## The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh and Twelfth |

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Page 29

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 are ... Page 30

**Parallelograms**upon the same base , and between the same parallels , are equal to one another . Let the**parallelograms**ABCD , EBCF be upon the same base BC , and between the same parallels AF , BC : the**parallelogram**ABCD shall be equal ... Page 31

1 . nated in the same point ; then , because ABCD is a

1 . nated in the same point ; then , because ABCD is a

**parallelogram**, AD is equal * to BC ; for the same reason EF is equal to BC ; wherefore AD is equal * to * 1 Ax . EF ; and DE is common ; therefore the whole , or the remainder ... Page 32

Producet AD both ways to the points E , F , and through B draw * BE parallel to CA ; and through C draw CF parallel to BD : therefore each of the figures EBCA , DBCF is at

Producet AD both ways to the points E , F , and through B draw * BE parallel to CA ; and through C draw CF parallel to BD : therefore each of the figures EBCA , DBCF is at

**parallelogram**: and EBCA is equal * to DBCF , because they are ... Page 33

If a

If a

**parallelogram**and a triangle be upon the same base , and between the same parallels ; the**parallelogram**shall be double of the triangle . * 37.1 . Let the**parallelogram**ABCD and the triangle BOOK I. PROP . XL , XLI . 39.### What people are saying - Write a review

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The Elements of Euclid: Viz. The First Six Books, Together With the Eleventh ... Euclid Euclid No preview available - 2018 |

### Common terms and phrases

added altitude angle ABC angle BAC base Book centre circle circle ABCD circumference common cone contained cylinder definition demonstrated described diameter difference divided double draw drawn equal equal angles equiangular equimultiples Euclid excess figure fore four fourth given angle given in position given in species given magnitude given ratio given straight line greater Greek half join less likewise logarithm magnitude manner meet multiple opposite parallel parallelogram pass perpendicular plane prism produced PROP proportionals proposition proved pyramid radius reason rectangle rectilineal figure remaining right angles segment shewn sides similar sine solid sphere square square of AC taken THEOR third triangle ABC wherefore whole