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

Table of contents

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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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page |< < (154) of 347 > >|
178154
In ſingulis enim figuris iuncta recta C D: erit in tribus primis circa maio-
rem axim, recta C D maior C A (cum circulus ex C A ſit ſectioni 1192. h ptus, ac propterea ſecet C D) ſed C A maior eſt G D, v thìc ad numeros
2, 3, &
5. oſtenſum eſt, ergo C D eò ampliùs maior erit ipſa G D, ſiue
quadratum C D maius quadrato G D, vel duo ſimul C I, I D maiora
duobus ſimul G I, I D, quare dempto communi D I, erit quadratum C I
maius quadrato G I, vnde punctum C cadet infra G:
ſed A C, D G ſi-
mul conueniunt ad partes axis B R, vt ad num.
1. oſtendimus, ergo ipſa-
rum occurſus erit vltra axim B R.
In quarta demum figura, eſt C D minor C A (cum circulus ex C A ſit
Ellipſi circumſcriptus ) &
C A minor G D, prout ad num. 6. huius 22ibidem. monſtrauimus, quare C D erit omnino minor G D, ſiue quadratum C D
minus quadrato G D, vel duo ſimul C I, I D minora duobus ſimul G I,
I D;
quamobré dempto I D, erit C I minus G I, ſiue punctum C occurſus
inferioris perpendicularis A C cadet ſupra G occurſum ſuperioris D G;
ſed tales perpendiculares A C, D G ſe mutuò ſecant (vt ſuperiùs oſten-
dimus ad num.
1.) ad partes axis B R, quare ipſarum occurſus erit inter
contactus, &
minorem axim, ſed reſpectu maiorem axim M L ſe mutuò
ſecant vltra M L, vti paulò ante demonſtrauimus.
Quare in Ellipſi oc-
curſus huiuſmodi perpendicularium A C, D G cadet in angulo quadran-
tis M L G, qui deinceps eſt quadranti M L B, ad cuius peripheriam M A
B ductæ ſunt perpendiculares A C, D G, &
c.
Pag. 147. ad finem Prop. 97.
quodque de _MAXIMIS_ ſimilibus Ellipſibus angulo rectilineo inſcriptis
facillimùm eſt demonſtrare.
FINIS.

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