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

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[211.] Pag. 131. poſt Prop. 84.
[212.] Pag. 144. ad calcem Prop. 93.
[213.] SCHOLIVM.
[214.] Pag. 147. ad finem Prop. 97.
[215.] FINIS.
[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.
[217.] FLORENTIÆ MDCLIX. Apud Ioſeph Cocchini, Typis Nouis, ſub Signo STELLÆ. _SVPERIORVM PERMISSV._
[218.] SERENISSIMO PRINCIPI LEOPOLODO AB ETRVRIA.
[219.] VINCENTII VIVIANI DE MAXIMIS, ET MINIMIS Geometrica diuinatio in V. conic. Apoll. Pergæi. LIBER SECVNDVS. LEMMA I. PROP. I.
[220.] LEMMA II. PROP. II.
[221.] THEOR. I. PROP. III.
[222.] LEMMA III. PROP. IV.
[223.] THEOR. II. PROP. V.
[224.] THEOR. III. PROP. VI.
[225.] LEMMA IV. PROP. VII.
[226.] THEOR. IV. PROP. VIII.
[227.] THEOR. V. PROP. IX.
[228.] SCHOLIVM.
[229.] THEOR. VI. PROP. X.
[230.] THEOR. VII. PROP. XI.
[231.] THEOR. VIII. PROP. XII.
[232.] THEOR. IX. PROP. XIII.
[233.] THEOR. X. PROP. XIV.
[234.] THEOR. XI. PROP. XV.
[235.] LEMMA V. PROP. XVI.
[236.] COROLL.
[237.] THEOR. XII. PROP. XVII.
[238.] THEOR. XIII. PROP. XVIII.
[239.] THEOR. XIV. PROP. XIX.
[240.] PROBL. I. PROP. XX.
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1831
VINCENTII VIVIANI
DE MAXIMIS, ET MINIMIS
Geometrica diuinatio in V. conic.
Apoll. Pergæi.
LIBER SECVNDVS.
LEMMA I. PROP. I.
Si recta linea vtcunque ſecta fuerit: quadratum totius æqua-
bitur quadrato vnius partis, vnà cum rectangulo ſub tota, &
di-
cta parte, tanquam ab vna linea, &
ſub altera parte contento.
ESTO data recta A B vtcunque ſecta in C. Dico quadratum
A B æquale eſſe quadrato alterius partis, nempe A C, vna
cum rectangulo ſub B A cum A C, tanquam vna linea, &

ſub reliqua parte B C comprehenſo.
Nam producta B A ſu-
matur A D æqualis ipſi BC.
Quoniam igitur D C eſt bifa-
riam ſecta in A, ipſique adiecta C B, erit
quadratum A B æquale rectangulo ſub
D B, B C, vnà cum quadrato C A;
ſed
DB linea conficitur ex D A cum A B, vel
143[Figure 143] ex A C cum A B;
ergo quadratum totius
A B æquatur quadrato partis C A, vna
cum rectangulo ſub B A cum A C, tan-
quam vna linea, &
ſub reliqua parte B C
comprehenſo.
Quod erat, & c.
LEMMA II. PROP. II.
Si quatuor quantitatum eiuſdem generis, prima ſuperet ſecun-
dam maiori exceſſu, quo tertia ſuperat quartam, aggregatum
extremarum maius erit aggregato mediarum.
SInt quatuor quantitates eiuſdem generis A, B, C, D, & prima A ſu-
peret ſecundam B, maiori exceſſu, quo tertia C ſuperat quartam D.
Dico aggregatum extremarum A, D maius eſſe aggregato mediarum B, C.

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