipiemus pro &aelig;quabili; lic&egrave;t omnin&ograve; &aelig;quabilis non &longs;it; ni&longs;i <lb/>tant&ugrave;m &aelig;quiualenter; dixi &aelig;quiualenter, quia eodem modo &longs;e habet hic <lb/>motus, ac &longs;i per inclinatam &longs;ur&longs;um LC impetu &longs;cilicet LC mobile pro&shy;<lb/>iiceretur; &longs;ed in hoc ca&longs;u de&longs;trueretur impetus ille per inclinatam &longs;im&shy;<lb/>plex; igitur &amp; mixtus; quia tamen ille qui remanet partim ex LA, par&shy;<lb/>tim ex LF eodem modo fer&egrave; &longs;e habet ac &longs;i totus LF intactus maneret; <lb/>hinc dictum e&longs;t &longs;upr&agrave; &aelig;quiualenter e&longs;&longs;e &aelig;quabilem. </s></p><p type="main"> 
  
 <s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 87.<emph.end type="center"/></s></p><p type="main"> <s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 87.<emph.end type="center"/></s></p><p type="main">
  
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 <s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 30.<emph.end type="center"/></s></p><p type="main"> <s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 30.<emph.end type="center"/></s></p><p type="main">
  
 <s><emph type="italics"/>Hinc in planis in&aelig;qualibus t&ugrave;m in longitudine, t&ugrave;ns in inclinatione, <lb/>pote&longs;t &longs;<gap/>iri ratio temporum, quibus percurruntur<emph.end type="italics"/>; &longs;int enim AC AR duo pla&shy;<lb/>na; &longs;it autem AE perpendicularis indefinita; diuidatur AC bifariam <lb/>in V ducta perpendiculari VB; ex B fiat circulus, &longs;ecabit puncta <lb/>ACE; &longs;ecat etiam AR; in D igitur AC, &amp; AD percurruntur &aelig;quali <lb/>tempore per Th. 27. &longs;imiliter fiat circulus ART eodem modos cert&egrave; A <lb/>R &amp; AT percurruntur &aelig;qualibus temporibus per Th. </s> <s><emph type="italics"/>Hinc in planis in&aelig;qualibus t&ugrave;m in longitudine, t&ugrave;ns in inclinatione, <lb/>pote&longs;t &longs;<gap/>iri ratio temporum, quibus percurruntur<emph.end type="italics"/>; &longs;int enim AC AR duo pla&shy;<lb/>na; &longs;it autem AE perpendicularis indefinita; diuidatur AC bifariam <lb/>in V ducta perpendiculari VB; ex B fiat circulus, &longs;ecabit puncta <lb/>ACE; &longs;ecat etiam AR; in D igitur AC, &amp; AD percurruntur &aelig;quali <lb/>tempore per Th. 27. &longs;imiliter fiat circulus ART eodem modos cert&egrave; A <lb/>R &amp; AT percurruntur &aelig;qualibus temporibus per Th. 27. igitur tempus, <lb/>quopercurritur AR, vel AD e&longs;t ad tempus, quo percurritur AR vt <lb/>tempus, quo percurritur AE ad tempus, quo percurritur AT; &longs;ed h&aelig;c <pb pagenum="211"/>&longs;unt vt radices AEAT, id e&longs;t tempus quo percurritur AE e&longs;t ad tem&shy;<lb/>pus, quo percurritur AT, vt AE ad mediam proportionalem inter AE <lb/>AT, vel vt AD ad mediam proportionalem inter AD AR; quippe AD <lb/>e&longs;t ad AR vt AE ad AT. </s></p><p type="main">
  
 <s>27. igitur tempus, <lb/>quopercurritur AR, vel AD e&longs;t ad tempus, quo percurritur AR vt <lb/>tempus, quo percurritur AE ad tempus, quo percurritur AT; &longs;ed h&aelig;c <pb pagenum="211"/>&longs;unt vt radices AEAT, id e&longs;t tempus quo percurritur AE e&longs;t ad tem&shy;<lb/>pus, quo percurritur AT, vt AE ad mediam proportionalem inter AE <lb/>AT, vel vt AD ad mediam proportionalem inter AD AR; quippe AD <lb/>e&longs;t ad AR vt AE ad AT. </s></p><p type="main"> 
  
