Exercise Manuals, Issue 3Ginn & Company, 1889 |
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Common terms and phrases
adjacent angles altitude Analysis apothem Auxiliary triangles base bisectors bisects centre chord circumference circumscribed construct a circle construct a triangle cubic decagon diagonals distance draw a line equidistant equilateral triangle equivalent find a point Find the area Find the length find the locus Find the radius Find the volume frustum given circle given length given line given point given square given triangle hypotenuse inches inscribed regular intersection isosceles trapezoid isosceles triangle join K₁ L₁ legs line drawn line parallel median method of loci middle points P₁ parallelogram perimeter perpendicular plane problem produced quadrilateral radii rectangle regular hexagon regular polygon rhombus right cone right cylinder right triangle secant segment similar slant height sphere square feet straight line tangent tangents drawn Theorem total surface trapezoid triangle ABC vertex vertices
Popular passages
Page 25 - Find the radii r, r' of the inscribed and circumscribed spheres, the surface S, and the volume V. 9. The same exercise for the regular octahedron. 11. The same exercise for the regular tetrahedron. 12. The same exercise for the regular octahedron. 13. The height of a frustum of a right cone is h, and the radii of its bases r, r' ; what is the volume of the largest regular four-sided frustum which can be made from it? 14. The volume of a right cone, whose slant height is equal to the diameter of its...
Page 77 - To find the locus of a point such that the difference of the squares of its distances from two given points A, B is constant.
Page 2 - 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.
Page 60 - 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 xii - 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 5 - The sum of the diagonals of a quadrilateral is less than the sum and greater than half the sum of tht. sides. * 21. Each side of a triangle is less than half the perimeter.
Page 60 - In every inscribed quadrilateral the product of the diagonals is equal to the sum of the products of the opposite sides.
Page xxiv - Theorem. The perimeters of two regular polygons of the same number of sides have the same ratio as their radii, or as their apothems.
Page 65 - Every straight line cutting the sides of a triangle (produced when necessary) determines upon the sides six segments, such that the product of three non-consecutive segments is equal to the product of the other three.
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...