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. </s>
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              Theorema
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              86.
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              Motus puncti L initio eſſet minor motu puncti V initio; </s>
              <s id="N1E803">id eſt poſito quod
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              demittatur ex V verſus A
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              ; </s>
              <s id="N1E80C">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; </s>
              <s id="N1E816">ſed motus per LC ini­
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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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              eſt ad motum per­
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              pendiculi FA vt FE ad FA; </s>
              <s id="N1E824">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. </s>
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            <p id="N1E82C" type="main">
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                <emph type="center"/>
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              Theorema
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              87.
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              </s>
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            <p id="N1E83A" type="main">
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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. </s>
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            <p id="N1E850" type="main">
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                <emph type="italics"/>
              Theorema
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              88.
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              </s>
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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. </s>
              <s id="N1E86A">v.g. punctum L; </s>
              <s id="N1E870">aſſumatur
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              arcus LQ æqualis arcui LA; </s>
              <s id="N1E876">ducatur recta AQ, in quam ducatur LK
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              perpendicularis: </s>
              <s id="N1E87C">dico motum in L per arcum LVA initio eſſe ad motum
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              per LA vt KA ad LA: </s>
              <s id="N1E882">ſimiliter ſit punctum V; </s>
              <s id="N1E886">aſſumatur VL æqualis
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              arcui VA; </s>
              <s id="N1E88C">& 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; </s>
              <s id="N1E894">idem dico de omnibus aliis: </s>
              <s id="N1E898">Ratio eſt, quia Tangens, quæ ducere­
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              tur in V eſſet parallela AX; igitur triangula vtrimque eſſent æqualia. </s>
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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. </s>
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              Theorema
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              89.
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              </s>
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            <p id="N1E8B5" type="main">
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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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              : </s>
              <s id="N1E8CA">cum
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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. </s>
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