## The Elements of Euclid |

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Page 11

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**diameter**of circle is a straight line drawn through the centre , and terminated both ways by the circumference . XVIII . A semicircle is the figure contained by a**diameter**and the part of the circumference cut off by that**diameter**. Page 39

THE opposite sides and angles of parallelograms are equal to one another , and the

THE opposite sides and angles of parallelograms are equal to one another , and the

**diameter**bisects them that is , divides them into two equal parts . N B. A parallelogram is a four sided figure , of which the opposite sides ure ... Page 40

equal to the angle BCD ; therefore the triangle ABC is equal c to the triangle BCD , and the

equal to the angle BCD ; therefore the triangle ABC is equal c to the triangle BCD , and the

**diameter**BC divides the parallelogram ACDB into two equal parts . Q. E. D. C 4 , 1 . PROP . XXXV . THEOR . See Note . Page 41

... and EBCA is equal 6 to DBCF , because b 35. 1 . they are upon the same base BC , and between the same parallels BC , EF ; and the triangle ABC is the half of the paralleloF Book 1. gram EBCA , because the

... and EBCA is equal 6 to DBCF , because b 35. 1 . they are upon the same base BC , and between the same parallels BC , EF ; and the triangle ABC is the half of the paralleloF Book 1. gram EBCA , because the

**diameter**AB bisects OF EUCLID . Page 42

Book 1. gram EBCA , because the

Book 1. gram EBCA , because the

**diameter**AB bisects e it ; and the triangle DBC is the half of the parallelogram DBCF , because C 34. 1 . the**diameter**DC bisects it : but the halves of equal things are d 7. Ax . equal d ; therefore the ...### 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