1868.] Mensuration of Superficies and Solids. 211 MENSURATION OF SUPERFICIES. Triangle Base X perpendicular. 2 " equilateral . . Square of any side X -433 Trapezoid 2 parallel sides X perpendicular distance between them. 2 Parallelogram .... Base X perpendicular. Trapezium Diagonal X by ^ sum of perpendiculars. Circle Diameter 2 X -T854 " Circumference X radius. 2 Parabola § of base X altitude. Ellipse . .... Transverse axis X conjugate axis X .1854 Cylinder Length X diameter X 3^. Cone Diameter of Base X length of side X 1.5108 Sphere Diameter 2 X 3.1416 The circumference of every circle is 3.1416 times its diameter, or 6.2832 times its radius, or half diameter. The circumference of an ellipse is that of a circle whose diameter is a mean between the two axes of the ellipse. MENSURATION OF SOLIDS. CUBICAL CONTENTS. Prism Area of base X height. Cylinder Area of base X height. Sphere Diameter 3 X .5236 Cone Base 2 X height X -2618 Paraboloid Diameter of base 2 X height X .3927 To find the area of a triangle whose perpendicular is not known : Call the sides A, B, and C, and half their sum call S ; then, Area = /S— a, S— b, S— c X S. In land survej'ing or measuring, to find the area of a figure which is bounded bj' lines of irregular curvature, as A, B, C, D, in the accompanying figure : The most convenient method is to draw the longest possible line (A, C) straight through the figure, and to divide it into equal parts, by transverse lines, as here ; then add together the lengths of all these perpendiculars, or offsets, divide the sum by the number of offsets, and multiply by the whole length of the line A, C.
