GEOMETRY. 361 



62. Divided proportion is when the difference of 

 the antecedent and consequent is compared either 

 with the consequent or with the antecedent. Thus 

 if 3 : 1 : : 12:4; then by division 3 1 : 1 : : 12 

 4:4and3 1 : 3 : : 12 4 : 12. 



63. Continued proportion is when the first is to the 

 second as the second to the third ; as the third to 

 the fourth ; as the fourth to the fifth ; and so on. 



64f. Compound ratio is formed by the multiplica- 

 tion of several antecedents and the several conse- 

 quents of ratios together, in the following manner : 



If A be to B as 3 to 5, B to C as 5 to 8, and C to 



Das8to6; then A will be D, as gg|-|?z:i; 



that is, A : D : : 1 : 2. 



6*5. To Bisect means to divide any thing into 

 two equal parts. 



66. To Trisect is to divide any thing into three 

 equal parts. 



67. To Inscribe is to draw one figure within 

 another, so that all the angles of the inner figure 

 shall touch either the angles, sides, or planes of the 

 external figure. 



68. To Circumscribe is to draw a figure round 

 another, so that either the angles, sides, or planes 

 of the circumscribed figure shall touch all the 

 angles of the figure within it. 



69. A Rectangle under any two lines means a 

 rectangle which has two of its sides equal to one of 

 the lines, and two of them equal to the other. Also 

 the rectangle under AB,CD, means ABxCD. 



70. Scales of equal parts. A scale of equal parts 

 is a straight line divided into any number of equal 

 parts -at pleasure. Each part may represent any 

 measure you please, as an inch, a foot, a yard, &c. 

 One of these is generally subdivided into parts of 

 the next denomination, or into tenths or hundredth^. 



