## The measure of the circle; perfected in January, 1845

### John Davis

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. 1854 Excerpt: ...forms an internal scroll, and over measure forms an external scroll. I have 36 straight strips, each 19 inches long and £ of an inch wide. I wish to know how many square inches there are in each strip, and how many square inches there are in the 36 strips, in proportion of square measure, and also in proportion of circular measure. When you work this, and understand it, you will see the difference between square measure and circular measure. Suppose a box be 2 feet long; how wide and how high must it be to contain half a yard square 1 Find the square of the length. 18 18 144 18 3)324 108 V 216 ( 14J 1 24)016 96 20 24 inches long. 24 ) 5832 ( 243 square inches. 48 103 96 72 72 0 V 243 ( 15.583, height and depth. 1 25 ) 143 125 305 ) 1800 1525 3108 ) 27500 24864 2636 Suppose I have a round stick, 50 feet long and 18 inches at the base, and running to a point. I wish to know the length of a string that is wound 3 times round each and every foot, commencing at the base and running to the extreme of the 12 inches, the same as a barber's pole is painted. I find the circle of the mean circumference, which is 9 inches:--9 9.5 3 ) 85.5 ( 28.5, the circle. Now I square the circle. 28.5 28.5 1425 2280 570 812.25 This is what the string rises, 4 X 4 = 16; 812.25 16 30 24 6 Answer: The string will be 359 feet, 7.4162 inches. A and B bought 300 acres of land for 600 dollars; each paid 300 dollars; A says to B, " Let me have my choice in the land, and my land shall cost me 75 cents an acre more than yours." The sum is 65 to 95. 80: 150:: 90 80: 150:: 65 80 80 95 ) 12000 ( 126, answer. 65 ) 12000 ( 184, answer. 95 65 250 550 190. 520 600 126, ana. 300 570 184, ans. 260 30, remainder. 310 40, remainder. 310:126:: 300 310: 184:: 300 300 300 310 ) 37800 ( 181, ...

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