## 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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Page 64

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**ABCD**be a parallelogram , of which the diameters are AC and BD ; the sum of the squares of AC and BD is equal to the sum of the squares of AB , BC , CD , DA . Let AC and BD intersect one another in E : and because the ver- tical angles ... Page 69

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**ABCD**be a circle , and AC , BD two straight lines in it , which cut one another in the point E , and do not both pass through the cen- tre : AC , BD do not bisect one another . For if it is possible , let AE be equal to EC , and BE to ... Page 70

... one upon each side of the shortest line . Let

... one upon each side of the shortest line . Let

**ABCD**be a circle , and AD its diameter , in which let any point F be taken which is not the centre : let the centre be E ; of all the straight lines FB , FC , FG , & c 70 ELEMENTS. Page 76

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**ABCD**be a circle , of which the di- ameter is AD , and the centre E ; and let BC be nearer to the centre than FG ; AD is greater than any straight line BC which is not a diameter , and BC greater than FG . From the centre draw EH , EK ... Page 80

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**ABCD**be a circle , and BAD , BED angles in the same segment BAED : The angles BAD , BED are equal to one another . Take F the centre of the circle**ABCD**: And . first , let the segment BAED be great- er than a semicircle , and join BF ...### 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