28 INVESTIGATION of fome 
or, to fpeak algebraically, the fum of the fixth power of chords 
drawn Trom either P or Q to the faid points, will be equal to 
twenty times a multiple of the fixth power of radius, by the 
number of the fides of the infcribed figure. 
In like manner, 
- 
wf. ae —_—_—_-4 ee 
Ac i” ee Os uidee Se en oe pices 
—} al aeons Bee ss, 
22 ae a INA aN oS 3 
Gd' +b _r+Od +7—Od_, ates x Od" 
r ; r 7 
&e. &c. - &e. 
And third proportionals to radius, perpendiculars from P and Q_ 
to right lines touching the circle in the points A, B, C, &c. and 
the cubes of faid perpendiculars are, taken together equal to 
anritiarXOc OE 40d + &e. pax FOP LOH 4 Be 
st AP'4.BP +CP + &. ,, AVHBQ'+6Q + &e. 
Oe ee hg oe eee 
Bur Oc + OF +0d + &c. = ”"" when the circumference 
2 
is equally divided in the points A, B, C, &c. or when a regular 
figure is circumfcribed about the circle, with its fides touching 
nr 
the fame in faid points, and 127 X—-=64%r:  Alfo 
—+} ——4 ——4 “ 
x OG, FOF Qe ESS ony = we Wherefore thefe 
te 
: : ars 
third proportionals are taken together equal to 8773 + 3 er os 
35.2 r3 
4 
; and four times their aggregate is equal to 35.273. Or, 
te 
