A B C ABCD adjacent altitude angle ABC apothem bisect centre chord circumference cone construct the triangle convex surface Corollary cylinder diagonals diameter distance divided dodecagon EATON'S ELEMENTARY ALGEBRA equal altitudes equally distant equiangular equilateral feet frustum GEOMETRY given angle given circle given line given point given side half the arc 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 PROBLEM propositions quadrilateral radii radius ratio rectangle regular polygon respectively equal rhombus right angles right prism right pyramid right triangle Scholium secant segment sides A D similar triangles slant height sphere straight line tangent THEOREM THEOREM VII trapezoid triangle ABC TRIGONOMETRY vertex
Page 33 - 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 71 - 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 48 - 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 17 - 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 10 - 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 19 - 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 58 - 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 59 - 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 56 - 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