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

Table of contents

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[201.] THEOR. IL. PROP. IIC.
Page: 172 (148)
[202.] THEOR. L. PROP. IC.
Page: 172 (148)
[203.] THEOR. LI. PROP. C.
Page: 173 (149)
[204.] PRIMI LIBRI FINIS.
Page: 174 (150)
[205.] ADDENDA LIB. I.
Page: 175 (151)
[206.] Pag. 74. ad finem Prim. Coroll.
Page: 175 (151)
[207.] Ad calcem Pag. 78. COROLL. II.
Page: 175 (151)
[208.] Pag. 87. ad finem Moniti.
Page: 175 (151)
[209.] Pag. 123. poſt Prop. 77. Aliter idem, ac Vniuerſaliùs.
Page: 175 (151)
[210.] COROLL.
Page: 177 (153)
[211.] Pag. 131. poſt Prop. 84.
Page: 177 (153)
[212.] Pag. 144. ad calcem Prop. 93.
Page: 177 (153)
[213.] SCHOLIVM.
Page: 177 (153)
[214.] Pag. 147. ad finem Prop. 97.
Page: 178 (154)
[215.] FINIS.
Page: 178 (154)
[216.] DE MAXIMIS, ET MINIMIS GEOMETRICA DIVINATIO In Qvintvm Conicorvm APOLLONII PERGÆI _IAMDIV DESIDERATVM._ AD SER ENISSIMVM PRINCIPEM LEOPOLDVM AB ETRVRIA. LIBER SECVNDVS. _AVCTORE_ VINCENTIO VIVIANI.
Page: 179
[217.] FLORENTIÆ MDCLIX. Apud Ioſeph Cocchini, Typis Nouis, ſub Signo STELLÆ. _SVPERIORVM PERMISSV._
Page: 179
[218.] SERENISSIMO PRINCIPI LEOPOLODO AB ETRVRIA.
Page: 181
[219.] VINCENTII VIVIANI DE MAXIMIS, ET MINIMIS Geometrica diuinatio in V. conic. Apoll. Pergæi. LIBER SECVNDVS. LEMMA I. PROP. I.
Page: 183 (1)
[220.] LEMMA II. PROP. II.
Page: 183 (1)
[221.] THEOR. I. PROP. III.
Page: 184 (2)
[222.] LEMMA III. PROP. IV.
Page: 185 (3)
[223.] THEOR. II. PROP. V.
Page: 186 (4)
[224.] THEOR. III. PROP. VI.
Page: 188 (6)
[225.] LEMMA IV. PROP. VII.
Page: 189 (7)
[226.] THEOR. IV. PROP. VIII.
Page: 191 (9)
[227.] THEOR. V. PROP. IX.
Page: 193 (11)
[228.] SCHOLIVM.
Page: 194 (12)
[229.] THEOR. VI. PROP. X.
Page: 195 (13)
[230.] THEOR. VII. PROP. XI.
Page: 195 (13)
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20725
THEOR. XV. PROP. XXI.
Semita MINIMARVM linearum, ducibilium à puncto com-
munis axis infinitarum Parabolarum, per eundem verticem ſi-
mul adſcriptarum, ad earundem ſectionum peripherias, eſt cir-
cumferentia Ellipſis, cuius tranſuerſum latus ſit ipſum axis ſe-
gmentum, inter aſſumptum punctum, & vertieem interceptum:
rectum verò eiuſdem tranſuerſi ſit duplum.
ESto Parabole A B C, cuius axis B D, in quo ſumptum ſit punctum D
à vertice B diſtans per interuallum æquale dimidio ſui recti B E: pa-
tet ipſam D B eſſe _MINIMAM_ ad peripheriam A B C; & ſi aliæ 119. huius
ad nu. 1. bolæ concipiantur per B adſcriptæ, quarum recta latera excedant B E,
conſtat ipſas cadere extra, qualis eſt M B N, & eandem D B (quæ 222. Co-
roll. 19.
pr. huius. nino erit minor dimidio ipſius rectilateris) ad eius peripheriam eſſe _MI-_ _NIMAM_. At ſi Parabolæ fuerint ipſi A B C per B verticem inſcriptæ,
339. huius
ad nu. 1.168[Figure 168] patet etiam ipſarum latera minora eſſe recto B E, ac ideo D E 44ex 2. Co
roll. 19.
pr. huius. libet ipſorum laterum dimidium excedere, & _MINIMAS_ ducibiles ex D,
ad harum Parabolarum peripherias pertingere, præter ad verticem B. Si
ergo quæratur, quàm delineent ſemitam harum _MINIMARV M_ extrema
puncta. Deſcribatur circa ſegmentum axis B D, tanquam circa tranſuer-
ſum latus, Ellipſis B F D G, cuius rectum ſit ipſum B E. Conſtat hanc
eſſe _MAXIMAM_ Parabolæ A B C per B verticem inſcriptibilem. 55ex 20.
pr. huius. huius peripheriam B F D G prædictarum _MINIMARV M_ eſſe tramitem.
Iungatur Ellipſis regula D E: & Parabolę A B C inſcribatur quælibet
alia F B G, quæ Ellipſis peripheriam ad vtranq; partem omnino ſecabit,

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