## The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh and Twelfth. The Errors, by which Theon, Or Others, Have Long Ago Vitiated These Books, are Corrected, and Some of Euclid's Demonstrations are Restored. Also, the Book of Euclid's Data, in Like Manner Corrected |

### From inside the book

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**polygons**, by more than four straight lines . XXIV . Of three sided figures , an equilateral triangle is that which has three equal sides . XXV . An isosceles triangle , is that which has only two sides equal . B XXVI . A scalene ... Page 174

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**polygons**have ; and the**polygon**ABCDE has to the**polygon**FGHKL the duplicate ratio of that which the side AB has to the side FG . Join BE , EC , GL , LH : and because the**polygon**ABCDE is similar to the**polygon**FGHKL , the angle BAE is ... Page 175

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**polygons**have to one another , the antecedents being ABE , EBC , ECD , and the consequents FGL , LGH , LHK : and the**polygon**ABCDE has to the**polygon**FGHKL the duplicate ratio of that which the side AB has to the homologous side FG ... Page 176

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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 212

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**polygon**BCDEF : therefore all the angles at the ba- ses of the triangles are together greater than all the angles of the**polygon**; and because all the angles of the triangles are together equal to twice as many right angles as there are ...### Other editions - View all

The Elements of Euclid: Viz, the First Six Books, Together with the Eleventh ... Robert Simson,Euclid Euclid No preview available - 2018 |

### Common terms and phrases

altitude angle ABC angle BAC base BC BC is equal BC is given bisected centre circle ABCD circumference cone cylinder demonstrated described diameter draw drawn equal angles equiangular equimultiples Euclid ex æquali excess fore given angle given in magnitude given in position given in species given magnitude given ratio given straight line gnomon greater join less Let ABC meet multiple parallel parallelogram parallelogram AC perpendicular point F polygon prism proportionals proposition Q. E. D. PROP radius ratio of AE rectangle CB rectangle contained rectilineal figure remaining angle right angles segment sides BA similar sine solid angle solid parallelopipeds square of AC straight line AB straight line BC tangent THEOR third triangle ABC triplicate ratio vertex wherefore