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

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155135LIBER II. inrecta, Φ Λ, & incidentem eiuſdem figuræ, nempè ipſam, 38, in
puncto, 4, igitur figuræ, BC, Π Ω, erunt duæ figurarum homolo-
11Defin. 11.
huius. garum ſolidorum, AP, V & , & , OX, Φ Λ, earum incidentes, & ,
LG, 38, erunt ſimiliter diuiſæ in punctis, E, 4, nam etiam altitu-
2217. Vndec.
Elem. dines propoſitorum ſimilium ſolidorum ſunt ſimiliter diuiſæ (ad ean-
dem partem ſub intellige) ſi igitur à punctis, O, Φ, duxerimus tan-
gentes figuras, BC, Π Ω, erunt iſtæ regulis homologarum earun-
dem figurarum parallelæ, vel pro regulis aliarum etiam aſſumi pote-
runt, & quę à punctis, X, Λ, ducentur prędictis parallelę occurrent
eiſdem figuris, & illas ex oppoſito prędictarum contingent, ita vt ha-
beamus (ſi & iſtæ ductæ intelligantur, quæ ſint, XC, Λ Ω,) oppc-
fitas tangentes figuræ, BC, quæ erunt, BO, CX, & figuræ, Π Ω,
quæ erunt, Π Φ, Ω Λ, necnon pro regulis homologarum earundem
haberi poterunt; vel igitur figuræ, BC, Π Ω, adiacent ſuis inciden-
tibus, OX, Φ Λ, totę ad eandem partem, & interius integrę exiſten-
tes, vel non, ſi ſic factum erit, quod volumus, ſi non transferantur
omnes lineæ figurarum, BC, Π Ω, regulis eiſdem tangentibus, in
33Vide A.
15. huius
propèfin. figuras ipſis, OX, Φ Λ, adiacentes, pro vt in Prop. 15. effectum eſt,
hinc autem reſultantes figurę ſint, OZX, Φ Γ Λ, quę per talem con-
ſtructionem ad eandem partem incidentium, & interius integrę nc-
bis proueniunt. Similiter ſi intelligamus ducta alia duo plana prędi-
ctis ęquidiſtantia, quę ſolida propoſita ita ſecent, vt fiant in ipſis non
vnica in ſingulis figura, ſed plures, ex. gr. in ſolido, AP, figurę, R,
I, & in, V & , figuræ, ℟, N, eadem autem ſecent figuras inciden-
tes in rectis, SY, Β Δ, & rectas, LG, 38, in punctis, K, {10/ }, dum-
modo hæc plana pariter ſecent altitudines dictas propoſitorum ſoli-
dorum ſimiliter ad eandem partem, erunt figurę, R, I, binę ſimiles, &
44E. Def. 10.
lib. 1. ſimiliter poſitę, ac figurę, ℟, N, . ſ. I, ſimilis ipſi, N, & , R, ipſi, ℟, &
linearum homologarum earundem regulæ ipſis, CX, Ω Λ, æquidi-
ſtabunt, ipſę autem rectę, S, Y; β, Δ, erunt earundem incidentes,
vt, S, β, ipſarum, R, ℟, & , Y, Δ, ipſarum, I, N, ſi igitur figurę,
R, I, ℟, N, non adiacent ſuis incidentibus, transferantur ſingula-
rum omnes lineę, regula ſemper, pro figuris, RI, ipſa, CX, & pro
55Videad
fig. A. figuris, ℟, N, ipſa, Ω Λ, in figuras adiacentes lineis homologis figu-
66Piop. 15.
huius. rarum, H {00/ }, Σ 2, vt ſint nobis inuentæ figuræ, S, Y, β Δ, quæ
adiaceant homologis lineis figurarum incidentium, H, {00/ }, Σ 2: Si
igitur eandem methodum ſeruemus in cæteris figuris, quæ ex lectio-
ne planorum tangentibus æquidiſtantium in dictis ſolidis producun-
tur, transferentes nempè omnes earum lineas homologas, regulis
ſemper ipſis, CX, Ω Λ, in figuras adiacentes lineis homologis figu-
rarum incidentium, H, {00/ }, Σ 2, quę reperientur totę ad eandem par-
tem, & interius integrę, tandem nobis erunt comparata duo

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