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

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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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Scan	Original
111	87
112	88
113	89
114	90
115	91
116	92
117	93
118	94
119	95
120	96
121	97
122	98
123	99
124	100
125	101
126	102
127	103
128	104
129	105
130	106
131	107
132	108
133	109
134	110
135	111
136	112
137	113
138	114
139	115
140	116

Scan	Original
111	87
112	88
113	89
114	90
115	91
116	92
117	93
118	94
119	95
120	96
121	97
122	98
123	99
124	100
125	101
126	102
127	103
128	104
129	105
130	106
131	107
132	108
133	109
134	110
135	111
136	112
137	113
138	114
139	115
140	116