Gummere's Surveying by Gummere John 1784-1845

Author:Gummere, John, 1784-1845. [from old catalog] & Sharpless, Isaac, 1848-1920, ed
Language: deu
Format: epub
Tags: Surveying
Publisher: Philadelphia, Porter & Coates
Published: 1880-03-25T05:00:00+00:00

product of the two diameters of the ellipse, by .7854, for the area.*

Note 1.—If the diaraeter of a circle be multiplied by 3.1416, the product will be the circumferenee; also if the circumferenee be divided by 3.1416, the quotient will be the diameter.

2. If the area of a circle be divided by .7854, the Square root of the quotient will be the diameter.

EXAMPLES.

1. How many acres are in a circle a mile in diameter? 1 mile=80ch.

80

6400

.7854

3141600 47124

5026.5600 Sq. Ch.=502 A. 2 R. 25 P. nearly. Or by Logarithms.

Square of 80 { |» ** ^90

H 180 1.903090

7854 -1.895091

5026.56 Sq. Ch. 3.701271

2. Required the area of an ellipse, the longer diameter of which measures 5.36 ch. and the shorter 3.28 ch.

* The demonstration of this rule in the case of the circle is given in Sharpless's Geometry, Book VI., .7854 = \k.

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