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

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3313LIBER I. iangentium, ideſt ipſas, Χ Δ, Υ Ζ, FQ, KL. Hìsìgitur
poſitis, voco ſolida, Γ β 3 Φ, AHBM, ſimilia; ſiguras verò, F
11_A. Def. @@._ GKD, ΧVΥΤ; dicθ figuras incidentes ſimilium ſolidorum iam
22_B. Def. _ dictorum, et oppoſitorum tangentium planorum, ℟ Δ, & Z; PQ,
Π L; ipſas autem figuras, β λ, Σ Φ, HE, CM, et eas, quarum
extenſa plana ſimiliter ad eandem partem diuidunt altitudines
ſolidorum, Γ β 3 Φ, AHBM, reſpectu dictorum tangentium
planorum ſumptas, & ſunt ſimiles, velbinæ ſimiles, & ſimiliter
inter ſe diſpoſitæ, voco figuras homologas dictorum ſolidorum,
33_C. Def. 11._ ſumptas, regulis earum duabus, vel dictis tangentibus planis.

SCHOLIVM.

_A_Duertendum eſt autem pro ſimilium figurarum nominatione,
dum voco eas ſimiles figuras ſiue planas, ſiue ſolidas, me intel-
ligere in eis d finitiones generales ſuperius allatas; dum verò eas
particulari nomine appello, intelligere definitiones particulares pro
ipſarum ſimilitudine ab alĳs, vel à me allatas, vt cum dicam, ſimi-
les coni ſectionum portiones, intelligam particularem in eis definitio-
nem, & cum dicam (ſimilta parallelogramma) intelligam in eis par-
ticularem definitionem ſimilium rectilinearum figurarum, & fic in
cæteris, licet vtramq; definitionem tum particularem, tum genera-
lem, de eiſdem figuris verificari inferius oſtendemus.

XII.

CVm fuerint quotcumque magnitudines eiuſdem ge-
neris vtcumque diſpoſitæ, prima ad vltimam dicitur
habere rationem compoſitam exrationibus primæ ad ſe-
cundam, ſecundæ ad tertiam, tertiæ ad quartam, & ſic de-
inceps vſq; ad vltimam.

XIII.

CVm vnum, & idem antecedens ad plura conſequen-
tia comparatum fuerit, ſingillatim ad vnumquodq;
comparare idem ad eadem conſequentia ſimul collecta, di-
cemus, colligere, vel, colligendo.

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