154 



MR. T. T. WILKINSON ON 



them shall be equal to the square upon the third tangent ;" — 

 and then, by considering this locus (a circle) and the circle 

 from which tangents are drawn to coincide, he determines the 

 required circle as in Mr. Butterworth's construction. 



PORISM. 



Proposed hy Mr. Charles Gill. 



" Two straight lines and a circle are given in position, and 

 the lines joining the centre of this circle and the centres of 

 two other circles are also given. It is required to find the 

 position and magnitude of these circles, so that if from any 

 point in the circumference of the given circle, perpendiculars 

 upon the lines, and tangents to the circles, be drawn, the 

 rectangle of these tangents may always be a mean proportional 

 between a certain given space and the rectangles of the 

 perpendiculars." 



Porismatic Construction. By Mr. Butterworth. 



" Let O be the centre of the given circle, and D E and F G 

 the lines given by position. From O demit O E and O G 

 perpendicular to DE and F G in E and G : — upon O E and 

 O G take O P and O Q equal to the given lines, and bisect 

 them in K and L ; then take K R and L S = third propor- 

 tionals to 2 O P and the radius of the circle, and = 200. 

 and the said radius, and with the centres P and Q, and radii 

 equal to sides of squares which are equal to 2 P O . E R, and 

 2 O O . L S, respectively, describe two circles, and they will 

 be those required." (Maih. Comp., Ques. 680.) Mr. Charles 

 Holt also gives an Analysis of this Porism, from which he 

 deduces a construction similar to the preceding. 



Porism. 

 Proposed hy Mr. Butterworth. 



** Having given an ellipse, and a point in one of its axes, a 

 right line may be found, such, that if any right line be 



