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

0239-01

126. V.
PROBLEMA AB ERUDITIS SOLVENDUM:
A
JOHANNE BERNOULLIO
IN ACTIS LIPSIENSIBUS
ANNI MDCXCIII.
PROPOSITUM.

QUæritur, qualis ſit curva A B C, quæ hanc habet
proprietatem, ut, ducta ubicunque tangente
B D terminata ab axe A E, portio ejus abſciſſa
A D ſit ad tangentem B D in ratione conſtan-
te M ad N.

126.1.

TAB. XLVI.
fig. 5.

Problema hoc ſolutu dignum eſt, & facile Mathemati-
corum applicationem meretur. In quacunque enim ratio-
ne ſit M ad N, curva A B C ſemper eadem facilitate mo-
tu quodam continuo deſcribi poteſt, non obſtante, quod
curva pro ratione M ad N magis vel minus compoſita
evadat; in caſu quippe rationis æqualitatis illico patet,
curvam A B C eſſe circulum: in reliquis ſi M ad N eſt ut
numerus ad numerum, erit quidem curva geometrica, ſe-
cus autem tranſcendentalis eſt. Quæritur generalis deter-
matio puncti in curva.

127. Tom. II. Ttt

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