## 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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**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 R angle ABC ... Page 18

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**angle**ECD is greater than the**angle**BCD ; wherefore the**angle**FDC is likewise greater than BCD ; much more then is ...**BAC**is equal to the**angle**EDF . For , if the triangle ABC be applied to DEF , so that the point B be on E , and the ... Page 19

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**angle BAC**coincides with the angle EDF , and is equal ( 8. Ax . ) to it . Therefore , if two triangles , & c . Q. E. D. PROP . IX . PROB . To bisect a given rectilineal angle , that is , to divide it into two equal angles . it . Let BAC ... Page 24

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**angles**. Let ABC be a triangle , and let its side BC be produced to D , the exterior**angle**ACD is greater than either of the interior op- posite**angles**CBA ,**BAC**. join Bisect ( 10. 1. ) AC in BE and produce it to F , and make EF equal ... Page 25

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**BAC**, ACB , as also CAB , ABC , are less than two right**angles**. Therefore any two**angles**, & c . Q. E. D .. 1 PROP . XVIII . THEOR . THE greater side of every triangle is opposite to the greater**angle**...**angle**ABC , is also greater than the ...### 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