Fabri, Honoré
,
Tractatus physicus de motu locali
,
1646
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<
chap
id
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N15AC3
">
<
pb
pagenum
="
107
"
xlink:href
="
026/01/139.jpg
"/>
<
p
id
="
N177E0
"
type
="
main
">
<
s
id
="
N177E2
">Si verò in noſtra hypotheſi ſpatium, quod reſpondet primæ parti tem
<
lb
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poris AC ſit idem cum illo, quod reſpondet eidem parti in ſententia
<
lb
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Galilei, id eſt æquale triangulo CAG, ſumma ſpatiorum erit minor in
<
lb
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noſtra hypotheſi triangulo AFN ſex triangulis æqualibus triangulo
<
lb
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ACG; igitur erit vt 10.ad 16. igitur minor 1/8. </
s
>
<
s
id
="
N177EE
">ſi verò diuidantur in 8.
<
lb
/>
temporis partes, triangulum AFN continebit 64. triangula æqualia
<
lb
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AXQ: </
s
>
<
s
id
="
N177F6
">at verò ſumma quæ reſpondet noſtræ hypotheſi 36.igitur minor
<
lb
/>
(7/16). denique ſi diuidantur in 16. partes, triangulum AFN continebit
<
lb
/>
256. triangula æqualia AYZ; at verò ſumma noſtra 136. igitur minor
<
lb
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(15/52) ſed nunquam erit minor 1/2. </
s
>
</
p
>
<
p
id
="
N17800
"
type
="
main
">
<
s
id
="
N17802
">Obſeruabis obiter dictum eſſe ſuprà ſummam rectangulorum CB CI
<
lb
/>
EK EN eſſe maiorem triangulo AFN, 2.quadratis æqualibus CB; </
s
>
<
s
id
="
N17808
">ſi
<
lb
/>
verò diuidatur tempus in 8. partes, ſumma rectangulorum eſt minor præ
<
lb
/>
cedenti ſummâ, toto quadrato æquali CB, id eſt 4.quadratis æqualibus
<
lb
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XB, id eſt 1/2 primæ differentiæ, quæ eſt ſumma duorum quadratorum
<
lb
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æqualium CB; </
s
>
<
s
id
="
N17814
">at ſi diuidatur in 16. partes, tempus AF, ſumma rectan
<
lb
/>
gulorum eſt minor præcedente 8. quadratis æqualibus QZ, vel ſubdu
<
lb
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plo quadrati CB, id eſt 1/4 primæ differentiæ quæ eſt ſumma duorum
<
lb
/>
quadratorum æqualium CB; </
s
>
<
s
id
="
N1781E
">ſi 4. partes temporis diuidantur in 8. de
<
lb
/>
trahitur 1/2 differentiæ, quæ eſt inter ſummam primam rectangulorum,
<
lb
/>
& triangulum AFN; </
s
>
<
s
id
="
N17826
">ſi diuidantur in 16. detrahitur 1/4 eiuſdem diffe
<
lb
/>
rentiæ; </
s
>
<
s
id
="
N1782C
">ſi diuidantur in 32. detrahitur 1/8, ſi in 64. (1/16); </
s
>
<
s
id
="
N17830
">atque ita deinceps,
<
lb
/>
& nunquam hæ minutiæ ſubtractæ in infinitum totam differentiam ex
<
lb
/>
haurient; hinc minutiæ iſtæ 1/2 1/4 1/8 (1/16) (1/32) (1/64) &c. </
s
>
<
s
id
="
N17838
">in infinitum non fa
<
lb
/>
ciunt vnum integrum; ſed hæc ſunt facilia. </
s
>
</
p
>
<
p
id
="
N1783E
"
type
="
main
">
<
s
id
="
N17840
">Quarta ratio, quam afferunt aliqui, eſt; </
s
>
<
s
id
="
N17844
">quia ſi cum eadem velocita
<
lb
/>
te acquiſita in fine temporis dati ſine augmento nouo moueatur mobi
<
lb
/>
le; </
s
>
<
s
id
="
N1784C
">haud dubiè acquiret duplum ſpatium tempore æquali tempori dato; </
s
>
<
s
id
="
N17850
">
<
lb
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v. g. ſit triangulum AFE; </
s
>
<
s
id
="
N17859
">ſitque velocitas acquiſita EF in 4. parti
<
lb
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bus temporis AE, vt iam ſuprà dictum eſt, ne cogar repetere: </
s
>
<
s
id
="
N1785F
">certè ſi du
<
lb
/>
catur velocitas EF in tempus AE, vel EL æquale; </
s
>
<
s
id
="
N17865
">habebitur rectan
<
lb
/>
gulum EK duplum trianguli AFE: </
s
>
<
s
id
="
N1786B
">ſed triangulum AFE eſt ſumma
<
lb
/>
ſpatiorum motus accelerati tempore AE, & rectangulum EK eſt ſum
<
lb
/>
ma ſpatiorum motus æquabilis cum velocitate EF; igitur duplum eſt
<
lb
/>
ſpatium motus æquabilis, quod erat demonſtrandum. </
s
>
<
s
id
="
N17875
">Præterea ſi diui
<
lb
/>
datur velocitas EF, & eius ſubdupla ducatur in tempus AE; habebitur
<
lb
/>
rectangulum æquale triangulo AFE, vt conſtat. </
s
>
<
s
id
="
N1787D
">Reſpondeo facilè ex di
<
lb
/>
ctis, hoc ipſum etiam ex noſtra hypotheſi proxime ſequi; </
s
>
<
s
id
="
N17883
">ſint enim duo
<
lb
/>
inſtantia; </
s
>
<
s
id
="
N17889
">haud dubie ſi non creſcit velocitas, ſecundo inſtanti æquale
<
lb
/>
ſpatium percurretur; </
s
>
<
s
id
="
N1788F
">ſi vero ſecundo inſtanti creſcat, percurrentur illo
<
lb
/>
motu 3.ſpatia; </
s
>
<
s
id
="
N17895
">& cùm velocitas
<
expan
abbr
="
ſecũdi
">ſecundi</
expan
>
<
expan
abbr
="
inſtãtis
">inſtantis</
expan
>
ſit dupla velocitatis primi
<
lb
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inſtantis, primo inſtanti ſit 1.gradus v.g. ſecundo erunt 2. gradus; </
s
>
<
s
id
="
N178A5
">igi
<
lb
/>
tur moueatur per duo inſtantia motu æquabili veloci vt 2. percurrentur
<
lb
/>
4. ſpatia; </
s
>
<
s
id
="
N178AD
">igitur totum ſpatium, quod percurritur motu veloci vt 2. per
<
lb
/>
2.inſtantia eſt ad totum ſpatium, quod percurritur æquali tempore mo-</
s
>
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