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

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

Table of contents

[91.] COROLLARIVM II.

[92.] LEMMA PRO ANTECED. PROP.

[93.] THEOREMA XX. PROPOS. XXIII.

[94.] COROLLARIVM.

[95.] THEOREMA XXI. PROPOS. XXIV.

[96.] COROLLARIVM.

[97.] THEOREMA XXII. PROPOS. XXV.

[98.] COROLLARIVM.

[99.] THEOREMA XXIII. PROPOS. XXVI.

[100.] THEOREMA XXIV. PROPOS XXVII.

[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.

8363LIBER I. L, ad, RT, vel vt, GΠ, ad, RZ, ſunt enim & ipſæ, GL, RT,
ſimiliter ad eandem partem ſectę in punctis, Π, Z, nam ſimiliter ſe-
cantur ac, FC, PO, in punctis, Λ, Γ, ergo etiam reliqua, I Π, ad,
QZ, erit vt tota, GΠ, ad totam, RZ, ideſt vt, FC, ad, PO. Eo-
dem modo oſtendemus, ΠH, ad, ZS, eſſe vt, FC, ad, PO, er-
go, IΠ, ad, QZ, erit vt, ΠH, ad, ZS, & permutando, IΠ, ad,
ΠH, erit vt, QZ, ad, ZS, ſunt ergo latera homologa, IH, QS,
ſimiliter ad eandem partem ſecta à præfatis planis, quod eodem mo-
do de quibuſcumq; homologis lateribus, quæ contingat dictis planis
ſecari, pariter oſtendemus, hoc verò demonſtrare propoſitum fuit.

_E_X boc autem Lemmate inſuper habetur nedum latera bomologa ſi-
milium ſolidorum, ſed etiam, ſi illa producantur vſq; ad oppoſita
tangentia plana, eorum reſidua, vel ipſa tota, eſſe vt eorum dictas al-
titudines.

THEOREMA XXVI. PROPOS. XXIX.

SI in duobus ſimilibus ſolidis iuxta defin. 9. vndec. Elem.
accipiantur, ac in eorumdem ambitu, duæ quæcumq;
ſimiles figurę planę tanquam baſes, quibus parallela ducan-
tur quæcumq; plana eadem ſecantia, necnon corum altitu-
dines, reſpectu dictarum baſium aſſumptas, ſimiliter ad ean-
dem partem diuidentia. Productæ ijſdem in ſolidis figuræ
ſimiles erunt iuxta definitionem 10. huius, & omnium ho-
mologæ duabus quibuſdam regulis æquidiſtabunt.

Sint ſimilia ſolida iuxta defin. 9. vndec. Elem. ipſa, AEFSOGo,
Tl & p f8s, in eorum autem ambitu capiantur ſimiles quæcumque
figurę planę, OGFS, f8 & p, quibus parallela ducantur duo quę-
cumque plana eadem ſecantia, necnon & altitudines reſpectu dicta-
rum baſium aſſumptas ſimiliter ad eandem partem diuidentia, ac in
ipſis ſolidis figuras, LHMP, YVZd, producentia. Dico has eſſe
ſimiles figuras planas icxta defin. 10. huius, omniumque ſic produ-
ctarum in dictis ſolidis homologas duabus quibuſdam regulis, vtex.
gr. ipſis, OS, fp, æquidiſtare. Igitur figurarum ambientium dicta
ſolida duæ aliæ ſimiles quæcumq; capiantur cum baſibus concurren-
tes, vt ex. gr. oOS, sfp, ſimilia triangula, ducantur autem pręfa-
tis baſibus oppoſita tangentia plana, AC, TR, ſecantia

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