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Colored diff for /texts/archimedes/xml/Attic/cevag_geome_01_la_1692.xml between version 1.15 and 1.16

version 1.15, 2002/08/18 15:51:15 version 1.16, 2002/08/18 18:41:08
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 <s>Similiter cum &longs;it, vt BA ad AE, ita CA <lb/>ad AF, etiam BC, EF inter&longs;e &aelig;quidi&longs;tabunt, &longs;eu ad hori&shy;<lb/>zontem &aelig;qualiter inclinabuntur, eruntque in ratione ea&shy;<lb/>dem, ac BA ad AE. </s> <s>Similiter cum &longs;it, vt BA ad AE, ita CA <lb/>ad AF, etiam BC, EF inter&longs;e &aelig;quidi&longs;tabunt, &longs;eu ad hori&shy;<lb/>zontem &aelig;qualiter inclinabuntur, eruntque in ratione ea&shy;<lb/>dem, ac BA ad AE. </s>
  
 <s>Idemque o&longs;tenditur de chordis CD, <lb/>FG, quare ex magni Galilei &longs;ententia de motu naturaliter <lb/>accelerato indubitanter &longs;equitur tempus decur&longs;us &longs;ph&aelig;r&aelig; <lb/>grauis ex B in D per binas chordas BC, CD ad tempus <lb/>decur&longs;us per vnicam BD, e&longs;&longs;e vt tempus decur&longs;us grauis <lb/>&longs;ph&aelig;r&aelig; ex E in G per binas EF, FG ad tempus decur&longs;us <lb/>per vnicam EG: cadem itidem ratione demon&longs;tratur (an&shy;<lb/>gulis pariter BAC, CAD bifariam &longs;ectis per rectas, qu&aelig; <lb/>&longs;imiles arcus BC, EF, ac CD, FG duas in partes diuidant) <lb/>ex quatuor vtrinque arcuum horum cordis, illas inter&longs;e <pb pagenum="57"/>homologas, &longs;imile&longs;que arcus &longs;ubtendentes ad horizonte m <lb/>e&longs;&longs;e &aelig;qualiter inclinatas, ac alteram alteri in ratione ea&shy;<lb/>dem, in qua &longs;unt rect&aelig; AB, AE &amp;c: ac propterea ex ea&shy;<lb/>dem Galilei &longs;cientia con&longs;tabit vtique, tempus decur&longs;us ex <lb/>B in C &longs;ph&aelig;r&aelig; grauis B per quatuor chordas quatuor par&shy;<lb/>tes arcus BCD &longs;ubtendentes ad tempus decur&longs;us per vni&shy;<lb/>cam BD, e&longs;&longs;e vt tempus decur&longs;us &longs;ph&aelig;r&aelig; grauis E ex E in <lb/>G per quatuor illis homologas chordas quatuor partes <lb/>arcus EFG pariter &longs;ubtendentes ad tempus decur&longs;us per <lb/>vnicam chordam EG: &amp; hoc &longs;emper ita euenire demon&shy;<lb/>&longs;trabitur quantacunque, &amp; maxima fuerit in perpetua an&shy;<lb/>gulorum bi&longs;ectione &aelig;qu&egrave;multiplicitas in vtroque arcu <lb/>talium chordarum homolog&egrave; &longs;umptarum, ac inter&longs;e pro&shy;<lb/>portionalium, &aelig;qualiterque ad horizontem inclinatarum: <lb/>Propterquam qu&ograve;d &longs;emper decur&longs;us ex B in D per aggre&shy;<lb/>gatum chordarum omnium in arcu BCD ad tempus de&shy;<lb/>cur&longs;us per &longs;olam chordam BD e&longs;&longs;e vt tempus decur&longs;us ex <lb/>E in G per aggregatum totidem chordarum in arcu EFG <lb/>ad tempus decur&longs;us per vnicam chordam EG; adeo vt de&shy;<lb/>nique iure optimo educi po&longs;&longs;e videatur, tempus decur&longs;us <lb/>grauis ex B in D per aggregatum infinitarum chordarum <lb/>totum arcum BCD con&longs;tituentium, &longs;eu tempus per ip&longs;um <lb/>arcum BCD ad tempus decur&longs;us per &longs;olam cordam BD <lb/>e&longs;&longs;e vt tempus decur&longs;us grauis ex E in G per aggregatum <lb/>totidem infinitarum chordarum dictis homolog&egrave; propor&shy;<lb/>tionalium, &aelig;qualiterque &longs;ingul&aelig; &longs;ingulis ad horizonte&mtail; <lb/>inclinatarum, ac totum arcum EFG conformantium, &longs;iue <lb/>vt tempus per ip&longs;um arcum EFG per &longs;olam chordam EG. <lb/></s> <s>Idemque o&longs;tenditur de chordis CD, <lb/>FG, quare ex magni Galilei &longs;ententia de motu naturaliter <lb/>accelerato indubitanter &longs;equitur tempus decur&longs;us &longs;ph&aelig;r&aelig; <lb/>grauis ex B in D per binas chordas BC, CD ad tempus <lb/>decur&longs;us per vnicam BD, e&longs;&longs;e vt tempus decur&longs;us grauis <lb/>&longs;ph&aelig;r&aelig; ex E in G per binas EF, FG ad tempus decur&longs;us <lb/>per vnicam EG: eadem itidem ratione demon&longs;tratur (an&shy;<lb/>gulis pariter BAC, CAD bifariam &longs;ectis per rectas, qu&aelig; <lb/>&longs;imiles arcus BC, EF, ac CD, FG duas in partes diuidant) <lb/>ex quatuor vtrinque arcuum horum cordis, illas inter&longs;e <pb pagenum="57"/>homologas, &longs;imile&longs;que arcus &longs;ubtendentes ad horizonte m <lb/>e&longs;&longs;e &aelig;qualiter inclinatas, ac alteram alteri in ratione ea&shy;<lb/>dem, in qua &longs;unt rect&aelig; AB, AE &amp;c: ac propterea ex ea&shy;<lb/>dem Galilei &longs;cientia con&longs;tabit vtique, tempus decur&longs;us ex <lb/>B in C &longs;ph&aelig;r&aelig; grauis B per quatuor chordas quatuor par&shy;<lb/>tes arcus BCD &longs;ubtendentes ad tempus decur&longs;us per vni&shy;<lb/>cam BD, e&longs;&longs;e vt tempus decur&longs;us &longs;ph&aelig;r&aelig; grauis E ex E in <lb/>G per quatuor illis homologas chordas quatuor partes <lb/>arcus EFG pariter &longs;ubtendentes ad tempus decur&longs;us per <lb/>vnicam chordam EG: &amp; hoc &longs;emper ita euenire demon&shy;<lb/>&longs;trabitur quantacunque, &amp; maxima fuerit in perpetua an&shy;<lb/>gulorum bi&longs;ectione &aelig;qu&egrave;multiplicitas in vtroque arcu <lb/>talium chordarum homolog&egrave; &longs;umptarum, ac inter&longs;e pro&shy;<lb/>portionalium, &aelig;qualiterque ad horizontem inclinatarum: <lb/>Propterquam qu&ograve;d &longs;emper decur&longs;us ex B in D per aggre&shy;<lb/>gatum chordarum omnium in arcu BCD ad tempus de&shy;<lb/>cur&longs;us per &longs;olam chordam BD e&longs;&longs;e vt tempus decur&longs;us ex <lb/>E in G per aggregatum totidem chordarum in arcu EFG <lb/>ad tempus decur&longs;us per vnicam chordam EG; adeo vt de&shy;<lb/>nique iure optimo educi po&longs;&longs;e videatur, tempus decur&longs;us <lb/>grauis ex B in D per aggregatum infinitarum chordarum <lb/>totum arcum BCD con&longs;tituentium, &longs;eu tempus per ip&longs;um <lb/>arcum BCD ad tempus decur&longs;us per &longs;olam cordam BD <lb/>e&longs;&longs;e vt tempus decur&longs;us grauis ex E in G per aggregatum <lb/>totidem infinitarum chordarum dictis homolog&egrave; propor&shy;<lb/>tionalium, &aelig;qualiterque &longs;ingul&aelig; &longs;ingulis ad horizonte&mtail; <lb/>inclinatarum, ac totum arcum EFG conformantium, &longs;iue <lb/>vt tempus per ip&longs;um arcum EFG per &longs;olam chordam EG. <lb/></s>
  
