## 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 |

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... angle , nor that the equal sides are opposite to

... angle , nor that the equal sides are opposite to

**equal angles**, nor , lastly , that things equal to the same thing are equal to one another ? By a scientific mind this information will not be thought lightly of ; and it is exactly that ... Page 23

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**equal**to the remainder ( 3. Ax . ) BG : But it has been shewn that BC is**equal**to BG ; wherefore AL and BC are each ...**angles**contained by those sides**equal**to one another , their bases , or third sides , shall be**equal**; and the ... Page 24

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**equal**, each to each , viz . the**angle**ABC to the**angle**DEF , and the**angle**ACB to DFE . For , if the triangle ABC ...**angles**of the one shall coincide with the remaining**angles**of the other , and be**equal**to them , viz . the**angle**... Page 25

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**equal**to the two CG , GB , each to each ; but the**angle**BFC is**equal**to the**angle**CGB ; wherefore the triangles BFC , CGB are**equal**( 3. 1. ) , and their remaining**angles**are**equal**, to which the**equal**sides are opposite ; therefore ... Page 26

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**equal**to one another . Join CD , and if possible let CB be**equal**to DB ; then , in the case in which the vertex of ...**angles**ECD , FDC upon the other side of the base CD are**equal**( 5. 1. ) to one ano- ther but the**angle**ECD is ...### 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