Fabri, Honoré
,
Tractatus physicus de motu locali
,
1646
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[Figure 42]
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poteſt declinari; </
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N2705A
">ſit enim circulus immobilis BDFC, mobilis FEG,
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punctum F poſt decurſum quadrantem FD extat ſupra planum hori
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zontis tota ID erecta; </
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<
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id
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N27062
">poſt decurſum verò ſemicirculum tota BK
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erecta æquali BF, vt conſtat; </
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<
s
id
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N27068
">igitur vertatur FBK, circa FB, donec incu
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bet perpendiculariter plano horizontali in BF; </
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<
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N2706E
">tùm circa FK, ita ere
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ctam vertatur planum, donec incubet DI, erecta in I, fiet planum, in quo
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deſcribetur linea huius motus; </
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<
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N27076
">aſſumatur autem DH æqualis AI; </
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<
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N2707A
">dico
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quod ducetur per FHK: </
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<
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id
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N27080
">ſimiliter inuenientur alia puncta, quod ſuffi
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ciat indicaſſe; </
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<
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id
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N27086
">eſt autem hic motus maximè inæqualis propter ratio
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nem, de qua ſuprà: </
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<
s
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N2708C
">ſed de his ſatis; </
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<
s
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N27090
">immò certum eſt punctum F ſuo
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motu prædicto deſcribere perfectum circulum duplum circuli rota
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ti, cuius centrum eſt D erectum in A, nam DH, DF, DK ſunt æqua
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les; </
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<
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id
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N2709A
">ſi enim circulus tangat in M, punctum F erectum toto arcu FM,
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reſpondebit perpendiculariter puncto O, ita vt OM ſit æqualis PB, vel
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HS, vel AN; erigatur autem OR, donec incubet perpendiculariter,
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extat ſuper AD erecta in A tota QR, ita OQ ſit æqualis AD. </
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<
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N270A5
">Sed
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quad. </
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<
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id
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N270AA
">AO eſt æquale quadratis AM, MO; igitur ſit quad. </
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<
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id
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N270AE
">AM qua
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dratum MO erit 8. igitur quadratum A 24. ſed extat ſuper MO, QR,
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æqualis OM; </
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<
s
id
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N270B6
">igitur ſi à D erecto ducantur duæ rectæ, altera ad Q, altera
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ad R, lineæ OR erectæ; </
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<
s
id
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N270BC
">certè DQ erit æqualis AO; </
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<
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N270C0
">eſt enim ipſi pa
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rallela; </
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<
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id
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N270C6
">tùm fiet triangulum ortogon ex tribus DQ, QR, DR; igitur
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quadr. </
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<
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id
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N270CC
">DR eſt æquale duobus DQ, QR, ſed DQ eſt æqualis A
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O; igitur quadr. </
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<
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N270D2
">DQ eſt 24. QR eſt æqualis OM; igitur quadr. </
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N270D6
">QR
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eſt 8. igitur quadratum DR eſt 32. ſed quadr. </
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<
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N270DB
">DF eſt 32. poſito
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quadrato AF 16.igitur DR erit æqualis DF; igitur circu
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lus duplus, &c. </
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<
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id
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N270E3
">quod erat demon
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ſtrandum.
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