## 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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**ABCD**and the triangle EBC be upon the same base BC and between the same pa- rallels BC , AE ; the parallelogram**ABCD**A is double of the triangle EBC . D E Join AC ; then the triangle ABC is equal ( 37. 1. ) to the triangle EBC , because ... Page 47

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**ABCD**and the triangle EBC be upon the same base BC and between the same pa- rallels BC , AE ; the parallelogram**ABCD**A is double of the triangle EBC . DE Join AC ; then the triangle ABC is equal ( 37. 1. ) to the triangle EBC , because ... Page 48

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**ABCD**be a parallelogram of which the diameter is AC ; let EH , FG be the parallelograms about AC , that is , through which AC passes , and let BK , KD be the other parallelograms , which make up the AH D whole figure**ABCD**and are there ... Page 49

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**ABCD**be the given rectilineal figure , and E the given rectili- neal angle . It is required to describe a parallelogram equal to**ABCD**, and having an angle equal to E. G i Join DB , and describe ( 42.1 . ) OF GEOMETRY . BOOK . I. 49. Page 50

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**ABCD**is equal to the whole parallelogram KFLM ; therefore the pa- rallelogram KFLM has been described equal to the given rectilineal figure**ABCD**, having the angle FKM equal to the given angle E. Which was to be done . COR . From this ...### 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