## Elements of Geometry and Trigonometry |

### From inside the book

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Page 142

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**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

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**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

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**prism**. Hence , the sum of these rectan- gles , or the convex surface of the**prism**, is equal to ( AB + BC + CD + DE + ÉA ) × AF ; that is , to the perimeter of the base of the**prism**multi- plied by its altitude . B Cor . If two right ... Page 145

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**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

... , 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 B to its base EA multiplied by half the perpendicular SF 146 GEOMETRY .### Other editions - View all

### 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 convex surface Cosine Cotang cylinder diagonal diameter dicular distance draw drawn equal angles equally distant equiangular equivalent figure formed four right angles frustum given angle given line gles greater homologous sides hypothenuse inscribed polygon intersection less Let ABC let fall logarithm measured by half number of sides oblique lines 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 sine solid angle solid described sphere spherical polygon spherical triangle square described straight line tang tangent THEOREM triangle ABC triangular prism vertex