Cavalieri, Buonaventura
,
Geometria indivisibilibvs continvorvm : noua quadam ratione promota
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LIBER II.
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planorum, necnon planorum earundem figurarum incidentium,
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nempè, HL, 3 Σ, quod ſerua.</
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<
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rum, H {00/ }, Σ 2, plurificari poſſunt, quę ſunt in eodem plano,
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vti apparet in figuris, S, Y, β, Γ, quę cum ſint in eodem plano ſunt
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tamen duæ figuræ, ideò vt ex duobus fiat vna tantum, adhuc om-
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nium linearum harum adiacentium figurarum aliam translationem
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regulis, HL, Σ 3, faciemus; </
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<
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">ducantur ergo per ipſas, LG, 38, duo
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plana, quorum & </
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ſectiones ſint ipſæ, 3 {12/ }, 8 {13/ }, LQ, GT, cum ipſis, 3 Σ, 82, LH,
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G {00/ }, angulos æquales continentes, & </
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<
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">agantur duę ex oppoſito tan-
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gentes figuras, OZX, Φ Γ Λ, parallelę ipſis, OX, Φ Λ, quę ſint ip-
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iæ, ZF, Γ 7, productæ cum reliquis tangentibus oppoſitis, OX, Φ
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Λ, donec occurrant planis, LT, 3 {13/ }, vt in punctis, E, F; </
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ctis rectis lineis, EF, 47. </
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<
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">Quia ergo, DE, ęquidiſtat ipſi, {00/ }G, &</
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Elem.</
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EF, ipſi, GT, angulus, DEF, æquatur angulo, {00/ } GT, & </
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ratione angulus, 647, probabitur æqualis ipſi, 28 {13/ }, vnde, quia,
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{00/ }GT, æquatur ipſi, 28 {13/ }, angulus, FED, erit æqualis angulo,
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746, & </
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<
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">cum ſit, vt, OX, ad, Φ Λ, vel vt, OE, ad, Φ 4, quia, L
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G, 38, ſunt lineæ incidentes ſimilium planarum figurarum, H {00/ },
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24. lib. 1.</
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Σ 2, vel vt, XE, ad, Λ 4, ita, EF, ad, 47, ſint autem, XE, Λ 4,
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comprehenſæ inter eaidem extremitates rectarum, EF, 47, & </
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metrum figurarum, OZX, Φ Γ Λ, eaſdem tangentes, ergo, EF, 4
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7, erunt incidentes ſimilium figurarum, OZX, Φ Γ Λ, & </
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rum tangentium, OE, ZF; </
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oppoſitæ tangentes figurarum, S, Y; </
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">β Δ, quarum duæ incidant ip-
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ſis, LG, 38, vt in, K, {10/ }, reliquæ vero in punctis, {11/ } {14/ }, planis, L
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T, 3 {13/ }, occurrant, iunctis, K {14/ }, {10/ } {11/ }, oſtendemus pariter ipſas, K
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{14/ }, {10/ } {11/ }, eſſe incidentes ſimilium figurarum, Y, Δ, vel ſimilium, S,
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β, & </
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<
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&</
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finem A.
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p. 15. hu-
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ius.</
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gurarum, S, Y, tum, β, Δ, regulis eiſdem tangentibus, vel ſemper
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regulis ipſis, OE, Φ 4, prius compoſitis illis, quę ſibi in directum e-
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runt, tum in figuris, S, Y, tum, β Δ, vt ex illis fiat vnica compoſita
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recta linea, prędictis in directum poſita in figura adiacente, qualis ſit,
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9 {10/ }, æqualis .</
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MK, æqualis compoſitæ ex his, quibus adiacent figuræ, S, Y; </
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dem habebimus figuras adiacentes ipſis incidentibus .</
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{11/ }, in quibus plures figuræ, S, Y, in vnam, MK {14/ }, & </
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