Fabri, Honoré
,
Tractatus physicus de motu locali
,
1646
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tertij ad ſecundum quàm quarti ad tertium, atque ita deinceps
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; </
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<
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">ſit enim
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primo inſtanti velocitas vt 1.ſecundo erit, vt 2.tertio, vt 3.quarto, vt 4.
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ſed maior eſt proportio 2.ad 1.quàm 3.ad 2. & hæc maior quàm 4. ad 3.
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atque ita deinceps; </
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<
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">ſimiliter maior eſt proportio ſpatij quod percurritur
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ſecundo inſtanti ad ſpatium, quod percurritur primo, quàm ſpatij, quod
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percurritur ſecundo inſtanti ad ſpatium, quod percurritur primo quàm
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ſpatij quod percurritur tertio ad ſpatium, quod percurritur ſecundo, at
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que ita deinceps; eſt enim eadem ratio ſpatiorum quæ ſingulis inſtanti
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bus reſpondent, quæ velocitatum, vt demonſtratum eſt ſuprà. </
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Theorema
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45.
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Minor eſt proportio totius ſpatij, quod acquiritur duobus instantibus ad to
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tum ſpatium, quod acquiritur vno, quàm ſit illius, quod acquiritur quatuor in
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ſtantibus ad aliud, quod acquiritur duobus
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; patet ex dictis; </
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<
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id
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">ſi enim primo
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inſtanti acquiritur vnum ſpatium, ſecundo acquiruntur 2.igitur duobus
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ſimul acquirantur 3. igitur proportio eſt vt 3.ad 1.Sed ſi duobus acqui
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runtur 3. ſpatia; </
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<
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id
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">certè 4.inſtantibus acquiruntur 10. igitur proportio eſt
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vt 10.ad 3. ſed proportio 10/3 eſt maior 3/1, erit adhuc maior proportio ſpa
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tij quod acquiretur 6. inſtantibus ad illud quod acquiritur tribus; eſt
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enim (21/6) vt patet. </
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Theorema
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46.
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Si componatur æquabilis motus ex ſubdupla velocitate maxima, & mini
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ma, æquali tempore, idem ſpatium percurretur hoc motu naturaliter accelera
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to
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; </
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<
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id
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">ſit enim maxima velocitas vt 6. minima vt 1. motu naturaliter acce
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lerato percurrentur ſpatia 21. cuius ſummæ termini ſunt 6.igitur 6. in
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ſtantibus conſtat hic motus; </
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<
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id
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">accipiatur ſubduplum maximæ, & minimæ
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velocitatis, ſcilicet 3 1/2. sítque velocitas motus æquabilis inſtantium 6.
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haud dubiè ſi ducantur 3 1/2 in 6 erunt 21.ratio ex eo petitur quod ſcili
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cet, vt habeatur ſumma progreſſionis arithmeticæ, debet addi primus
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terminus maximo, & aſſumi ſubduplum totius; </
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<
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id
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">illudque ducere in nu
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merum terminorum per regulam arithmeticam; </
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<
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id
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">atqui eadem eſt ratio
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velocitatum, quæ ſpatiorum; vt dictum eſt ſuprà; ſcilice, in ſingulis
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inſtantibus. </
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Theorema
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47.
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Si aſſumantur partes temporis majores; quæ ſcilicet pluribus inſtantibus
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constent, ſerueturque eadem accelerationis progreſſio arithmetica, ſpatium
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quod ex ſumma huius progreſſionis reſultabit, erit minus vero,
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ſint enim 6.in
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ſtantia, & cuilibet iuxta progreſſionem prædictam ſuum ſpatium reſpon
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deat, haud dubiè ſpatium ſecundi erit duplum ſpatij primi, & tertium
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triplum, &c. </
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<
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">vt conſtat ex dictis; </
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<
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">igitur erunt ſpatia 21. iam verò aſſu
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mantur 3. partes temporis, quarum quælibet ex 2. conſtet inſtantibus; </
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<
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primæ parti tria ex prædictis ſpatiis reſpondeant; </
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<
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id
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">certè ſi ſeruetur pro
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greſſio arithmetica, ſecundæ reſpondebunt 6. & tertiæ 9. igitur totum
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ſpatium erit 18. minus vero quod erat 21. ſi verò aſſumantur tantùm 2.
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partes, quarum quælibet tribus inſtantibus conſtet; </
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<
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