Huygens, Christiaan
,
Christiani Hugenii opera varia; Bd. 2: Opera geometrica. Opera astronomica. Varia de optica
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ET HYPERBOLÆ QUADRATURA.
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tione, diviſione, & </
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trapezii A B F P: </
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">triangulum autem A B P & </
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<
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xml:space
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A B F P ſupponimus eſſe quantitates inter ſe analyticas; </
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<
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proinde ſector A B I P illis analytica eſſe non poteſt, hoc
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eſt ex quantitatum ipſis A B P, A B F P analyticarum addi-
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tione, ſubductione, multiplicatione, diviſione & </
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<
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extractione componi non poteſt; </
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<
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<
s
xml:id
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">proinde ex hoc capite
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nulla poteſt exhiberi ratio inter triangulum A B P & </
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<
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rem A B I P, cum evidens ſit illam non eſſe analyticam. </
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dicet fortè aliquis rationem inter triangulum A B P & </
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<
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">ſecto-
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rem A B I P omnifariam variari poſſe; </
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<
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xml:space
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">& </
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<
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">proinde poſſe eſſe
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inter ſe in ratione qualibet data ſive analytica ſive etiam com-
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menſurabili: </
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<
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xml:space
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">reſpondeo hoc eſſe veriſſimum, ſed in hoc ca-
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ſu ratio inter triangulum A B P & </
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<
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">trapezium A B F P non
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erit analytica; </
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<
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<
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">proinde ex dato circulo ellipſe vel hyper-
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bola nunquam dabitur in analyticis triangulum A B P, quod
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ex prædictis clariſſimè patet. </
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<
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">etiamſi ex prædicto capite non
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poſſimus comprehendere rationem inter triangulum A B P & </
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ſectorem A B I P, poſſumus tamen ejus aliquam habere cogni-
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tionem, ex eo quod ſector A B I P ſit terminatio ſeriei con-
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vergentis datæ; </
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<
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">ex hac conſideratione poſſibile eſt inve-
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nire quantitatem datæ commenſurabilem cujus differentia à
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ſectore A B I P minor fuerit quacunque quantitate propoſi-
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ta, ad hoc enim ſemper recurrendum eſt, cum de quantita-
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tibus quibuscunque incommenſurabilibus tractant practici,
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& </
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">in hac noſtra approximatione praxis non erit operoſior
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quam in multis aliis etiam quantitatum analyticarum appro-
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ximationibus, immo multo brevior, facilior & </
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<
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illis Vietæ ſectionibus angularibus, quæ tamen ſummæ ma-
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theſeos utilitati in praxem reducuntur. </
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re circuli quadratura diutius æſtimetur ignorari: </
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demonſtratum ſit rationem circuli ad diametri quadratum
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non eſſe analyticam, vanum certè erit & </
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talem impoſterum quærere: </
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">at rejectis quantitatibus analyti-
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cis, vix credo ullam poſſe eſſe notiorem hisce noſtrarum ſe-
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rierum convergentium terminationibus, ſicut ex ſequentibus
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pleniſſimè apparebit.</
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