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according algebraic altitude applied arrangements base becomes called circle coefficient common consequently considered contains cube Demonstration denominator denoted determine difference divide dividend division divisor double employed equal equation equivalent evident example exponent expression extract factors figures follows four fraction given gives greater greatest hence known less letters logarithm manner means measure meet method multiplied necessary negative observed obtain operation parallel perpendicular plane polygon positive preceding problem proportion proposed proposed equation pyramid question quotient radical radius ratio reason reduced reference remainder represent resolve respect result right angles root rule sides similar simple square straight line substituting subtract suppose surface taken tens term THEOREM third tion triangle units unity unknown quantity whence whole
Page 9 - If two triangles have the three sides of the one equal to the three sides of the other, each to each, the triangles are congruent.
Page 63 - The areas of two triangles which have an angle of the one equal to an angle of the other are to each other as the products of the sides including the equal angles. A D A' Hyp. In triangles ABC and A'B'C', To prove AABC A A'B'C' A'B' x A'C ' Proof. Draw the altitudes BD and B'D'.
Page 101 - Which proves that the square of a number composed of tens and units, contains the square of the tens plus twice the product of the tens by the units, plus the square of the units.
Page 8 - Any side of a triangle is less than the sum of the other two sides...
Page 122 - ... is negative in the second member, and greater than the square of half the coefficient of the first power of the unknown quantity, this equation can have only imaginary roots.
Page 180 - CD, &c., taken together, make up the perimeter of the prism's base : hence the sum of these rectangles, or the convex surface of the prism, is equal to the perimeter of its base multiplied by its altitude.
Page 54 - The sum of the squares on the sides of a parallelogram is equal to the sum of the squares on the diagonals.
Page 185 - The convex surface of a cone is equal to the circumference of the base multiplied by half the slant height.