Improved Geometrical Plotting Quadrant, &c. 165 

 following problems; A, B, C, being the triangle under con- 

 sideration; then, since the /. ACE is by Euclid (I. 20.) 

 equal to the a BAG, it is evident that this angle will be 

 shown, or may be set, by means of the divisions on the arc 

 FG: also, that since GBE and IGB are also equal, the arc 

 HI, with the addition of 90° (for the angle EBA), will 

 show the Z CBA of the triangle; it is equally evident that 

 the arc FH will show the sum of the two angles BC A and 

 AC F, at the same time that the lengths of all the sides may 

 be read off, on the divisions or scales, on CA, CB, and 

 BA. Therefore, 



First. — To construct or set a Triangle, having two of its 

 Angles and the Side bet it can them given. 

 Set the limb CG, to the division at G, upon the arc an- 

 swering to one of the angles, say A, and make it fast ; then 

 to this z A add the other given angle (which we will call C), 

 and set the other limb CH, and make it fast at the divi- 

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

 then on the limb CG seek the length of the given side C A ; 

 next, push the perpendicular up of 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 CH, say in the point B, when it is evident that the 

 degrees on the arc HI, added to 90°, is equal to the angle B, 

 and that the other sides. C B and B A, may be read off there- 

 on. Or supposing CBD to be the triangle, whose angles 

 B and C, and side BC, are given, we have only to move the 

 Jimbs so as to make I H equal to B, and HG equal to C, 

 and then to bring the lop of the perpendrular to touch CM, 

 at the division B, answering to the side C B, when the other 

 angle D will be shown by the division on the are GF, addinu; 

 90° thereto; and the remaining sides CD and BD may be 

 read off on their respective scales. 



Second. — To set a Triangle, having iuo Sides and the An « I c 



included betivecn t/u/u given. 



Let ABC be the triangle, Aid and AC the given sides, 



and A the given angle : first set the limb CG to the division 



L 3 answering 



