Fabri, Honoré
,
Tractatus physicus de motu locali
,
1646
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N15AC3
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main
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<
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105
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026/01/137.jpg
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quirentur æquales velocitatis gradus; </
s
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<
s
id
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N17634
">ſit autem BI, menſura velocitatis,
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lb
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quam acquirit mobile cadens ex ſua quiete in fine primæ partis tempo
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ris AB; </
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<
s
id
="
N1763C
">certè in fine ſecundæ partis temporis BC acquiret velocitatem,
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quæ coniuncta cum priore BI faciet duplam CH, & in fine tertiæ par
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tiæ CD triplam DG; </
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>
<
s
id
="
N17644
">denique in fine quartæ DE quadruplam EF; </
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<
s
id
="
N17648
">quip
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pe cum in parte BC remaneat tota velocitas B, & acquiratur æqualis; </
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<
s
id
="
N1764E
">
<
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certè in fine BC eſt velocitas CH dupla illius quæ commenſuratur BI.
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ſimiliter in parte CD remanebit vtraque, & accedet altera; </
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>
<
s
id
="
N17655
">igitur eſt ve
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lb
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locitas DG tripla BI, & EF eſt quadrupla: Similiter ita ſe ratio habet
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cuiuſlibet alterius partis inter AB ad aliam alterius partis inter BC, vt
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lineæ ductæ parallelæ BICH, &c. </
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>
<
s
id
="
N1765F
">igitur cum ſpatium acquiſitum reſ
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pondeat exercitio huius velocitatis; </
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>
<
s
id
="
N17665
">ſitque inſtanti B vt BI, & inſtanti
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C vt CH; </
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>
<
s
id
="
N1766B
">certè tempore AB eſt vt triangulum AIB; </
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>
<
s
id
="
N1766F
">nam ſpatium AIB
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eſt collectio omnium linearum, quæ duci poſſunt parallelæ in tempore
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AB; </
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>
<
s
id
="
N17677
">idem dico de trapezo CBIH, qui eſt triplus trianguli IBA; </
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<
s
id
="
N1767B
">& de
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lb
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trapezo GDCH, qui eſt quintuplus; </
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>
<
s
id
="
N17681
">igitur triangulum HCA eſt qua
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lb
/>
druplum IBA; </
s
>
<
s
id
="
N17687
">quia hæc triangula ſunt vt quadrata laterum; </
s
>
<
s
id
="
N1768B
">igitur ſpa
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tium acquiſitum temporibus AB, BC, eſt ad ſpatium acquiſitum tempo
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re AB, vt triangulum HCB ad triangulum IBA; </
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>
<
s
id
="
N17693
">igitur vt quadratum
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AB ad quadratum AC; </
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>
<
s
id
="
N17699
">igitur vt quadratum temporis AB ad quadra
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tum temporis AC; igitur ſpatia diuerſis temporibus decurſa ſunt vt qua
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drata temporum, quibus ſingula decurruntur. </
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>
</
p
>
<
p
id
="
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type
="
main
">
<
s
id
="
N176A3
">Hæc ratio ad ſpeciem videtur eſſe demonſtratiua, deficit tamen à ve
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lb
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ra demonſtratione; </
s
>
<
s
id
="
N176A9
">primo, quia ſupponit inſtantia infinita, quæ multi
<
lb
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paſſim negabunt in tempore; </
s
>
<
s
id
="
N176AF
">immò aliquis vltrò demonſtrare tentaret
<
lb
/>
non eſſe infinita; </
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>
<
s
id
="
N176B5
">itaque ex ſuppoſitione quod ſint tantùm finita inſtan
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tia aſſumantur 4. æqualia AC, CD, DE, EF, certè cum inſtans ſit to
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lb
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rum ſimul, velocitatem habet æquabilem ſibi toti reſpondentem; </
s
>
<
s
id
="
N176BD
">igitur
<
lb
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inſtanti AC reſpondeat velocitas, cuius menſura ſit ABCG; </
s
>
<
s
id
="
N176C3
">haud du
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lb
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biè inſtanti CD reſpondebit velocitas CH, ſcilicet dupla AB; </
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>
<
s
id
="
N176C9
">nam re
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manet primus velocitatis gradus acquiſitus primo inſtanti: </
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>
<
s
id
="
N176CF
">ſed alter æ
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qualis acquiritur; </
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>
<
s
id
="
N176D5
">igitur eſt duplus prioris; </
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>
<
s
id
="
N176D9
">igitur reſpondet lineæ DK.
<
lb
/>
quæ tripla eſt AB, & quarto lineæ FN, quæ eſt quadrupla AB; </
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>
<
s
id
="
N176DF
">igitur
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lb
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creſcit ſpatium, vt rectangula CB, DH, EK, FM; </
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>
<
s
id
="
N176E5
">ſed hæc creſcunt iuxta
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lb
/>
progreſſionem numerorum 1.2.3.4. nec aliter res eſſe poteſt ex ſuppoſi
<
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tione quod ſint inſtantia finita; </
s
>
<
s
id
="
N176ED
">quod alibi ex profeſſo tractamus: </
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>
<
s
id
="
N176F1
">quippe
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illa quæſtio pertinet ad Metaphyſicam, non verò ad phyſicun; </
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>
<
s
id
="
N176F7
">nam vel
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ſingula aliquid addunt, vel nihil: aliquid addunt haud dubiè; </
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>
<
s
id
="
N176FD
">igitur con
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ſiderantur tantùm 4. inſtantia prima AC, CD, DE, EF, in ſua ſcrie; </
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>
<
s
id
="
N17703
">certè
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lb
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non poſſunt aliam progreſſionem facere quàm eam, quæ eſt iuxta hos
<
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/>
numeros 1.2.3.4.vnde non fit per triangula ſed per rectangula minima;
<
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igitur linea AF præcedentis figuræ non eſt recta, ſed denticulata, qualis
<
lb
/>
eſſet ABGHIKLMN, ſed longè minoribus gradibus, ſeu denticulis. </
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<
s
id
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N1770F
">
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Hinc quò rectangula CB, DH, &c. </
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>
<
s
id
="
N17713
">fient maiora in partibus ſcilicet tem
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lb
/>
poris ſenſibilibus, ſeruata ſcilicet in illis progreſſione numerorum 1.2.3. </
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