Huygens, Christiaan - Christiani Hugenii opera varia; Bd. 2: Opera geometrica. Opera astronomica. Varia de optica

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78366CHRISTIANI HUGENII ad B H, ita K G ad C H. Ergo major erit ratio E G ad
C H, quam duplicata ejus, quam habet K G ad C H. Qua-
re major ratio E G ad K G, quam K G ad C H. Ideoque
duæ ſimul E G, C H omnino majores duplâ K G. Et ſumptis
omnium trientibus, erunt trientes utriuſque E G & C H ſi-
mul majores duabus tertiis K G. Quamobrem addito utrim-
que ipſius C H triente, erit triens E G cum duabus tertiis
C H, major duabus tertiis K G cum triente C H. Hiſce
vero minor etiam eſt arcus C G . Igitur duæ tertiæ C 11per praced. ſimul cum triente ipſius E G majores omnino ſunt eodem ar-
cu C G. Unde ſumptis omnibus toties quoties arcus C G
circumferentiâ totâ continetur, erunt quoque duæ tertiæ pe-
rimetri polygoni C D, cum triente perimetri polygoni E F,
majores circuli totius circumferentiâ. Quod fuerat oſtenden-
dum.

Omnis igitur circumferentiæ arcus quadrante minor, mi-
nor eſt ſinus ſui beſſe & tangentis triente.

Problema I. Prop. X.

Peripheriæ ad diametrum rationem invenire
quamlibet veræ propinquam.

MInorem eſſe peripheriæ ad diametrum rationem quam tri-
plam ſeſquiſeptimam: majorem vero quam 3 {10/71}, Archi-
medes oſtendit inſcripto circumſcriptoque 96 laterum po-
lygono. Idem verò hic per dodecagona demonſtrabimus.

Quia enim latus inſcripti circulo dodecagoni majus eſt par-
tibus 5176 {3/8}, qualium radius continet 10000: duodecim la-
tera proinde, hoc eſt, perimeter inſcripti dodecagoni major
erit quam 62116 {1/2}: perimeter autem hexagoni inſcripti eſt
radii ſextupla, ideoque partium 60000. Igitur dodecagoni
perimeter perimetrum hexagoni excedit amplius quam par-
tibus 2116 {1/2}. Quare triens exceſſus major erit quam 705 {1/2}. Igi-
tur dodecagoni perimeter unà cum triente exceſſus, quo pe-
rimetrum hexagoni ſuperat, major erit aggregato

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