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.
[202.] THEOR. L. PROP. IC.
[203.] THEOR. LI. PROP. C.
[204.] PRIMI LIBRI FINIS.
[205.] ADDENDA LIB. I.
[206.] Pag. 74. ad finem Prim. Coroll.
[207.] Ad calcem Pag. 78. COROLL. II.
[208.] Pag. 87. ad finem Moniti.
[209.] Pag. 123. poſt Prop. 77. Aliter idem, ac Vniuerſaliùs.
[210.] COROLL.
[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.
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COROLL.
HInc, data ratione maioris inæqualitatis, hoc eſt D E, ad E H, &
differentia A C inter duo s terminos ignotos A G, G C, qui de-
beant eſſe in data ratione, eruitur quomodo reperiantur ipſi termini A G,
G C.
Facta enim fuit vt D H differentia primorum, ad H E minorem ter-
minum, ita data differentia A C, ad aliam C G, &
reperti ſunt quæſiti
termini A G, G C, Nam ſtatim oſtenſum fuit eſſe A G ad G C, vt D E
ad E H.
THEOR. XII. PROP. XVII.
Si fuerit in angulo rectilineo quælibet applicata, à qua hinc
inde ab eius termino æqualia ſegmenta ſint abſciſſa, &
per v-
num diuiſionis punctum deſcribatur Hyperbole, cuius aſympto-
ti ſint latera dati anguli, ipſa per alterum punctum neceſſariò
tranſibit.
SIt in angulo A B C applicata quæcunque A C, quæ inæqualiter ſece-
tur in D, &
ſumatur C E æqualis A D. Dico ſi per punctum D de-
ſcribatur Hyperbole, cuius aſymptoti ſint B A, B C, ipſam omnino tran-
ſire per E.
Quod huiuſmodi Hyper-
162[Figure 162] bole tranſiens per D, alibi
ſecet applicatam A C, pa-
tet.
Nam ſi eam continge-
ret in D, eſſet A C æquali-
ter ſecta in D:
quod 113. ſecun-
di conic.
contra hypoteſim.
Secet er-
go in F;
& erit F C 228. ibid. lis A D, ſed eſt quoque E
C eidem A D ęqualis, qua-
re F C, E C ęquales erunt;
hoc eſt punctum F congruet
cum ipſo E;
quare Hyper-
bole D F, quæ in angulo aſymptotali A B C deſcribitur per D, omnino
tranſit per E.
Quod erat demonſtrandum.

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