PROPERTIES of the CIRCLE. 55 
“Wusnstons Aa'+AlyAc+Ad =Aa + Ab + Ac Ad 
aD Re Sa wea amer tensed ait 
yes = NX ar , and DM + Dy + DH + DN’ 
LE EO an eee 
“DM 4. DV + DA + DN x 2 aN rs ogi met 
éN,, Des 
“2 16 
Now, it is evident, that perpendiculars drawn from the point 
D to’the fides of the figures; ate’ refpectively 7 + DM, 7 — DM, 
r+ DV, r—DV,r+ DH, r— DH, r+ DN, r— DN. 
bur EDM 4 7 DM = ar + 2xDM, 
74+ DV + ASN er sok DNs 
74DH +r—DH = 27 + 2x DH, 
SoD ce r— Dt =2rt+ 2X DN. 
WHEREFORE the fum of their fquares is equal'to Nxr’ + 
2x DM +DV+DH'+DN =NxXr+Nx GD nce 
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. 
7 DM + 7—DM’ = 2r3 + 67 xX DM, 
7+DV + 7—DV =2arnt 6rx DV, 
74+ DH cay 9mm) = 2 4 67x DH: 
7+ DN +7—DN = 277+ 6rX DN. 
ay WHEREFORE, 
