An Elementary Geometry |
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... Angles 64 Exercises 68 BOOK V. POLYEDRONS . Prisms , Cylinders 69 Pyramids , Cones 75 The Sphere 82 Exercises 86 PROBLEMS OF CONSTRUCTION Exercises BOOK VI . 89 106 PLANE GEOMETRY . INTRODUCTORY DEFINITIONS . 1. Mathematics is the.
... Angles 64 Exercises 68 BOOK V. POLYEDRONS . Prisms , Cylinders 69 Pyramids , Cones 75 The Sphere 82 Exercises 86 PROBLEMS OF CONSTRUCTION Exercises BOOK VI . 89 106 PLANE GEOMETRY . INTRODUCTORY DEFINITIONS . 1. Mathematics is the.
Page 78
... cone is a right pyramid ( 33 ) , this demon- stration includes the frustum of a , cone . If , therefore , R and r = the radii of the two bases of the 78 SOLID GEOMETRY .
... cone is a right pyramid ( 33 ) , this demon- stration includes the frustum of a , cone . If , therefore , R and r = the radii of the two bases of the 78 SOLID GEOMETRY .
Page 79
... cone , and S its slant height , its convex surface = ( 2 πR + 2 πν ) S = ( π R + πr ) S If r ' the radius of a section midway between and parallel to the bases , the convex surface 2πγ ' δ THEOREM X. 46. If two pyramids having equal ...
... cone , and S its slant height , its convex surface = ( 2 πR + 2 πν ) S = ( π R + πr ) S If r ' the radius of a section midway between and parallel to the bases , the convex surface 2πγ ' δ THEOREM X. 46. If two pyramids having equal ...
Page 83
... cone , and is equal to BCX circ . PO ( 45 ) . But the triangles BCH and POG are similar ( II . 21 ) ; therefore or ( III . 28 ) BC : BHor KL = GO : PO BC : KL = circ . GO : circ . PO ... BCX circ . P 0 = K L × circ . GO That is , the ...
... cone , and is equal to BCX circ . PO ( 45 ) . But the triangles BCH and POG are similar ( II . 21 ) ; therefore or ( III . 28 ) BC : BHor KL = GO : PO BC : KL = circ . GO : circ . PO ... BCX circ . P 0 = K L × circ . GO That is , the ...
Page 85
... cone whose slant height is 5 feet and whose base has a radius of 2 feet ? How many square feet in the whole surface ? 11. How many cubic feet in a right quadrangular pyramid whose alti- tude is 10 feet , and whose base is 3 feet square ...
... cone whose slant height is 5 feet and whose base has a radius of 2 feet ? How many square feet in the whole surface ? 11. How many cubic feet in a right quadrangular pyramid whose alti- tude is 10 feet , and whose base is 3 feet square ...
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Common terms and phrases
ABC and DEF ABCD adjacent altitude angle ABC apothem base and altitude bisect centre chord circ circumference coincide cone construct the triangle convex surface Corollary cube cylinder diameter distance divided dodecagon EATON'S equal altitudes equally distant equiangular equilateral feet frustum given angle given circle given line given point given side given square given triangle half the arc hexagon homologous sides hypothenuse included angle infinite number inscribed internal angles intersection isosceles triangle Let ABCDEF line joining mean proportional measured by half number of sides opposite sides parallel planes parallelogram parallelopiped perimeter perpendicular plane parallel propositions quadrilateral radii radius ratio rectangle regular polygon respectively equal rhombus right angles right prism right pyramid right triangle Scholium secant segment similar triangles slant height sphere tangent THEOREM VIII trapezoid triangle ABC vertex
Popular passages
Page 25 - Four quantities are in proportion when the ratio of the first to the second is equal to the ratio of the third to the fourth.
Page 30 - If any number of quantities are proportional, any antecedent is to its consequent as the sum of all the antecedents is to the sum of all the consequents. Let a : b = c : d = e :f Now ab = ab (1) and by Theorem I.
Page 27 - If the product of two quantities is equal to the product of two others, the...
Page 43 - The area of a regular polygon is equal to half the product of its perimeter and apothem.
Page 11 - If two triangles have two sides, and the included angle of the one equal to two sides and the included angle of the other, each to each, the two triangles are equal in all respects.
Page 23 - If two triangles have two sides of one respectively equal to two sides of the other, but the third sides unequal...
Page 20 - ... polygon, is equal to twice as many right angles as the polygon has sides minus two.
Page 49 - A Circle is a plane figure bounded by a curved line every point of which is equally distant from a point within called the center.
Page 70 - A right cylinder is a solid described by the revolution of a rectangle about one of its sides.
Page 64 - DEFINITIONS. 1 . A straight line is perpendicular to a plane, when it is perpendicular to every straight line of the plane which it meets.