Huygens, Christiaan
,
Christiani Hugenii opera varia; Bd. 2: Opera geometrica. Opera astronomica. Varia de optica
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ni diviſi per z ad alteram partem æquationis transferantur,
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ductisque omnibus in z, diviſio deinde fiat per terminos in
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quibus initio non erat z, exiſtere tunc ipſam quantitatem z
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ab una æquationis parte; </
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<
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echoid-s4877
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xml:space
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">uti hîc fiet z = - {3ey
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+ aeyx/3exx - aey}.
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</
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<
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xml:space
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">Atque hinc intelligo ad conſequendam quantitatem z, po-
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nendos tantum eos terminos æquationis ſecundæ, qui deſcri-
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pti ſunt ex terminis æquationis primæ in quibus y, ſublato
<
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tantum denominatore z, mutatiſque ſignis + & </
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<
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xml:space
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">-. </
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<
s
xml:id
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xml:space
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preserve
">Dein-
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de dividendo iſtos terminos per eos qui deſcripti ſunt ex ter-
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minis æquationis primæ in quibus x. </
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<
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xml:space
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preserve
">Porro ex omnibus, tam
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diviſis quàm dividentibus, patet rejici poſſe e, adeo ut in hoc
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exemplo fiat z = - {y
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style
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3 + ayx/3xx - ay}. </
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<
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xml:id
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echoid-s4882
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xml:space
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preserve
">Itaque rejicitur {e/z} ex
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terminis qui deſcripti ſunt ab iis qui habent y. </
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>
<
s
xml:id
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xml:space
="
preserve
">Sic autem
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deſcriptos eos ſuperius diximus ut ducerentur in idem
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{e/z}, præponereturque numerus dimenſionum y. </
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>
<
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xml:id
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echoid-s4884
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xml:space
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preserve
">Itaque ni-
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hil requiri apparet ad terminos hoſce (quatenus ad definien-
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dam quantitatem z hic adhibentur) ex terminis æquationis
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/>
primæ, in quibus y, deſcribendos, quam ut præponamus
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tantum iis numerum dimenſionum quas in ipſis habet y, ſigna-
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que + & </
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<
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xml:space
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">- invertamus. </
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<
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xml:space
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">Sic nempe ab y
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- axy, deſcribetur
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- 3y
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style
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emph
>
+ axy. </
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>
<
s
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echoid-s4887
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xml:space
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preserve
">A terminis verò qui deſcripti ſunt à terminis æ-
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quationis primæ in quibus x, cum tantum e hîc rejiciendum
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lb
/>
patuerit, cumque hos ita prius deſcriptos dixerimus ut unum
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x mutaretur in e, præponereturque numerus dimenſionum
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ipſius x; </
s
>
<
s
xml:id
="
echoid-s4888
"
xml:space
="
preserve
">apparet eos, quatenus h@c ad conſtituendum diviſo-
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rum adhibentur, ſic tantum deſcribi opus eſſe ex terminis pro-
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/>
poſitæ æquationis in quibus x, ut præponatur iis numerus di-
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menſionum ipſius x, ac deinde unum x auferatur. </
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>
<
s
xml:id
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echoid-s4889
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xml:space
="
preserve
">Sic nem-
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pe ab x
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- axy deſcribetur 3x
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- axy; </
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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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">dempto ubique x
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uno, fiet 3xx - ay. </
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>
<
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xml:space
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">Atque ex his ratio regulæ ab initio poſitæ
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manifeſta eſt. </
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<
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xml:space
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preserve
">Nam quod ſigna + & </
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>
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xml:space
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">- in terminis qui deſcri-
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buntur ab iis in quibusy, hîc immutanda diximus, in </
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