C *93 ] 
XXX V . Some New Properties in Conic Sec - 
tions, difcovered by Edward Waring, M, A. 
Lucahan ProfeJJor of the Mathematics in 
the IJniverfity op Cambridge, and F R. S. 
to Charles Morton, M. D. Sec. R . S. 
T H E O R. I. 
Read June 21, QIT ellipsis APBQC R D S E T, &c. 
defcribantur circa earn duo polygona 
[Tab. XIII. Fig. i.J [abcdef^ &c. pqrstv, 6cc.) 
eundem laterum numerum habentia, 6c quorum latera 
ad refpedtiva contadtuum pundta (APBQCR DS,6cc.) 
in duas asquales partes dividuntur, i. e. a l\— Ab, 
— Be, cC — Cd, 6cc. p? — Py, yQ^Qr, 
r X = R J, 6cc. 6c erit fumma quadratorum ex fin- 
gulis unius polygoni lateribus aequalis fummiE qua- 
dratorum ex iingulis alterius polygoni lateribus, i. e. 
a b -\- bc -\-cd~ -|- d e z 4- e f z 4- , 6cc. — p q~-\~ 
qr+rs'+sf+tv'-y, 6cc. 
Cor. Ducantur lineae AB, B C, CD, DE, EF, 
6cc. PQ^QR, RS, ST, TV, &c. 6c erit 
AB 2 + BC 1 -1- CD 1 + DE 2 4-EF z -f 6cc. = 
+ QR 2 + RS*-fST*-f TV x -\-&c. 
C c 
Vol. LIV. 
THEOR. 
