Full text: Volumen secundum. Opera geometrica. Opera astronomica. Varia de optica. (2)

CHRIST. HUGENII torum differentia eſt {{1/4}ggoo/pp} - ox + {ppxx/gg} - yy + 2 ly - ll
+ {2nxy/z} + {2lnx/z} - {nnxx/zz}. Ergo hæc æquatur rectangulo
Y S X, hoc eſt quadrato I X minus quadrato I S, hoc eſt
{{1/4}ggoo/pp} - mm; quia I X = {{1/2}go/p} & I S = m. In qua æqua-
tione deleto utrinque {{1/4}ggoo/pp}, invenietur y = l - {nx/z} +
√mm - ox + {ppxx/gg} , ut oportebat.

In Secundo calu rectangulum Q C O æquatur quadrato
L C minus quadrato L O; & rectangulum Y S X quadrato
I S minus quadrato I X. Unde rurſus valor Y idem qui ca-
ſu primo invenietur.

120.1.

fig. 5.

Sit tertius caſus quo habeatur - mm, ſitque æquatio y = l
- {nx/z} + √- mm + ox + {ppxx/gg} , producta GN occurrat al-
teri aſymptoto in D. Hîc jam eadem ratione qua prius, ap-
parebit L O vel LQ eſſe {{1/2}go/p} + {px/g}, & L C = y + {nx/z} - l. Et propter hyperbolam erit rectangulum Q C O = rectan-
gulo D N G ſeu quadrato N G, hoc eſt {{1/4}ggoo/pp} + mm, quia
X I = {{1/2}go/p}, & I S = m, quorum quadratis æquale fecimus
quadratum G N. Rectangulum autem Q C O æquatur qua-
drato L O minus quadrato L C, hoceſt {{1/4}ggoo/pp} + ox + {ppxx/gg}
- yy - {2nxy/z} — {nnxx/zz} + 2 ly + {2nlx/z} - ll. Ergo hoc
æquale {{1/4}ggoo/pp} + mm. In qua æquatione deleto rurſus utrin-

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