### Δημοφιλή αποσπάσματα

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 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...
Σελίδα 56 - ... a — b, b— a, a— c, c— a, b— c, c— b.
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.