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CHAPTER VII-KRASUREMENT OF AREAS.
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62. In the case of a semiciroular field of a diameter measuring 12. and of another) field having a diameter of 36 in measure what is the oiroumference and what the area !
The role for arriving at the minutely accurate valuos relating to an elliptical figure :--
63. The square of the (shorter) diameter is multiplied by 6 and the square of twice the length (as measured by the longer diameter) is added to this. The square root of this sum gives) the measure of the circumference. This measure of tho circumforence multiplied by one-fourth of the shorter) diameter gives the minutely accurate measure of the area of an elliptical figure.
An e: ample in illustration thereof.
84. In the case of an elliptical figure, the length (as moasured by the longer diameter) is 36, and tho broudth (as measured by the shorter diameter) is 12. Tell me, after caloulation, what the measure of the circumference is, and what the minutoly acourato measure of the area.
The rule for arriving at the minutoly acourato valuos in relation to a conchiform figuro :--
05. The maximum moasure of the) breadth (of the figure), diminished by half (the measure of the broadth) of the mouth, and (then) multiplied by the square root of 10, gives rise to the measure of the perimeter. The square of half tho (maximum)
69. Il a represents the measure of the longer diameter and b that of the shorter diameter of an ollipse, then, k'cording to the rule given here, the oir. onmference is V 66 + 4a, and the area in bx V 60' + tal. It may be noted that this stanse, u found in the M88., omits to mention that the square root of the quantity is to be taken for arriving at the value of the cironmferonoo. The formula for the area given here is only an approximation, at noon to be based on the analogy of the srea of a circle us represented by ad *-. where d is the diameter and rd in the circumforenco. 864. Algebraically, circumference = (
a m ) * 10;
2
arow = [ {6-4m) **}'+4)*]x vio; whero a ia tho monsivo of the
