Main  History  Search  Repository tree

[BACK] Return to bianc_locam_01_la_1615.xml CVS log [TXT][DIR] Up to [CVSROOT] / texts / archimedes / xml

Colored diff for /texts/archimedes/xml/Attic/bianc_locam_01_la_1615.xml between version 1.54 and 1.55

version 1.54, 2002/08/15 00:20:57 version 1.55, 2002/08/15 00:36:20
Line 2537 
Line 2537 
  
 Euclidis percipi pote&longs;t. </s> Euclidis percipi pote&longs;t. </s>
  
 <s>vt propterea ben&egrave; ij <lb/>&longs;entiant, inter quos pr&aelig;cipui &longs;unt Toletus, &amp; Zabarella, qui a&longs;&longs;erunt, Ari&longs;t. <lb/></s> <s>vt propterea ben&egrave; ij <lb/>&longs;entiant, inter quos pr&aelig;cipui &longs;unt Toletus, &amp; Zabarella, qui a&longs;&longs;erunt, Ari&longs;t. <lb/>Mathematicas &longs;cientias tamquam typum perfecti&longs;simarum &longs;cientiarum <lb/>&longs;ibi ob oculos propo&longs;ui&longs;&longs;e; ex quo typo ver&aelig; &longs;cienti&aelig; de&longs;criptionem his li&shy;<lb/>bris complectaretur.</s></p><p type="main">
  
 <s>Mathematicas &longs;cientias tamquam typum perfecti&longs;simarum &longs;cientiarum <lb/>&longs;ibi ob oculos propo&longs;ui&longs;&longs;e; ex quo typo ver&aelig; &longs;cienti&aelig; de&longs;criptionem his li&shy;<lb/>bris complectaretur.</s></p><p type="main"> 
  
 <s><arrow.to.target n="marg22"></arrow.to.target></s></p><p type="margin"> <s><arrow.to.target n="marg22"></arrow.to.target></s></p><p type="margin">
  
Line 3829 
Line 3827 
  
 <s>Tex. 31. <emph type="italics"/>(Vtuntur etiam Mathematici infinito)<emph.end type="italics"/> <expan abbr="aliqu&atilde;do">aliquando</expan> Mathematici du&shy;<lb/>cunt lineas quantumuis longas, &longs;eu indefinit&aelig; longitudinis, quas etiam in&shy;<lb/>finitas appellant: &amp; hoc modo vtuntur infinito, vt infra tex. </s> <s>Tex. 31. <emph type="italics"/>(Vtuntur etiam Mathematici infinito)<emph.end type="italics"/> <expan abbr="aliqu&atilde;do">aliquando</expan> Mathematici du&shy;<lb/>cunt lineas quantumuis longas, &longs;eu indefinit&aelig; longitudinis, quas etiam in&shy;<lb/>finitas appellant: &amp; hoc modo vtuntur infinito, vt infra tex. </s>
  
 <s>71. ip&longs;e Ari&longs;t. <lb/></s> <s>71. ip&longs;e Ari&longs;t. <lb/>exponit. </s>
  
 <s>exponit. </s> 
  
 <s>alio pr&aelig;terea modo vtuntur infinito, vt quando &longs;upponunt data <lb/>quauis quantitate po&longs;&longs;e &longs;umi maiorem, vel etiam minorem in infinitum, vt <lb/>patet ex 6. po&longs;tulato primi Elem.  <s>alio pr&aelig;terea modo vtuntur infinito, vt quando &longs;upponunt data <lb/>quauis quantitate po&longs;&longs;e &longs;umi maiorem, vel etiam minorem in infinitum, vt <lb/>patet ex 6. po&longs;tulato primi Elem.
  