 <s>Quocirca permutando, tempus, decur&longs;us &longs;ph&aelig;r&aelig; grauis B <lb/>per arcum BCD ad tempus decur&longs;us &longs;ph&aelig;r&aelig; grauis E per <lb/>arcum &longs;imilem, &longs;imiliterque po&longs;itum EG erit vt tempus <lb/>decur&longs;us per chordam BD ad tempus decur&longs;us per chor&shy;<lb/>dam EG; &longs;ed ex eadem Galilaica &longs;cientia de motu, tempus <lb/>decur&longs;us per chordam BD ad tempus decur&longs;us per &aelig;qua-<pb pagenum="58"/>iter inclinatam EG e&longs;t in &longs;ubduplicata ratione ip&longs;aru&mtail; <lb/>chordarum BD, EG; ergo tempus quoque decur&longs;us ex B <lb/>per arcum BCD ad tempus decur&longs;us ex E per arcum EFG <lb/>e&longs;t in eadem &longs;ubduplicata ratione chord&ecedil; BD ad chordam <lb/>EG, quod o&longs;tendendum propo&longs;uimus. </s></p><p type="main"> <s>Quocirca permutando, tempus, decur&longs;us &longs;ph&aelig;r&aelig; grauis B <lb/>per arcum BCD ad tempus decur&longs;us &longs;ph&aelig;r&aelig; grauis E per <lb/>arcum &longs;imilem, &longs;imiliterque po&longs;itum EG erit vt tempus <lb/>decur&longs;us per chordam BD ad tempus decur&longs;us per chor&shy;<lb/>dam EG; &longs;ed ex eadem Galilaica &longs;cientia de motu, tempus <lb/>decur&longs;us per chordam BD ad tempus decur&longs;us per &aelig;qua-<pb pagenum="58"/>iter inclinatam EG e&longs;t in &longs;ubduplicata ratione ip&longs;aru&mtail; <lb/>chordarum BD, EG; ergo tempus quoque decur&longs;us ex B <lb/>per arcum BCD ad tempus decur&longs;us ex E per arcum EFG <lb/>e&longs;t in eadem &longs;ubduplicata ratione chord&ecedil; BD ad chordam <lb/>EG, quod o&longs;tendendum propo&longs;uimus. </s></p><p type="main">
  

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