Viviani, Vincenzo - De maximis et minimis, geometrica divinatio : in qvintvm Conicorvm Apollonii Pergaei

Viviani, Vincenzo, De maximis et minimis, geometrica divinatio : in qvintvm Conicorvm Apollonii Pergaei

Table of contents

[41.] THEOR. IV. PROP. XI.

[42.] COROLL.

[43.] MONITVM.

[44.] LEMMA III. PROP. XII.

[45.] ALITER idem breuiùs.

[46.] ITER VM aliter breuiùs, ſed negatiuè.

[47.] COROLL.

[48.] THEOR. V. PROP. XIII.

[49.] COROLL. I.

[50.] COROLL. II.

[51.] COROLL. III.

[52.] THEOR. VI. PROP. XIV.

[53.] COROLLARIVM.

[54.] THEOR. VII. PROP. XV.

[55.] THEOR. VIII. PROP. XVI.

[56.] THEOR. IX. PROP. XVII.

[57.] MONITVM.

[58.] THEOR. X. PROP. XVIII.

[59.] Definitiones Secundæ. I.

[60.] II.

[61.] III.

[62.] IV.

[63.] V.

[64.] VI.

[65.] VII.

[66.] VIII.

[67.] IX.

[68.] THEOR. XI. PROP. XIX.

[69.] COROLL. I.

[70.] COROLL. II.

5232 ſibus proportionales: qua-

29[Figure 29] re ſemi-Parabole EBC ad
EDC, ſiue tota ABC ad
totam ADC, ſuper ea-
dem baſi AC, & circa eã-
dem diametrum BE, eſt vt
altitudo FA ad AG. At
ſi concipiatur altera Para-
bole QST, cuius baſis QT
æqualis ſit baſi AC, alti-
tudo verò SV ſit æqualis
ipſi GA (quæcunq; ſit in-
clinatio baſis cum diame-
tro SZ) ipſa, per præcedẽ-
tem propoſitionem, ęqua-
lis erit Parabolę ADC, ac
ideo QST ad ABC eandem habebit rationem, quàm ADC ad ABC, vel
quàm altitudo GA, ſiue SV ad FA. Vnde Parabolæ æqualium baſium
ſunt inter ſe vt altitudines. Quod erat, & c.

THEOR. VIII. PROP. XVI.

Sirecta linea ſemi-Parabolen ad extremum baſis contingens
cum diametro conueniat, & intra ipſam ſuper eadem baſi deſcri-
pta ſit Parabole, cuius diameter ſit dimidium diametri ſemi-Para-
bolæ, ac ei æquidiſtet; erit trilineum à contingente, producta dia-
metro, & conuexa ſemi-Parabolica linea contentum, æquale tri-
lineo à diametro, conuexa Parabolica, & concaua ſemi-Parabo-
lica comprehenſo.

ESto ſemi-Parabole ABC, cuius baſis AC, & contingens AE diametro
CB occurrens in E, & iuncta AB, ac bifariam ſecta AC in F, agatur F
GH æquidiſtans CB, & ſuper baſi AC cum diametro GF, quod eſt dimidium
CB, deſcripta ſit Parabole AGC, (quæ cadet tota intra ABC:) Dico 1113. h. lineum AEBHA æquale eſſe trilineo AHBCGA.

Sed ad hoc demonſtrandum, videndum eſt primò, quomodo cuilibet tri-
lineo ex prædictis, circumſcribi poſſint figuræ ex æquè altis, & numero æ-
qualibus parallelogrammis, & c.

Per continuam igitur biſectionem, diuidatur contingens AE, vel baſis AC
in quotcunq; partes æquales CD, DL, LM, MF & c. : & per diuiſionum pun-
cta D, L, M, F, & c. ducãtur ipſi CBE æquidiſtantes D1, L2, M3, F4, & c. quæ
ſemi-Parabolen ſecent in Q, R, K, H & c. Parabolen verò in N, O, P, G, & c. ;
& ex B, Q, R, K & c. : ducantur BY, QZ, R& , KI & c. : ipſi AE parallelæ, quæ
intra ſemi-Parabolen ABC cadent (cum ſint contingenti æquidiſtantes) vel
extra trilineum AEBHA. Hac ergo methodo circumſcribetur trilineo figu-
ra EBYZ& I & c. ex æquè altis parallelogrammis & c.

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