## 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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**third**sides , equal ; and the two triangles shall be equal ; and their other angles shall be equal , each to each , viz . those to which the equal sides are opposite . Let ABC , DEF be two triangles which have the two sides AB , AC ... Page 26

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**third**side . * Let ABC be a triangle ; any two sides of it together are greater than the**third**side , viz . the sides BA , AC greater than the side BC ; and AB , BC greater than AC ; and BC , CA greater than AB . Produce BA to the point ... Page 27

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**third**( 20. 1 . ) * Let A , B , C be the three given straight lines , of which any two whatever are greater than the**third**, viz . A and B greater than C ; A and C greater than B ; and B and C than A. It is required to make a triangle ... Page 30

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**third**angle of the other . Let ABC , DEF be two triangles which have the angles ABC , BCA equal to the angles DEF ...**third**angle B C E F BAC to the**third**angle EDF . For , if AB be not equal to DE , one of them must be the greater . Let ... Page 31

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**third**angle BAC to the**third**an- gle EDF . B D HCE F Next , let the sides which are opposite to A equal angles in each tri- angle be equal to one an- other , viz . AB to DE ; likewise in this case , the other sides shall be equal , AC ...### 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