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.

3212GEOMETRIÆ alias, Ω Δ RQ, cum prædictis angulos æquales continentes, ℟
Ω Δ, PRQ, proregulis homolog arum accipiemus, hoc . n. fieri
pθſſe demonſtrabitur in Prop. 23. buius, quę erunt cum planis, Δ
Υ, QK, concurrentes. Siergo ducantur prædictarum ſimilium

8[Figure 8] figurarum, β λ, HE, Σ Φ, CM, oppoſitæ tangentes, parallelæ
regulis, Ω Δ, RQ, ex. g. ſiguræ, β Λ, oppoſitæ tangentes, β Τ,
Λ S, & , HE, ipſæ, HD, EI, & , Σ Φ, ipſæ, Σ Ο, Φ V, & tan-
demipſius, CM, ipſæ, CN, MG, quæ productæ ſi opus ſit, oc-
currant planis, Δ Υ, QK, inpunctis, T, S; OV; D, I; N, G;
iungantur autem, TS, OV, DI, NG, et ipſęreperiantur eſſe
incidentes ſimilium figurarum, β λ, HE, Σ Φ, CM, et dicta-
rum oppoſitarum tangentium.

Conſimiliter, ſectis eiſdem ſolidis alĳs planis dictis planis tan-
gentibus paralle@is, altitudine ſque dictas ſimiliter ad candem,
partem ſecantibus, ſemper conceptæ in ſolidis figuræ ſint ſimiles,
velbinę ſimiles, & c. & earumdem homologarum oppoſitę tangen-
t es parallelę pręfatis regulis, Ω Δ, RQ, ſint productę vſque ad
plana, Δ Υ, QK; occurrantque illis in punctis, quę ſiiungan-
tur rectis lineis, ipſę iungentes ſint dictarum ſimilium ſigurarum,
& ductarum oppoſitarum tangētium ſemper incidentes, quæ om-
nes iaceantin planis, Δ Υ, QK, per quarum extrema tranſeant
lineę, ΧVΥΤ, FGKD, et interius lineæ, 4 N 6 I, 7085,
& conting at figuras, ΧVΥΤ, FGKD, eſſe ſimiles, earumque
homologas dictas incidentes, & ipſarum regulas eſſe communes
ſectiones planorum, in quibus iacent, & oppoſitorum

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