Ceva, Giovanni
,
Geometria motus
,
1692
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Scholium.
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Vides, quàm breuiter rei diſficillimæ demonſtrationem at
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tulimus, nec dubium, quin illa extendi queat ad quaſcum
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que lineas decurſuum, dummodo ſimiles, ac ſimiliter poſitas in
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ijſdem, vel æqualibus ab horizonte planis elenatis, quemad
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modum Dominus Viuianus pulcherrimè propoſuit.
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Exemplum III.
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PROP. XXXV. THEOR. XXVIII.
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tionem habentia ſunt homologè vt longitudines
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planorum. </
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Tab.
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8.
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fig.
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3.</
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AB. (hæc Torricellij propoſitio,
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eſt, hancque
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eandem veritatem ex noſtris principijs demonſtrare
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eſt, non vt de re illa dubitemus, immò contrà, quòd de eą
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plenè ſatisfacti ſimus, ex eo rurſus demonſtrandam ſuſce
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pimus, vt exinde methodus noſtra, quàm vera ſit, eluceſ
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cat) Momentum deſcenſus inplano AC ad id deſcenſus ſu
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per plano AB eſt vt AB ad AC; ſunt autem
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deſcendentiũ
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grauium, etiam ſuper planis inclinatis motus, quos ſimpli
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ces appellamus, inter ſe ſimiles, nempe quorum geneſes
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ſunt rectangula; ergo habebimus ſimplices geneſes, vnam,
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cuius altitudo AC amplitudoque AB; alteram, cuius am
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plitudo AC, altitudo autem AB; itaque propoſitis ſpatijs
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AC, AB, primiſque velocitatibus AB, AC, ſi fiat AB ad AC
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vt CA ad EA, erit EA ad AB duplicata
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tẽporum
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, & ideo
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ratio temporum per AC, AB erit CA ad AB. </
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