## The Elements of Euclid |

### From inside the book

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Page 17

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**equal**to the base EF ; and the triangle ABC to the triangle DEF ; and the other**angles**, to which the**equal**sides are opposite , shall be**equal**each to each , viz . the**angle**ABC to the B**angle**DEF , and the**angle**ACB to DFE . CE ט F ... Page 18

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**angles**of the one ad Jare**equal**to the remaining an gles of the other , each to each , to which the**equal**sides are op- sposite ; wiz . the**angle**ACF to the**angles**ABG , and the**angle**AFC to the ...**angle**ABC**equal**18 THE ELEMENTS. Page 19

Euclid Robert Simson. Let ABC be a triangle having the

Euclid Robert Simson. Let ABC be a triangle having the

**angle**ABC**equal**to the Вовк L.**angle**ACB ; the side AB is also ...**angles**, & c , Q. E. D. Cor . Hence every equiangular triangle is also equilateral . is not PROP . VII . THEOR ... Page 21

... angle BAC coincides with the angle EDF , and is equal to it . Therefore if twob 8. Ax . triangles , & c . Q. E. D. PROP . IX . PROB . TO bisect a given rectilineal angle , that is , to di- vide it into two

... angle BAC coincides with the angle EDF , and is equal to it . Therefore if twob 8. Ax . triangles , & c . Q. E. D. PROP . IX . PROB . TO bisect a given rectilineal angle , that is , to di- vide it into two

**equal angles**. Let BAC be the ... Page 22

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**angles**to a given straight line , from a given point in the same . Let AB be a given straight line , and C a point given in it : See Note . it is required to draw a straight ...**angle**CBE is**equal**to the**angle**22 THE ELEMENTS A ...### Common terms and phrases

altitude angle ABC angle BAC base BC BC is equal BC is given bisected Book XI centre circle ABCD circumference cone cylinder demonstrated described diameter draw drawn equal angles equiangular equimultiples Euclid 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 pyramid Q. E. D. PROP radius ratio of BC rectangle CB rectangle contained rectilineal figure right angles segment sides BA similar solid angle solid parallelopiped square of AC straight line AB straight line BC tangent THEOR third tiples triangle ABC triplicate ratio vertex wherefore