Huygens, Christiaan
,
Christiani Hugenii opera varia; Bd. 2: Opera geometrica. Opera astronomica. Varia de optica
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AD RESP. JAC. GREG.
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terit, quoniam tunc ignotum erit, quomodo terminatio com-
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poſita ſit ex primis & </
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<
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xml:space
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<
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xml:space
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quomodo probabitur per
<
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ejus Propoſitionem, termina-
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tionem non eſſe {7/3}. </
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<
s
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xml:space
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">Ut ergo concludatur, rationem Circu-
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li ad quadratum diametri ejus non eſſe analyticam, demon-
<
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ftrari non ſolum debet, quod ſector Circuli non ſit ana-
<
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lyticus indefinite ad figuram ſuam inſcriptam, licet illa de-
<
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/>
monſtratio non careat ſuâ pulchritudine, ſed quod illud etiam
<
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verum ſit in omni caſu definito.</
s
>
<
s
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</
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<
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<
s
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xml:space
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">Dico præterea, ſi quantitates a & </
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>
<
s
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xml:space
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">b maneant indetermi-
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natæ, terminationem forte reduci ad æquationem ex iis, qua-
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rum radices dari nequeunt; </
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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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">contrarium probari per
<
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e-
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jus Propoſitionem, neque per Supplementum, non poterit, ni-
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hilominus ſi illa terminatio reducta ſit ad quandam æquatio-
<
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nem ejus naturæ, crederem Quadraturam Geometricè eſſe in-
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ventam per interſectionem quarundam linearum curvarum,
<
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quæ in Geometriâ admittuntur.</
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<
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">Di-
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cam tantum, has, ſicuti locum amplius non habent poſt cor-
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rectionem Dn. </
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<
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">Gregorii, ita antea firmo fundamento nixas
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fuiſſe; </
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<
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">quoniam omiſſa diviſione neceſſariâ per a@ b in tot
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locis propoſitionis
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. </
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talem diviſionem eſſe poſſibilem, & </
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credidiſſe, in compoſitione de qua agitur indefinitas ad-
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mitti debere quantitates.</
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<
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">Tranſeo igitur ad comparationem noſtrarum methodorum
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pro dimenſione Circuli proxima: </
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approximationes quarum fundamentum ſunt ipſius propo-
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fitiones
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, & </
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<
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. </
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<
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">eaſdem eſſe cum iis, quas dedi in tra-
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ctatu de Circuli magnitudine; </
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">ubi demonſtravi eadem illa
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Theoremata, ſcil. </
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">ſi Polygonum in Circulo inſcriptum ſit
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a; </
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<
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xml:space
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Circuli minus eſſe quam {1/3}a + {2/3} d , ſed majus quam {4/3}
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pag. 361.
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pr.
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{1/3} a , poſito c pro Polygono inſcripto quod duplo
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prop.
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habeat laterum numerum quam a vel d. </
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