PLOTTtNG <iuAl>RANf, LEVEL, AND CALCULAToiR* ^^J 



ation ; then since the Z A C E, is by Euclid (I, 90) equal 

 to the Z B A C, it is evident that this angle will be shown, or 

 may be set, by means of the divisions on the arc F G; also, 

 that since C B E> and I C B, are also eq^ual, the arc H I,' 

 with the addition of 90*^ (for the angle E B A), will show the 

 Z C B A, of the triangle ; it is equally evident, that the a7X 

 F H will show the sum of the two Zs B C A, and AC F, af 

 the same time that the lengths of alt the sides may be read 

 off", on the divisions or scales, on C A, C B, and B A. 

 Therefore : 



First, — To construct or set a triangle, having two of its angles 

 and the side hetioeen them given. 

 Set the limb C G, to the division at G upon the arc an- to set a triaa- 

 sweriug to one of tlie angles, say A, and make it fast, then S^® "^ which 2 

 to this ZA add the (rther given angle, (which we will call C) side between 

 and set the other limb C H, and make it fast at the division them are glv^, 

 H, on the arc answering to the sum of their degrees; then on 

 the limb C G seek the length of the given side C A ; next, 

 push the perpendicular up or down, till the parallel cuts the 

 point A, (always observing, the divided edges are those you 

 Work to), and by the help of the mill-headed nut, move the 

 perpendicular, till its top corner just touches the limb C H, 

 say in the point B; when it is evident that the degrees oa 

 the arc H I, added to 90°, is equal to the angle B, and that 

 the other sides C B, and B A, may be read orf thereon. Or 

 supposing C B D 16 be the triangle, whose angles B and C 

 and side B C are given, we have only to move the limbs so as 

 to make 1 H equttl to B, and H G equal to C, and then to 

 bnngthe top of the perpendicular to touch C H, at the divi-* 

 sion B, answerii'g to the sideSl^ B, when the other Z D will 

 be shown by the division on the arc G F, adding 90° thereto ; 

 and the remaining sides C D and B D may be read off on 

 their respective scales. 



Second. — To set a triangle, having fivo sides and iht angle 

 included between them given. 



Let A B C be the triangle, A B aud A C the given sides, T\7o sides and 

 and A the given angle; iirst set the litnb C G to the division ^^^ ^"g'® ^2- • 

 answering to A, then bring the parallel up to the point A, any J^Ien. 



