PROPERTIES of the CIRCLE. 55 



Wherefore Aa + Al? +Ac" + Ad — Aa -f A3 + Ac -f Ad 



x l2^_ -NX 3JL + j and DM* -f DV* + DH + DN 4 

 4 16 



- DM 4. DV + DH 4- DN X ^— = s2 7£- X DG = 



6N „ DG 4 



Now, it is evident, that perpendiculars drawn from the point 

 D to the fides of the figures, are refpeclively r -f- DM, r — DM,, 

 r + DV, r — DV, r + DH, r — DH, r -f- DN, r — DN. 



But r + DM + r — DM = 2 r* -J- 2 X DM , 



,. _j_ d v + r — DV = 2 r* + 2 X DV , 



r + DH + r — DH 5= 2 r* + 2 X DH , 



r + DN + r — DN = 2 r 2 -f 2 X DN . 



Wherefore the fum of their fquares is equal to Nxr' + 



2 X DM 1 + W + DH 2 + DN' 1 = N X r* + N X — > "nee 



2 



the circle which paffes through the points D, M, V, G, H, N, is 

 equally divided by the points M, V, H, N. This is Prop. 5. 

 of Dr Stewart's Theorems. 



r + DM + r — DM = 2 r) + 6 r X DM , 



r-f-DV + r — DV = 2 r3 -f 6rXDV, 



r + DH 3 -f- r-DH 3 = 2 r3 4. 6 r X Eh\ 



r + DN 3 4- r — DN 3 = %r* -f 6r X DN*. 



Wherefore, 



