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 , pentagonal , 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 , pentagonal , 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 ) x AF ; that is , to the perimeter of the base of the prism multi- plied by its altitude . B Cor . If two right ...
... prism . Hence , the sum of these rectan- gles , or the convex surface of the prism , is equal to ( AB + BC + CD + DE + EA ) x AF ; that is , to the perimeter of the base of the prism multi- plied by its altitude . B Cor . If two right ...
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 E F S A B to its base EA multiplied by half the perpendicular SF 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 E F S A B to its base EA multiplied by half the perpendicular SF 146 GEOMETRY .
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Common terms and phrases
adjacent adjacent angles altitude angle ACB angle BAC ar.-comp base multiplied bisect Book centre chord circ circumference circumscribed common cone consequently convex surface cylinder diagonal diameter dicular distance draw drawn equal angles equally distant equation equiangular equivalent figure formed four right angles frustum given angle given line gles greater homologous sides hypothenuse inscribed circle inscribed polygon intersection less Let ABC let fall logarithm measured by half number of sides opposite parallelogram parallelopipedon pendicular perimeter perpen perpendicular plane MN polyedron polygon ABCDE prism proportional PROPOSITION pyramid quadrant quadrilateral quantities radii radius ratio rectangle regular polygon right angled triangle S-ABC Scholium secant secant line segment side BC similar solid angle solid described sphere spherical polygon spherical triangle square described straight line tang tangent THEOREM triangle ABC triangular prism vertex