< «8. )

Sed diximus, quod K E ad EG, ut K A ad A G: i. e. - y —- 0 ..

b ■+ y x

di nx -d- cy ay -4- b x nx — cy

x n — y b y n — y

Unde invenitur X an x xy-¥x bnx 5 —ddbn x-ddnxy—naddy-y- nbddx— X ac x y y—x b c xxy~i~d db c y-hrd d c y y — addyy — bddxy.

„ bc xbbe bbddcx xbbcjyx

Et quia n —-, sit-.v5-, quia xx =

a a a a ,

xbbe xbbcddx xbbcyyx

dd — yy■ Est autem- x * — ---, quia x x —

a au

— xbbe xy y ddbcyx

dd~~- yy. Ergo --—-• —-— X ac xy y -+• ddcyy — —

Addyy bddxy.

Et divisis omnibus per y & ductis in a

— xb b e xy — ddbc x —• x a ac xy -dr d de ay — a addy — bddaxa b ddx — cbddx -+■ ac ddy -baaddy — xaacxy-d'Xbbcxy

abddx — cb ddx ac ddy -b a addy .. .

-----— xy , qux xquatio elt

X /t 4 e —f* % b b c ^

ad Hypcrbolam.

Vel quia bc = na,

abdd — an ddx ■+ ac ddy H* a addyXaac ■+• xbbe

— xy.

add ^ _ fbx — fnx - 4 - sey -+• f ay

Sit — T77— Pi Er S°- ~ ---= *>•

Unde porro non difficulter invenitur sequens Constructio : Jungantur B A,A C, & applicato seorsim ad utramque Quadrato Radii A D, fiant indeA P, AQj & juncto P Qj dividatur ipsa bifariam in R, & per punctum Rducantur R D, R N, sese ad Rectos Angulos secantes, quorumque R D, sitparallela A D, qux dividet bifariam Angulum B AC. Erunt jam R D, R NAfymptoti Oppositarum Hyperbolarum, quarum altera per Centrum A transi-re debet, quxque secabunt Circumferentiam in punctis H quxsitis. Transi-bunt autem Hyperbolx per Puncta P, G.

Ratio Constructionis apparet, ductis P y, & Q_£, perpendicularibus inadd „ . „ ap _ „ p n

A M.Fit enim Ay— -— sive* ; Lc A ^ —-. Item Py -*

a a bb c c

&QS =

pb

p c -i' p a _ p b — p n

Quare AO=-—& OR = -- . Un-

X G

i c

de Cxtera facilia»

Mirari