## The Elements of Euclid |

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Page 39

THE opposite sides and angles of

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 diameter BC divides 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 . ?**PARALLELOGRAMS**upon the ... Page 41

**PARALLELOGRAMS**upon equal bases , and between the same parallels , are equal to one another . с Let ABCD , EFGH be A D E H**parallelograms**upon equal bases BC , FG , and between the same parallels AH , BG ; the**parallelogram**ABCD is ... Page 42

Book 1. gram EBCA , because the diameter AB bisects e it ; and the triangle DBC is the half of 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 ... Page 43

IF a

IF a

**parallelogram**and triangle be uport the same base , and between the same parallels ; the parallel - gram shall be double of the triangle . Book I. Let the**parallelogram**ABCD and the triangle EBC OF EUCLID .### 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