Hirsch's Collection of Examples Formulae and Calculations on the Literal Calculus and Algebra |
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Hirsch's Collection of Examples, Formulæ, and Calculations, on the Literal ... Meier Hirsch No preview available - 2016 |
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a²x a²x² a³p a³x AB² ABCDEF arise assume calculation circumference coefficients combinations consequently contains convex angle denote determine different values divide division draw the line eliminate equa equal EXAM following equations foregoing formula four further given angle given circle given equation given point given proportion gives Hence irrational magnitudes Let ABCD fig likewise multiply numerical expressions obtain parallel permutations polygon primitive root PROB quadrilateral radical exponents radius rational equation rational functions recurring transpositions SECTION segment semicircle sides sixth degree solution solve substitute symmetrical functions three roots tion transformed equation Trapez trapezium triangle ABC values of forms x¹³
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Page 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...
Page 20 - ... are proportionals. Let the two triangles ABC, DEF have one angle in the one equal to one angle in the other, viz. the angle BAC to the angle EDF, and the sides about...
Page 199 - Of all the lines that can be drawn from a given point to a given line, the perpendicular is the shortest.
Page 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.
Page 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.
Page 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.
Page 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.
Page 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.