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

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

Table of contents

[101.] COROLLARIVM.

[102.] THEOREMA XXV. PROPOS. XXVIII.

[103.] DEFINITIO.

[104.] SCHOLIV M.

[105.] LEMMA I.

[106.] LEMMA II.

[107.] LEMMA III.

[108.] LEMMA IV.

[109.] COROLLARIVM.

[110.] LEMMA V.

[111.] COROLLARIV M.

[112.] LEMMA VI.

[113.] COROLLARIVM.

[114.] THEOREMA XXVI. PROPOS. XXIX.

[115.] THEOREMA XXVII. PROPOS. XXX.

[116.] LEMMA.

[117.] THEOREMA XXVIII. PROPOS. XXXI.

[118.] DEFINITIO.

[119.] DEFINITIO.

[120.] THEOREMA XXIX. PROPOS. XXXII.

[121.] THEOREMA XXX. PROPOS. XXXIII.

[122.] THEOREMA XXXI. PROPOS. XXXIV.

[123.] COROLLARIVM.

[124.] THEOREMA XXXII. PROPOS. XXXV.

[125.] COROLLARIVM.

[126.] THEOREMA XXXIII. PROPOS. XXXVI.

[127.] THEOREMA XXXIV. PROPOS. XXXVII.

[128.] COROLLARIVM.

[129.] THEOREMA XXXV. PROPOS. XXXVIII.

[130.] THEOREMA XXXVI. PROPOS. XXXIX.

188168GEOMETRIÆ lela eſt ipſi, ED. Ducaturintra trapezia parallela ipſi, AB, vtcun-

108[Figure 108] 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.

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-

109[Figure 109] 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
11PerD. Co
toll. 23.
huius. 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
229. huius.

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