## 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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**join**FC , GB . Α Because AF is equal to AG , and AB to AC , the two sides FA , AC are equal to the two GA , AB , each to each ; and they contain the angle FAG common to the two triangles AFC , AGB ; therefore the base FC is equal ( 4. 1 ... Page 17

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**join**DC ; therefore , because in the triangles DBC , ACB , DB is equal to AC , and BC common to both , the two sides DB , BC are equal to the two AC , CB , each to each ; and the angle DBC is equal to the angle ACB ; therefore the base ... Page 19

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**join**DE , and upon it describe ( 1. 1. ) an equilateral triangle DEF ; then**join**AF ; the straight line AF bisects the angle BAC . Because AD is equal to AE , and AF is common to the two triangles DAF , EAF ; the two sides DA , AF , are ... Page 24

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**join**Bisect ( 10. 1. ) AC in BE and produce it to F , and make EF equal to BE ;**join**also FC , and produce AC to G. Because AE is equal to EC , and BE to EF ; AE , EB are equal to CE , EF , each to each ; and the angle AEB is equal ( 15 ... Page 28

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**join**DE . and make ( 22. 1. ) the trian- gle AFG , the sides of which D shall be equal to the three straight lines CD , DE , CE , so that CD be equal to AF ; E F G B CE to AG ; and DE to FG ; and because DC , CE are equal to FA , AG ...### 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