## Elements of Geometry and Trigonometry |

### From inside the book

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Page 139

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**S**by any plane**ABCDE**; from O , a point in that plane , draw to the several angles the straight lines AO , OB , OC , OD , OE . The sum of the angles of the triangles ASB , BSC , & c . formed about the vertex**S**, is equal to the sum of ... Page 143

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**S**, and terminating in the different sides of the same polygon**ABCDE**. The polygon**ABCDE**is called the base of the pyramid , the point**S**the vertex ; and the triangles ASB , BSC , CSD , & c . form its convex or lateral sur- face . 11 ... Page 145

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**S**-**ABCDE**, of which SO is the altitude , be cut by the plane abcde ; then will Sa : SA :: So : So , and the same for the other edges : and the polygon abcde , will be similar to the base ABCDE . B D First . Since the planes ABC , abc ... Page 146

Adrien Marie Legendre. Cor . 1. Let

Adrien Marie Legendre. Cor . 1. Let

**S**-**ABCDE**, S - XYZ be two pyramids , hav- ing a common vertex and the same altitude , or having their bases situated in the same plane ; if these pyramids are cut by a plane parallel to the plane of ... Page 160

... ABC be a triangular pyramid , ABC - DEF a triangular prism of the same base and the same altitude ; the pyramid will be equal to a third of the prism . Cut off the pyramid F - ABC ...

... ABC be a triangular pyramid , ABC - DEF a triangular prism of the same base and the same altitude ; the pyramid will be equal to a third of the prism . Cut off the pyramid F - ABC ...

**S**-**ABCDE**be a pyramid . T dollag 160 GEOMETRY .### Other editions - View all

### Common terms and phrases

adjacent adjacent angles altitude angle ACB angle BAC ar.-comp base multiplied bisect Book VII centre chord circ circumference circumscribed common cone convex surface Cosine cylinder diagonal diameter dicular distance divided draw drawn 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 parallelogram parallelopipedon pendicular perimeter perpen perpendicular perpendicular let fall 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 Cotang slant height solid angle solid described sphere spherical polygon spherical triangle square described straight line tang tangent THEOREM triangle ABC triangular prism vertex