Huygens, Christiaan
,
Christiani Hugenii opera varia; Bd. 2: Opera geometrica. Opera astronomica. Varia de optica
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CHRISTIANI HUGENII
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ſcriptiones ſectionum Conicarum, quæ fiunt per inſtrumen-
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ta, haberemus inde & </
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<
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<
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xml:space
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ctam conſtructionem omnium Problematum, quæ ad hanc
<
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quadraturam reducuntur; </
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<
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xml:space
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">ut inter alia ſunt, determinatio
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punctorum Catenariæ, & </
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<
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xml:space
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xml:space
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">Si enim B Y ſit =
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A C, quæ ſumitur in axe Catenariæ, id eſt D B = DC ap-
<
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plicata ejus C G erit = Y X; </
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>
<
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xml:space
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">& </
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>
<
s
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xml:space
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">eadem quoque Y X eſt lo-
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garithmus rationis quam habet A D ad P D; </
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<
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xml:space
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">id eſt, æqualis
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eſt diſtantiæ duarum linearum A D, P D, vel aliarum duarum qua-
<
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rumcunque, quæ eandem habent rationem, ordinatarum per-
<
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pendicularium ad Aſymptoton lineæ logarithmicæ, quæ habet
<
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D A pro Subtangente univerſali; </
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>
<
s
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xml:space
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">unde poſſunt inveniri logarith-
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mi tabularum, prout demonſtravi in additione ad diſſertationem
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de cauſa gravitatis. </
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<
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xml:space
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">Leibnitius, qui primus initium fecit redu-
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ctionis curvæ Catenariæ ad leges Geometriæ, ipſam illam
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lineam ope veræ Catenæ tenuiſſimæ formatam, dixit inſer-
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vire poſſe inventioni logarithmorum, vel quadraturæ Hy-
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perboles; </
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<
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xml:space
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">licet ad id cognita requiratur (ut quidem ipſe no-
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verat) longitudo rectæ, quam vocat curvæ Parametrum,
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cujus inventionem non demonſtrat. </
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<
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xml:space
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">Ita ut noſtra qua-
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dratrix in his uſibus præferenda videatur, quia poſt de-
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ſcriptionem Parameter ejus, quæ eſt univerſalis ejus Tan-
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gens, datur.</
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<
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">Sed quoniam hæc materia me perduxit ad conſideratio-
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nem Catenariæ quæ elegantiſſimis hujus temporis Geome-
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trarum inquiſitionibus occaſionem præbuit, libet hic addere
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quam inveni peculiarem ſatis methodum qua hæc delincatur cur-
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va, quod eſt omnium difficillimum inter ea quæ de hac ſibi inqui-
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renda propoſuere Mathematici. </
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>
<
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xml:space
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">Inter illa, quæ inſerenda dedi in
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actis Lipſienſibus cum pulcris & </
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noullii inventis, dixi, me reduxiſſe conſtructionem vel
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inventionem punctorum hujus lineæ ad quadra@uram curvæ,
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cujus æquatio eſt a
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= aaxx + yyxx ; </
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<
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<
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xml:space
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">me
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">Vide ſupra
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pag. 29@.</
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ſe, hanc quadraturam dependere à cognitione ſummæ ſe-
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cantium arcuum circuli, quæ æqualiter creſcerent per mi-
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nima; </
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<
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">quæ ſumma jam dudum reducta fuerat ad </
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