## 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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**Q. E. D.**B C**Cor**. Hence every equiangular triangle is also equilateral . PROP . VII . THEOR . Upon the same base , and on the same side of it , there cannot be two tri- angles , that have their sides which are terminated in one ... Page 31

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**Q. E. D. COR**. 1. From this it is manifest , that if two straight lines cut one another , the angles which they make at the point of their intersec- tion , are together equal to four right angles . Cor . 2. And hence , all the angles ... Page 42

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**Q. E. D. Cor**. 1. All the interior angles of any rectilineal figure are equal to twice as many right angles as the figure has sides , wanting four right angles . For any rectilineal figure ABCDE can be divided into as many tri- angles ... Page 55

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**Q. E. D.**PROP . IV . THEOR . B D E If a straight line be divided into any two parts , the square of the whole line ... (**Cor**. 46. 1. ) . Wherefore CGKB is a square , and it is upon the side CB . For the same reason HF also is a ... Page 56

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**Q. E. D. COR**. From the demonstration , it is manifest that the parallelograms about the diameter of a square are ... ( Cor . 4. 2. ) ; therefore gnomon CMG = AD.DB. To each add LG = CD2 , then gnomon CMG + LG = AD.DB + CD2 , But CMG ...### 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