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 aa:iom 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 -f 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. 



