## The Elements of Euclid |

### From inside the book

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**angle**BAC**equal**to the**angle**EDF , the base BC shall be**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 ... Page 18

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**angle**FBC is**equal**to the**angle**GCB , and the**angle**BCF to the**angle**CBG : and , since it has been demonstrated , that the whole**angle**ABG is**equal**to the whole ACF , the parts of which , the**angles**CBG , BCF are also**equal**; the remaining ... Page 19

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**equal**to one another , and likewise their sides CB , DB , that are terminated in B. Join CD ; then , in the case in which the vertex of each of the tri-**angles**is without the other triangle , because AC is**equal**to AD , the**angle**ACD is ... Page 21

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

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

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**angles**DCF , ECF , d 10. Def . is a right**angle**. Wherefore , from the given point C , in the given straight line AB , FC has been drawn at right**angles**to AB . Which was to be done . 1 ...**angle**CBE is**equal**to the**angle**22 THE ELEMENTS.### Other editions - View all

The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ... Robert Simson,Robert Euclid No preview available - 2016 |

The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ... Robert Simson,Euclid No preview available - 2015 |

### 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 AE rectangle CB rectangle contained rectilineal figure remaining angle right angles segment sides BA similar solid angle solid parallelopiped square of AC straight line AB straight line BC tangent THEOR third triangle ABC triplicate ratio vertex wherefore