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

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Page 56

Draw within it any straight line AB , and bisect * it in D ; from the point D draw * DC at right angles to AB , and produce it to E , and bisect CE in F : the point F shall be the centre of the

Draw within it any straight line AB , and bisect * it in D ; from the point D draw * DC at right angles to AB , and produce it to E , and bisect CE in F : the point F shall be the centre of the

**circle ABC**. Page 57

D D A E B E For if it do not , let it fall , if possible , without , as AEB : find * D the centre of the

D D A E B E For if it do not , let it fall , if possible , without , as AEB : find * D the centre of the

**circle ABC**; and join DA , DB ; in the circumference AB take any point F , join DF , and produce it to E : then because DA A is ... Page 58

If in a

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

Let the two

Let the two

**circles ABC**, CDG cut one another in the points B , C ; they shall not have the same centre . ... and draw any straight line EFG meeting them in F and G : and because E is the centre of the**circle ABC**, EC is equal t to EF ... Page 60

Let

Let

**ABCD**be a**circle**, and AD its diameter , in which let any point F be taken which is not the centre : let the centre be E : of all the straight lines FB , FC , 4 FG , & c . that can be drawn from F to the circumference , FA shall be ...### 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