Fabri, Honoré
,
Tractatus physicus de motu locali
,
1646
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Theorema
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58.
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Impetus naturalis non decreſcit etiam in arcu deſcenſus
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; probatur quia
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creſcit, vt dictum eſt ſuprà, igitur non decreſcit. </
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Theorema
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59.
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Deſtruitur impetus violentus pro rata. </
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">id eſt, qua proportione eſt frustrà;
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v.g. </
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">ſit impetus per AD inclinatam ſurſum, & alius per AB perpendi
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cularem deorſum; </
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id
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">haud dubiè motus erit per AC; </
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<
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id
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">igitur concurrunt
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ad motum AC motus AB & AD, vel potiùs impetus; </
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<
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">igitur debet de
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ſtrui impetus in ea proportione, in qua AC eſt minor AG, id eſt com
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poſita ex AD, DC, quod impetus AB non poſſit deſtrui; </
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<
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">totum id
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quod deſtruetur detrahetur impetui AD; </
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">igitur aſſumatur DF ſcilicet
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differentia AC, & AG; impetus deſtructus ita ſe habet ad impetum
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AD, vt DF ad AD, & ad reſiduum impetum ex AD, vt DF ad FA,
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quæ omnia conſtant ex Th.7. ſit ergo AC fig. </
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">49. perpendicularis ſur
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ſum, AD inclinata, AB horizontalis; ſit impetus violentus reſpondens
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AD, & naturalis DG, ducatur AGK, ex AD detrahatur DF, id eſt
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differentia AG & compoſitæ ex AD. DG, ſupereſt AF, cui aſſumitur
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æqualis GK, ex qua detrahitur KH, id eſt differentia GL, & compoſitæ
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ex GK, KL, ſupereſt GH, cui LO accipitur æqualis, cui detrahitur
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OM, id eſt differentia LP & compoſitæ ex LO, OP, ſupereſt ML, cui
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æqualis accipitur PR, atque ita deinceps. </
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">Porrò demonſtratur deſtrui
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impetum violentum iuxta hanc proportionem; </
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id
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">quia deſtruitur, qua
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proportione eſt fruſtrà, pro rata per Ax.2.& Th.7.ſed totus impetus qui
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concurrit ad ſecundam lineam AG, eſt compoſitus ex AD, GD; </
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<
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">quia ſi
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naturalis ſolus eſſet, percurreret ſpatium æquale DG; </
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">ſi verò ſolus eſſet
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violentus percurreret ſpatium æquale AD; </
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">igitur vterque ſimul ſumptus
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eſt vt
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, ex AG. DG. igitur ſi ea proportione eſt fruſtrà, qua motus
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deficit, cùm AG ſit motus; </
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">certè motus eſt ad impetum, vt AG ad
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compo-ſitã
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ſitam</
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ex AD. DG; </
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">igitur deficit motus tota DF quæ eſt differentia AG &
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ex AD. DG; </
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<
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id
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">igitur impetus eſt fruſtrà in ratione DF; </
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>
<
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id
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">igitur de
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bet deſtrui in ratione DF; </
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<
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id
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">ſed impetus DG ſeu naturalis nihil deſtrui
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tur per Th.57. & 58. igitur ex violento AD deſtruitur DF; </
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<
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">igitur ſu
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pereſt tantum AF vel æqualis GK; </
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">ſimiliter impetui GK & KL re
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ſpondet motus GL, ſed GL eſt minor compoſita ex GK & KL ſeg
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mento KH; </
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<
s
id
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">igitur eſt fruſtrà impetus in ratione KH; </
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>
<
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">igitur deſtruitur
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in eadem ratione KH, non ex naturali KL; </
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<
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id
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">igitur ex violento GK;
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igitur ſupereſt tantum GH, vel æqualis LO, in qua ſimiliter procedi
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tur. </
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Corollarium
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1.
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