## 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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**shewn**that BC is equal to BG ; wherefore AL and BC are each of them equal to BG ; and things that are equal to the same are equal to one another ; therefore the straight line AL is equal to BC . Wherefore , from the given point A , a ... Page 33

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**shewn**that it is not equal to AB ; therefore AC is greater than AB . Wherefore the greater angle , & c . Q. E. D. PROP . XX . THEOR . Any two sides of a triangle are together greater than the third side . Let ABC be a triangle ; any two ... Page 34

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**shewn**that BA , AC are greater that BE , EC ; much more then are BA , AC B greater than BD , DC . C Again , because the exterior angle of a triangle ( 16. 1. ) is greater than the interior and opposite angle , the exterior angle BDC of ... Page 37

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**shewn**that it is B not equal to it : therefore E C F the angle BAC is greater than the angle EDF . Wherefore , if two triangles , & c . Q. E. D. PROP . XXVI . THEOR . If two triangles have two angles of the one equal to two angles of ... Page 41

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**shewn**that the angle AGK is equal to the angle GHF ; therefore also AGK is equal to GKD ; and they are alternate angles ; therefore AB is parallel ( 27.1 . ) to CD . Where- fore straight lines , & c . Q. E. D. A G B E H -I K C D PROP ...### 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