 <s>Galileus ver&ograve; demon&longs;trat rationem i&longs;torum temporum e&longs;&longs;e compo&longs;i&shy;<lb/>tam ex ratione longitudinem planorum &amp; ex ratione &longs;ubduplicata al&shy;<lb/>titudinum eorumdem permutatim accepta: pro quo ob&longs;erua &agrave; Galileo <lb/>rationem duplicatam appellari duplam, &amp; &longs;ubduplicatam appellari &longs;ub&shy;<lb/>duplam. </s></p><p type="main"> <s>Galileus ver&ograve; demon&longs;trat rationem i&longs;torum temporum e&longs;&longs;e compo&longs;i&shy;<lb/>tam ex ratione longitudinem planorum &amp; ex ratione &longs;ubduplicata al&shy;<lb/>titudinum eorumdem permutatim accepta: pro quo ob&longs;erua &agrave; Galileo <lb/>rationem duplicatam appellari duplam, &amp; &longs;ubduplicatam appellari &longs;ub&shy;<lb/>duplam. </s></p><p type="main">
  
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 <s>Th. 63. eiu&longs;dem incidenti&aelig; cum EA fig. </s> <s>Th. 63. eiu&longs;dem incidenti&aelig; cum EA fig. </s>
  
 <s>Th. </s> <s>Th. 65. igitur <lb/>globus A incidat per DB, &amp; globus B per MB, ita vt punctum conta&shy;<lb/>ctus &longs;it B, &amp; linea connectens centra FA; determinatio noua ratione in&shy;<lb/>cidenti&aelig; e&longs;t vt BH, cui addatur HF &aelig;qualis AY fig. </s>
  
 <s>65. igitur <lb/>globus A incidat per DB, &amp; globus B per MB, ita vt punctum conta&shy;<lb/>ctus &longs;it B, &amp; linea connectens centra FA; determinatio noua ratione in&shy;<lb/>cidenti&aelig; e&longs;t vt BH, cui addatur HF &aelig;qualis AY fig. </s> 
  
 <s>alterius ratione <lb/>motus impre&longs;&longs;i &agrave; globo B; tota determinatio erit BF; a&longs;&longs;umatur MT <lb/>&aelig;qualis BF: dico nouam lineam qu&aelig;&longs;itam e&longs;&longs;e B<foreign lang="greek">q</foreign> mixtam &longs;cilicet ex <lb/>BF BM, quod probatur vt &longs;upr&agrave;. </s></p><p type="main"> <s>alterius ratione <lb/>motus impre&longs;&longs;i &agrave; globo B; tota determinatio erit BF; a&longs;&longs;umatur MT <lb/>&aelig;qualis BF: dico nouam lineam qu&aelig;&longs;itam e&longs;&longs;e B<foreign lang="greek">q</foreign> mixtam &longs;cilicet ex <lb/>BF BM, quod probatur vt &longs;upr&agrave;. </s></p><p type="main">
  
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 <s>in fig. </s> <s>in fig. </s>
  
 <s>Th. </s> <s>Th. 65. determinatio noua <lb/>po&longs;ita perpendiculari &longs;it ad priorem vt AZ ad AF, ita vt per mediam <lb/>aquam conficiat tant&ugrave;m &longs;patium A<foreign lang="greek">d</foreign> v. </s>
  
 <s>65. determinatio noua <lb/>po&longs;ita perpendiculari &longs;it ad priorem vt AZ ad AF, ita vt per mediam <lb/>aquam conficiat tant&ugrave;m &longs;patium A<foreign lang="greek">d</foreign> v. </s> 
  
 <s>g. </s> <s>g. </s>
  

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