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

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Page 3

A

A

**diameter**of a circle is a straight line drawn through See N. 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 the ... Page 29

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 are ... Page 30

Also , their

Also , their

**diameter**bisects them : for AB being equal to CD , and BC common , the two AB , BC are equal to the two DC , CB , each to each ; and the angle ABC has been proved equal to the angle BCD ; therefore the triangle ABC is equal ... Page 32

... and between the same parallels BC , EF ; and the triangle ABC is the half of the parallelogram EBCA , because the

... and between the same parallels BC , EF ; and the triangle ABC is the half of the parallelogram EBCA , because the

**diameter**AB bisects * it ; and the triangle DBC is the half of the parallelogram DBCF , because the**diameter**DC * Ax ... Page 34

ABC , because the

ABC , because the

**diameter**AC divides it into two equal * parts ; wherefore ABCD is also double of the triangle EBC . Therefore , if a parallelogram , & c . B * 34. 1 . Q. E. D. PROP . XLII . PROB . # 10. 1 . # 23. 1 . * 31.1 . + Def .### 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