THE LANCASHIBE GE0METEB8 AND THEIR WEITIKGS. 



155 



drawn through the given point, and from the points where it 

 meets the curve perpendiculars be demitted upon the line to 

 be found, their rectangle will be a constant magnitude." 



Porismatic Construction. By Mr. Charles Uolt. 



** Let P be the given point in the transverse axis A B of 

 the given ellipse A D B C ; O its centre. Erect P K perpen- 

 dicular to A B ; apply O K = O A ; make O L = O P ; join 

 L K, perpendicular to which draw K H to intersect A B pro- 

 duced in H ; then through H draw G H I perpendicular to 

 A B, and G I will be the line required." (Math. Comp.y 

 Ques. 700.) Mr. Butterworth also gives a construction of 

 this Porisra. 



PORISM. 



Proposed hy Mr. John, Kay. 



** Given the points C, D, A, B, in the same straight line. 

 Now a straight line may be found, such, that any ellipse 

 being described upon A B, as its axis, tangents drawn from 

 C, D, will intersect in the line to be found." 



Porismatic Construction. By Mr. Butterworth. 



" Upon A B as a diameter, describe a circle, to which from 

 C and D, draw the tangents C F and D S, intersecting each 

 other in P, and through the point P draw the indefinite per- 

 pendicular E P, and it will be the line required." (Math. 

 Comp., dues. 702.) Mr. Holt also gives an elegant Analysis 

 and Construction. 



It would not be difficult to enlarge considerably on this and 

 other interesting topics, but the specimens already adduced 

 may suffice to shew that the Lancashire Geometers had caught 

 the true spirit of the Ancient Analysis. At the same time 

 it cannot be doubted that they failed to profit to the extent 

 they might have done by the fragments of systematic research 



