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| <author>Jordanus de Nemore</author> | <author>Jordanus de Nemore</author> |
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| <title>Liber de ponderibus</title> | <title>Liber de ponderibus</title> |
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| <text><front><section><pb xlink:href="050/01/001.jpg" /><pb xlink:href="050/01/002.jpg" /></section></front> | <text><front><section><pb xlink:href="050/01/001.jpg" /> |
| | <p type="head"> |
| | <s><emph type="center"/>LIBER IORDANI <lb/> |
| | NEMORARII VIRI CLARISSIMI, <emph.end type="center"/></s> |
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| | <p type="head"> |
| | <s><emph type="center"/>DE PONDERIBUS PROPOSITIONES XIII.<emph.end type="center"/></s> |
| | </p> |
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| | <p type="head"> |
| | <s><emph type="center"/>& earundem demon&longs;trationes, mul­<lb/>tarumque rerum rationes &longs;anè <lb/>pulcherrimas comple­<lb/>ctens, nunc in lu­<lb/>cem editus.<emph.end type="center"/></s> |
| | </p> |
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| | <p type="head"> |
| | <s><emph type="center"/>Cum gratia & priuilegio Imperiali, Petro Apiano Ma<lb/>thematico Ingol&longs;tadiano ad xxx. annos conce&longs;&longs;o.<emph.end type="center"/></s> |
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| | <figure/> |
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| | <s><emph type="center"/>M. D. XXXIII.<emph.end type="center"/></s> |
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| | <pb xlink:href="050/01/002.jpg" /><p type="main"><s>[empty page]</s></p></section></front> |
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| <body><chap><pb xlink:href="050/01/003.jpg" /><pb xlink:href="050/01/004.jpg" /><pb xlink:href="050/01/005.jpg" /></chap><chap><pb xlink:href="050/01/006.jpg" /><p> | <body><chap><pb xlink:href="050/01/003.jpg" /><p type="main"><s>[dedication not transcribed]</s></p><pb xlink:href="050/01/004.jpg" /><p type="main"><s>[dedication not transcribed]</s></p><pb xlink:href="050/01/005.jpg" /><p type="main"><s>[dedication not transcribed]</s></p></chap><chap><pb xlink:href="050/01/006.jpg" /><p type="main"> |
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| <s id="id.0.0.05.04">Grave igitur in parte inferiori, sive moveatur si­<lb/>ve quiescat, levius est secundum situm.</s></p><p> | <s id="id.0.0.05.04">Grave igitur in parte inferiori, sive moveatur si­<lb/>ve quiescat, levius est secundum situm.</s></p><p type="main"> |
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| <s id="id.0.0.06.05">Ex eadem enim violentia sit totus ad quietem motus, et ipsa quies, <lb/>sicut patet ex prædictis, unde idem forte sit locus quietum naturaliter di­<lb/>versarum.</s></p><p> | <s id="id.0.0.06.05">Ex eadem enim violentia sit totus ad quietem motus, et ipsa quies, <lb/>sicut patet ex prædictis, unde idem forte sit locus quietum naturaliter di­<lb/>versarum.</s></p><p type="main"> |
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| <s id="id.0.0.07.04">Sunt itaque suppositiones septem.</s></p></chap><chap><p> | <s id="id.0.0.07.04">Sunt itaque suppositiones septem.</s></p></chap><chap><p type="main"> |
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| <s id="id.0.0.09.01.post">Prima <lb/>est, Omnis ponderosi motum ad medium esse.</s></p><p> | <s id="id.0.0.09.01.post">Prima <lb/>est, Omnis ponderosi motum ad medium esse.</s></p><p type="main"> |
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| <s id="id.0.0.10.01.post">Secunda, Quanto gra­<lb/>vius tanto velocius descendere.</s></p><p> | <s id="id.0.0.10.01.post">Secunda, Quanto gra­<lb/>vius tanto velocius descendere.</s></p><p type="main"> |
