E *94 ] 
T H E O R. II. 
Iifdem pofitis fit O centrum ellipfeos, St ducantu? 
linear OA, OP, OB, OQ, OC, OR, OD, OS, 
Sec. erit 
OA 2 + OB i + OC 1 4-OD t 4-&c. = OP l 4- 
OQ^+ OR* + OS* + Sec. 
Cor. Ducantur etiam lineas Oa , O p, Ob, O q. 
Of, Or, O d, O s, Sec. & erit 
Oa’ + O^ 1 4. Of 1 -)- 0 <T 4 - Sec. = Op'Jr- 
o q ' -)~ Or 2 -)- Or-)- &c. 
Haec etiam vera funt de polygonis inter conjugatas 
hyperbolas eodem modo defcriptis. 
T H E O R. IIL 
Sit conica fe&io MPQJISTM &c. [Fig. 2.] 
cnjus diameter fit A L, et ejus ordinata M L'; fit 
M p = M 'u, & confequenter Ly> — L-u. 
Ducantur linear pq, qr , rj, j/, &c. quae re- 
fpedtive tangant conicam fedtionem in pundtis P, Q, 
R, S» T, Sec. St erit contentum 
/>Px yQj< rR x Sj X See. =zPq x Qr X R JX 
Sf 1 x T-yx Sec. ve], quod idem eft, fumma omni- 
um hujus generis rationum (P p : P y, Q q ; Qr, 
R r : Rj, S j : S/, Sec.) erit nihilo aequalis. 
Cor. 1. Sit elliplis PQRSTV Sec. circa earn deferi- 
batur quodcunque polygonum (/> q r s t u w, Sec.), 
[Fig- 
