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

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148128GEOMETRIÆ

A. DEMONSTRATIONIS SECTIO I.

SInt duæ quæcunque figuræ planæ ſimiles, ABD, ΦΣΛ. Dico
eaſdem eſſe in dupla ratione linearum, vel laterum homologo-
11Coroll. 1.
lib. 1. rum, earundem. Ducantur ipſarum oppoſitę tangentes, AK, FM,
figuræ, ABD, & , Φ Π, Δ Ω, ſiguræ, Φ Σ Λ, quæ homologis ea-
rum lineis æquidiſtent, deinde ſint intradictas oppoſitas tangentes
ductæ, KM, Π Ω, taliter, vt illæ ſint incidentes dictarum ſimilium
22Coroll. 2.
9. lib. 1. figurarum, & tangentium, hoc facto, diuidantur ipſæ incident@s, K

87[Figure 87] M, Π Ω, ſimil@ter, & ad eandem
partem vtcunq; in punctis, L, Γ,
per quæ puncta ſint ductæ ipſæ, B
L, Σ Γ, quarum portiones figuris
interceptę ſint, BE, ID, in figu-
ra, ABD, & , Σ 2, 3 Λ, in figu-
ra, Φ Σ Λ, ſumatur autem ex, BL,
recta æqualis vtriſque ſimul, BE,
ID, ter ninans in, KM, quæ ſit,
QL, & pariter ipſius, Σ 2, 3 Λ, ſit
ſumpta æqualis, Τ Γ, term nans
in, Π Ω, & in puncto, Γ, ſicq; fiat
de cæteris, quæ ipſis tangentibus
æquidiſtant, & manent intra figu-
rarum ambitum, quibusn m è in
eadem rectitudine ſun antur rectæ
æquales in ipſis, KM, ΠΩ, termi-
natæ, erunt igitur omnium in@en-
tarum linearum reliqui termini in
alia quadam inea, quæ inc pi@t in
puncto, K, & deſinet in, M, pro
figura, ABD, & quæ incip e in Π, & deſinet in, Ω, pro figura,
Φ Σ Λ, ſint iſtę lineę, KQM, Π Ω; patet igitur figuram, KQM,
333. huius. eſſe æqualem ipſi, ABD, & Π Ω, ipſi, Φ Σ Λ, nam omnes earum
lineæ ſumptæ regulis, FM, Δ Ω, ſunt æquales, quod ex ip a con-
ſtructione patet; dicantur autem iſtæ conſtruct ones, translationes
omn um linearum ſ gurarum, ABD, ΦΣΛ, in figuras, KQA, Π
Τ Ω, ipſi, KM, ΠΩ adiacentes, effectę regulis dictis tangent bus.
Patet vlterius figuras, KQM, ΠΤΩ, eſſe ſim les, nam homologę
figurarum, ABD, ΦΣΛ, (quia illę ſunt ſimiles) ſunt vt incidentes,
44Coroll. 1.
22. lib. 1. KM, ΠΩ, eæden autem in figuras, KQM,ΠΤΩ, modo dicto,
translatæ ſunt (ſimui in vnam rectam coniunctis, quæ diuiſæ

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