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| <s id="id.0.0.11.01.post">Tertia, Gravius ess in descendendo,<lb/> quanto eiusdem motus ad medium est rectior.</s></p><p> | <s id="id.0.0.11.01.post">Tertia, Gravius ess in descendendo,<lb/> quanto eiusdem motus ad medium est rectior.</s></p><p type="main"> |
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| <s id="id.0.0.12.01.post">Quarta, Secundum si­<lb/>tum gravius esse, quanto in eodem situ minus obliquus est descensus.<lb/></s></p><p> | <s id="id.0.0.12.01.post">Quarta, Secundum si­<lb/>tum gravius esse, quanto in eodem situ minus obliquus est descensus.<lb/></s></p><p type="main"> |
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| <s id="id.0.0.13.01.post">Quinta, Obilquiorem autem descensum minus capere de directo, in eadem <lb/>quantitate.</s></p><p> | <s id="id.0.0.13.01.post">Quinta, Obilquiorem autem descensum minus capere de directo, in eadem <lb/>quantitate.</s></p><p type="main"> |
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| <s id="id.0.0.14.01.post">Sexta, Minus grave aliud alio esse secundum situm, quan­<lb/>to descensus alterius consequitur contrario motu.</s></p><p> | <s id="id.0.0.14.01.post">Sexta, Minus grave aliud alio esse secundum situm, quan­<lb/>to descensus alterius consequitur contrario motu.</s></p><p type="main"> |
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| <s id="id.0.0.15.01.post">Septima, Situm<lb/> æqualitatis esse æquidistantiam superficiei orizontis.</s></p><p> | <s id="id.0.0.15.01.post">Septima, Situm<lb/> æqualitatis esse æquidistantiam superficiei orizontis.</s></p><p type="main"> |
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| <s id="id.0.0.16.03">Sunt itaque tredecim.</s></p><pb xlink:href="050/01/008.jpg" /></chap><chap><p> | <s id="id.0.0.16.03">Sunt itaque tredecim.</s></p><pb xlink:href="050/01/008.jpg" /></chap><chap><p type="main"> |
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| <s id="id.0.0.18.01.prop">PROPOSITIO PRIMA.<lb/></s><s>Inter quælibet duo gravia est velocitas descenden<lb/>do proprie, et ponderum eodem ordine sumpta pro<lb/>portio, descensus autem, et contrarii motus, proportio eadem, sed permutata.<lb/></s></p><p> | <s id="id.0.0.18.01.prop">PROPOSITIO PRIMA.<lb/></s><s>Inter quælibet duo gravia est velocitas descenden<lb/>do proprie, et ponderum eodem ordine sumpta pro<lb/>portio, descensus autem, et contrarii motus, proportio eadem, sed permutata.<lb/></s></p><p type="main"> |
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| <s id="id.0.0.19.05">Oportet enim, quanto illud exce­<lb/>dit, tanto id isto excedi.</s><s>Et per consequens, quanto illud quod est gravi­<lb/>us, velocius ascendit, tanto levius movetur contrarie.</s></p><pb xlink:href="050/01/009.jpg" /><figure id="id.050.01.009.1.jpg" xlink:href="050/01/009/1.jpg"/><pb xlink:href="050/01/010.jpg" /><pb xlink:href="050/01/011.jpg" /></chap><chap><p> | <s id="id.0.0.19.05">Oportet enim, quanto illud exce­<lb/>dit, tanto id isto excedi.</s><s>Et per consequens, quanto illud quod est gravi­<lb/>us, velocius ascendit, tanto levius movetur contrarie.</s></p><pb xlink:href="050/01/009.jpg" /><figure id="id.050.01.009.1.jpg" xlink:href="050/01/009/1.jpg"/><pb xlink:href="050/01/010.jpg" /><pb xlink:href="050/01/011.jpg" /></chap><chap><p type="main"> |
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| <s id="id.0.0.20.01.prop">PROPOSITIO SECUNDA.<lb/></s><s> Cum fuerit æquilibris positio æqualis, æquis pon<lb/>deribus appensis, ab æqualitate non discedet, etsi ab <lb/>æquidistantia separetur, ad æqualitatis situm revertetur.<lb/></s></p><p> | <s id="id.0.0.20.01.prop">PROPOSITIO SECUNDA.<lb/></s><s> Cum fuerit æquilibris positio æqualis, æquis pon<lb/>deribus appensis, ab æqualitate non discedet, etsi ab <lb/>æquidistantia separetur, ad æqualitatis situm revertetur.<lb/></s></p><p type="main"> |
