Cavalieri, Buonaventura
,
Geometria indivisibilibvs continvorvm : noua quadam ratione promota
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LIBER I.
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GM, ideſt, vt, AD, ad, GH, ergo permutando, BA, ad, AD,
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Elem.</
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erit vt, IG, ad, GH, & </
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">anguli, BAD, IGH, ſunt æquales, er-
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go, BAD, IGH, erunt triangula ſimilia, ergo anguli, ADB, G
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HI, æquales erunt, ſunt autem ęquales etiam, ADF, GHO, er-
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go reliqui, BDF, IHO, erunt æquales, eſt verò, BD, ad, DA,
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vt, IH, ad, HG, &</
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">, AD, ad, DF, vt, GH, ad, HO, ergo ex
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æquali, BD, ad, DF, eſt vt, IH, ad, HO, ergo triangula, BD
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F, IHO, pariter ſimilia erunt, & </
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<
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">anguli, DFB, HOI, inter ſe,
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necnon, DBF, HIO, inter ſe ęquales, ergo anguli, ABF, GIO,
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ADF, GHO, erunt etiam ęquales, & </
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<
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æquiangulę, & </
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">cum, BA, ad, DF, FB, binæ ſint in eadem ratio-
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ne cum, IG, GH, HO, OI, patet, quod etiam circa ęquales an-
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gulos ſunt latera proportionalia, ergo ipſæ figuræ, BADF, IG
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HO, ſimiles erunt. </
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<
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">Eodem autem modo oſtendemus ſimiles eſſe, B
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CEF, IMNO, patet autem ipſas, BF, IO, eſſe earum latera ho-
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mologa, quod erat demonſtrandum.</
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<
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tamen in eodem plano conſtituta) ad quę anguli ſolidi æquales ter-
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minantur, illaq; </
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">iungatur rectis lineis, fient ſimiles pyramides trian-
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@ti El.</
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gulatæ comprehenſæ ſub triangulis, ijſdem rectis lineis iungentibus
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contentis.</
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GL, iuxta def.</
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">& </
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ijs accepta quatuor quęcumq; </
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cta, nempè, A, H, C, D, in vno,
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&</
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">, F, O, G, L, in alio ſolido, quæ
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non ſint in eodem plano, ſed ad an-
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gulos ęquales conſtituta, iungantur-
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querectis lineis, AH, AC, CD, C
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H, HD; </
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L, LO, ſiue hęc iungentia ſint ipſo-
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rum ſimilium ſolidorum latera. </
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copyramides, AHCD, FOGL,
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ſimiles eſſe. </
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ramides continentia ſunt in ambitu
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ſolidorum, vt ex.</
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finitione, vel non ſunt in ambitu, tunc autem probandum eſt nihi-
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lominus eſſe ſimilia, vt non ſint in ambitu ipſa triangula, ACH, </
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