Synopsis
This historic book may have numerous typos and missing text. Purchasers can usually download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1805 edition. Excerpt: ...accord ing to the construction of prob. 31. sect. 1. fig. 10. PI. 18. Rule, Find the sum of the areas of the sectors AF G B, F K E L, B I C M, and E G C D, by prob. 16. sect 4. from which subtract the area of the lozenge G IH K, and the difference will be the required area.-Prob. 22. To find the area of an ellipse ACBD, fig. 11, PI. 18,. Rule. Rule. Multiply continually together the two diameters A B, CD, and the number 11. Divide the last product by 14, and the quotient will be the area nearly true. Example. What will be the area of the ellipse ADB C A, its transverse A B being 15 feet, and its conjugate C D 10 feet? ii X i; x io-117j85 Square feet = area re. '4 quired. Another method still nearer. Rule. Multiply continually together the two diameters, and the number 0,7854, and the product will be the area of the ellipse. Example. What will be the area of the ellipse ADBCA, its transverse A B being 25 inches, and conjugate CD 18 inches? 0,7854 X 25 X 18 = 353,43 square inches = area required. Brob. 23. To find the area of the parabola A B C A, fig. 12. PI. 18. Rule. Rule. Multiply the base A C by the height D Bf land the of the product will be the area. Example, What will be the area of the parabola A B C A, its base A C being 20 feet, and its height D B 12 feet? 20 X 12 = 240,-2 X 2 = 160 square feet = area required. SECT. V. MENSURATION OF SOLIDS, DEFINITIONS. 1.-A. Solid, is a body contained under three dimensions, or extended in length, breadth, and thickness. 2. Solids are measured by cubes, whose sides are each an inch, a foot, a yard, &c. and the solidity, capacity, or content of any figure, is computed by the number of such cubes as are contained in it. 3. Solidities are terminated, either by one sur face, face, as a globe,...
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