170 Improved Geometrical Plotting Quadrant, &c. 



things which it will perform, some it is hoped useful and 

 some amusing, amongst which may he enumerated multi- 

 plication, division, rule of three, double rule of three, &c; 

 determining the area or sides of any sort of triangle from 

 any proper data; determining the inscribing or inscribed 

 circle of any triangle, square, or polygon ; showing a mean 

 proportional between two numbers, Sec. 



It is presumed that an instrument, if perfectly made, on 

 a large scale, would be found very useful and accurate in 

 various practical calculations, as well for making them as 

 for proving them after made in figures. 



The following are specimens of the manner of calculating 

 by this instrument : 



First Question. — If £.100 in 12 Months produce SO Shil- 

 lings Interest, what will £.200 produce in 18 Months', 

 and also, what will it produce in 1 2 Months r 

 On the base line of the instrument set £. 100. On the 

 perpendicular set SO, for shillings interest. Then bring the 

 lower limb to intersect, which angle will then be, as per 

 question, equal to 12 months at all places on the base: hav- 

 ing so fixed the lower limb, move forward the perpendicular 

 till it intersect the lower limb at the height 12 on the per- 

 pendicular; then raise the perpendicular to 18, and to the 

 extremity thereof fix the upper limb to intersect, which 

 angle will then be in proportion as 18 to 12 to the lower 

 limb, being equal to the different times. The limbs being 

 so fixed, it is only requisite to move the perpendicular to 

 200 on the base ; and, raising the perpendicular till it inter- 

 sect the upper limb, you will have thereon the answer, 240 

 shillings; and at the same time, at the intersection on the 

 lower limb, 160, being the interest for 12 months only. 



Second Question. — To determine the inscribed or inscribing 

 Circle of any Polygon, the Side being given; for example 

 the Hexagon, whose Side is 100 Feet. 

 Set one of the limbs to half the angle included in the re- 

 quired side of the hexagon (i e. 30 degrees), then set the 

 perpendicular to the height of half the side given, being as 

 per question 50. Then move the perpendicular till the ex- 

 tremity 



