An Elementary Geometry |
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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 ...
... 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 ...
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... Exercises 64 68 BOOK V. POLYEDRONS . Prisms , Cylinders Pyramids , Cones The Sphere Exercises 8828 69 75 82 86 BOOK VI . PROBLEMS OF CONSTRUCTION 89 Exercises 106 PLANE GEOMETRY . INTRODUCTORY DEFINITIONS . 1. Mathematics is the.
... Exercises 64 68 BOOK V. POLYEDRONS . Prisms , Cylinders Pyramids , Cones The Sphere Exercises 8828 69 75 82 86 BOOK VI . PROBLEMS OF CONSTRUCTION 89 Exercises 106 PLANE GEOMETRY . INTRODUCTORY DEFINITIONS . 1. Mathematics is the.
Page 83
... 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 = AFX circ . GA . L G H M D Let ABCDEF be a regular semi - decagon inscribed ...
... 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 = AFX circ . GA . L G H M D Let ABCDEF be a regular semi - decagon inscribed ...
Page 84
... sphere equal to AFX circ . GA 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 = 2π RX 2 R = 4 π R2 , or π D2 п That is ...
... sphere equal to AFX circ . GA 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 = 2π RX 2 R = 4 π R2 , or π D2 п That is ...
Page 88
... sphere is four times the surface of one of its great circles . ( 62 ; III . 32. ) 94. Definition . A polyedron is circumscribed about a sphere when its faces are each tangents to the sphere . In this case the sphere is inscribed in the ...
... sphere is four times the surface of one of its great circles . ( 62 ; III . 32. ) 94. Definition . A polyedron is circumscribed about a sphere when its faces are each tangents to the sphere . In this case the sphere is inscribed in the ...
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Common terms and phrases
A B C ABCD adjacent altitude angle ABC apothem arcs A B base and altitude bisect centre chord circ circumference cone construct the triangle convex surface Corollary cube 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 VII 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.