Fabri, Honoré
,
Tractatus physicus de motu locali
,
1646
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trorſum poteſt duci linea LA breuior arcu LVA; igitur per concauum
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LVA non deſcenderet mobile. </
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Theorema
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86.
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Motus puncti L initio eſſet minor motu puncti V initio; </
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<
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demittatur ex V verſus A
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; </
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<
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">demonſtro, quia eodem modo ſe habet in L,
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atque ſi eſſet in puncto L
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LC, vt pater; </
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<
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tio eſt ad motum per LA vt ND ad NA vel vt LC ad LA per Th.55.
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at verò motus in V vel in F initio per FE
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Tãgentem
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eſt ad motum per
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pendiculi FA vt FE ad FA; </
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<
s
id
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">ſed eſt maior ratio FE ad FA, quàm LE
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ad LA, vt conſtat; igitur motus initio in V eſt minor quàm in L
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initio. </
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Theorema
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87.
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Hinc eſt inuerſa ratio motus funependuli vulgaris & plani inclinati recti,
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in quibus motus ſupremi puncti eſt maior motu cuiuſlibet alterius pun
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cti, vnde inciperet motus, cum tamen hic ſit minor: porrò poſſet eſſe
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funependulum KLA dum vel LVA eſſet orbis durus quem media di
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uideret rima quaſi ecliptica globi penduli ex K fune extenſo, & per ri
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mam incerto KL, vel quod faciliùs eſſet ſi KL eſſet priſma durum, quod
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circa K immobile moueri ſeu volui poſſet. </
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Theorema
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88.
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Alia via facilior occurrit, quæ mihi videtur non eſſe omittenda qua propor
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tiones illæ diuerſi motus demonstrari poſſent,
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ſit. </
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<
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">v.g. punctum L; </
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arcus LQ æqualis arcui LA; </
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perpendicularis: </
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<
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">dico motum in L per arcum LVA initio eſſe ad motum
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per LA vt KA ad LA: </
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arcui VA; </
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">& in hanc perpendicularis VX.dico motum in V per arcum
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VA eſſe ad motum per ipſum perpendiculum VA vt XA ad rectam
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VA; </
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<
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">Ratio eſt, quia Tangens, quæ ducere
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tur in V eſſet parallela AX; igitur triangula vtrimque eſſent æqualia. </
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v.g. FEA & FYA: item motus in P eſt ad motum per ipſum perpen
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diculum, vt Tangens PM ad PA, vt conſtat ex dictis. </
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Theorema
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89.
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Hinc totus motus per LA perpendiculum eſt ad totum motum per arcum
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LVA, vt omnes chordæ ductæ ab A ad omnia puncta quadrantis AVL
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ſimul ſumptæ ad totidem ſubduplas chordarum ductarum ab A ad alterna
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puncta totius ſemicirculi ALQ vel ad totidem
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ſimul ſumptas
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: </
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<
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enim motus in L per arcum LVA ſit ad motum in L por ipſum perpen
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diculum LA vt ſubdupla AQ ad LA, & motus in V per arcum in A
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ſit ad motum in V per rectam VA, vt ſubdupla chordæ AL ad rectam
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VA, atque ita deinceps per Th.88. certè omnia antecedentis ſimul ſum
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pta habent illam rationem ad omnia conſequentia ſimul ſumpta, vt con
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ſtat; igitur totus motus, &c. </
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