Inhaltsangabe
This historic book may have numerous typos and missing text. Purchasers can download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1796. Excerpt: ... Mensuration of Superficies. Book Vi. 63 Problem 7. To find the circumference of a circle, the diameter being known. Every carpenter will tell you that, if the diameter of a circle be 7, thecirumference is 22; and this is sufficiently exact for common mensuration. Therefore state by the rule of three direct, as 7 is to 22 so is the diameter to the circumference nearly. Or more exactly, as 113 is to 355. Problem 8. To measure a circle. It is manifest that the greater number of sides a polygon has, the nearer it approaches to a circle, and consequently, (with respect to practical mensuration) itmaybe conceived to be a regular polygon of an indefinitely large number of sides; and therefore, by the last problem, its area may be found, by multiplying half the circumference by half the diameter, (as the perpendicular in such cafe is the radius of a circle.) This proportion is generally called Archimedes proportion. It was known to Archimedes and Appollonius Pergaus about 2000 years ago. The proportion of 113 to 355 is generally cited, as the proportion of Vieta or Metius. Probably, it will never be found strictly speaking exact. If the diameter is 1. the circumference has been computed to be 3.14159165358979, &c. to more than 100 places of decimals, and even then they could not be affirmed to be exact. „..» BOOK VII. Of the Rationality of the Mensuration of Sol1ds. Being the Application of Book IV. Problem 1. To measure a cube. Cube the number of feet, inches, or yards, Use. which a side measures in length. For instance; suppose the side os a cube is equal to 2 feet, then 2 multiplied by 2 is equal to 4; and 4 multiplied by 2 is equal to 8 (the cube of 2) the numLer of cubic feet it contains. The truth of which is (hewn by experiment, in illustrating...
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