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

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

Table of contents

[61.] COROLLARIVM.

[62.] THEOREMA IV. PROPOS. VII.

[63.] THEOREMA V. PROPOS. VIII.

[64.] COROLLARIV M.

[65.] THEOREMA VI. PROPOS. IX.

[66.] COROLLARIVM.

[67.] THEOREMA VII. PROPOS. X.

[68.] THEOREMA VIII. PROPOS. XI.

[69.] COROLLARIV M.

[70.] LEMMA PRO ANTECED. PROP.

[71.] THEOREMA IX. PROPOS. XII.

[72.] COROLLARIV M.

[73.] THEOREMA X. PROPOS. XIII.

[74.] THEOREMA XI. PROPOS. XIV.

[75.] THEOREMA XII. PROPOS. XV.

[76.] SCHOLIVM.

[77.] THEOREMA XIII. PROPOS. XVI.

[78.] COROLLARIVM.

[79.] THEOREMA XIV. PROPOS. XVII.

[80.] COROLLARIVM.

[81.] THEOREMA XV. PROPOS. XVIII.

[82.] COROLLARIVM.

[83.] THEOREMA XVI. PROPOS. XIX.

[84.] COROLLARIVMI.

[85.] COROLLARIVM II.

[86.] THEOREMA XVII. PROPOS. XX.

[87.] THE OREMA XVIII. PROPOS. XXI.

[88.] COROLLARIVM.

[89.] THEOREMA XIX. PROPOS. XXII.

[90.] COROLLARIVM I.

3010GEOMETRIÆ deinde inter eadem plana tangentia eiſdem æquidiſtantia
11D. Def.2. vtcumque plana ducta fuerint, altitudines ſolidorum, re-
ſpectu dictorum tangentium ſumptas, ſimiliter ad eandem
partem diuidentia, reperiamus figuras exhis planis in di-
22A.Def.10. ctis ſolidis conceptas eſſe ſimiles, vel ſi plures producan-
tur, tot numero in vno, quot in alio ſolido produci, quæ
33E.Def.10. fint binæ ſimiles, & quæ ſunt vnius ſolidi ſimiliter inter ſe
diſpoſitę, ac quę ſunt alterius, & omnium homologas dua-
bus quibuſdam rectis lineis communiter, tamquam earum-
dem regulis, æquidiſtare. (ſic. n. earum homologæ cum
quibuſuis alijs duabus regulis angulos æquales cum præ-
dictis facientibus, vt infra Prop. 23. huius oſtendetur, e-
tiam haberi poterunt) Vnde ſiregulæ homologarum acci-
piantur cum incidentibus planis concurrentes, & conce-
ptarum in ſolidis ſimilium figurarum ductæ in ſingulis op-
poſitæ tangentes præfatis regulis Parallelę producantur, ſt
opus ſit, quouſq; prædictis incidentibus planis occurrant,
& binarum quarumcumque oppoſitarum tangentium pun-
cta occurſuum iungantur rectis lineis, etiam has iungentes
reperiamus ſingulas eſſe incidentes ſuarum ſimilium figu-
rarum, & oppoſitarum tangentium, ac omnes dictas inci-
dentes concipi in figuris ſimilibus, quarum, & ipſæ inci-
dentes ſint homologæ, & omnium regulæ communes ſe-
ctiones planorum incidentium, & oppoſitorum planorum
tangentium. Has omnes, inquam, conditiones ſimilia ſo-
lida in vniuerſum habere ſuppono.

B.

44B

IPſæ autem figuræ planæ ſimiles, quæ capiunt omnes di-
ctas incidentes, vocentur. Figuræ incidentes dictorum
ſimilium ſolidorum, & oppoſitorum tangentium iam du-
ctorum.

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