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.

9171LIBERI.

SImiles coni, & cylindriſunt, quorum & axes, & baſium diame-
tri eandem inter ſe proportionem habent. Euclid. lib. 11. Elem.
defin. 24.

Verum, quia ſupradicta definitonon

48[Figure 48] eſt niſi cylindrorum, & conorum re-
ctorum, ideo aliam, quę affertur à Com-
mandino tum de rectis, tum etiam de
ſcalenis illi ſubiungo, quam ſufficiet o-
ſtendere cum mea ſuptadicta concor-
dare, nam hęcCommandinieam, quam
Euclides attulit, inuoluit.

SImiles coni, & cylindri, ſiue recti, ſiue ſcaleni ſunt, quando per
axes ductis planis ad rectos angulos baſibus, communes ſectio-
nes eorum, & baſium cum axibus æquales angulos continentes, ean-
dem inter ſe, quam axes, proportionem habent: Commandinus lo-
co definitionis ſupra citatæ.

Sint coni, BEC, GMN, & cylindri, AC, FN, ſimiles iuxta
11Defin. 11. proximam definitionem. Dico eoſdem eſſe ſimiles iuxta meam ſu-
pradictam. Vt autem in ſimul pro conis, & cylindris fiat demon-
ſtratio, ſupponanturconi, & cylindri iam dicti eſſe in eiſdem baſi-
bus, & circa eoſdem axes; ducantur ergo in ipſis plana per axes, qui
ſint, EO, MR, quoniam ergo latera cylindrorum ſunt ſuis axibus
parallela, ideò dicta plana tranſibunt per latera cylindrorum, ſiue
22Ex. def. 3.
& 4. Cor. cylindricorum, AC, FN, & per latera conorum, ſiue conicorum,
EBC, MGN, quia per eorum vertices intra ipſos ducuntur, ſint
autem dicta plana ea, quę ſint ad rectos angulos baſibus, quorum &
baſium communes ſectiones, quæ ſint, BC, GN, cum axibus æ-
quales angulos continentes eandem interſe, quam axes proportio-
nem habeant, vt fert definitio, fient igitur in cylindricis parallelo-
gramma, vt, AC, FN, & in conicis triangula, vt, BEC, GMN,
33Ex Cor. 5.
& ex 16.
huius.& quia anguli, BOE, GRM, ſunt ęquales, ideò etiam ipſi, BCD,
GNH, ſunt æquales, & eſt, BC, ad, CD, vt, GN, ad, NH,
ideò parallelogramma, AC, FN, & triangula, BEC, GMN, e-
runt ſimilia iuxta definitionem Euclidis, & ideò etiam iuxta meam,
& quia ipſæ, AD, BC, FH, GN, tangunt figuras, AC, FN,
4427. huius.

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