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

Table of contents

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[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.
[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.
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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-
tes 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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