## An Elementary Geometry |

### From inside the book

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**sphere**. Thus the whole constitutes a single Theorem , without an unnecessary link in the chain of reasoning . These five Books , including Ratio and Proportion , are pre- sented in eighty - one Propositions , covering only seventy ... Page

... 64 Exercises 68 BOOK V. POLYEDRONS . Prisms , Cylinders Pyramids , Cones The

... 64 Exercises 68 BOOK V. POLYEDRONS . Prisms , Cylinders Pyramids , Cones The

**Sphere**Exercises 86 8828 69 75 PROBLEMS OF CONSTRUCTION Exercises BOOK VI . · . 89 106 PLANE GEOMETRY . INTRODUCTORY DEFINITIONS . 1. Mathematics is the. Page 83

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**sphere**K may be described ; then the surface of the**sphere**is equal to the diameter A F multi- plied by the circumference of the circle whose radius is GA , or — A F × circ . G A. L G C M D Let A B C D E F be a regular semi - decagon ... Page 84

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**sphere**equal to AFX circ . G A 62. Corollary . Let S the surface of the**sphere**, C = the circumference , R = the radius , D = the diameter , then we have ( III . 30 ) C = 2π R , or π D Therefore S = 2 TRX 2 R = 4 π R2 , or π D2 П ... Page 86

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**sphere**whose radius is 6 feet ? 21. How many cubic feet in a**sphere**whose radius is 8 feet ? 22. What is the ratio of the volumes of two**spheres**whose radii are as 4 : 8 ? 23. Are**spheres**always similar solids ? Are cones ? 24. What ...### Other editions - View all

### Common terms and phrases

A B C A B equal ABCD adjacent altitude angle ABC apothem base and altitude centre chord circ circumference cone construct the triangle convex surface Corollary cylinder diagonals 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 half the arc hexagon homologous sides hypothenuse included angle infinite number inscribed internal angles intersection isosceles triangle Let ABCDEF line joining lines A B measured by half number of sides opposite sides parallel planes parallelogram parallelopiped perimeter perpendicular plane parallel 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 107 - To describe an isosceles triangle, having each of the angles at the base double of the third angle.

Page 5 - If, at a point in a straight line, two other straight lines, upon the opposite sides of it, make the adjacent angles together equal to two right angles, these two straight lines shall be in one and the same straight line.

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 27 - If the product of two quantities is equal to the product of two others, the...

Page 12 - In an isosceles triangle the angles opposite the equal sides are equal.

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 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 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 23 - If two triangles have two sides of one respectively equal to two sides of the other, and the angles contained by those sides supplementary, the triangles are equal in area.

Page 70 - A Cylinder is a solid figure, described by the revolution of a rectangle about one of its sides, which remains fixed.