## The Elements of Euclid |

### From inside the book

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Page 17

AB to DE , and AC to DF ; A D Book I. and the

AB to DE , and AC to DF ; A D Book I. and the

**angle BAC**equal to the angle ÉDF , 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 ... Page 20

The

The

**angle BAC**is en qual to the angle EDF . For , if the tri . angle ABC be applied 10 DEF , so B CE F that the point B be on E , and the straight line BC upon EF ; the point C shall also coincide with the point F. Because BC is equal ... Page 21

Therefore if two b 8. Ax . triangles , & c . Q. E. D. PROP . IX . PROB . sect it . TO bisect a given rectilineal

Therefore if two b 8. Ax . triangles , & c . Q. E. D. PROP . IX . PROB . sect it . TO bisect a given rectilineal

**angle**, that is , to divide it into two equal**angles**. Let**BAC**be the given rectilineal**angle**, it is required to bi . Page 26

IF one side of a triangle be produced , the exterior

IF one side of a triangle be produced , the exterior

**angle**is greater than either of the interior opposite**angles**. a 10 ... BC be produced to D , the exterior**angle**ACD is greater than either of the interior opposite**angles**CBA ,**BAC**. Page 27

1 these add the

1 these add the

**angle**ACB ; therefore the**angles**ACD , ACB Book I. are greater than the**angles**ABC , ACB ; but ACD ... In like manner , it may be demonstrated , that**BAC**, ACB , as also CAB , ABC , are less than two right**angles**...### 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