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

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Page 35

Let ABCD be a parallelogram , of which the diameter is AC ; and EH , GF parallelograms about AC , that is , through which AC

Let ABCD be a parallelogram , of which the diameter is AC ; and EH , GF parallelograms about AC , that is , through which AC

**passes**; and BK , KD the other parallelograms which make up thewhole figure ABCD , which are therefore called ... Page 57

If a straight line drawn through the centre of a circle bisect a straight line in it which does not

If a straight line drawn through the centre of a circle bisect a straight line in it which does not

**pass**through the centre , it shall cut it at right angles : and if it cut it at right angles , it shall bisect it . Page 58

If in a circle two straight lines cut one another , which do not both

If in a circle two straight lines cut one another , which do not both

**pass**through the centre , they do not bisect each other . Let ABCD be a circle , and AC , BD two straight lines in it which cut one another in the ... Page 59

... to the line which

... to the line which

**passes**through the centre is always greater than one more remote : and from the same point there can be drawn only two straight lines that are equal to one another , one upon each side of the shortest line , 20.1 . Page 60

... FK is equal + to FH ; that is , a line nearer to that which

... FK is equal + to FH ; that is , a line nearer to that which

**passes**through the centre , is equal to one which is more remote ; which has been proved to be impossible . Therefore , if any point be taken , & c . Q. E. D. GF ,体 23.### 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