Fabri, Honoré
,
Tractatus physicus de motu locali
,
1646
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107
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026/01/139.jpg
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<
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N177E0
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<
s
id
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N177E2
">Si verò in noſtra hypotheſi ſpatium, quod reſpondet primæ parti tem
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poris AC ſit idem cum illo, quod reſpondet eidem parti in ſententia
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Galilei, id eſt æquale triangulo CAG, ſumma ſpatiorum erit minor in
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noſtra hypotheſi triangulo AFN ſex triangulis æqualibus triangulo
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ACG; igitur erit vt 10.ad 16. igitur minor 1/8. </
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<
s
id
="
N177EE
">ſi verò diuidantur in 8.
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temporis partes, triangulum AFN continebit 64. triangula æqualia
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AXQ: </
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<
s
id
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N177F6
">at verò ſumma quæ reſpondet noſtræ hypotheſi 36.igitur minor
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(7/16). denique ſi diuidantur in 16. partes, triangulum AFN continebit
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256. triangula æqualia AYZ; at verò ſumma noſtra 136. igitur minor
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(15/52) ſed nunquam erit minor 1/2. </
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<
p
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N17800
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type
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<
s
id
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N17802
">Obſeruabis obiter dictum eſſe ſuprà ſummam rectangulorum CB CI
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EK EN eſſe maiorem triangulo AFN, 2.quadratis æqualibus CB; </
s
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<
s
id
="
N17808
">ſi
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verò diuidatur tempus in 8. partes, ſumma rectangulorum eſt minor præ
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cedenti ſummâ, toto quadrato æquali CB, id eſt 4.quadratis æqualibus
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XB, id eſt 1/2 primæ differentiæ, quæ eſt ſumma duorum quadratorum
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æqualium CB; </
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<
s
id
="
N17814
">at ſi diuidatur in 16. partes, tempus AF, ſumma rectan
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gulorum eſt minor præcedente 8. quadratis æqualibus QZ, vel ſubdu
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plo quadrati CB, id eſt 1/4 primæ differentiæ quæ eſt ſumma duorum
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quadratorum æqualium CB; </
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>
<
s
id
="
N1781E
">ſi 4. partes temporis diuidantur in 8. de
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trahitur 1/2 differentiæ, quæ eſt inter ſummam primam rectangulorum,
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& triangulum AFN; </
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>
<
s
id
="
N17826
">ſi diuidantur in 16. detrahitur 1/4 eiuſdem diffe
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rentiæ; </
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<
s
id
="
N1782C
">ſi diuidantur in 32. detrahitur 1/8, ſi in 64. (1/16); </
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>
<
s
id
="
N17830
">atque ita deinceps,
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& nunquam hæ minutiæ ſubtractæ in infinitum totam differentiam ex
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haurient; hinc minutiæ iſtæ 1/2 1/4 1/8 (1/16) (1/32) (1/64) &c. </
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<
s
id
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N17838
">in infinitum non fa
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ciunt vnum integrum; ſed hæc ſunt facilia. </
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</
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<
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N1783E
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type
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main
">
<
s
id
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N17840
">Quarta ratio, quam afferunt aliqui, eſt; </
s
>
<
s
id
="
N17844
">quia ſi cum eadem velocita
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te acquiſita in fine temporis dati ſine augmento nouo moueatur mobi
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le; </
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>
<
s
id
="
N1784C
">haud dubiè acquiret duplum ſpatium tempore æquali tempori dato; </
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>
<
s
id
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N17850
">
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v. g. ſit triangulum AFE; </
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<
s
id
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N17859
">ſitque velocitas acquiſita EF in 4. parti
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bus temporis AE, vt iam ſuprà dictum eſt, ne cogar repetere: </
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>
<
s
id
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N1785F
">certè ſi du
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catur velocitas EF in tempus AE, vel EL æquale; </
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<
s
id
="
N17865
">habebitur rectan
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gulum EK duplum trianguli AFE: </
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<
s
id
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N1786B
">ſed triangulum AFE eſt ſumma
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ſpatiorum motus accelerati tempore AE, & rectangulum EK eſt ſum
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ma ſpatiorum motus æquabilis cum velocitate EF; igitur duplum eſt
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ſpatium motus æquabilis, quod erat demonſtrandum. </
s
>
<
s
id
="
N17875
">Præterea ſi diui
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datur velocitas EF, & eius ſubdupla ducatur in tempus AE; habebitur
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rectangulum æquale triangulo AFE, vt conſtat. </
s
>
<
s
id
="
N1787D
">Reſpondeo facilè ex di
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ctis, hoc ipſum etiam ex noſtra hypotheſi proxime ſequi; </
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>
<
s
id
="
N17883
">ſint enim duo
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inſtantia; </
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<
s
id
="
N17889
">haud dubie ſi non creſcit velocitas, ſecundo inſtanti æquale
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ſpatium percurretur; </
s
>
<
s
id
="
N1788F
">ſi vero ſecundo inſtanti creſcat, percurrentur illo
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motu 3.ſpatia; </
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<
s
id
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N17895
">& cùm velocitas
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expan
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ſecũdi
">ſecundi</
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>
<
expan
abbr
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inſtãtis
">inſtantis</
expan
>
ſit dupla velocitatis primi
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inſtantis, primo inſtanti ſit 1.gradus v.g. ſecundo erunt 2. gradus; </
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<
s
id
="
N178A5
">igi
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tur moueatur per duo inſtantia motu æquabili veloci vt 2. percurrentur
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4. ſpatia; </
s
>
<
s
id
="
N178AD
">igitur totum ſpatium, quod percurritur motu veloci vt 2. per
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2.inſtantia eſt ad totum ſpatium, quod percurritur æquali tempore mo-</
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