$6 INVESTIGATION of fo 



ome 



Wherefore, the fum of the cubes of the perpendiculars, 

 drawn from the point D to the fides of the figure, is zNx^ 3 + 



6r X DM 1 + DV* + DH 2 + DN* = Nxr3 + 6rX — • 



4 



This is Prop. 23. Stewart's Theor. When DG = r, the Aim 

 of the cubes of the perpendiculars is zn N X - x ^ = N X 



* 3 ' . rh This is Prop. 22. Dr Stewart's Theor. 

 1.2.3 



When DG = r, or D coincides with A, the fum of the cubes 



AC \ B A t' 



of the perpendiculars is equal to -77— + — f- — — _|_ & r . 



-i_8 



and, confequently, we get AG -j- AB + AT +, &c. s 



XNXr tf = NX2or 5 = NX^..2 3 / = NX2o X r* = 



1.2.3 



NXior4X AC/ + AB' + AT 2 +, &c. 



If, therefore, the circumference of a circle be divided into an 

 even number of equal parts, and from the points of divifion 

 chords be drawn to any point in the circumference, the fum of 

 the fixth powers of thefe chords is equal to the fum of their 

 fquares, multiplied by ten times the fourth power of radius. 



f^TDM -f r — DM = 2 r* + 12 r* X DM + 2 X DM , 

 ?+DV 4 4- r-DV 4 = 2 r* + 12 r 1 X DV* -f 2 X DV 4 , 



r + DH + r-7 DH* = 2 r* -f 12 r 2 X DH + 2 X DH , 

 r -f DN 4 + r-DN 4 = 2 r* -f 12 r 2 X DN* + 2 X DN 4 . 



Wherefore 



