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

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

Table of contents

[31.] VIII.

[32.] IX.

[33.] SCHOLIVM.

[34.] A. X.

[35.] B.

[36.] C.

[37.] D. IV.

[38.] E.

[39.] APPENDIX PRIOR Pro explicatione Definit. 10. antecedentis.

[40.] A. XI.

[41.] B.

[42.] C.

[43.] APPENDIX POSTERIOR Pro declaratione Definit. II.

[44.] SCHOLIVM.

[45.] XII.

[46.] XIII.

[47.] XIV.

[48.] XV.

[49.] POSTVLATA I.

[50.] II.

[51.] PROBLEMA I. PROPOS. 1.

[52.] COROLLARIVM.

[53.] PROBLEMA II. PROPOS. II.

[54.] PROBLEMA III. PROPOS. III.

[55.] SCHOLIVM.

[56.] THEOREMA I. PROPOS. IV.

[57.] COROLLARIVM I.

[58.] COROLLARIVM II.

[59.] THEOREMA II. PROPOS. V.

[60.] THEOREMA III. PROPOS. VI.

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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