or THE MOTION OF A SYSTEM. 217 



for both the right angled triangles formed by the divi- 

 sion of the base: we have therefore a'^—a'^—h" — c^: 

 hxxi a"'-a"^=.{a'—a:') (of -\-a")z=:{a'—a") a, and ¥—c^:= 



(6 + c)(6-c): consequently a'_a"=-^^±^^^^\ 



326, Lemma B. If an angle of a rectan- 

 gular parallelepiped be cut off by a plane 

 passing through three of its diagonals, the 

 three planes perpendicular to the section, and 

 passing through the edges meeting in the 

 angle, will be perpendicular to the opposite 

 sides of the section. 



For the perpendicular falling from the solid angle on the 

 diagonal between the sides or edges a and b will divide 

 that diagonal into two segments, of which the difference is 



equal to -—-, (325), and the perpendicular from the 



opposite angle of the section will fall on the same point, for 

 in this case the difference of the squares of the sides is a^-\-c^ 

 — (h^ + c^), which is equal to a^ — ¥, and the diagonal is 

 common to both triangles: but both the perpendiculars 

 being perpendicular to the same line, the plane in which 

 they lie will be perpendicular to this 

 line and to the section; and this 

 plane passes tlirough the edge in 

 question. 



327. Lemma C. If an angle of a parallele- 

 piped be cut off by a plane, the square of the 

 area of the section will be equal to the sum of 



