DIFFERENTIAL CALCULUS. -01 



7. IV-'Ve that three parabolas of maximum latus rectum 

 can he drawn circumscribing a given triangle ; and that if a, /?, y 

 be the angles which the sides muke with the axis of any one 

 of them, 



cot a + cot ft + cot y = 0. 



958. Find the plane sections of greatest and least area which 

 can be drawn through a given point on the surface of a paraboloid 

 of revolution : proving tha f ., if 0,, S be the angles which the 

 planes of maximum and minimum section make with the a 



3 



tan O tan O = - . 



'. If x, y, z be the distances of any point in a plain- from 

 three given points, andy(aj, y, z) be a maximum or minimum; 



1 .// _J __ # = 1 I//. 

 iu(y, z) lie sin (c, x) dy sin (x,y) tls ' 



(y, z) denoting the angle between the distances y, z. 



960. If A, E, C, D be four points not in on<- plane, and P 

 a p"int the sum of whose distances from A, 1>, C', JJ is a. mini 

 mum ; then will 



PA. PA //;//; PC. PC* PD.PD' 



AA' r,r, CC' 



PA, PR, PC, PD meeting the opposite laces of the tctrahedm 

 in A', ff, a, !>'. 



1 . If A, B, C t D be four points not in one plane, and P a 

 point at \vhicli 



ia a maximum or minimuin, tin n will 



v,l. PCDA ?oL /'/>.(/; wl /'.:/ 



