## The Elements of Euclid |

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Page 18

AG equal to AF , the less , and

AG equal to AF , the less , and

**join**FC , GB . 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 ; as be 4 ... Page 19

1 . equal to AC , the less , and

1 . equal to AC , the less , and

**join**DC ; thereА fore , because in the triangles DBC , ACB , DB is equal to AC , and BC common to D both , the two sides DB , BC are equal to the two AC , CB , each to each ; and the angle DBC is equal ... Page 21

AD ;

AD ;

**join**DE and upon it describe b А b1.1 . an equilateral triangle DEF ; then**join**AF ; the straight line AF bisects the angle BAC . Because AD is equal to AE , and D E AF is common to the two triangles DAF , EAF ; the two sides DA ... Page 22

F upon DE describe b the equib 1.1 , lateral triangle DFE , and

F upon DE describe b the equib 1.1 , lateral triangle DFE , and

**join**FC ; the straight line FC drawn from the given point C is at right angles to the given straight line AB . Steven Because DC is equal to CE ... Page 26

A Bisect • AC in E ,

A Bisect • AC in E ,

**join**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 , B each to each ; and the angle C AEB is equal b ...### What people are saying - Write a review

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### Other editions - View all

The Elements of Euclid: The Errors, by Which Theon, Or Others, Have Long Ago ... Robert Simson,Robert Euclid No preview available - 2015 |

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

### Common terms and phrases

added altitude angle ABC angle BAC base Book centre circle circle ABCD circumference common cone cylinder definition demonstrated described diameter divided double draw drawn equal equal angles equiangular equimultiples excess fore four fourth given angle given in position given in species given magnitude given ratio given straight line greater Greek half join less likewise magnitude manner meet multiple Note opposite parallel parallelogram pass perpendicular plane prisms produced PROP proportionals proposition pyramid radius reason rectangle rectangle contained remaining right angles segment shown sides similar sine solid solid angle sphere square square of AC taken THEOR third triangle ABC wherefore whole