150 



MR. T. T. WILKINSON ON 



Companion fot 1806; — or by reducing the porismatic pro- 

 perty said to exist into the form of an equation and then 

 treating it by the Method of Indeterminate Co-efRcients, as 

 is done by Gompertz, Epsilon, Baker, and Rangeley in 

 the Companion, Galloway in the Repository, Davies in the 

 Mathematician and in the Edinburgh Transactions, and more 

 recently still by Gompertz again in his valuable Hints on 

 Porisms, lately published. When by any of these means 

 the entities required to be found, have been found, the 

 requisite Constructions are indicated by the process, and the 

 Demonstrations of the Porisms are reduced to those of ordi- 

 nary Indeterminate Theorems. 



The principal Porisms which engaged the attention of the 

 Lancashire Geometers occur in the concluding volume of the 

 Mathematical Companion. Three of them form the Prize 

 Questions for the years 1822-3-4, and were severally proposed 

 by Mr. Lowry, under the signature of " P. P.," and Mr. Kay. 

 Did space permit, both the algebraical and geometrical solu- 

 tions are well worthy of transcription, as specimens of the 

 modes in which such inquiries may be treated ; but as I am 

 concerned only with those by Lancashire Geometers, the 

 enunciations and constructions must suffice for the present 

 occasion. 



PORISM. " 



Projyosed by " P. P.," Mr. John Lowry. 



" Two points and a circle being given by position, two 

 straight lines may be found which will also be given by 

 position, such, that if from the given points two straight lines 

 be drawn to any point in the circumference of the circle, the 

 rectangle contained by these lines will be a mean proportional 

 between a certain given space and the rectangle contained by 

 the perpendiculars drawn from that point upon the straight 

 lines which are to be found." 



