Elements of Geometry and Trigonometry |
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Page 142
... prism . 4. The equal and parallel polygons ABCDE , FGHIK , are called the bases of the prism ; the parallelograms taken together constitute the lateral or convex surface of the prism ; the equal straight lines AF , BG , CH , & c . are ...
... prism . 4. The equal and parallel polygons ABCDE , FGHIK , are called the bases of the prism ; the parallelograms taken together constitute the lateral or convex surface of the prism ; the equal straight lines AF , BG , CH , & c . are ...
Page 143
... prism . In every other case the prism is oblique , and the altitude less than the side . 7. A prism is triangular , quadrangular , pentagoral , hex- agonal , & c . when the base is a triangle , a quadrilateral , a pentagon , a hexagon ...
... prism . In every other case the prism is oblique , and the altitude less than the side . 7. A prism is triangular , quadrangular , pentagoral , hex- agonal , & c . when the base is a triangle , a quadrilateral , a pentagon , a hexagon ...
Page 144
... prism . Hence , the sum of these rectan- gles , or the convex surface of the prism , is equal to ( AB + BC + CD + DE + EA ) × AF ; that is , to the perimeter of the base of the prism multi- plied by its altitude . Cor . If two right prisms ...
... prism . Hence , the sum of these rectan- gles , or the convex surface of the prism , is equal to ( AB + BC + CD + DE + EA ) × AF ; that is , to the perimeter of the base of the prism multi- plied by its altitude . Cor . If two right prisms ...
Page 145
... prism , if drawn parallel to the base , is also equal to the base . PROPOSITION III . THEOREM . If a pyramid be cut by a plane parallel to its base , 1st . The edges and the altitude will be divided proportionally . 2d . The section ...
... prism , if drawn parallel to the base , is also equal to the base . PROPOSITION III . THEOREM . If a pyramid be cut by a plane parallel to its base , 1st . The edges and the altitude will be divided proportionally . 2d . The section ...
Page 146
... , therefore , which form the convex surface of the prism are all equal to each other . But the area of either of these triangles , as ESA , is equal F S B which to its base EA multiplied by half the perpendicular 146 GEOMETRY .
... , therefore , which form the convex surface of the prism are all equal to each other . But the area of either of these triangles , as ESA , is equal F S B which to its base EA multiplied by half the perpendicular 146 GEOMETRY .
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Common terms and phrases
adjacent altitude angle ACB angle BAC ar.-comp base multiplied bisect Book VII centre chord circ circumference circumscribed common cone consequently convex surface Cosine Cotang cylinder diagonal diameter dicular distance divided draw drawn equal angles equally distant equations equivalent feet figure find the area formed four right angles frustum given angle given line gles greater homologous sides hypothenuse inscribed circle inscribed polygon intersection less Let ABC logarithm number of sides opposite parallel parallelogram parallelopipedon pendicular perimeter perpen perpendicular plane MN polyedron polygon ABCDE PROBLEM proportional PROPOSITION pyramid quadrant quadrilateral quantities radii radius ratio rectangle regular polygon right angled triangle S-ABCDE Scholium secant segment similar sine slant height solid angle solid described sphere spherical polygon spherical triangle square described straight line tang tangent THEOREM triangle ABC triangular prism vertex
Popular passages
Page 241 - In every plane triangle, the sum of two sides is to their difference as the tangent of half the sum of the angles opposite those sides is to the tangent of half their difference.
Page 19 - If two triangles have the three sides of the one equal to the three sides of the other, each to each, the triangles are congruent.
Page 232 - ... the logarithm of a fraction is equal to the logarithm of the numerator minus the logarithm of the denominator.
Page 168 - The radius of a sphere is a straight line drawn from the centre to any point of the surface ; the diameter or axis is a line passing through this centre, and terminated on both sides by the surface.
Page 18 - America, but know that we are alive, that two and two make four, and that the sum of any two sides of a triangle is greater than the third side.
Page 169 - The convex surface of a cylinder is equal to the circumference of its base multiplied by its altitude, Fig.
Page 20 - In an isosceles triangle the angles opposite the equal sides are equal.
Page 86 - The areas of two triangles which have an angle of the one equal to an angle of the other are to each other as the products of the sides including the equal angles. A D A' Hyp. In triangles ABC and A'B'C', To prove AABC A A'B'C' A'B' x A'C ' Proof. Draw the altitudes BD and B'D'.
Page 225 - B) = cos A cos B — sin A sin B, (6a) cos (A — B) = cos A cos B + sin A sin B...
Page 168 - CIRCLE is a plane figure bounded by a curved line, all the points of which are equally distant from a point within called the centre; as the figure ADB E.