N. B. There being two fuch-like arch-lines in the 2d. fector as in the 1ft. in that cafe you take the whole inftead of half. PROBLEM VII. To find the area of the fegment of a Circle. Take the difference between the area of the fector under the fame arch with the fegment, and the area of the triangle under the chord and radius, for the area of the fegment. Note. It may fometimes happen that you may meet with mixt or compound figures, fuch as are compofed of rectilineal and curvileneal figures figures together: To find the area of fuch, you muft first find the area of the feveral figures of which the whole compound figure is compofed, and add all the areas together, the fum will be the area of the whole compound figure. Some general rules for finding the fuperficial content of round or fquare figures, &c. For round pillars, multiply the length by the circumference. For fquare pillars, add the fides or breadths together, and multiply the total by the length. For cones, multiply half the length by the largeft circumference. For pyramids, add all the breadths at the base together, and multiply half the length by the total. For globes, multiply the area of the greatest circle by 4, it gives the content. STER E STEREOMETRY, TEa OR MENSURATION OF SOLIDS, Eacheth how to meafure and give up the content of all folid bodies, which are fuch as do confist of length, breadth, thickness, &c. PROBLEM 1. To find the folidity of any Cube, Prifm, or Cylinder. A prifm, &c. is a folid body constituted of an infinite series of equal areas, that of its bafe being one of the terms, and its height the number of all the terms; hence therefore may be deducted the following rule. Multiply the area of the bafe by the depth or perpendicular altitude, and the product fhall be the folid content. Note. In the following examples, the folid figures are formed more to anfwer the purpofe they are defign'd for, than for perfpectives; as alfo there is this advantage, that the learner may very eafily form an idea to make others by them. Solid content 6.859 |