A complete and practical solution book for the common school teacher . moving in this beautiful curve, we are constrained to ac-knowledge that all our boasted knowledge is as nothing in the won-drous dispensation of Him who telleth the number of the stars andcalleth them all by their names. 95. In Fig. 78, AA is the major axis, or the diameterwhich passes through the foci. BB is the minor axis, or thediameter which is perpendicular to the major axis. To Find the Area.—Multiply half the sum of the two diametersby it and the residt is the area. PROBLEM the axes of an ellipse are 60 and 80
A complete and practical solution book for the common school teacher . moving in this beautiful curve, we are constrained to ac-knowledge that all our boasted knowledge is as nothing in the won-drous dispensation of Him who telleth the number of the stars andcalleth them all by their names. 95. In Fig. 78, AA is the major axis, or the diameterwhich passes through the foci. BB is the minor axis, or thediameter which is perpendicular to the major axis. To Find the Area.—Multiply half the sum of the two diametersby it and the residt is the area. PROBLEM the axes of an ellipse are 60 and 80 ft., what are the areas of thetwo segments into which it is divided by a line perpendicular to themajor axis, at the distance of 10 ft. from the center? Solution. (1) Let ADAD represent a cir- cle, EAS the segment ofthe ellipse ABAB, andDAD the segment of thecircle. (2) CG=10 ft., DG2=AGxGA, or ft. (3) DG = V1500, or ft. (4) DD= ft. (5) The area of DAD= (h*+2b) +f of ^= sq. ft. (6) Area of the segment of circle : the area of the segment. FIG. 78. MENSURATION. 197 of the ellipse::CB : CA. (7) .. : the segment of the ellipse:: 40 : 30. (8) From which we find the area of the segment of the ellipse to be sq. ft. (9) The area of the ellipse is (40X 30)tt= sq. ft. (by the above rule). — = sq. ft., areaof EAS. Note.—This problem was prepared by the author for the TeachersReview. We wish to prepare an extensive work on the ellipse in thefuture. VI. CATENARIAN CURVE. 96. A curve formed by a chain or rope of uniform density,hanging freely from any two points not in the same verticalline. The catenary was first observed by Galileo, who proposed it as theproper figure for an arch of equilibrium. He imagined it to be thesame as the parabola. Its properties were first investigated by JohnBernovilli, Huygens and Leibnitz. It is now universally adopted insuspension bridges. Each wire assumes its own catenary curve.
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