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:


Note to user

Dear user,

In response to current developments in the web technology used by the Goobi viewer, the software no longer supports your browser.

Please use one of the following browsers to display this page correctly.

Thank you.

powered by Goobi viewer