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Page 199 - If a straight line meet two straight lines, so as to make the two interior angles on the same side of it taken together less than two right angles...
Page 292 - THE rectangle contained by the diagonals of a quadrilateral inscribed in a circle, is equal to both the rectangles contained by its opposite sides.* Let ABCD be any quadrilateral inscribed in a circle, and join AC, BD ; the.
Page 292 - The rectangle contained by the diagonals of a quadrilateral inscribed in a circle is equal to the sum of the two rectangles contained by its opposite sides.
Page 298 - He finds as a general law that a ray, passing from a rarer to a denser medium, is refracted towards the perpendicular : if...
Page 194 - Give him threepence, since he must make gain out of what he learns.
Page 56 - IJandnotwith any special problem. course, that most astronomers mean by 'the universe' the sphere of which the centre is the centre of the earth and the radius is a line drawn from the centre of the earth to the centre of the sun.
Page 145 - At a given point in a given straight line, to make a rectilineal angle equal to a given rectilineal angle. Let AB be the given straight line, and A the given point in, it, and DCE the given rectilineal angle ; it is required to make...
Page 53 - If a straight line be divided into any two parts, the square of the whole line is equal to the squares of the two parts, together with twice the rectangle contained by the parts.
Page 176 - To describe an isosceles triangle, having each of the angles at the base double of the third angle.
Page 133 - Pythagoras changed the study of geometry into the form of a liberal education, for he examined its principles to the bottom and investigated its theorems in an immaterial and intellectual manner.