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Hirsch's Collection of Examples, Formulæ, and Calculations, on the Literal ...
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ABCD according already angle arise assume base calculation circle coefficients combinations consequently contains degree denote depends describe determine distance divide division draw the line drawn easily eliminate equal EXAM EXAMPLE figure five foregoing formula four fourth function further given equation gives Hence known likewise magnitudes manner means measure meets merely method multiply necessary numerical expressions obtain parallel perpendicular polygon position possible powers preceding PROB problem proportion quadrilateral radical exponents radius rational recurring remaining REMARK roots SECTION seen sides similar solution solve substitute third tion transformed transposition triangle types values of forms
Σελίδα 110 - IF a straight line be bisected, and produced to any point: the rectangle contained by the whole line thus produced, and the part of it produced, together with the square...
Σελίδα 199 - Of all the lines that can be drawn from a given point to a given line, the perpendicular is the shortest.
Σελίδα 83 - Find the diameter of a circle whose area is equal to the sum of the areas of two circles whose diameters are 12 in.
Σελίδα 81 - He also showed how to find the sums of the first, second, third, &c., powers of the roots of an equation in terms of the coefficients.
Σελίδα 82 - Find the length of the radius of a circle whose area is equal to the sum of the areas of four circles of 10 in., 15 in., 18 in., and 24 in.
Σελίδα 82 - No portion of the column capital should be considered effective which lies outside of the largest 90° cone that can be included within the outlines of the column capital. When a square, or other symmetrically shaped capital is used, c is 'the diameter of a circle whose area is equal to the area of the base of the largest 90° pyramid which can be included within the outlines of the column capital.
Σελίδα 111 - DEF have equal bases and unequal altitudes. ... A ABC > A DEF. (Why ?) .•. A ABC is a maximum. QED Ex. 1015. To divide a given line into two parts so that the rectangle contained by the segments is a maximum. Ex. 1016. In the hypotenuse of a right triangle to find a point so that the sum of the squares of perpendiculars drawn from the point upon the arms is a minimum.