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A B C ABCD adjacent apotheme applied base bisectors Book calculate centre chord circle circumference coincide common consequently constructed COROLLARY curve DEFINITIONS described diagonals diameter difference direction distance divide draw drawn equal equal angles equivalent exterior extremities ference figures formed four geometrical given given point gives greater half height homologous hypothesis included inscribed intersect join length less limit magnitude manner mean measure meet mètres middle opposite sides parallel parallelogram passes perimeter perpendicular placed plane portion PROBLEM proportional prove quadrilateral quantity radii radius ratio rectangle regular polygon relation result right angles right-angled triangle secant segments side A B sides similar square straight line summit surface taken tangent term THEOREM third triangle triangle ABC twice unity
Page 29 - All the interior angles of any rectilineal figure, together with four right angles, are equal to twice as many right angles as the figure has sides.
Page 168 - A point moves so that the difference of the squares of its distances from two fixed points is constant. Show that the locus is a straight line. Hint. Draw XX' through the fixed points, and YY/ through their middle point.
Page 168 - Show that the locus of a point such that the sum of the squares of its distances from two fixed points is constant, is a circle.
Page 168 - The sum of the squares of two sides of a triangle is equal to twice the square of half the third side, plus twice the square of the median drawn to the third side.
Page 127 - The area of a rectangle is equal to the product of its base and altitude.
Page 56 - BOC, inscribed in a segment less than a semicircle, is an obtuse angle ; for it is measured by half of the arc BAC, greater than a semi-circumference.
Page 1 - Things which are double of the same thing, are equal to each other. 7. Things which are halves of the same thing, are equal to each other. 8. The whole is greater than any of its parts. 9. The whole is equal to the sum of all its parts. 10. All right angles are equal to each other. II. From one point to another, only one straight line can be drawn.
Page 85 - Fig. 121. parallel to BC, the angles of the quadrilateral AEFD are equal to those of the quadrilateral ABCD; but the proportion of the sides is different. Also, without changing the four sides...
Page 101 - Scholium. The right-angled triangle is the only one in which the sum of the squares of two sides is equivalent to the square of the third ; for if the angle contained by the two sides is acute, the sum of their squares will be greater than the square of the opposite side ; if obtuse, it will be less.