## The Elements of Euclid |

### From inside the book

Results 1-5 of 100

Page 17

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

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 18

b Book I. equal to AC , and let the straight lines AB , AC be produced to SD and E , the

b Book I. equal to AC , and let the straight lines AB , AC be produced to SD and E , the

**angle ABC**shall be equal to the angle ACB , and the angle CBD to the angle BCE . In BD take any point F , and from AE the greater , cut off a 3. Page 19

Let ABC be a triangle having the

Let ABC be a triangle having the

**angle ABC**equal to the Book L angle ACB ; the side AB is also equal to the side Ac . For if AB be not equal to AC , one of them is greater than the other : let AB be the greater , and from it cut off DB ... Page 20

a Book L But if one of the vertices , as D , be within the other triangle . ... For , if the tri .

a Book L But if one of the vertices , as D , be within the other triangle . ... 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 ... Page 24

For , if the angle CBA be equal to ABD , each of them is a А E D B C D B C . def . ... Again , because the angle DBA is equal to the two angles DBE , EBA , add to these ' equals the

For , if the angle CBA be equal to ABD , each of them is a А E D B C D B C . def . ... Again , because the angle DBA is equal to the two angles DBE , EBA , add to these ' equals the

**angle ABC**; there fore the angles DBA , ABC are equal ...### What people are saying - Write a review

We haven't found any reviews in the usual places.

### 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