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| <s id="id.0.0.21.02">Secundum patet per quartam suppositi­<lb/>onem quartam, vocatur autem illud situs, quod circulus dicitur, sicut patet per <lb/>prædicta.<figure id="id.050.01.011.1.jpg" xlink:href="050/01/011/1.jpg"/></s></p><pb xlink:href="050/01/012.jpg" /><figure id="id.050.01.012.1.jpg" xlink:href="050/01/012/1.jpg"/><pb xlink:href="050/01/013.jpg" /></chap><chap><p> | <s id="id.0.0.21.02">Secundum patet per quartam suppositi­<lb/>onem quartam, vocatur autem illud situs, quod circulus dicitur, sicut patet per <lb/>prædicta.<figure id="id.050.01.011.1.jpg" xlink:href="050/01/011/1.jpg"/></s></p><pb xlink:href="050/01/012.jpg" /><figure id="id.050.01.012.1.jpg" xlink:href="050/01/012/1.jpg"/><pb xlink:href="050/01/013.jpg" /></chap><chap><p type="main"> |
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| <s id="id.0.0.22.01.prop">Cum fuerint appen­<lb/>sorum pondera æqua<lb/>lia, non motum faciet in<lb/>æquilibri appendicu­<lb/>lorum inæqualitas.</s></p><p> | <s id="id.0.0.22.01.prop">Cum fuerint appen­<lb/>sorum pondera æqua<lb/>lia, non motum faciet in<lb/>æquilibri appendicu­<lb/>lorum inæqualitas.</s></p><p type="main"> |
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| <s id="id.0.0.23.01">Non debet hic sumi inæ­<lb/>qualitas appendiculorum pon­<lb/>dere, sed longitudine proba­<lb/>tur sic.</s><s>Si fiat motus in una par<lb/>te, ergo pars alia est minus gra­<lb/>vis, per suppositionem secundam, <lb/>sed positum est prius appenso<lb/>rum pondera esse æqualia; ergo.<lb/></s></p><pb xlink:href="050/01/014.jpg" /></chap><chap><p> | <s id="id.0.0.23.01">Non debet hic sumi inæ­<lb/>qualitas appendiculorum pon­<lb/>dere, sed longitudine proba­<lb/>tur sic.</s><s>Si fiat motus in una par<lb/>te, ergo pars alia est minus gra­<lb/>vis, per suppositionem secundam, <lb/>sed positum est prius appenso<lb/>rum pondera esse æqualia; ergo.<lb/></s></p><pb xlink:href="050/01/014.jpg" /></chap><chap><p type="main"> |
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| <s id="id.0.0.24.01.prop">Quodlibet pondus in quamcumque partem discedat secundum situm sit levius.<lb/></s></p><p> | <s id="id.0.0.24.01.prop">Quodlibet pondus in quamcumque partem discedat secundum situm sit levius.<lb/></s></p><p type="main"> |
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| <s id="id.0.0.25.01">Manifestum est hoc per suppositionem quartam.</s></p><pb xlink:href="050/01/015.jpg" /><figure id="id.050.01.015.1.jpg" xlink:href="050/01/015/1.jpg"/></chap><chap><p> | <s id="id.0.0.25.01">Manifestum est hoc per suppositionem quartam.</s></p><pb xlink:href="050/01/015.jpg" /><figure id="id.050.01.015.1.jpg" xlink:href="050/01/015/1.jpg"/></chap><chap><p type="main"> |
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| <s id="id.0.0.26.01.prop">Si fuerint brachia æquilibris inæqualia, æquali­<lb/>bus ponderibus appensis, ex parte longioris fiet motus.<lb/></s></p><p> | <s id="id.0.0.26.01.prop">Si fuerint brachia æquilibris inæqualia, æquali­<lb/>bus ponderibus appensis, ex parte longioris fiet motus.<lb/></s></p><p type="main"> |
