Huygens, Christiaan
,
Christiani Hugenii opera varia; Bd. 2: Opera geometrica. Opera astronomica. Varia de optica
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CHRIST. HUGENII
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torum differentia eſt {{1/4}ggoo/pp} - ox + {ppxx/gg} - yy + 2 ly - ll
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+ {2nxy/z} + {2lnx/z} - {nnxx/zz}. </
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<
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xml:space
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">Ergo hæc æquatur rectangulo
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Y S X, hoc eſt quadrato I X minus quadrato I S, hoc eſt
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{{1/4}ggoo/pp} - mm; </
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<
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xml:space
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xml:space
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xml:space
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">In qua æqua-
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tione deleto utrinque {{1/4}ggoo/pp}, invenietur y = l - {nx/z} +
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√mm - ox + {ppxx/gg} , ut oportebat.</
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xml:space
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">In Secundo calu rectangulum Q C O æquatur quadrato
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L C minus quadrato L O; </
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">& </
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<
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xml:space
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">rectangulum Y S X quadrato
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I S minus quadrato I X. </
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ſu primo invenietur.</
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<
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<
s
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xml:space
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">Sit tertius caſus quo habeatur - mm, ſitque æquatio y = l
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- {nx/z} + √- mm + ox + {ppxx/gg} , producta GN occurrat al-
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teri aſymptoto in D. </
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">Hîc jam eadem ratione qua prius, ap-
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parebit L O vel LQ eſſe {{1/2}go/p} + {px/g}, & </
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<
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xml:space
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</
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<
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xml:space
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">Et propter hyperbolam erit rectangulum Q C O = rectan-
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gulo D N G ſeu quadrato N G, hoc eſt {{1/4}ggoo/pp} + mm, quia
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X I = {{1/2}go/p}, & </
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<
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xml:space
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">I S = m, quorum quadratis æquale fecimus
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quadratum G N. </
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<
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xml:space
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">Rectangulum autem Q C O æquatur qua-
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drato L O minus quadrato L C, hoceſt {{1/4}ggoo/pp} + ox + {ppxx/gg}
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- yy - {2nxy/z} — {nnxx/zz} + 2 ly + {2nlx/z} - ll. </
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<
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æquale {{1/4}ggoo/pp} + mm. </
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