An Elementary Geometry

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Thompson, Brown & Company, 1872 - Geometry - 110 pages

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Page 35 - figure bounded by a curved line called the circumference, every point of which is equally distant from a point within called the centre ; as ABD E. 2, The Radius of a circle is a line drawn from the centre to the circumference • as C D.
Page 72 - CD, &c. are called zones. 91. The area of a zone Is equal to the product of its altitude by the circumference of a great circle. 92. Zones on the same or equal spheres are as their altitudes. 93. The surface of a sphere is four times the surface of one of its great circles.
Page 50 - ANGLES. DEFINITIONS. - / 1. A straight line is perpendicular to a plane when it is perpendicular to every straight line of the plane which it meets. Conversely, the plane, in this case, is perpendicular to the line. The foot of the perpendicular is the point in which it meets the plane.
Page 19 - Corollary. The area of a square is the square of one of its sides. THEOREM III. 10. The area of a parallelogram is equal to the product of its base and altitude. Let DF be the altitude of the
Page 12 - A proportion is transformed by Division when in each couplet the difference of the antecedent and consequent is compared with the antecedent or with the consequent. THEOREM I. 12. In a proportion the product of the extremes is equal to the product of the means. Let
Page 21 - therefore the area of a trapezoid is equal to the product of its altitude and the line joining the middle points of the sides •which are not parallel. THEOREM VI. 16. A line drawn parallel to one side of a triangle divides
Page 60 - its base by its altitude ; therefore the volume of any prism is equal to the product of its base by its altitude. 26. Corollary. As a cylinder is a right prism, this demonstration includes the cylinder. If, therefore, R = the radius
Page 61 - Pyramid is one whose base is a regular polygon and in which the perpendicular from the vertex passes through the centre of the base. 32. The Slant Height of a right pyramid is the perpendicular distance from the vertex to the base of any one of its lateral faces ; as A C.
Page 58 - Cor. 1. A section made by a plane parallel to the base is equal to the base. 18. Cor. 2. A section of a cylinder made by a plane parallel to the base is a circle equal to the base. THEOREM III. 19. Prisms having equivalent bases and equal altitudes are equivalent. Let

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