## 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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**polygons**, by more than four straight lines ΧΙΧ . Of three sided figures , an equilateral triangle is that which has three equal sides . XX . An isosceles triangle is that which has only two sides equal . ΔΑΔ ΧΧΙ . A scalene triangle ... Page 141

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**polygons**have ; and the**polygon**ABCDE has to the**polygon**FGHKL a ratio duplicate of that which the side AB has to the side FG . Join BE , EC , GL , LH : and because the**polygon**ABCDE is simi- lar to the**polygon**FGHKL , the angle BAE is ... Page 142

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**polygon**ABCDE to the**polygon**FGHKL : but the triangle ABE has to the triangle FGL , the duplicate ratio of that which the side AB has to the homologous side FG . Therefore also the**polygon**ABCDE has to the**polygon**FGHKL the duplicate ... Page 161

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**polygon**inscribed in a circle , is less than the circumference of the circle . COR . 2. If from a point two straight lines be drawn touching a cir- cle , these two lines are together greater than the arch intercepted be- tween them ... Page 162

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**polygons**, of the same number of sides , inscribed in circles , are similar , and are to one another as the squares of the diameters of the circles . Let ABCDEF and GHIKLM be two equilateral**polygons**of the same number of sides ...### 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