## 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

Results 6-10 of 11

Page 204

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**parallelepipeds**which have the same altitude , are to one another as their bases , Let AB , CD be solid**parallelepipeds**of the same altitude : they are to one another as their bases ; that is , as the base AE to the base CF , so is the ... Page 205

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**parallelepiped**CD as the triangle AME to the parallelogram LG . PROP . IX . THEOR . Solid**parallelepipeds**are ...**parallelepipeds**, of which the bases are the parallelograms AC and GK , and the altitudes , the perpendicu- lars let ... Page 206

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**parallelepipeds**Y and Z on these bases . Then , if the upright**parallelepipeds**AF and GO be constitut- . ed on the bases AC and GK , with the altitudes AE and GM , they will be equal to the**parallelepipeds**Y and Z ( 7. 3. Sup . ) . Now ... Page 207

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**parallelepipeds**, which have their bases and altitudes reciprocally proportional , are equal ; and**parallelepipeds**which are equal , have their bases and altitudes reciprocally proportional . Let AG and KQ be two solid**parallelepipeds**... Page 208

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**parallelepipeds**, & c . Q. E. D. COR . 1. If as AB to KL , so KL to m , and as KL to m , so is m ton , then AB is ton as the solid AG to the solid KQ . For the ratio of AB to n is triplicate of the ratio of AB to KL ( def . 12. 5 ...### 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