## Elements of Geometry: Containing the First Six Books of Euclid, with a Supplement on the Quadrature of the Circle and the Geometry of Solids ; to which are Added Elements of Plane and Spherical Trigonometry |

### From inside the book

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**prism**is a solid figure contained by plane figures , of which two that are opposite are equal , similar , and parallel to one another ; and the others are parallelograms . V. A parallelepiped is a solid figure contained by six ... Page 199

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**prisms**. Let AB be a solid parallelopiped , and DE , CF the diagonals of the opposite parallelograms AH , GB , viz . those which are drawn betwixt the equal angles in each ; and because CD , FE are each of them pa- rallel to GA , though ... Page 200

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**prism**CAE is equal to the**prism**CBE ( 1. 3. Sup . ) , and the solid AB is cut into two equal**prisms**by the plane CDEF . Q. E. D. A E N. B. The insisting straight lines of a parallelepiped , mentioned in the following propositions , are ... Page 201

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**prisms**DAG , HLN are equal ( 1.3 . Sup . ) . If therefore the**prism**LNH be taken from the solid , of which the base is the parallelogram AB , and FDKN the plane opposite to the base ; and if from this same solid there be taken the**prism**... Page 204

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**prism**BNM is to the parallelepiped CD as the triangle AEM to the parallelogram LG . For by the last Cor . the**prism**BNM is to the**prism**DPG as the triangle AME to the triangle CGF , and therefore the**prism**BNM is to twice the**prism**...### Other editions - View all

### Common terms and phrases

ABC is equal ABCD altitude angle ABC angle ACB angle BAC angle EDF arch AC base BC bisected centre circle ABC circumference cosine cylinder definition demonstrated diameter draw equal angles equiangular equilateral equilateral polygon equimultiples Euclid exterior angle fore four right angles given straight line greater hypotenuse inscribed join less Let ABC Let the straight line BC magnitudes MDCCCXX meet multiple opposite angle parallel parallelepipeds parallelogram perpendicular polygon prism PROB produced proportionals proposition Q. E. D. COR Q. E. D. PROP radius ratio rectangle contained rectilineal figure remaining angle segment semicircle shewn side BC sine solid angle solid parallelepipeds spherical angle spherical triangle straight line AC THEOR third touches the circle triangle ABC triangle DEF wherefore