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altitude Analysis angle base bisectors centre chord circumference circumscribed construct construct a circle containing cubic cylinder denote described determine diagonals diameter difference distance divide draw drawn equal equidistant equilateral triangle equivalent feet figure Find the area Find the volume formed four frustum given circle given line given point given triangle greater half height hexagon hypotenuse inches inscribed intersection isosceles triangle join legs length line parallel mean meet middle points opposite parallel parallelogram passes perimeter perpendicular plane position problem produced proportional Prove pyramid quadrilateral radii radius ratio rectangle regular regular polygon respectively rhombus right cone right triangle secant segment sides similar solution sphere square square feet straight line surface tangent Theorem third touch transform trapezoid triangle ABC vertex vertices volume wide yards
Page 79 - To find the locus of a point such that the sum of the squares of its distances from two given points A, B is constant.
Page 6 - A pyramid 15 ft. high has a base containing 169 sq. ft. At what distance from the vertex must a plane be passed parallel to the base so that the section may contain 100 sq.ft.?
Page xiv - The straight line joining the middle points of two sides of a triangle is parallel to the third side, and equal to half of it.
Page 62 - In any triangle, the product of two sides is equal to the square of the bisector of the included angle plus the product of the segments of the third side. Hyp. In A abc, the bisector t divides c into the segments, p and q. To prove ab = t
Page 81 - OP= 4 inches, r = 4 inches. 16. To find the locus of points from which two given circles will be seen under equal angles. Show that the distances from any point in the locus to the centres of the two circles are as the radii of the circles; this reduces the problem to Ex. 12. 17. To find the locus of the points from which a given straight line is seen under a given angle. 18. To find the locus of the vertex of a triangle, having given the base and the ratio of the other two sides. 19. To find the...
Page xxiii - AREAS. 175. Definitions. Equivalent figures, area of a figure, units of area, transformation of a figure. 176. Theorem. Two rectangles having equal bases are to each other as their altitudes; and two rectangles having equal altitudes are to each other as their bases. 177. Theorem. Any two rectangles are to each other as the products of their bases and altitudes. 178. Theorem. Area of a rectangle = base X altitude. 179. Theorem. Area of a square = square of one side. 180. Theorem. Area of a parallelogram...
Page xiv - A straight line drawn parallel to the base of a triangle, bisecting one of the sides, bisects the other also ; and the part intercepted between the two sides is equal to half the base. 72. Theorem. The median of a trapezoid is' parallel to the bases and equal to half their sum. 73. Theorem. Equidistant parallels divide every secant into equal parts. BOOK II. THE CIRCLE. THE CIRCLE AND STRAIGHT LINES. 74. Definitions. Circumference, circle, radius, diameter, arc, chord, semi-circumference, segment,...
Page 33 - A cone, whose slant height is equal to the diameter of its base, is inscribed in a given sphere, and a similar cone is circumscribed about the same sphere.
Page xiv - An isosceles trapezoid is a trapezoid whose non-parallel sides are equal. A pair of angles including only one of the parallel sides is called a pair of base angles. Pairs of base angles The median of a trapezoid is parallel to the bases and equal to onehalf their sum.