Full text: Viviani, Vincenzio: De maximis et minimis, geometrica divinatio

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 inſcri- 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.

213.1.

92. h

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 de- 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.

213.1.

ibidem.

214. Pag. 147. ad finem Prop. 97.

quodque de _MAXIMIS_ ſimilibus Ellipſibus angulo rectilineo inſcriptis
facillimùm eſt demonſtrare.

215. FINIS.

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