32 BENJ. PIKE'S, JR., DESCRIPTIVE CATALOGUE. 



line, set it in the arch described, and the angle formed by 

 lines drawn through these points is 35 degrees. The de- 

 grees contained in an angle to be measured, are found in 

 nearly the same manner. 



Price, in ivory, 6 inch, 88cts.; 12 inch, $3. 00 to $8.00. 

 " in brass, " " $1.50 " " $3.00. 



The Sector. (Fig. 36, page 35.) Of all mathematical 

 instruments that have been contrived to facilitate the art of 

 drawing, there is none so extensive in its use as the sector. 

 It is a universal scale. It not only contains the most useful 

 lines, but by its nature renders them of general application ; 

 uniting, as it were, angles and parallel lines, the rule and 

 the compass. The sector is usually six inches long when 

 closed, and forms a rule of twelve inches long when open. 

 The sector consisting of two pairs, or legs, movable upon a 

 central joint, it is requisite that the lines should be laid on 

 the sector by pairs, viz. one of a sort on each leg, and all 

 of them issuing from the centre ; all of the same length, 

 and every two containing the same angle. The scales or 

 lines graduated upon the faces of the instrument, and which 

 are used as sectoral lines, are, 1, two scales of equal parts 

 called the line of lines, and marked L ; 2, two scales of 

 chords, marked c ; 3, two scales of secants, marked s ; 4, a 

 line of polygons, marked POL. Upon the other face ; 5, 

 two lines of sines, marked s ; 6, two lines of tangents, mark- 

 ed T ; 7, another line of tangents extending from 45 to 75 

 degrees ; the first only extending to 50. Besides these, 

 when the sector is quite opened, there is on one side, 1, 

 Gunter's line of artificial numbers, marked N ; 2, line of 

 artificial sines, marked s : 3, line of artificial tangents, 

 marked T ; and on the other side a line of twelve inches 

 divided in tenths, and on the edge, the foot divided into 

 100 parts. To explain the proper use of all these sectoral 

 lines would require more space than can be given in this 

 work. A few examples will be given. 



1. In the line of equal parts. Having three numbers 

 given to find a fourth proportional. To do this, take in 

 your compasses the lateral extent of sixteen divisions in the 

 line of lines, and apply it by a proper opening of the sector 

 from 4 to 4 in these lines ; then take the parallel distance 

 from 7 to 7 in your compasses, with the same opening of 

 the sector, and apply one foot of the compasses to the com- 