Line 5473 
Line 5469 
  
 <s>Nunc ad textus declarationem, in <lb/>quo continetur Geometrica demon&longs;tratio rotunditatis Are&aelig;, quam &longs;ic bre&shy;<lb/>uiter prius veteres excogitarunt: Viderunt prim&ograve; Solem in Area apparere <lb/>in orbem, &amp; con&longs;imiliter: hinc intulerunt nece&longs;&longs;e e&longs;&longs;e apparere etiam per <lb/>con&longs;imiles, &longs;iue &aelig;quales refractionis angulos; quia diuer&longs;i anguli, diuer&longs;am <lb/>etiam <expan abbr="appar&etilde;tiam">apparentiam</expan> efficiunt: atqui con&longs;imiles, &longs;iue &aelig;quales refractionis an&shy;<lb/>gulos nece&longs;&longs;e e&longs;t in circulum <expan abbr="c&otilde;&longs;titui">con&longs;titui</expan>, vt mox con&longs;tabit; cau&longs;a igitur rotun&shy;<lb/>ditatis huius, e&longs;t angulorum refractionis &aelig;qualitas. </s> <s>Nunc ad textus declarationem, in <lb/>quo continetur Geometrica demon&longs;tratio rotunditatis Are&aelig;, quam &longs;ic bre&shy;<lb/>uiter prius veteres excogitarunt: Viderunt prim&ograve; Solem in Area apparere <lb/>in orbem, &amp; con&longs;imiliter: hinc intulerunt nece&longs;&longs;e e&longs;&longs;e apparere etiam per <lb/>con&longs;imiles, &longs;iue &aelig;quales refractionis angulos; quia diuer&longs;i anguli, diuer&longs;am <lb/>etiam <expan abbr="appar&etilde;tiam">apparentiam</expan> efficiunt: atqui con&longs;imiles, &longs;iue &aelig;quales refractionis an&shy;<lb/>gulos nece&longs;&longs;e e&longs;t in circulum <expan abbr="c&otilde;&longs;titui">con&longs;titui</expan>, vt mox con&longs;tabit; cau&longs;a igitur rotun&shy;<lb/>ditatis huius, e&longs;t angulorum refractionis &aelig;qualitas. </s>
  
 <s>Sed iam textum Ari&longs;t. <lb/></s> <s>Sed iam textum Ari&longs;t. <lb/>qui geometricam huius rci continet demon&longs;trationem, explicemus. </s>
  
 <s>qui geometricam huius rci continet demon&longs;trationem, explicemus. </s> 
  
 <s>Suppo&shy;<lb/>nit igitur prim&ograve; Ari&longs;t.  <s>Suppo&shy;<lb/>nit igitur prim&ograve; Ari&longs;t.
  
Line 5651 
Line 5645 
  
 <s>Deinde vt &longs;e habet F, ad K G. ita &longs;it <lb/>B, ad aliam, qu&aelig; &longs;it K P, in eadem figura per 12. 6. &amp; &agrave; puncto P, ad M, iun&shy;<lb/>gatur recta P M. </s> <s>Deinde vt &longs;e habet F, ad K G. ita &longs;it <lb/>B, ad aliam, qu&aelig; &longs;it K P, in eadem figura per 12. 6. &amp; &agrave; puncto P, ad M, iun&shy;<lb/>gatur recta P M. </s>
  
 <s>Dico P, e&longs;&longs;e polum circuli, quem dixi Iridis, &amp; in quem li&shy;<lb/>ne&aelig; &agrave; K, procedentes turbinis formam effingunt, probatur autem ab Ari&longs;t. <lb/></s> <s>Dico P, e&longs;&longs;e polum circuli, quem dixi Iridis, &amp; in quem li&shy;<lb/>ne&aelig; &agrave; K, procedentes turbinis formam effingunt, probatur autem ab Ari&longs;t. <lb/>in &longs;equentibus.</s></p><p type="main">
  
 <s>in &longs;equentibus.</s></p><p type="main"> 
  
 <s><arrow.to.target n="marg167"></arrow.to.target></s></p><p type="margin"> <s><arrow.to.target n="marg167"></arrow.to.target></s></p><p type="margin">
  
