Ceva, Giovanni
,
Geometria motus
,
1692
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tionem, ac GF ad IH, motus, qui fiunt iuxta illas geneſes,
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vocentur inter ſe ſimiles, & ipſæ geneſes dicentur ſimilium
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motuum; quod verò attinet ad rectas AE, BD, GF, IH apel
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labimus applicatas ad homologa puncta A, B, G, I propor
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tionales. </
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PROP. VI. THEOR. VI.
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">SI in imaginibus temporum homogeneis, applicatæ v
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nius fuerint ad homologa puncta, proportionales ap
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plicatis alterius imaginis, motus, quorum ſunt ipſæ imagi
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nes, ſimiles erunt. </
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ſint homogeneæ, & cum GI ad IK ſit vt AB ad BC, habeat
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quoque AL ad BM eandem rationem, ac GN ad IO. Di
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co, motus, quorum ſunt illæ imagines temporum inter ſe ſi
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miles eſſe. </
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Tab.
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2.
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fig.
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3.</
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ſcilicet EAC, FGK interſe homogeneæ. </
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BM, vt GN ad IO, erit conuertendo BM ad AL vt IO ad
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GN; ſed vt BM ad AL ita ob geneſim EA ad DB, & vt IO
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ad GN, ſic FG ad HI. ergo EA ad DB eſt vt FG ad HI, erat
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autem vt AB ad BC ita etiam GI ad IK, ergo motus ſunt
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ſimiles, & ipſæ imagines ſimilium motuum. </
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Def.
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2.
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huius.
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Def.
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7.
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huius.
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PROP. VII. THEOR. VII.
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<
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punctis homologè ſumptis proportionales applicatis
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alterius imaginis, motus iuxta ipſas imagines erunt ſimi
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les, ideoque ipſæ imagines ſimilium motuum. </
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Tab.
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2.
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fig.
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4.</
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<
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">Velocitatum imagines ſint ABCD, NPRT, ſitque AB
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ad EF in eadem ratione, in qua NP ad TR; Dico exiſtenti
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bus etiam BF ad FC, vt PQ ad QR eſſe propoſitas imagi
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nes ſimilium motuum. </
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