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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Willebrordi Snellii tota innititur, quæque demonſtraſſe ipſe
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videri voluit, argumentatione uſus quæ meram quæſiti pe-
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titionem continet. </
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eſt imprimis & </
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<
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. XIII.
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. XVI.</
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I diametro circuli ſemidiameter in directum adji-
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ciatur, & </
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">ab adjectæ termino recta ducatur quæ
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circulum ſecet, occurr atque tangenti circulum ad ter-
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minum diametri oppoſitum: </
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gentis arcu adjacente abſciſſo minorem.</
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<
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Fig. 1.</
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ſit A C ſemidiametro æqualis. </
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quæ circumferentiam ſecundò ſecet in E; </
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<
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genti in L, ei nimirum quæ circulum contingit in termino
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diametri B. </
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">Dico interceptam B L arcu B E minorem eſſe.
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">Jungantur enim A E, E B, poſitâque A H ipſi A E æqua-
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li ducatur H E & </
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Denique ſit E G diametro A B ad angulos rectos, E D ve-
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ro tangenti B L. </
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">Quoniam igitur iſoſceles eſt triangulus
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H A E, erunt anguli inter ſe æquales H & </
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autem angulus A E B rectus eſt, etiam recto æquales erunt
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duo ſimul H E A, K E B. </
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H K B uni recto æquantur, quoniam in triangulo H K B
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rectus eſt angulus B. </
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<
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">Ergo demptis utrimque æqualibus,
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hinc nimirum angulo H, inde angulo H E A, relinquen-
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tur inter ſe æquales anguli K E B, H K B. </
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igitur iſoſceles eſt K B E, ejuſque latera æqualia E B, B K. </
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Eſt autem B D æqualis E G. </
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B E excedit E G. </
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ad A B, erunt duæ ſimul A G, A B majores duplâ A E .</
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Ideoque A E, hoc eſt, A H minor quam dimidia </
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