Line 6789 
Line 6781 
  
 <s>Qvidquid Mathematicum in his qu&aelig;&longs;tionibus occurret, illud, vt <lb/>plurimum per paraphra&longs;im exponemus, ita tamen, vt tex. </s> <s>Qvidquid Mathematicum in his qu&aelig;&longs;tionibus occurret, illud, vt <lb/>plurimum per paraphra&longs;im exponemus, ita tamen, vt tex. </s>
  
 <s>Ari&longs;t. <lb/></s> <s>Ari&longs;t. <lb/>&amp; figur&aelig; textui re&longs;pondentes per eam, quantum fieri poterit re&shy;<lb/>&longs;tituantur, &amp; &longs;i qu&aelig; &longs;e offerent difficilia, pro viribus &longs;oluantur. <lb/></s>
  
 <s>&amp; figur&aelig; textui re&longs;pondentes per eam, quantum fieri poterit re&shy;<lb/>&longs;tituantur, &amp; &longs;i qu&aelig; &longs;e offerent difficilia, pro viribus &longs;oluantur. <lb/></s> 
  
 <s>E&longs;t autem nonnullis in locis textus tam gr&aelig;cus, qu&agrave;m latinus ade&ograve; corrup&shy;<lb/>tus, ac deprauatus, vt nullo modo emendari queat.</s></p><p type="head"> <s>E&longs;t autem nonnullis in locis textus tam gr&aelig;cus, qu&agrave;m latinus ade&ograve; corrup&shy;<lb/>tus, ac deprauatus, vt nullo modo emendari queat.</s></p><p type="head">
  
Line 8349 
Line 8339 
  
 <s>&longs;ed cau&longs;a e&longs;t, quia in <lb/>vortice aqua ip &longs;a &longs;piratim circumcurrens tandem in centrum, vbi demer&shy;<lb/>gitur de&longs;cendit; nece&longs;&longs;e igitur e&longs;t, vt etiam ea, qu&aelig; in ip&longs;a &longs;unt, &longs;imul cum <lb/>illa ad centrum per plures conuolutiones deducantur. </s> <s>&longs;ed cau&longs;a e&longs;t, quia in <lb/>vortice aqua ip &longs;a &longs;piratim circumcurrens tandem in centrum, vbi demer&shy;<lb/>gitur de&longs;cendit; nece&longs;&longs;e igitur e&longs;t, vt etiam ea, qu&aelig; in ip&longs;a &longs;unt, &longs;imul cum <lb/>illa ad centrum per plures conuolutiones deducantur. </s>
  
 <s>C&aelig;terum &longs;i quis ve&shy;<lb/>lit Mechanicam facultatem &longs;eri&ograve; aggredi, nequaquam paucis his ab Ari&longs;t. <lb/></s> <s>C&aelig;terum &longs;i quis ve&shy;<lb/>lit Mechanicam facultatem &longs;eri&ograve; aggredi, nequaquam paucis his ab Ari&longs;t. <lb/>traditis, <expan abbr="eis&qacute;">eisque</expan>; leui brachio pertractatis, contentus &longs;it: ver&ugrave;m Archimedem <lb/>de Aqu&aelig;ponderantibus, Commandinum, ac Lucam Valerium de centro <lb/>grauitatis &longs;olidorum, ac tandem Guidi Vbaldi Mechanica adeat, vbi hu&shy;<lb/>ius &longs;cienti&aelig; admiranda plurima, <expan abbr="ea&qacute;">eaque</expan>; firmi&longs;&longs;im&egrave; demon&longs;trata reperiet.</s></p><figure></figure><p type="head">
  
 <s>traditis, <expan abbr="eis&qacute;">eisque</expan>; leui brachio pertractatis, contentus &longs;it: ver&ugrave;m Archimedem <lb/>de Aqu&aelig;ponderantibus, Commandinum, ac Lucam Valerium de centro <lb/>grauitatis &longs;olidorum, ac tandem Guidi Vbaldi Mechanica adeat, vbi hu&shy;<lb/>ius &longs;cienti&aelig; admiranda plurima, <expan abbr="ea&qacute;">eaque</expan>; firmi&longs;&longs;im&egrave; demon&longs;trata reperiet.</s></p><figure></figure><p type="head"> 
  