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| <s id="id.0.0.27.02">Ex parte <lb/>longioris describitur circulus maior, et sic patet per suppositionem tertiam <lb/>quod pondus secundum situm est gravius.</s></p><pb xlink:href="050/01/016.jpg" /><figure id="id.050.01.016.1.jpg" xlink:href="050/01/016/1.jpg"/><figure id="id.050.01.016.2.jpg" xlink:href="050/01/016/2.jpg"/><pb xlink:href="050/01/017.jpg" /><figure id="id.050.01.017.1.jpg" xlink:href="050/01/017/1.jpg"/><pb xlink:href="050/01/018.jpg" /><pb xlink:href="050/01/019.jpg" /><figure id="id.050.01.019.1.jpg" xlink:href="050/01/019/1.jpg"/><figure id="id.050.01.019.2.jpg" xlink:href="050/01/019/2.jpg"/><pb xlink:href="050/01/020.jpg" /><figure id="id.050.01.020.1.jpg" xlink:href="050/01/020/1.jpg"/></chap><chap><p> | <s id="id.0.0.27.02">Ex parte <lb/>longioris describitur circulus maior, et sic patet per suppositionem tertiam <lb/>quod pondus secundum situm est gravius.</s></p><pb xlink:href="050/01/016.jpg" /><figure id="id.050.01.016.1.jpg" xlink:href="050/01/016/1.jpg"/><figure id="id.050.01.016.2.jpg" xlink:href="050/01/016/2.jpg"/><pb xlink:href="050/01/017.jpg" /><figure id="id.050.01.017.1.jpg" xlink:href="050/01/017/1.jpg"/><pb xlink:href="050/01/018.jpg" /><pb xlink:href="050/01/019.jpg" /><figure id="id.050.01.019.1.jpg" xlink:href="050/01/019/1.jpg"/><figure id="id.050.01.019.2.jpg" xlink:href="050/01/019/2.jpg"/><pb xlink:href="050/01/020.jpg" /><figure id="id.050.01.020.1.jpg" xlink:href="050/01/020/1.jpg"/></chap><chap><p type="main"> |
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| <s id="id.0.0.28.01.prop">Cum unius ponderis sint appensa, et a centro mo­<lb/>tus inæqualiter distent, et si remotum secundum di­<lb/>stantiam propinquius accesserit ad directionem, alio <lb/>non moto secundum situm, illo levius fiet.<lb/></s></p><p> | <s id="id.0.0.28.01.prop">Cum unius ponderis sint appensa, et a centro mo­<lb/>tus inæqualiter distent, et si remotum secundum di­<lb/>stantiam propinquius accesserit ad directionem, alio <lb/>non moto secundum situm, illo levius fiet.<lb/></s></p><p type="main"> |
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| <s id="id.0.0.29.03">Est enim semicirculus minor, quem tunc fuit.</s></p><figure id="id.050.01.021.1.jpg" xlink:href="050/01/021/1.jpg"/><pb xlink:href="050/01/022.jpg" /></chap><chap><p> | <s id="id.0.0.29.03">Est enim semicirculus minor, quem tunc fuit.</s></p><figure id="id.050.01.021.1.jpg" xlink:href="050/01/021/1.jpg"/><pb xlink:href="050/01/022.jpg" /></chap><chap><p type="main"> |
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| <s id="id.0.0.30.01.prop">Aequis ponderibus in æquilibri appensis, si æqua<lb/>lia sint appensibilia, alterum autem circum <lb/>volubile appenditur, graviua erit secundum situm.<lb/></s></p><p> | <s id="id.0.0.30.01.prop">Aequis ponderibus in æquilibri appensis, si æqua<lb/>lia sint appensibilia, alterum autem circum <lb/>volubile appenditur, graviua erit secundum situm.<lb/></s></p><p type="main"> |
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| <s id="id.0.0.31.01">Circumvolubile dicitur, quando perpendiculum potest habere decli<lb/>nationem plus largam, quam brachia libræ, ut sit, quando in circulo pendet <lb/>secundum angulum rectum fixum, dicitur, quando nullam contingit habere de­<lb/>clinationem perpendiculorum, nisi secundum brachium, et est in situ æqua­<lb/>litatis inter brachium et perpendiculum angulus rectus, probatur.</s><s>Sint <lb/>appensa æqualia, ut vult positio, in pondere, sed non in longitudine, tunc <lb/>illud quod est circumvolubile, maiorem circulum constituit in causa, <lb/>quia plus declinat propter circumvolutionem, et sic pondus ibi gravius <lb/>est secundum situm, cum eius descensus sit rectior.</s></p><p> | <s id="id.0.0.31.01">Circumvolubile dicitur, quando perpendiculum potest habere decli<lb/>nationem plus largam, quam brachia libræ, ut sit, quando in circulo pendet <lb/>secundum angulum rectum fixum, dicitur, quando nullam contingit habere de­<lb/>clinationem perpendiculorum, nisi secundum brachium, et est in situ æqua­<lb/>litatis inter brachium et perpendiculum angulus rectus, probatur.</s><s>Sint <lb/>appensa æqualia, ut vult positio, in pondere, sed non in longitudine, tunc <lb/>illud quod est circumvolubile, maiorem circulum constituit in causa, <lb/>quia plus declinat propter circumvolutionem, et sic pondus ibi gravius <lb/>est secundum situm, cum eius descensus sit rectior.</s></p><p type="main"> |
