RULES FOR ASCERTAINING SQUARE NUMBERS. gQ 2 



made of iron, light and elegant, and every plate or pannet, 

 that fitted them, might be pointed with any kind oi device 

 imagination and taste might devise, beautiful as the ancient 

 painted windows of cathedrals, and they would endure for 

 centuries. 



But I need not farther expatiate on this subject. If frflhi Conclusion; 

 the above hints, anyone would enter upon it with that kind 

 of spirit the thing' requires, select ingenious mechanics, and 

 study to introduce it with lightness, elegance, and taste; 

 wfien it is considered, that the price in general would be less 4 



than mahogany, that it would be handsomer and more du- 

 rable, that it is the production of our Own nation, and that 

 it would give employment io vast numbers of our own 

 countrymen ; I flatter myself with the idea, that in a great 

 many instances', it would be adopted; 



I am, Sir, 

 Birmingham* Your obedient humble servant, 



Caroline Street, March 16, 1809. B. COOK. 



±1. 



Oh ascertaining Square Numbers and Biquadratics by Inspect 

 tion. By W. Saint, Esq; 



To Mr. NICHOLSON. 



SIR, 



Woolwich * March \5th, i&0£. 



JLjLaVING frequently experienced, in the solution of To ascertain by 



questions involving a quadratic equation, and more particu- inspection 



1»m1 v in such as relate to the diophantine algebra, a consi- wllel ; iCr :i 



J r a ' number be a 



durable degree ©f inconvenience and trouble from not being pe feet square 



able to ascertain whether a number be a perfect square Or woulJ °' u ' n 



not, without the tedious operation of extracting its rout; trouble. 



I have thought, that the following rules or propositions, 



which I have accompanied with their demonstrations, might 



prove useful to many of your readers, by enabling them, on 



inspection, to ascertain a great vauety of forms of numbers, 



U 4 which 