 <s><emph type="italics"/>IN LIBELLVM DE MVNDO<emph.end type="italics"/></s></p><p type="head"> <s><emph type="italics"/>IN LIBELLVM DE MVNDO<emph.end type="italics"/></s></p><p type="head">
  
Line 9160 
Line 9148 
  
 <s>Lib. 1. cap.  <s>Lib. 1. cap.
  
 7. <emph type="italics"/>(Faber enim, &amp; Geometra diuer&longs;o modo rectum angulum <lb/><expan abbr="vtriq;">vtrique</expan> con&longs;iderant: ille quatenus <expan abbr="&longs;ol&utilde;">&longs;olum</expan> ad opus vtile e&longs;t, hic ver&ograve; cum ve&shy;<lb/>ritatis &longs;peculator &longs;it, quid, &amp; qualis &longs;it, indagat)<emph.end type="italics"/> Id quod dicit Ari&longs;t. <lb/></s> 7. <emph type="italics"/>(Faber enim, &amp; Geometra diuer&longs;o modo rectum angulum <lb/><expan abbr="vtriq;">vtrique</expan> con&longs;iderant: ille quatenus <expan abbr="&longs;ol&utilde;">&longs;olum</expan> ad opus vtile e&longs;t, hic ver&ograve; cum ve&shy;<lb/>ritatis &longs;peculator &longs;it, quid, &amp; qualis &longs;it, indagat)<emph.end type="italics"/> Id quod dicit Ari&longs;t. <lb/>confirmatur ex eo, quod Fabri omnes vtuntur amu&longs;&longs;i, &longs;eu norma, <lb/><figure id="fig130"></figure><lb/>qu&aelig; nihil aliud e&longs;t qu&agrave;m angulus rectus, qu&aelig; vulg&ograve; <lb/>&longs;quadra dicitur, vt eius auxilio angulum ip&longs;um re&shy;<lb/>ctum in opus conferant, <expan abbr="&longs;ic&qacute;">&longs;icque</expan>; norm&aelig;, aut amu&longs;&longs;is du&shy;<lb/>ctu &longs;ua ip&longs;i opera ad angulos rectos, ide&longs;t quadrata, <lb/>conficiunt. </s>
  
 <s>confirmatur ex eo, quod Fabri omnes vtuntur amu&longs;&longs;i, &longs;eu norma, <lb/><figure id="fig130"></figure><lb/>qu&aelig; nihil aliud e&longs;t qu&agrave;m angulus rectus, qu&aelig; vulg&ograve; <lb/>&longs;quadra dicitur, vt eius auxilio angulum ip&longs;um re&shy;<lb/>ctum in opus conferant, <expan abbr="&longs;ic&qacute;">&longs;icque</expan>; norm&aelig;, aut amu&longs;&longs;is du&shy;<lb/>ctu &longs;ua ip&longs;i opera ad angulos rectos, ide&longs;t quadrata, <lb/>conficiunt. </s> 
  
 <s>Geometra ver&ograve; con&longs;iderat eundem an&shy;<lb/>gulum, quatenus fit &agrave; linea &longs;uper lineam aliam per&shy;<lb/>pendiculariter in&longs;i&longs;tente, vt e&longs;t in definit. </s> <s>Geometra ver&ograve; con&longs;iderat eundem an&shy;<lb/>gulum, quatenus fit &agrave; linea &longs;uper lineam aliam per&shy;<lb/>pendiculariter in&longs;i&longs;tente, vt e&longs;t in definit. </s>
  
