Huygens, Christiaan, Christiani Hugenii opera varia; Bd. 2: Opera geometrica. Opera astronomica. Varia de optica

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250514CHRISTIANI HUGENII Tangentis proprietatem; Problema, quod mihi apparuit
difficillimum. Solutio Marchionis exſtat in 34. Diario Pari-
ſienſi anni ultimi, quare hanc hic non trado.
Alterum eſt ejus reſponſum de aliâ curvâ valde cognitâ, &
quam Carteſius aliter adhuc conſideravit, ut & Huddenius
eo tempore, quo negotia Reip. non impediebant, quo-
minus vacaret ſtudiis. Curva in fig. 4. exhibetur, fo-
11TAB. XLVI.
fig. 4. lium A B C H circumſcribit & utrimque ſeſe extendit juxta
Aſymptoton E F G. Æquatio ejus eſt x3 + y3 = xyn ſi A D
ponatur x in recta, quæ cum diametro C A format angulum
45 graduum; perpendicularis DB, vel D H, vel D K, y; &
n recta data. Cum ipſi indicaſſem, me inveniſſe qua-
draturam hujus curvæ, & quod contentum folii A B C H
eſſet = {1/6} nn id eſt {1/3} quadrati diametri A C; quod ſpa-
tium infinitum inter Aſymptoton & ambo curvæ brachia
etiam ejuſdem magnitudinis eſſent; & quod quadratura ge-
neralis ſegmentorum exprimeretur per unicum terminum;
ille invenit veram illam quadraturam generalem. Scilicet quod
contentum ſegmentorum A H vel A K exprimatur per {nxx/6y}
& ſegmenti A B per {nyy/6x}; ſed ulterius mihi affirmat ſe eo
perveniſſe per tres diverſas vias; quod miror, cum per-
ſuaſum habeam me non parum profeciſſe unicam dete-
gendo.
98[Figure 98]

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