Ceva, Giovanni
,
Geometria motus
,
1692
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Ex mechani
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cis,</
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PROP. XXII. THEOR. XVII.
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Tab.
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7.
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fig.
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1.</
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">IMagines velocitatum, ſeu ſpatia, quæ curruntur accele
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ratis motibus, ſunt vt ſolida ab imaginibus ſimplicium
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motuum, ex quibus ipſi gignuntur accelerati. </
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da ab ipſis imaginibus (angulis ACQ, GHD ſemper re
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ctis, aut ſaltem æqualibus) intelligantur ABCRQ, GLHD.
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Dico, vt ſunt interſe iſta ſolida, ſic eſſe homologè ſpatium
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exactum tempore AC motu accelerato ex ſimplici motu
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imaginis ABC ad ſpatium tranſactum tempore GH motu
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item accelerato ex ſimplici imagine priori homogeneą
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GLH: ſecetur ſolidum ABCRQ plano æquidiſtanti QCR, </
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quod faciat in ſolido ipſo ſectionem TSVX: erit hæc figu
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ra prorſus ſimilis, ac æqualis conterminæ ABVI; quare
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cum in accelerato motu velocitas, quæ habetur momen
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to C ad velocitatem momento S ſit vt imago ABC ſim
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plex ad ſegmentum eius ABVS: erit etiam QCR æqualis
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ABC ad ſectionem ſolidi TSVX, quæ æquatur ABVS, vt
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illa eadem velocitas momento C mobili inhærens ad ve
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locitatem momento S alterius accelerati motus. </
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tem ſectio TSVX ad libitum ſumpta; ergo ſolidum ABC
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QR poteſt ſumi merito vt imago velocitatum accelerati
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motus, cuius ſimplex imago ABC: & eodem modo ſoli
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dum alterum vicem geret imaginis velocitatum alterius
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motus ex ſimplici imagine GLH, itaque erit ob homoge
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neitatem ſpatium tranſactum motu accelerato iuxta ſim
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plicem imaginem ABC ad ſpatium tranſactum motu ac
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celerato iuxta ſimplicem imaginem GLH,
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AC,
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GH, vt ſolidum ABCQR ad ALHD, </
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