Fabri, Honoré, Tractatus physicus de motu locali, 1646

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              Theorema
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              47.
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              Facilè cognoſcitur, in qua proportione potentia applicata puncte A faciliùs
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              vertat rotam, quàm applicata puncto F in circulo ſcilicet horizontali
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              ; </s>
              <s id="N222D0">ſit enim
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              ſolus vectis FC, cuius centrum ſit E; </s>
              <s id="N222D6">certè ſi vertatur in circulo hori­
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              zontali, potentia applicata extremitati C faciliùs verſabit, quàm appli­
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              cata puncto F, iuxta proportionem CE ad EF, vel ad HE; igitur po­
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              tentia applicata puncto H, vectis CF eſt eiuſdem momenti, cuius eſt ea­
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              dem applicata puncto F, quia æqualem prorſus effectum, ſcilicet impe­
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              tum, debet producere in vecte CF, vt moueatur in circulo horizontali
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              circa centrum E. </s>
              <s id="N222E7">Probatur vlteriùs, quia motus, æquabiles ſcilicet, ſunt
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              vt ſpatia, impetus vt motus, vires vt impetus; </s>
              <s id="N222ED">igitur applicata potentiæ
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              in C producat impetum in vecte CF, vt vertatur in plano horizontali, &
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              C eo motu acquirat CS ſegmentum CE ſectorem CES; </s>
              <s id="N222F5">ſegmentum
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              verò FE ſectorem FEV; </s>
              <s id="N222FB">applicetur autem eadem potentia in F, vt ver­
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              tatur, idem vectis FC, & producatur in F impetus æqualis impetui an­
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              tè producto in C; </s>
              <s id="N22303">haud dubiè punctum F percurret arcum FG eo tem­
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              pore, quo C priore motu percurrebat CS, vt patet; </s>
              <s id="N22309">quia arcus CS eſt
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              æqualis quadranti FG; igitur ſegmentum FE quadrantem FEG, & ſeg­
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              mentum EC quadrantem CED. </s>
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              Theorema
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              48.
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              Ex his determinantur omnes aliæ proportiones
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              ; </s>
              <s id="N2232A">ſi enim fit vectis AC
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              (quem ſuppono æqualem in omnibus ſuis partibus & volubilem circa
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              centrum E in plano horizontali) & applicetur potentia in puncto A, in
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              quo producat minimum impetum, quem poteſt immediatè producere ex
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              hypotheſi toties repetita, ita vt dato tempore percurrat A arcum AK, ſi
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              ſit vectis AH, & applicetur potentia in A, mouebit faciliùs, quàm AC
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              iuxta proportionem 8/5; </s>
              <s id="N2233A">nam in vecte AC ſpatium eſt compoſitum ex
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              gemino ſectore AEK, CES, & in vecte AH ſpatium eſt compoſitum
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              ex ſectore AEK & ZEH, qui ſubquadruplus eſt AEK; </s>
              <s id="N22342">igitur hoc ſpa­
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              tium totum confectum hoc vltimo motu eſt ad prius ſpatium vt 5. ad 8.
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              igitur & motus; </s>
              <s id="N2234A">igitur & impetus; </s>
              <s id="N2234E">ſed quò minor eſt impetus, eſt maior
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              facilitas; igitur facilitas vltimi motus eſt ad facilitatem primi, vt 8. ad 5.
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              idem dico, ſi applicetur potentia in H. </s>
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              <s id="N22359">Si verò retento ſemper eodem vecte AC applicetur potentia tùm in
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              A, tùm in F, facilitas motus potentiæ applicatæ in A eſt ad facilitatem
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              motus potentiæ applicatæ in F, vt AE ad FE, vel vt AB ad AK, vel
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              vt AEB ad AEK, quæ omnia conſtant ex dictis; igitur applicata in F
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              in vecte AC eſt ad applicatam in F in vecte FE vt 5. ad 8. ſed hæc ſunt
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              ſatis clara, nec vlteriore explicatione indigent. </s>
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              Theorema
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              49.
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              Hinc quò propiùs ad centrum applicatur potentia, eò maior eſt difficultas
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              motus
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              ; </s>
              <s id="N22382">igitur ſi applicetur ipſi centro mathematicè conſiderato eſt infi­
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              nita difficultas; </s>
              <s id="N22388">igitur nulla potentia ſuperare poſſet hanc difficultatem; </s>
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