PROPERTIES of the CIRCLE. 29 
to fpeak algebraically, eight times the fum of the fourth powers 
of perpendiculars from either P or Q to the fides of a Tegular 
figure of a greater number of fides than four circumfcribed 
about the circle, and touching it in the points A, B, C, &c. are 
equal to thirty-five times the multiple of the fourth power of 
radius by the number of the fides of the figure. This is Dr 
STEWART’s 25th theorem. 
- Anp ifa regular figure of a greater number of fides than four 
be infcribed in the circle, having its angles in the points A, B, C, 
&c. the eighth powers of the chords drawn from either P or Q_ 
to the points A, B, C, &c. (to {peak algebraically) is equal to 
your =n xX ae 2'.r° = feventy times a multiple of the 
eighth power of radius by the number of the fides of the fi- 
gure. - , 
In like manner, 
mbOcsr sae a iggy Oe 
—— =2rs-+a0rxOc +——» 
Le r 
Se a a CY ge W7 aan 
en hon OF + Tone 
r wa 
on =a p 
rtOd ara = 2r3420rxOd + 13x 
&e. &c. 
—SS §- ——_ 5 | — 
5 
WHEREFORE 2 gL e F ease | 
$s 
r4+-Od +r—Od 
ROR T=Or 
+ &c. = 2273410073} sn om — equal (by Cor. 3.) to 
AP. HBP ohGP 48.4 AQ +BQ. +00. + &e. chen 
= TT Te as r Sa aa Sa 
the circle is equally divided in the points A, B, CG, &c. 
; AND 
