Cavalieri, Buonaventura - Geometria indivisibilibvs continvorvm : noua quadam ratione promota

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157137LIBER II. planorum, necnon planorum earundem figurarum incidentium,
nempè, HL, 3 Σ, quod ſerua.

B. SECTIO II.

NVnc quia figuræ iam dictæ adiacentes homologis lineis figura-
rum, H {00/ }, Σ 2, plurificari poſſunt, quę ſunt in eodem plano,
vti apparet in figuris, S, Y, β, Γ, quę cum ſint in eodem plano ſunt
tamen duæ figuræ, ideò vt ex duobus fiat vna tantum, adhuc om-
nium linearum harum adiacentium figurarum aliam translationem
regulis, HL, Σ 3, faciemus; ducantur ergo per ipſas, LG, 38, duo
plana, quorum & oppoſitorum planorum tangentium communes
ſectiones ſint ipſæ, 3 {12/ }, 8 {13/ }, LQ, GT, cum ipſis, 3 Σ, 82, LH,
G {00/ }, angulos æquales continentes, & agantur duę ex oppoſito tan-
gentes figuras, OZX, Φ Γ Λ, parallelę ipſis, OX, Φ Λ, quę ſint ip-
iæ, ZF, Γ 7, productæ cum reliquis tangentibus oppoſitis, OX, Φ
Λ, donec occurrant planis, LT, 3 {13/ }, vt in punctis, E, F; 4, 7, iun-
ctis rectis lineis, EF, 47. Quia ergo, DE, ęquidiſtat ipſi, {00/ }G, & ,
1116. Vnd@
Elem. EF, ipſi, GT, angulus, DEF, æquatur angulo, {00/ } GT, & eadem
ratione angulus, 647, probabitur æqualis ipſi, 28 {13/ }, vnde, quia,
{00/ }GT, æquatur ipſi, 28 {13/ }, angulus, FED, erit æqualis angulo,
746, & cum ſit, vt, OX, ad, Φ Λ, vel vt, OE, ad, Φ 4, quia, L
G, 38, ſunt lineæ incidentes ſimilium planarum figurarum, H {00/ },
22Corollat.
24. lib. 1. Σ 2, vel vt, XE, ad, Λ 4, ita, EF, ad, 47, ſint autem, XE, Λ 4,
comprehenſæ inter eaidem extremitates rectarum, EF, 47, & peri-
metrum figurarum, OZX, Φ Γ Λ, eaſdem tangentes, ergo, EF, 4
7, erunt incidentes ſimilium figurarum, OZX, Φ Γ Λ, & oppoſita-
rum tangentium, OE, ZF; Φ 4, Γ 7. Similiter ſi ſic producantur
3324. lib. 1. oppoſitæ tangentes figurarum, S, Y; β Δ, quarum duæ incidant ip-
ſis, LG, 38, vt in, K, {10/ }, reliquæ vero in punctis, {11/ } {14/ }, planis, L
T, 3 {13/ }, occurrant, iunctis, K {14/ }, {10/ } {11/ }, oſtendemus pariter ipſas, K
{14/ }, {10/ } {11/ }, eſſe incidentes ſimilium figurarum, Y, Δ, vel ſimilium, S,
β, & oppoſitarum tangentium extremarum, quæ ad puncta, K 14,
& , {10/ }, {11/ }, terminantur. Si igitur transferamus omnes lineas tum fi-
44Vide ad
finem A.
p. 15. hu-
ius. gurarum, S, Y, tum, β, Δ, regulis eiſdem tangentibus, vel ſemper
regulis ipſis, OE, Φ 4, prius compoſitis illis, quę ſibi in directum e-
runt, tum in figuris, S, Y, tum, β Δ, vt ex illis fiat vnica compoſita
recta linea, prędictis in directum poſita in figura adiacente, qualis ſit,
9 {10/ }, æqualis . i. compoſitæ ex his, quibus adiacent figuræ, β Δ, & ,
MK, æqualis compoſitæ ex his, quibus adiacent figuræ, S, Y; tan-
dem habebimus figuras adiacentes ipſis incidentibus . ſ. MK {14/ }, 9 {10/ }
{11/ }, in quibus plures figuræ, S, Y, in vnam, MK {14/ }, & β, Δ, in

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