Full text: Volumen secundum. Opera geometrica. Opera astronomica. Varia de optica. (2)

CHRISTIANI HUGENII nus triente minoris. Quare ſi à ſexdecim inſcripti dodecago-
ni lateribus duo latera inſcripti hexagoni, hoc eſt, diameter
circuli deducatur, reliqua circuli circumferentiâ minor erit,
aut ſi ab octo dodecagoni lateribus radius deducatur, reliqua
minor erit circumferentiæ ſemiſſe. Hoc autem ad conſtructio-
nem mechanicam utile eſt, quoniam exigua eſt differentia,
ſicut poſtea oſtendetur.

Manifeſtum etiam, in omni arcu qui ſemicircumferen-
tiâ minor ſit, ſi ad ſubtenſam addatur triens exceſſus quo
ſubtenſa ſinum ſuperat, compoſitam arcu minorem eſſe.

31. Theor . VIII. Prop . VIII.

CIrculo dato, ſi ad diametriterminum contingens
ducatur, ducatur autem & ab oppoſito diametri
termino quæ circumferentiam ſecet occurratque tan-
genti ductæ: erunt interceptæ tangentis duæ tertiæ
cum triente ejus quæ ab interſectionis puncto dia-
metro ad angulos rectos incidet, ſimul arcu abſciſ-

Eſto circulus centro A, diametro B C; & ducatur ex C
recta quæ circulum contingat C D: huic autem occurrat
ducta ab altero diametri termino recta B D, quæ circumfe-
rentiam ſecet in E: ſitque E F diametro B C ad angulos re-
ctos. Dico tangentis interceptæ C D duas tertias ſimul cum
triente ipſius E F, arcu E C majores eſſe. Jungantur enim
A E, E C; & ducatur tangens circulum in E puncto, quæ
tangenti C D occurrat in G. Erit igitur G E ipſi G C æqua-
lis, itemque D G; nam ſi centro G circumferentia deſcriba-
tur quæ tranſeat per puncta C, E, eadem tranſibit quoque
per D punctum, quoniam angulus C E D rectus eſt. Oſten-
ſum autem fuit ſuprà, duas tertias quadrilateri A E G C una
cum triente trianguli A E C ſimul majores eſſe ſectore A E C . Eſtque quadrilaterum A E G C æquale triangulo baſin ha-

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