Huygens, Christiaan
,
Christiani Hugenii opera varia; Bd. 2: Opera geometrica. Opera astronomica. Varia de optica
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GEOMET. VARIA.
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o x; </
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">eritque punctum N in hyperbola quæſita, quæ proin-
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de rurſus data erit.</
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<
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">Sumpta enim in caſu primo A B = x ad arbitrium, eique
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">fig. 4.</
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applicata B C = y in angulo dato, quæ ad hyperbolam in-
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ventam terminetur, oſtendendum ſit quod</
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<
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<
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xml:space
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">y = l - {nx/z} + √mm - ox + {ppxx.</
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xml:space
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">Occurrat B C utrinque ſi opus ſit producta, aſymptotis
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in O & </
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">Ex conſtructione eſt I X vel I Y = {{1/2}og/p},
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I V = {{1/2}ogg/pp}, Ratio verò data I K ad K L, eadem nempe
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quæ z ad n. </
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">angulus I K L datus eſt. </
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tio I K ad I L, quæ ſit ea quæ z ad a. </
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ad I L ita I V ad I M, erit I M = {{1/2}aogg/zpp}. </
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">Ut autem I M ad
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IX, hoc eſt ut {{1/2}aogg/zpp} ad {{1/2}go/p}, ſive ut ag ad pz, ita M L,
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ſive M I minus I L, hoc eſt, {{1/2}aogg}zpp - {ax/z} ad L O vel L Q;
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</
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">quæ itaque erit {{1/2}og/p} - {px/g}. </
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xml:space
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erit B L = l - {nx/z}, quà ablatâ à B C=y, fit L C = y - l + {nx/z}. </
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Propter hyperbolam verò erit rectangulum Q C O æquale
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rectangulo Y S X. </
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quadrato L O minus quadrato L C, hoc eſt quadrato ab
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{{1/2}go/p} - {px/g} minus quadrato ab y - l + {nx/z}: </
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