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| <s id="id.0.0.32.02">Cum enim <lb/>aliquis voluit experiri, an ita esset; posuit in æquilibri pondera æqua<lb/>lia, cuius appendentia erunt filo composita, quæ motum habent a bra­<lb/>chiis alienum, etiam propter perpendiculorum flexus incognitis experimentum<lb/><figure id="id.050.01.022.1.jpg" xlink:href="050/01/022/1.jpg"/>fallax, quare experiens ve­<lb/>ritatis irrisorem, et acce­<lb/>pto cum casu, quod secundum <lb/>æquidistantiam a medio mo­<lb/>tus propter perpendicula, <lb/>ex terminis brachiorum li­<lb/>neæ sic describuntur utrumque <lb/>intelligit, quod prius nega­<lb/>vit, quod est, quia preter mu­<lb/>tationes brachiorum alii non <lb/>erunt flexus, et ex hoc non <lb/>conclusit secundum rectos <lb/>angulos idem congruere, cum <lb/>motus brachiorum simili­<lb/>ter contingit.</s></p><pb xlink:href="050/01/023.jpg" /></chap><chap><p> | <s id="id.0.0.32.02">Cum enim <lb/>aliquis voluit experiri, an ita esset; posuit in æquilibri pondera æqua<lb/>lia, cuius appendentia erunt filo composita, quæ motum habent a bra­<lb/>chiis alienum, etiam propter perpendiculorum flexus incognitis experimentum<lb/><figure id="id.050.01.022.1.jpg" xlink:href="050/01/022/1.jpg"/>fallax, quare experiens ve­<lb/>ritatis irrisorem, et acce­<lb/>pto cum casu, quod secundum <lb/>æquidistantiam a medio mo­<lb/>tus propter perpendicula, <lb/>ex terminis brachiorum li­<lb/>neæ sic describuntur utrumque <lb/>intelligit, quod prius nega­<lb/>vit, quod est, quia preter mu­<lb/>tationes brachiorum alii non <lb/>erunt flexus, et ex hoc non <lb/>conclusit secundum rectos <lb/>angulos idem congruere, cum <lb/>motus brachiorum simili­<lb/>ter contingit.</s></p><pb xlink:href="050/01/023.jpg" /></chap><chap><p type="main"> |
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| <s id="id.0.0.33.01.prop">Si fuerint brachia libræ proportionalia ponderi­<lb/>bus appensorum, ita, ut in breviori gravius appenda<lb/>tur, æque gravia erunt secundum situm.<lb/></s></p><p> | <s id="id.0.0.33.01.prop">Si fuerint brachia libræ proportionalia ponderi­<lb/>bus appensorum, ita, ut in breviori gravius appenda<lb/>tur, æque gravia erunt secundum situm.<lb/></s></p><p type="main"> |
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| <s id="id.0.0.34.01">Si pondus gravius tantum valet in termino breviori, quantum bra­<lb/>chium libræ longius in suo loco, et similiter pondus minus in breviori, <lb/>tunc dico, sic valebunt secundum situm, quando non essent sic secundum <lb/>naturam, necessario erunt pondera secundum situm æqualia, quia pon­<lb/>dus et brachium hic valet per oppositum totum reliquum, quia propter neu<lb/>trum pondus declinat, sicut patet propositione huius prima.</s></p><figure id="id.050.01.023.1.jpg" xlink:href="050/01/023/1.jpg"/><pb xlink:href="050/01/024.jpg" /><pb xlink:href="050/01/025.jpg" /></chap><chap><p> | <s id="id.0.0.34.01">Si pondus gravius tantum valet in termino breviori, quantum bra­<lb/>chium libræ longius in suo loco, et similiter pondus minus in breviori, <lb/>tunc dico, sic valebunt secundum situm, quando non essent sic secundum <lb/>naturam, necessario erunt pondera secundum situm æqualia, quia pon­<lb/>dus et brachium hic valet per oppositum totum reliquum, quia propter neu<lb/>trum pondus declinat, sicut patet propositione huius prima.</s></p><figure id="id.050.01.023.1.jpg" xlink:href="050/01/023/1.jpg"/><pb xlink:href="050/01/024.jpg" /><pb xlink:href="050/01/025.jpg" /></chap><chap><p type="main"> |
