102 



JAMES CLERK MAXWELL. 



[CHAP. IV. 



segment ACCCB containing an equal angle. Join BC and produce to 

 H, BH is a tangent, for suppose H to be the end of the rod, and take 

 any point O, n CH + m CA < n OH + n OA, therefore is without the 

 curve. 



CP is an apioid, CT is a circle, and CL is a meloid, with A and B 

 as foci. 



PROPOSITION 7 PROBLEM. 



To draw a tangent to an apioid from any point in the same, the 

 foci and the ratio being given. 



It is required to draw a tangent to the apioid at the point C. 

 Join BC, and draw a circle as in Prop. 3. Join AD, and produce it. 

 Make AP : PD : : n : m. Join CP, and draw CK at right angles to PC. 

 Describe a circle through P, C, K, and it was proved in Prop. 7 of the 

 Oval that if any point be taken and DO, AO joined, DO : AO : : m : n. 

 Suppose to be both in the circle and in the apioid, join BO, then 

 LO : AO : : m n, but DO : AO : m : n .'. LO = DO, but LO < DO .-. the 

 circle is without the apioid ; therefore a tangent C T to the circle at C 

 is a tangent to the apioid. 



AXIOM 1. 



It is possible for a circle to be described touching any given curve 

 internally. 



PROPOSITION 8. 



To draw a tangent to a meloid at any point C. 



Case 1. Let the curve be concave towards B. Describe the circle 

 POCK as in Prop. 7 : it will be wholly within the meloid. At C 

 draw a tangent to the circle : it is also a tangent to the meloid.. For 



