^26 PLOTTING QUADEANT, LEVEL, AND CALCULATOR. 



of any triangle, square, or polygon, showing a mean propor- 

 tional between two numbers, &o. 



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 tigures. 



The following are specimens of the manner of calculating 

 by this instrument. 



First Question. — Jf £\Q0 in 12 months produce 80 shillijigs 

 interest, what will ^£'200 produce in 18 months, and also 

 what will it produce in 12 months? 



Question in On the base line of the instrument set ^100. On the 



«d by U ^^^ 'perpendicular set 80 for shillings interest. Then bring the 

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

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

 ing so fixed the loiver limb, move forward the perpendicular 

 till it intersects the lower limb at the height 12 on the perpenri 

 dicular, then mise the perpendicular to 18, and to the extre- 

 inity thereof fix the upper limb to intersect, which angle will 

 then be in proportion as 18 to 12 to the loicer limb, being 

 equal to the different times. The limbs being so fixed, it is 

 only requisite to move the perpendicular to 200 ©n the base; 

 and, raising the perpendicular till it intersects the upper limb, 

 you will have thereon the answer 240 shillings, and at the 

 same time, at the intersection on the lower limb, l6o, beijig 

 the interest for 12 months only. 



' Question second. — To determine the imcrihed or inscribing 



circle of any polygon, the side being given; for exampUi 

 a hexagon the side ojtvhich is 100 Jeet. 



To determine Set one of the limbs to half the angle included in the 



the inscribed or • i • i /. i i /• i » i . .i 



inscribing cir- »'ec(uired side ot the hexiigon (i. e, 30 degrees), then set the 



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

 per question 60. Then move the perpendicular till the ex- 

 tiTmity intersects the limb before set, on which, at such inter- 

 section, will be denoted the radius of the inscribing circle, 

 and at the same time may be seen on the base the radius of 

 the inscribed circle. 



Question 



