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

VARIA DE OPTICA. Et diviſis omnibus per y & ductis in a
- 2bbcxy - ddbcx - 2aacxy + ddcay = - aaddy - bddax
abddx - cbddx + acddy + aaddy = 2aacxy + 2bbcxy
{abddx - cbddx + acddy + aaddy/2aac + 2bbc} = xy, quæ æquatio
eſt ad Hyperbolam.

Vel quia bc = na, {abddx - anddx + acddy + aaddy/2aac + 2bbc} = xy.

Sit {add/aa + bb} = p; Ergo {pbx - pnx + pcy + pay/2c} = xy.

Unde porrò non difficulter invenitur ſequens Conſtructio: jungantur B A, A C, & applicato ſeorſim ad utramque
Quadrato Radii A D, fiant inde A P, A Q; & juncto P Q,
dividatur ipſa bifariam in R, & per punctum R ducantur
R D, R N, ſeſe ad Rectos Angulos ſecantes, quorumque
R D, ſit parallela A M, quae dividet bifariam Angulum B A C. Erunt jam R D, R N Aſymptoti oppoſitarum Hyperbola-
rum, quarum altera per Centrum A tranſire debet, quæque
ſecabunt Circumferentiam in punctis H quæſitis. Tranſibunt
autem Hyperbolæ per Puncta P, Q.


fig. 6.

Ratio Conſtructionis apparet, ductis P γ, & Q ζ, per-
pendicularibus in A M. Fit enim A γ = {add/aa + bb} ſive p; & A ζ = {ap/c}. Item P γ = {pn/c}, & Q ζ = {pb/c}. Quare A O = {pc + pa/2c},
& O R = {pb - pn/2c}. Unde Cætera facilia.

pag. præced. lin. pen. lege - 2acxyy
lin ult. lege - addyy - bddxy:

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