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.
Page:Architectural Review and American Builders' Journal, Volume 1, 1869.djvu/337
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