Full text: Cavalieri, Bonaventura: Geometria indivisibilibvs continvorvm

GEOMETRIÆ lela eſt ipſi, ED. Ducaturintra trapezia parallela ipſi, AB, vtcun-
que, VC, ſecans, XA, in, S, & , O
B, in, T, ſunt igitur triangula, AO
B, VOT, ſimilia, & pariter ſunt ſi-
milia triangula, AXB, SXC, ergo,
AB, ad, VT, erit vt, BO, ad, OT,
. i. vt, BX, ad, XC, (quia, VC, pa-
rallela eſtipſi, AB, & conſequenter
ipſi, OX,) . i. vt, AB, ad, SC, er-
go, VT, SC, erunt & ae; quales. & eo-
rum quadrata pariter & ae; qualia, ſic au-
tem de cæteris ipſi, AB, parallelis
idem oſtendetur, ergo omnes lineæ
trapezij, AERB, erunt & ae; quales omnibus lineis trapeZij, AIDB,
regula, AB, & conſequenter ipſa trapezia erunt & ae; qualia, & omnia
eorundem quadrata pariter & ae; qualia, quod oſtendere opus erat.

253.1.

Iux. diff. 1.
Sexti Ele-
ment.
4. Sex. El.
0188-01

254. THEOREMA XXVIII. PROPOS. XXVIII:

SI parallelogrammum, & trapezium habuerint commu-
nem baſim vnum ęquidiſtantium laterum trapezij, quod
ſit ſumptum pro regula; Omnia quadrata parallelogrammi
ad omnia quadrata trapezij erunt, vt quadratum dictæ baſis
ad rectangulum ſub parallelis lateribus trapezij, cum, {1/3},
quadrati differentiæ dictorum laterum & ae; quidiſtantium.

Sit parallelogrammum, AC, & trapezium, IBCO, cuius late-
rum & ae; quidiſtantium alterum, vt, BC, ſit communis baſis ipſi, & trapezio, & regula. Dico ergo omnia quadrata, AC, ad omnia qua-
drata trapezij, IBCO, eſſe vt quadratum,
BC, ad rectangulum ſub, BC, IO, vna
cum, {1/3}, quadrati differentiæ ipſarum, B
CIO. Sumatur in, DA, ipſa, ED, & ae; -
qualis ipſi, IO, & iungatur, BE, & per,
E, ipſis, AB, DC, parallela ducatur, E
M: Omnia ergo quadrata trapezij, EBC
D, perlineam, EM, diuiduntur in omnia
quadrata trianguli, EBM, & in omnia
quadrata, MD, & in rectangula ſub tri-
angulo, EBM, & , EC, bis ſumpta; ad horum ergo ſingula com-
paremus omnia quadrata, AC. Igitur omnia quadrata, AC, ad

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