Huygens, Christiaan
,
Christiani Hugenii opera varia; Bd. 2: Opera geometrica. Opera astronomica. Varia de optica
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DE CIRCULI MAGNIT. INVENTA.
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benti duplam C G, hoc eſt, C D, & </
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<
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<
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angulum vero A E C æquale triangulo baſin ipſi E F æqua-
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lem habenti & </
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<
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">altitudinem dictam A C. </
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<
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xml:space
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">Itaque apparet duas
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tertias quadrilateri A E G C ſimul cum triente trianguli A E C
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æquari triangulo qui baſin habeat compoſitam ex duabus ter-
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tiis C D & </
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<
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">triente E F, altitudinem vero radii A C. </
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<
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re ejuſmodi quoque triangulum majus erit ſectore A E C.
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</
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<
s
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xml:space
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">Unde liquet baſin ipſius, hoc eſt, compoſitam ex duabus
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tertiis ipſius C D & </
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<
s
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xml:space
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">triente ipſius E F, majorem eſſe arcu
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C E. </
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<
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<
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. IX.
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. IX.</
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<
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">OMnis circuli circumferentia minor eſt duabus
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tertiis perimetri polygoni æqualium laterum ſibi
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inſcripti & </
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<
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xml:space
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">triente perimetri polygoni ſimilis circum-
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ſcripti.</
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<
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</
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<
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<
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">Eſto Circulus cujus A centrum; </
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<
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">inſcribatur ei polygo-
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<
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Fig. 1.</
note
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num æquilaterum, cujus latus C D: </
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cumſcribatur lateribus ad priora parallelis, quorum unum ſit
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E F. </
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xml:space
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">Dico circuli totius circumferentiam minorem eſſe dua-
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bus tertiis ambitus polygoni C D & </
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<
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ni E F. </
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<
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">Ducatur namque diameter circuli B G, quæ ſimul
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inſcripti polygoni latus C D medium dividat in H, & </
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cumſcripti latus E F in G, (conſtat autem G fore punctum
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contactus lateris E F,) Et ponatur H L æqualis ipſi H G,
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& </
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<
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<
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">producantur, occurrátque B C
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lateri E F in K, producta autem A C incidet in E angu-
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lum polygoni circumſcripti. </
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<
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">Quoniam igitur H L æqualis
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H G, erit B L dupla ipſius A H: </
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">Ideoque ut G A ad A H,
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ita G B ad B L. </
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">Major autem eſt ratio H B ad B L, quam
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G B ad B H; </
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<
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">quoniam hætres ſeſe æqualiter excedunt G B,
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H B, L B. </
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G A ad A H, quam duplicata rationis G B ad B H. </
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autem G A ad A H, ita eſt E G ad C H; </
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