Ceva, Giovanni
,
Geometria motus
,
1692
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to F motu compoſito currens; verùm quia quadratum ex
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PR ęquatur rectangulo ORQ vnà cum quadrato ex PQ, &
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eſt ob hyperbolam rectangulum ORQ æquale quadrato
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ex HI, vel PK; ergo PR quadratum æquale erit duobus ſi
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mul quadratis PQ, PK; itaque PR erit gradus velocitatis
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prædicti mobilis in F momento P, compoſitoque motu
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currentis iuxta curuam parabolicam. </
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M, cum mobile eſſet in D velocitas compoſiti motus foret
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MS poteſtate æqualis duabus MT, ML, ac demum in A
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initio motus velocitas eſt HI: quare HISM erit imago ve
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locitatis motus compoſiti dum mobile punctum deſcripſe
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rit curuam parabolicam AFD, eſtque illa imago imagini
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bus diuiſorum, ſeu ſimplicium, motuum homogenea; ergo
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conſtat baſim etiam BD ad parabolam AFD eandem ha
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bere rationem, quam rectangulum HILM ad quadrili
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neum HISM. </
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Def.
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7.
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primi
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& pr.
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12.
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pri
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mi huius.
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Cor. </
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4.
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hu.
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Pr.
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2.
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primi
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huius.
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Ex pr.
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12.
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hu.
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Pr.
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3.
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huius.
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Pr.
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11.
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l.
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2.
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co
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nic.
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Def.
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3.
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prima
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huius.
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Corollarium. I.
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Patet, cum latera compoſiti motus ſint duo, & ſibi ipſis per
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pendicularia, tunc gradum velocitatis eìuſdem motus compo
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ſiti æqualem eſſe potentiâ duobus ſimul gradibus, quos habet
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mobile eodem momento, ac ſi ſeorſim intelligatur in ipſis ferri
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lateribus.
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Corollarium. II.
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Si verò conſiderentur imagines primi ſecundique Caſus
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interſe homogenea, erit vt quadrilineum HISM primi ad
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quadrilineum ijſdem literis notatum ſecundi caſus, vt cur
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ua illa parabolica ad hanc ſecundi caſus parabolam.
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