# Rodgers' Mensuration; Elements of Mensuration

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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. 1862 edition. Excerpt: ...tha arc, and altitude the cosine of half the arc; as, A B C. Two sectors, segments, or arcs of circles are similar when they correspond to equal angles at the pentre 7 CIRCULAR AND ANGULAR MEASURE. This measure is applied to the measurement of circles and angles. 60 seconds (").... make 1 minute, ' 60 minutes..... "1 degree, 30 degrees....." 1 sign, S. 12 signs, or 360 degrees.. "1 circle, C. ARCS OF CIRCLES. PROBLEM VI. The number of degrees in a circular arc and the radius of the circle being given, to find the length of the arc. RULE. First find the circumference of the circle whose radius is given. Then as 360 degrees is to the number of degrees in the arc, so is the circumference to the required arc. EXPLANATION. The circumference is the length of 360 degrees, and we wish to find the length of the number of degrees in the arc, therefore as an arc is less than a circumference, we have by simple proportion as 360: number of in the arc:: circumference: arc. Examples. 1. What is the length of an arc of 95 whose diameter is 5 inches? Solution. 5 in. X 3.1416 = 15.703 in., the circumference. 360: 95:: 15.708 in.: 4.145 in., the arc. Res. 4.145 inches. 2. What is the length of an arc of 30, the radius of the circle being 7 feet? 3. What is the length of an are of 30 5' 7," the radius of the circle being 20 feet? 4. What is the length of a degree of the earth's circumference, if its equatorial diameter is 7926 miles? 5. How far is an inhabitant of any place on the equator carried in 5 hours, the diameter of the earth being 7926 miles? PROBLEM VII. The chord of the, arc and the chord of half tho, arc being given, to find the length of the arc, RULE, From 8 times the chord of half the are, subtract the chord of the whole arc, ...