362 GEOMETRY. 



Scales may be constructed in a variety of ways. 

 The most usual manner is to make an inch, or some 

 aliquot part of an inch to represent a foot ; and 

 then they are called inch scales, three-quarter- 

 inch scales, half-inch scales, quarter-inch scales, &c. 

 They are usually drawn upon ivory or box-wood. 



71. An axiom is a manifest truth, not requiring 

 any demonstration. 



72. Postulates are things required to be granted 

 true, before we proceed to demonstrate a propo- 

 sition. 



73. A proposition is when something is either 

 proposed to be done, or to be demonstrated, and is 

 either a problem or a theorem. 



74. A problem is when something is proposed to 

 be done ; as some figure to be drawn. 



75. A theorem is when something is proposed to 

 be demonstrated or proved. 



76. A lemma is when a premise is demonstrated, 

 in order to render the thing in hand the more easy. 



77- A corollary is an inference drawn from the 

 demonstration of some proposition. 



78. A scholium is when some remark or observa- 

 tion is made upon something mentioned before. 



79 The sign = denotes that the quantities be- 

 twixt which it stands are equal. 



80. The sign + denotes that the quantity after 

 it is to be added to that immediately before it. 



81. The sign denotes that the quantity after 

 it is to be taken away or subtracted from the quan- 

 tity preceding it. 



Geometrical Problems. 



Prob.l. To divide a given line, AB(P1. 4.), 

 into two equal parts. 



