Full text: Volumen secundum. Opera geometrica. Opera astronomica. Varia de optica. (2)

CHRIST. HUGENII = T E: tunc junge VD, ductâque ipſi parallelâ I K, e pun-
cto K, ubi occurrit ipſi D L, duc parallelam aſymptoto
K A, ſecantem D V in F, C O in X, & Logarithmicam in
A. Tum rectæ A X & F K ſimul ſumtæ erunt æquales cur-
væ C D.

Solutio hujus Problematis, prout ego invenio, poteſt et-
iam reduci ad quadraturam curvæ, cujus Æquatio eſt
a 4 = xxyy - aayy, quæ, ut & altera, dependet à quadratu-
ra Hyperboles, uti poſſem ſatis facile demonſtrare; ſed
conſtructio à modo deſcripta non differt.

Neſcio, an multæ lineæ curvæ hanc habeant proprietatem
ut ipſarum longitudines per ipſas curvas menſurari queant; interim ecce unam, quam haud ita pridem inveni, dignam, ut
videbis, quæ & ob alia etiam notetur; Eſt curva A X K O
extenſa in infinitum ſecundum rectam D N, quæ eſt ejus a-
ſymptos, ad quam A D, tangens ad verticem A, inſiſtit
perpendicularis; curvæ princeps & ſimpliciſſima pro-
prietas eſt, ut omnis tangens inter punctum contactus & aſymptoton, ut K N, ſit æqualis lineæ A D; curva pariter ex-
tenditur ad alteram partem hujus perpendicularis A D. Ut
invenias rectam lineam æqualem portioni hujus curvæ datæ a
vertice A, ut A K (ſic enim invenies alias portiones quaſcun-
que) duc K P perpendicularem ad A D, & deſcripto arcu
circuli P Q, qui habeat centrum D & radium D P, quæ-
re in A B parallelâ Aſymptoto punctum B, quod ſit centrum
circumferentiæ circuli, quæ tranſit per A & tangit arcum PQ,
quod facile eſt; porro ductâ rectâ B D, ſume in illâ DY = DA,
& e puncto Y duc parallelam Aſymptoto uſque ad curvam in
X, tunc Y X erit æqualis curvæ A K; Et natura hujus lineæ
talis eſt, ut ſi ſumas tot proportionales quot volueris, in re-
cta A D, incipiendo a D, ut DS, DI, DP & ducas applica-
tas SR, IO, PK: partes interceptæ curvæ, ut R O, O K,
omnes ſint æquales.

125.1.

TAB. XLVI.
fig. 2.

Ad quadraturam Hyperboles quoque inſervit curva hæc; nam
eadem recta Y X facit cum A D rectangulum æquale ſpatio
Hyperbolico A D E V, terminato lineis A D, E V perpen-

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