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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26983 rectæ D H F æquidiſtabit, cum & hæc quoque ſit eidem diametro ordina-
tim ducta.
Iam in ſingulis figuris erit portio L E M æqualis portioni A B C, 1140. h. eſt quoque portio D E F eidem portioni A B C æqualis, ex hypotheſi,
quare duæ portiones L E M, D E F inter ſe æquales erunt, ſed vtraque eſt
de eadem ſectione, &
circa communem diametrum E H I, & ſuper baſes
parallelas, ergo baſis L I M tota congruet cum baſi D H F, vnde &
pun-
ctum I cum puncto H;
quare ſegmenta E I, E H inter ſe æqualia erunt,
ac propterea erit, in prima, ſegmentum quoque E H æquale B G, &
in re-
liquis erit H E ad E O, vt G B ad B O.
Quod primò oſtendere propone-
batur.
222[Figure 222]
Sint iam in tertia figura duæ portiones æquales A N C, D P F ſemi- El-
lipſi maiores, quarum ſegmenta diametrorum ſint G N, H P, &
commune
centrum O.
Dico item eſſe G N ad N O, vt H P ad P O.
Producantur diametri N G, P H, ad B, E.
Et cum portiones A N C, D P F ſint æquales, & ſemi- Ellipſi maiores
erunt quoque reliquæ A B C, D E F de eadem Ellipſi inter ſe æquales,
ſed ſemi- Ellipſi minores;
quare erit, vt ſupra oſtendimus, G B ad B O,
vt H E ad E O, &
conuertendo, & diuidendo O G ad G B, vt O H ad
H E, &
eſt G B ad B O, vel ad O N, vt H E ad E O, vel ad O P, ergo,
ex æquali G O ad O N, vt H O ad O P, &
componendo, G N ad N O,
vt H P ad P O.
Quod vltimò erat, & c.

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