Huygens, Christiaan
,
Christiani Hugenii opera varia; Bd. 2: Opera geometrica. Opera astronomica. Varia de optica
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CIRCULI ET HYPERBOLÆ
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QUADRATURA.</
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">Sit circuli, ellipſeos vel hyperbolæ ſegmentum B I P
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Fig. 1. 2. 3.</
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cujus centrum A: </
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ſegmentum in punctis, B, P, tangentes ducantur re-
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ctæ B F, P F, ſe invicem ſecantes in puncto F; </
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<
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ducatur (ſi opus ſit) recta A F ſegmentum interſecans in
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puncto I & </
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<
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<
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ctæ B I, P I.</
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">Dico trapezium B A P I eſſe medium propor-
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tionale inter trapezium B A P F, &
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triangulum B A P.</
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">Quoniam recta A Q ducitur per F concurſum duarum re-
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ctarum F B, F P, ſegmentum in punctis B, P, tan-
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gentium; </
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">igitur recta A Q rectam B P contactuum
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puncta jungentem bifariam ſecabit in puncto Q; </
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triangulum A B Q eſt æquale triangulo A Q P, & </
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gnlum F B Q triangulo F Q P; </
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<
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">igitur triangulum A B F
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æquale eſt triangulo A P F; </
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midium trapezii A B F P: </
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lum A B I eſſe dimidium trapezii A B I P; </
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A B Q eſt dimidium trianguli A B P: </
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A B F, A B I, A B Q, eandem habeant altitudinem, in-
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ter ſe ſunt ut baſes, ſed eorum baſes nempe A F, A I, A Q,
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ſunt continuè proportionales; </
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<
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">igitur ipſa quoque triangu-
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la ſunt continuè proportionalia; </
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mirum trapezia A B F P, A B I P, & </
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ſunt continuè proportionalia in ratione A F ad A I, quod
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demonſtrare oportuit.</
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