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

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

Table of contents

[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.

[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.

5030GEOMETRIÆ

THEOREMA XI. PROPOS. XIV.

SI duæ figuræ planæ non exiſtentes in eodem plano fue-
rint ſimiles, æquales, & ſim iliter poſitæ, illæ erunt cu-
iuſdam cylindrici oppoſitæ baſes.

Sint duæ ſimiles figuræ planæ, & æquales, AQTO, FDNC,
non exiſtentes in eodem plano, & ſimiliter poſitæ. Dico eas eſſe
cuiuſdam cylindrici oppoſitas baſes. Quoniam enim ſunt ſimiliter
poſitæ erunt inter ſe æquidiſtantes, & earum incidentes pariter inter
11D. Def. 10 ſe æquidiſtantes, ducantur oppoſitæ tangentes figuræ, AQTO,
quæ ſint, TP, AB, & figuræ, FDNC, quæ ſint, FH, NL,
22Coroll. 1.
huius. quæque ſint regulæ homologarum earumdem ſimilium figurarum,
& ſint incidentes earum, & ſimilium figurarum ipſę, BP, HL, quę
erunt parallelæ, & quia ſunt incidentes ſimilium figurarum, AT,
33D. Def. 10. FN, & oppoſitarum tangentium iam ductarum, ideò ad eaſdem ex
eadem parte efficient angulos æquales, igitur angulus, BPT, erit
44B. Def. 10. æqualis angulo, HLN, & ideò etiam, PT, ęquidiſtabitipſi, LN,
55Excõuer.
ſa 10. Vn-
dec. Ele.

23[Figure 23]& , BA, ipſi, FH, iungantur, BH, PL,
quoniam ergo, AT, FN, ſunt ſimiles,
& æquales, earum homologæ erunt pa-
riter æquales, ſunt autem incidentes, BP,
HL, vt ipſæ homologæ, vt colligitur in
Coroll. 1. ſequentis Propoſit. 22. indepen-
denter ab hac Propoſitione, ergo, BP, H
L, erunt æquales, & ſunt æquidiſtantes,
ergo eas iungentes, BH, PL, erunt ęqua-
les, & æquidiſtantes. Diuidantur ipſę in-
cidentes, BP, HL, ſimiliter ad eandem
6610. Sexti
Elem. partem in punctis, E, M, G, K, & iun-
gantur, EG, MK, erit ergo, MP, ęqua-
lis ipſi, KL, & , EM, ipſi, GK, & , BE,
ipſi, HG, nam quia, BP, HL, ſimiliter
diuiduntur in his punctis, earum partes ſunt, vt ipſæ integræ, illæ
verò ſunt æquales, & ideò etiam homologæ partes ſunt æquales, &
eas iungentes, PL, MK, EG, BH, erunt æquales, & æquidiſtan-
7715. Vnde-
cimi El. tes, ducatur à puncto, K, verſus figuram, FN, ipſa, KR, æquidi-
ſtans ipſi, NL, quia ergo, MK, æquidiſtat ipſi, PL, & , RK,
ipſi, NL, planum per, MK, KR, tranſiens æquidiſtat tranſeunti
per, PL, LN, ſecet hoc planum tranſiens per, MK, KR, pla-
num, AT, productum, in recta, SM, & iungantur, SR, VI,

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