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



mencement of these lines, and the other will fall on 28, the 

 number required. For as 4 is to 7 so is 16 to 28. 



2. In the Lines of Chords. Suppose it required to lay 

 off an angle equal to 25 degrees, with any convenient 

 opening of the sector, take the extent in the lines marked 

 c, from 60 to 60, and with it describe an arch indefinitely ; 

 then, with the same opening of the sector, take the parallel 

 distance from 25 to 25, and set it in the arch described, 

 lines drawn from these points in the arch to its centre, will 

 give the angle required. 



3. In the Lines of Sines. The lines of sines, tangents, 

 ind secants, are used in conjunction with the line of lines in 

 the solution of all the cases of plain trigonometry ; thus, 

 suppose we are 230 feet from a spire, or elevation, the 

 n eight of which we wish to measure, we ascertain the angle 

 rormed at that distance by the base and point of the spire 

 Dy means of a quadrant, and find it to be 36 degrees and 

 30 minutes ; consequently, the other angle being its com- 

 plement must be 53^ degrees ; we now take the lateral 

 distance, 230, from the line of lines, and make it a parallel 

 from 53;f degrees to 53^ degrees in the line of lines ; then 

 the parallel distance between 36 j in the same lines, will 

 reach lateially from the centre to 170 in the line of lines, 

 for the height of the spire 170 feet. 



4. Polygons. If we open the sector any convenient 

 distance, and take with the compasses the distance 6 and 6 

 on these lines, and inscribe a circle, the whole circumference 

 will be divided by it into 6 parts ; then, if you take the 

 distance 4 and 4 on the same lines, it will be divided into 

 four parts, and you have a square inscribed in the circle ; 

 if you take 7 and 7 you have a heptagon, or seven sided 

 figure, and so on with all the divisions of these scales. 



A great number of problems of much interest may be 

 solved by means ot these, and the other lines of the sector. 



Price, in ivory, $1.50. 

 " in brass, $1.50. 



Architect's Scale. (Fig. 3"/, page 37.) Scales are usually 

 divided into tenths ; those expressly for architects are divided 

 into twelve parts, to correspond to the measure used by 

 carpenters and masons. They are usually made of ivory, 

 and six, nine, and twelve inches long ; one side is slanted 

 off ai each edge, having scales of |, |, |, 1 inch, marked 



