Huygens, Christiaan
,
Christiani Hugenii opera varia; Bd. 2: Opera geometrica. Opera astronomica. Varia de optica
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EPISTOLA.
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aliâ aſſumptâ formâ quantum libet arctè ſeſe conſtringentibus e-
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laberetur. </
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<
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xml:space
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">Verum age, inſpiciamus jam quo rem deducas, poſt-
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eaquam verbi continere novam ſignificationem elicuiſti, eâque
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vetera theoremata tam ſcitè interpolaſti. </
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<
s
xml:id
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xml:space
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">In Corollario propo-
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ſitionis 40. </
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<
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">lib. </
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<
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<
s
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xml:space
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">quò tam ſæpe provocas, id unum egiſſe vi-
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deris, unas ex aliis difficultates nectendo, ut ſi quis argumen-
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tationis tuæ tenorem conſectari cupiat, is defeſſus abſiſtat pri-
<
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uſquam ad finem pervenerit. </
s
>
<
s
xml:id
="
echoid-s1054
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xml:space
="
preserve
">Ego ad eum uſque locum te ſecu-
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tus ſum, ubi ſpatia Y & </
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<
s
xml:id
="
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xml:space
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">Z aſſumi jubes: </
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<
s
xml:id
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xml:space
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">Inde non ulterius pro-
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cedendum putavi. </
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<
s
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xml:space
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preserve
">Adeo enim manifeſto vitio atque ἀγεωμετρησίἀ
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ibi laborat conſtructio tua, ut tibimet ipſi exploratum id eſſe du-
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bitare nequeam: </
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>
<
s
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xml:space
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">ſed quoniam alia evadendi ratio non occurre-
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bat, ſperaſti, credo, in tanta obſcuritate nemini illud facile
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animadverſum iri. </
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<
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xml:id
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xml:space
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preserve
">Dein, inquis, aſſumantur duo plana Hyper-
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bolica Y & </
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<
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xml:space
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">Z, rectis alteri aſymptotorum parallelis incluſa. </
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<
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xml:id
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xml:space
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">Nullâ
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aliâ præcautione aſſumuntur quam quod rectis alteri aſympto-
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torum parallelis includi ea neceſſe ſit. </
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<
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xml:space
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">De magnitudine utriuſ-
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que aut ratione quam inter ſe ſervare debeant nihil præcipis. </
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<
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xml:space
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">I-
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gitur quamlibet magnum aut parvum unum quodque eorum
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abſcindi poterit. </
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<
s
xml:id
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echoid-s1064
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xml:space
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">Mox tamen rationem ſpatii Y ad Z cum aliis
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rationibus comparare inſtituis, quas prius ſecundum certam de-
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terminationem aſſumpſiſti, tibique hoc demonſtrandum propo-
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nis, Rationem totalem planorum X ad T tam eſſe multiplicem ra-
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tionis totalis planorum Y ad Z, quàm ratio totalis ſolidorum G H
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ad I K multiplicata eſt rationis totalis ſolidi L M ad N O. </
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<
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">Quid-
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nam, quæſo, abſurdius, quam de quantitate ejus rationis ali-
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quid enunciare, quæ prorſus in certa ſit ac vaga? </
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<
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xml:space
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">Equidem ex
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hoc ſolo ſatis liquere puto, quam fruſtra primæ Quadraturæ
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ſuppetias ferre tentaveris, cum in eo quod præcipuè tibi ex-
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plicandum erat, tam inſigniter delinquas. </
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<
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xml:space
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">In tribus reliquis an
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meliore fortunâ uſus ſis, ſi me inquirere oporteat, talentum
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non meream. </
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<
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xml:space
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">Id tamen ſcito perpetuum adverſus vos argumen-
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tum fore, quod rationem peripheriæ ad diametrum quam ſin-
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gulis quadraturis datam eſſe profitemini, ipſi tamen exhibere
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non poteſtis; </
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<
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xml:space
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">non autor ipſe Quadraturæ, non tot ejus diſci-
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puli, qui tot jam annis in id incumbunt, ut paucioribus Ilium
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expugnatum ſit. </
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<
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">Datam eſſe rationem, Euclides definivit, </
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