Huygens, Christiaan
,
Christiani Hugenii opera varia; Bd. 2: Opera geometrica. Opera astronomica. Varia de optica
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GEOMET. VARIA.
"/>
nihil opus eſſe deſcribi, cum utrobique mox delendi forent,
<
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atque adeo illos tantum ſcribendos in quibus unum e vel plu-
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ra inſunt, ut in exemplo noſtro - 2ce + 4ex + 2ee; </
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<
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xml:space
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que æquandos nihilo. </
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<
s
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xml:space
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">Sed etiam illos quibus plura quam u-
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num e inerunt, ſcribi ſruſtra apparet, cum diviſione facta
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per e delendos poſtea conſtet, ut paulò ante diximus. </
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<
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xml:space
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">Ita-
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que nulli præterea ab initio deſcribendi inter terminos poſte-
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riores quam quibus inerit e ſimplex.</
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</
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<
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<
s
xml:id
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xml:space
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">Hi autem termini ex terminis prioribus facilè deducuntur,
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cum conſtet nihil aliud eſſe quam ſecundos terminos poteſta-
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tum ab x + e, quia cæteri omnes plura quam unum e vel nullum
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habent. </
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<
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xml:id
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xml:space
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">Adeo ut ubicunque in prioribus terminis habe-
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tur x, ſcribendum ſit in poſterioribus e; </
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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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">ubi habe-
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tur xx in prioribus, ponendum 2ex in poſterioribus; </
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<
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xml:space
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<
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xml:space
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">ubi
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x
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in prioribus, in poſterioribus 3exx, atque ita deinceps.
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</
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<
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xml:id
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xml:space
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">Dicti autem termini ſecundi cujuſque poteſtatis x + e exipſa
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poteſtate x facilè deſcribuntur mutando unum x in e, & </
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<
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præponendo numerum dimenſionum ipſius x, ita enim ab
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xx fit 2ex, & </
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<
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xml:space
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">ab x
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, 3exx; </
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<
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xml:space
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">atque in cæteris pari modo. </
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Itaque ex terminis prioribus in quibus x, quos ſolos conſi-
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derandos eſſe patuit, facilè etiam termini poſteriores, ii
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quos nihilo adæquandos diximus, deſcribuntur; </
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<
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xml:space
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cando tantum ſingulos in numerum dimenſionum quas in ipſis
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habet x. </
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<
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xml:space
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">Nam mutare unum x in e ne quidem opus eſt, cum
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eodem redeat, ſive omnes poſtea per e ſive per x dividan-
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tur, & </
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<
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xml:space
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">ex his quidem aperta eſt ratio compendii ad primam
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partem regulæ pertinentis: </
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<
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xml:space
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">nunc ad alteram veniamus quæ
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eſt hujuſmodi.</
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<
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xml:space
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">Si termini quos maximum aut minimum deſignare volu-
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mus fractiones habeant in quarum denominatore occurrat
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quantitas incognita, delendæ primùm ſunt quantitates co-
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gnitæ ſi quæ adſint; </
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<
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xml:space
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">deinde ſi reliquæ quantitates non ha-
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beant eundem denominatorem, eò reducendæ ſunt. </
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<
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xml:space
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termini ſinguli numeratorem fractionis conſtituentes, du-
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cendi in terminos ſingulos denominatoris, productaque
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ſingula multipla ſumenda ſecundum numerum quo </
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