## 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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Page 31

... angles . Cor . 2. And hence , all the angles made by any number of straight lines meeting in one point , are together equal to four right angles . PROP . XVI . THEOR . If one side of a triangle be produced , the

... angles . Cor . 2. And hence , all the angles made by any number of straight lines meeting in one point , are together equal to four right angles . PROP . XVI . THEOR . If one side of a triangle be produced , the

**exterior angle**is ... Page 32

... angles together are less than two right angles . Produce BC to D ; and be- cause ACD is the

... angles together are less than two right angles . Produce BC to D ; and be- cause ACD is the

**exterior angle**of the triangle ABC , ACD is greater ( 16. 1. ) then the interior and opposite angle ABC ; to each of these add the angle ACB ... Page 34

... angle . Let the two straight lines BD , CD be drawn from B , C , the ends of the side BC of the triangle ABC , to ...

... angle . Let the two straight lines BD , CD be drawn from B , C , the ends of the side BC of the triangle ABC , to ...

**exterior angle**of a triangle ( 16. 1. ) is greater than the interior and opposite angle , the**exterior angle**BDC ... Page 38

... angle GCB is equal to the angle DFE but DFE is , by the hypothesis , equal to the angle BCA ; wherefore also the angle BCG is equal to the angle BCA , the less to the greater ...

... angle GCB is equal to the angle DFE but DFE is , by the hypothesis , equal to the angle BCA ; wherefore also the angle BCG is equal to the angle BCA , the less to the greater ...

**exterior angle**AEF is greater ( 16. 1. ) 38 ELEMENTS. Page 39

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**exterior angle**AEF is greater ( 16. 1. ) than the interior and oppo site angle EFG ; but it is also equal to it , which is impossible therefore , AB and CD being produced , do not meet towards B , D. In like manner it may be ...### 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