THE LANCASHIRE GEOMETERS AND THEIR WRITINGS. 



163 



the point where it cuts the circle, draw P Q parallel and = 

 2zm. Through Q draw xQu, to make the <FClx = 

 < a; a P ; lastly, bisect zx in F by drawing the line E F H 

 parallel to zm, which will be the line required." (Math. 

 Comp., dues. 639.) 



Mr. Butterwortb, at the close of his demonstration, remarks 

 that, " if there be two lines parallel to A D and B D, and at 

 equal and given distances from them, a right line may be 

 found, such, that the sum of the squares of the perpendiculars 

 demitted from any point of the arc A B, upon the lines 

 AD and B D, together with r times the square of the per- 

 pendicular upon the line to be found, will be a constant 

 magnitude." 



PORISM. 



Proposed by Mr. Thomas Baker. 



" Three circles being given in magnitude and position, it is 

 required to find the magnitude and position of another circle, 

 such, that if tangents be drawn from any point in the circum- 

 ference of one of the given circles to the other three, the sum 

 of the squares of the tangents to the two given circles may be 

 equal to the square of the tangent to the circle which is to be 

 found." 



Porismatic Construction. By Mr, Butterworth. 



" Let O, P, Q, be the centres of the given circles ; join 

 P Q, and bisect it in C, and join O C, which produce till 

 C R = O C ; then with centre R and radius equal to the side 

 of a square = 2 O C* + P F' + Q G^ — O E* — 2 Q C% 

 describe a circle, and it will be that required." (Math. Comp., 

 Q,ues. 657.) 



Mr. Wright, in his solution to this Porism, considers the 

 Lemmatical Problem of " having three circles given in position 

 and magnitude, to determine the locus of a point from which 

 tangents being drawn, the sum of the squares upon two of 



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