## The Elements of Euclid |

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Page 15

CA , CB to the points A , B ;

CA , CB to the points A , B ;

**ABC**shall be an equilateral**triangle**. a Because the point A is the centre of the circle BCD , AC is cqual e to AB ; and because the point B is the centre of the cir . c 15. Deficle ACE , BC is equal to BA ... Page 17

For , if the

For , if the

**triangle ABC**be applied to DEF , so that the poi A may be on D , and the straight line AB upon DE ; the point B shall coincide with the point . E , because AB is equal to DE ; and AB coinciding with DE , AC shall coincide ... Page 18

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

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 ... 1 . therefore the base FC is equal to the base GB , and the**triangle**AFC to the**triangle**AGB ; and the remaining ... Page 21

Describe upon it an equilateral

Describe upon it an equilateral

**triangle ABC**, and bisect 2 1.1 . the angle ACB by the straight line CD . AB is cut into two b 9.1 . equal parts in the point D. Book 1 . Bécause AC is equal to CB , OF EUCLID . 21. Page 26

IF one side of a

IF one side of a

**triangle**be produced , the exterior angle is greater than either of the interior opposite angles . a 10. 1 . Y D b 15. 1 . Let**ABC**be a**triangle**, and let its side BC be produced to D , the exterior angle ACD is greater ...### 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