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| <s id="id.0.0.35.01.prop">Si duo oblonga unius grossiciei per totum &longs;imilia <lb/>et pondere et quantitate æqualia, appendantur, ita, <lb/>ut alterum erigatur, et alterum orthogonaliter depen<lb/>deat, ita etiam, ut termini dependentis, et medii alte­<lb/>rius, eadem sit a centro distantia, secundum hunc situm<lb/>æque gravia fient.<lb/></s></p><p> | <s id="id.0.0.35.01.prop">Si duo oblonga unius grossiciei per totum &longs;imilia <lb/>et pondere et quantitate æqualia, appendantur, ita, <lb/>ut alterum erigatur, et alterum orthogonaliter depen<lb/>deat, ita etiam, ut termini dependentis, et medii alte­<lb/>rius, eadem sit a centro distantia, secundum hunc situm<lb/>æque gravia fient.<lb/></s></p><p type="main"> |
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| <s id="id.0.0.36.02">probatur sic, Gravitas naturalis est æqualis utro<lb/>bique propositum ut violentum, similiter, quia semicirculi sunt æquales, <lb/>ergo æque gravia secundum situm sunt appensa.</s></p><pb xlink:href="050/01/026.jpg" /><figure id="id.050.01.026.1.jpg" xlink:href="050/01/026/1.jpg"/></chap><chap><p> | <s id="id.0.0.36.02">probatur sic, Gravitas naturalis est æqualis utro<lb/>bique propositum ut violentum, similiter, quia semicirculi sunt æquales, <lb/>ergo æque gravia secundum situm sunt appensa.</s></p><pb xlink:href="050/01/026.jpg" /><figure id="id.050.01.026.1.jpg" xlink:href="050/01/026/1.jpg"/></chap><chap><p type="main"> |
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| <s id="id.0.0.37.01.prop">Si canonium fuerit symmetrum magnitudine, et sub<lb/>stantiæ eiusdem, dividitaturque in duas partes inæqua­<lb/>les, et suspendatur in termino minoris portionis pon<lb/>dus, quod faciat canonium paralellum epipedo ori­<lb/>zontis, proportio ponderis illius, ad superabundan­<lb/>tiam ponderis maioris portionis canonii ad minorem,<pb xlink:href="050/01/027.jpg" /> est sicut proportio totius canonii ad duplum longitu<lb/>dinis minoris portionis.</s></p><p> | <s id="id.0.0.37.01.prop">Si canonium fuerit symmetrum magnitudine, et sub<lb/>stantiæ eiusdem, dividitaturque in duas partes inæqua­<lb/>les, et suspendatur in termino minoris portionis pon<lb/>dus, quod faciat canonium paralellum epipedo ori­<lb/>zontis, proportio ponderis illius, ad superabundan­<lb/>tiam ponderis maioris portionis canonii ad minorem,<pb xlink:href="050/01/027.jpg" /> est sicut proportio totius canonii ad duplum longitu<lb/>dinis minoris portionis.</s></p><p type="main"> |
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| <s id="id.0.0.38.13">Sicut ista probatur geometrice, ita possunt omnes pro­ba<lb/>ri per missæ per proportionem illarum linearum, et angulorum suorum constructorum.<lb/></s></p><figure id="id.050.01.027.1.jpg" xlink:href="050/01/027/1.jpg"/><pb xlink:href="050/01/028.jpg" /></chap><chap><p> | <s id="id.0.0.38.13">Sicut ista probatur geometrice, ita possunt omnes pro­ba<lb/>ri per missæ per proportionem illarum linearum, et angulorum suorum constructorum.<lb/></s></p><figure id="id.050.01.027.1.jpg" xlink:href="050/01/027/1.jpg"/><pb xlink:href="050/01/028.jpg" /></chap><chap><p type="main"> |
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| <s id="id.0.0.39.01.prop">Si fuerit proportio ponderis in termino minoris<lb/>portionis suspensi ad superabundantiam ponderis ma­<lb/>ioris portionis ad minorem, sicut proportio totius lon<lb/>gitudinis canonii ad duplam longitudinem minoris por<lb/>tionis, erit canonium paralellum empipedo orizontis.</s></p><p> | <s id="id.0.0.39.01.prop">Si fuerit proportio ponderis in termino minoris<lb/>portionis suspensi ad superabundantiam ponderis ma­<lb/>ioris portionis ad minorem, sicut proportio totius lon<lb/>gitudinis canonii ad duplam longitudinem minoris por<lb/>tionis, erit canonium paralellum empipedo orizontis.</s></p><p type="main"> |
