Huygens, Christiaan - Christiani Hugenii opera varia; Bd. 1: Opera mechanica

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11974CHRISTIANI HUGENII gens A B, eodem arcu C B major erit. quod erat demon-
11De motu
IN Cy-
CLOIDE.ſtrandum.

PROPOSITIO XIX.

IIsdem poſitis, ſi tertia recta prioribus parallela
22TAB. VIII.
Fig. 5. D K circulum ſecet, quæ tantundem diſtet ab ea
quæ remotior eſt à centro quantum hæc à reliqua
A F: Erit pars tangentis in B, à parallela me-
dia, & ultimo addita D K, intercepta, nimirum
B D, major arcu B C.

Hoc enim manifeſtum eſt cum B D fiat ipſi B A æqualis,
quam oſtendimus arcu B C majorem eſſe.

PROPOSITIO XX.

SI arcus circuli, ſemicircumferentia minor, A B,
33TAB. VIII.
Fig. 6. in partes quotlibet ſecetur lineis rectis paralle-
lis, quæ & inter ſe, & cum rectis ſibi parallelis
per terminos arcus ductis, æqualia intervalla con-
ſtituant, quales ſunt C D, E F, G H, K L & c.
ducanturque ad terminum arcus alterutrum A, &
ad reliqua omnia ſectionum puncta rectæ circumfe-
rentiam tangentes, omnes in eandem partem, &
ut unaquæque occurrat proximæ dictarum paralle-
larum; cujusmodi ſunt tangentes A C, D E, F G,
H K & c. Dico has tangentes, dempta prima A C,
ſimul ſumptas, minores eſſe arcu propoſito A B.
Easdem vero omnes, non omiſſa A C, majores eſſe
arcu A B diminuto parte extrema N B, hoc eſt,
majores arcu A N.

Ponamus enim primo perallelarum aliquas tranſire ab

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