Monantheuil, Henri de
,
Aristotelis Mechanica
,
1599
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<
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">Propoſitionis conuerſio. </
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Naui æqualiter prouecta, atque palmula retroceßit: motus capitis
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remi proprius duplus eſt motus nauis.
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Si enim C H æqualis ponatur B D, quoniam eidem B D æqua
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lis eſt H E in parallelogrammo, æquales igitur erunt C H &
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H E ax. 1. </
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<
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id
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">Et ſic dupla erit C E ipſius H E: & eadem C E
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dupla ipſius B D. </
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<
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>æquales porro ſunt C E & A E prop 26. lib. 1.
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</
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<
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>Dupla ergo erit A E rectæ B D. </
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>ſed recta A E decurſa eſt à ca
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pite remi, & B D à ſcalmo, quantùm autem prouehitur ſcalmus,
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tantùm & nauis. </
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id
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">Igitur ſi nauis tantùm fuerit prouecta, quantùm
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remi palmula retroceßit, duplum conficit caput remi motu proprio
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eius interualli, quod nauis conficit. </
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<
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id
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">quod fuit demonſtrandum.
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Nauis decurrens minus ſpatium: quam caput remi decurrat: maius
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tamen eius dimidio: magis prouehitur: quam palmula retrocedat:
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minus autem dimidio: minus.
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In poſtremo diagrammate ponatur B D minor, quam A E:
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ſed eius dimidio maior. </
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id
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">Dico quod ipſa B D maior eſt, quam C H.
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</
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id
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">Nam B D & H E æquales ſunt, ad hæc A E & C E æqua
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les ſunt. </
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id
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">maior igitur erit H E dimidio ipſius A E. </
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<
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>quapropter
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reliqua C H minor dimidio erit eiuſdem A E. </
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id
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erit C H quam B D. </
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<
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id
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">Interuallum autem B D, id eſt quod nauis
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confecit, interuallum vero C H remi palmula in contrarium de
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currit. </
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id
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">Ideo prior pars theorematis vera. </
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id
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">Poſterior autem ſimiliter
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oſtendetur. </
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id
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">Si enim B D minor eſt dimidio ipſius A E, minor
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igitur erit & H E dimidio eiuſdem A E. </
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id
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">Et quoniam A E &
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C E æquales ſunt. </
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<
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id
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">Reliqua igitur C H dimidio eiuſdem A E
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maior erit. </
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<
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id
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">Et proinde minor erit B D quam C H. </
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<
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id
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minus interuallum decurret in anteriora: quam remi palmula in
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contrarium. </
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id
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Hinc & ex præcedenti infertur, quod ſi caput remi motu pro
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prio decurrat interuallum maius, quam nauis, ſiue duplum, ſiue du
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plo minus, ſiue maius: ſemper interuallum nauis adiuncto ei quod
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palmula retroceſſerit, æquale erit ei, quod à capite remi motu proprio
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conficitur.
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