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| <s id="id.0.0.40.03">Prius enim osten­<lb/>debatur, brachio longiori pondus in situ coæquari, vel correspondere, <lb/>igitur per suppositionem sextam, neque brachium pondus, neque pondus bra­<lb/>chium sequitur motu contrario.</s></p><pb xlink:href="050/01/029.jpg" /></chap><chap><p> | <s id="id.0.0.40.03">Prius enim osten­<lb/>debatur, brachio longiori pondus in situ coæquari, vel correspondere, <lb/>igitur per suppositionem sextam, neque brachium pondus, neque pondus bra­<lb/>chium sequitur motu contrario.</s></p><pb xlink:href="050/01/029.jpg" /></chap><chap><p type="main"> |
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| <s id="id.0.0.41.01.prop">Ex iis manifestum est, quoniam si fuerit canonium sim<lb/>metrum magnitudine, et zona eiusdem notum longitudine <lb/>et pondere, et dividatur in duas partes inæquales da­<lb/>tas, tunc possibile est nobis invenire pondus, quod <lb/>cum suspensum fuerit a termino minoris portionis, fa<lb/>ciet canonium paralellum empipedo orizontis.</s></p><p> | <s id="id.0.0.41.01.prop">Ex iis manifestum est, quoniam si fuerit canonium sim<lb/>metrum magnitudine, et zona eiusdem notum longitudine <lb/>et pondere, et dividatur in duas partes inæquales da­<lb/>tas, tunc possibile est nobis invenire pondus, quod <lb/>cum suspensum fuerit a termino minoris portionis, fa<lb/>ciet canonium paralellum empipedo orizontis.</s></p><p type="main"> |
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| <s id="id.0.0.42.01">Illa probatio satis patet ex prædictis.</s></p><figure id="id.050.01.029.1.jpg" xlink:href="050/01/029/1.jpg"/><pb xlink:href="050/01/030.jpg" /></chap><chap><p> | <s id="id.0.0.42.01">Illa probatio satis patet ex prædictis.</s></p><figure id="id.050.01.029.1.jpg" xlink:href="050/01/029/1.jpg"/><pb xlink:href="050/01/030.jpg" /></chap><chap><p type="main"> |
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| <s id="id.0.0.43.01.prop">Si fuerit canonium datum longitudine, spissitudi<lb/>ne, et gravitate, et dividatur in duas partes inæqua­<lb/>les, fueritque suspensum a termino minoris portionis <lb/>pondus datum, quod faciet canonium paralellum <lb/>empipedo orizontis, longitudo uniuscuiusque portio <lb/>data erit.</s></p><p> | <s id="id.0.0.43.01.prop">Si fuerit canonium datum longitudine, spissitudi<lb/>ne, et gravitate, et dividatur in duas partes inæqua­<lb/>les, fueritque suspensum a termino minoris portionis <lb/>pondus datum, quod faciet canonium paralellum <lb/>empipedo orizontis, longitudo uniuscuiusque portio <lb/>data erit.</s></p><p type="main"> |
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| <s id="id.0.0.44.01">Probatur sic, Longitudine totius canonii nota, et pondere noto, pone <lb/>pedem circini in centro medii motus, et constitue circulum super mino­<lb/>rem portionem, quæ secabit per diffinitionem circuli æqualem de bra­<lb/>chio longiori, parti autem reliquæ æquatur portio ablata a termino ubi<pb xlink:href="050/01/031.jpg" />pendet pondus, quia ex hac exceditur brachium brachio, unde sequitur<lb/>quæsitum.</s></p><figure id="id.050.01.031.1.jpg" xlink:href="050/01/031/1.jpg"/></chap><chap><p> | <s id="id.0.0.44.01">Probatur sic, Longitudine totius canonii nota, et pondere noto, pone <lb/>pedem circini in centro medii motus, et constitue circulum super mino­<lb/>rem portionem, quæ secabit per diffinitionem circuli æqualem de bra­<lb/>chio longiori, parti autem reliquæ æquatur portio ablata a termino ubi<pb xlink:href="050/01/031.jpg" />pendet pondus, quia ex hac exceditur brachium brachio, unde sequitur<lb/>quæsitum.</s></p><figure id="id.050.01.031.1.jpg" xlink:href="050/01/031/1.jpg"/></chap><chap><p type="main"> |
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