Line 12070 
Line 12056 
  
 1. Priorum, &longs;ecto <lb/>3. cap.  1. Priorum, &longs;ecto <lb/>3. cap.
  
 3. de hac trianguli proprietate annotaui, cuius etiam &longs;&aelig;pius Ari&longs;t. <lb/></s> 3. de hac trianguli proprietate annotaui, cuius etiam &longs;&aelig;pius Ari&longs;t. <lb/>meminit, nunquam tamen verbum illud, internos, pr&aelig;terquam hic, addi&shy;<lb/>dit; vt autem ben&egrave; intelligas quinam &longs;int hi anguli interni, &amp; qui externi, <lb/>&amp; quod etiam rectis externi &aelig;quiualeat, lege qu&aelig; ad tex. </s>
  
 <s>meminit, nunquam tamen verbum illud, internos, pr&aelig;terquam hic, addi&shy;<lb/>dit; vt autem ben&egrave; intelligas quinam &longs;int hi anguli interni, &amp; qui externi, <lb/>&amp; quod etiam rectis externi &aelig;quiualeat, lege qu&aelig; ad tex. </s> 
  
 <s>39. primi Po&longs;ter, <lb/>&longs;unt annotata.</s></p><p type="head"> <s>39. primi Po&longs;ter, <lb/>&longs;unt annotata.</s></p><p type="head">
  
Line 12920 
Line 12904 
  
 <s>videas Lector, qu&agrave;m &longs;yncer&egrave; natu&shy;<lb/>ralis philo&longs;ophi&aelig; profe&longs;&longs;or vera de Mathematicis loquatur, ita vt etiam eas <lb/>illi pr&aelig;ferat. </s> <s>videas Lector, qu&agrave;m &longs;yncer&egrave; natu&shy;<lb/>ralis philo&longs;ophi&aelig; profe&longs;&longs;or vera de Mathematicis loquatur, ita vt etiam eas <lb/>illi pr&aelig;ferat. </s>
  
 <s>Iacobus autem Zabarella in toto &longs;uo opere logico, perpetu&ograve; <lb/>Mathematicas demon&longs;tcationes, vt poti&longs;&longs;imas agno&longs;cit, <expan abbr="exempla&qacute;">exemplaque</expan>; Ari&longs;t. <lb/></s> <s>Iacobus autem Zabarella in toto &longs;uo opere logico, perpetu&ograve; <lb/>Mathematicas demon&longs;tcationes, vt poti&longs;&longs;imas agno&longs;cit, <expan abbr="exempla&qacute;">exemplaque</expan>; Ari&longs;t. <lb/>geometrica exponit tanquam vera, &amp; omnino rebus ip&longs;is accommodata; <lb/>quare non e&longs;t, cur vnum, aut alterum ip&longs;ius locum hic de&longs;cribamus. </s>
  
 <s>geometrica exponit tanquam vera, &amp; omnino rebus ip&longs;is accommodata; <lb/>quare non e&longs;t, cur vnum, aut alterum ip&longs;ius locum hic de&longs;cribamus. </s> 
  
 <s>illud <lb/>non pr&aelig;termittam, ip&longs;um fateri &longs;e bis, teru&egrave; totum Euclidem &longs;edul&ograve; perle&shy;<lb/>gi&longs;&longs;e, vt prob&egrave; po&longs;&longs;et Ari&longs;t.  <s>illud <lb/>non pr&aelig;termittam, ip&longs;um fateri &longs;e bis, teru&egrave; totum Euclidem &longs;edul&ograve; perle&shy;<lb/>gi&longs;&longs;e, vt prob&egrave; po&longs;&longs;et Ari&longs;t.
  
