De Curvarum Par. L

131

F R O P. XXXI.

‘Parallelis radiis in fpharam incidentibus 3 re -fraBorum ab axe remotorum errorem a principalifoco determinare .

In schern. 58. sit NBM sphaera, Ccentrum ejus,C B semidiameter incidentibus radiis parallela, A Nradius incidens &r N K refractus ejus, occurrens axiseu scmidiametro CBinK; 8c posito F principalifoco, i. e. in quem radii prope axem jacentes con-gregantur, quaerendus erit error F K. Demitte er-go perpendiculares C E in N K, & N G in C K, &dic G B — s, G B := „v & C K = #, atque ex na-tura circuli erit NGq = 2<?A? — x x, cui addeG K q, hoc est: zz-{~ 2xz — 2 a z-\- x x — 2 ax—j— a aj prodibit N K q ~zz-j-2 xz — 2 az-^ra a. Jam, cum N G sit ad C E ut sinus incidenti» adsinum refractionis, sive ut I ad R, & propter similitu-dinem triangulorum CEK&NGK, NK&CK sintin eadem ratione, erit II. RR :: (NK q. CKq : :)z z -f- 2 x z. — 2 a z -+• a a. z & adeoque 11 z z =zz~h 2 xz — 2a z 4-in RR,& facta reductione

’>Z:

iRR«-2 RRat* —RRRR —II

—, extractdque radice

RR * — R R x —J— R d l laa —> zRRöa - H— R R **

; _ RR.— U. : '