Line 13854 
Line 13836 
  
 <s>Porr&ograve; inter practicas omnium pr&aelig;&longs;tanti&longs;&longs;i&shy;<lb/>ma e&longs;t Geometria practica; quis enim non admiratur, c&ugrave;m audit Geome&shy;<lb/>tram &longs;olo vi&longs;u inacce&longs;&longs;as etiam magnitudines qua&longs;cunque, vt turres, vel <lb/>montes men&longs;urare?</s></p><p type="main"> <s>Porr&ograve; inter practicas omnium pr&aelig;&longs;tanti&longs;&longs;i&shy;<lb/>ma e&longs;t Geometria practica; quis enim non admiratur, c&ugrave;m audit Geome&shy;<lb/>tram &longs;olo vi&longs;u inacce&longs;&longs;as etiam magnitudines qua&longs;cunque, vt turres, vel <lb/>montes men&longs;urare?</s></p><p type="main">
  
 <s>Ex quibus liquid&ograve; con&longs;tant Mathematicas habere perfecti&longs;&longs;imas <expan abbr="dom&otilde;-&longs;trationes">domon&shy;<lb/>&longs;trationes</expan>, quarum cau&longs;&ecedil; ita ab effectu di&longs;tinguntur, vt nullis calumnijs &longs;int <lb/>obnoxi&aelig;: quare etiam &longs;i aduer&longs;arij conuincant, qu&ograve;d neutiquam faciunt, <lb/>Geometriam, &amp; Arithmeticam illis carere; reliquis tamen pr&aelig;dictis con&shy;<lb/>cedere coguntur: <expan abbr="eas&qacute;">easque</expan>; per omne <expan abbr="cau&longs;ar&utilde;">cau&longs;arum</expan> genus excurrere, qu&ograve;d tan&shy;<lb/>ta pr&aelig;terea euidentia pr&aelig;&longs;tant, vt nibl ambiguum, nihil contro&shy;<lb/>uer&longs;um relinquatur: Mathematic&ecedil; <expan abbr="namq;">namque</expan> te&longs;te etiam Ari&longs;t. <lb/></s> <s>Ex quibus liquid&ograve; con&longs;tant Mathematicas habere perfecti&longs;&longs;imas <expan abbr="dom&otilde;-&longs;trationes">domon&shy;<lb/>&longs;trationes</expan>, quarum cau&longs;&ecedil; ita ab effectu di&longs;tinguntur, vt nullis calumnijs &longs;int <lb/>obnoxi&aelig;: quare etiam &longs;i aduer&longs;arij conuincant, qu&ograve;d neutiquam faciunt, <lb/>Geometriam, &amp; Arithmeticam illis carere; reliquis tamen pr&aelig;dictis con&shy;<lb/>cedere coguntur: <expan abbr="eas&qacute;">easque</expan>; per omne <expan abbr="cau&longs;ar&utilde;">cau&longs;arum</expan> genus excurrere, qu&ograve;d tan&shy;<lb/>ta pr&aelig;terea euidentia pr&aelig;&longs;tant, vt nibl ambiguum, nihil contro&shy;<lb/>uer&longs;um relinquatur: Mathematic&ecedil; <expan abbr="namq;">namque</expan> te&longs;te etiam Ari&longs;t. <lb/>1. Elenchorum non &longs;unt contentio&longs;&aelig;. </s>
  
 <s>1. Elenchorum non &longs;unt contentio&longs;&aelig;. </s> 
  
 <s>Vnde &longs;it, vt to&shy;<lb/>ta h&aelig;c ade&ograve; digna, <expan abbr="atq;">atque</expan> admiranda cognitio &longs;it <lb/>mera veritas, qu&aelig; omnium &longs;cientiarum finis <lb/>atque anim&aelig; no&longs;tr&aelig; cibus e&longs;t.</s></p><p type="head"> <s>Vnde &longs;it, vt to&shy;<lb/>ta h&aelig;c ade&ograve; digna, <expan abbr="atq;">atque</expan> admiranda cognitio &longs;it <lb/>mera veritas, qu&aelig; omnium &longs;cientiarum finis <lb/>atque anim&aelig; no&longs;tr&aelig; cibus e&longs;t.</s></p><p type="head">
  

Legend:
Removed from v.1.54 
changed lines
 Added in v.1.55