## The Elements of Euclid |

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Page 68

See Notes TO find the centre of a given

See Notes TO find the centre of a given

**circle**. Let**ABC**be the given**circle**; it is required to find its centre . Draw within it any straight line AB , and bisect a it in D ; from the point D draw b DC at right angles to AB ... Page 69

C > Let ABC be a circle , and A , B any two points in the circumference ; the straight line drawn from A to B shall ... tre of the

C > Let ABC be a circle , and A , B any two points in the circumference ; the straight line drawn from A to B shall ... tre of the

**circle ABC**, and join AD , D DB , and produce DF , any straight line meeting the circumference AB , to E ... Page 71

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 . F Let**ABCD**be a**circle**, and AC , BD two straight lines in.it which cut one another in the point E , and do ... Page 72

Let the two

Let the two

**circles ABC**, CDE touch one another internally in the point C : they have not the same centre . ... and draw any straight line FEB meeting them in E and B ; C and because F is the centre of the**circle ABC**, CF is equal to FB ... Page 73

... 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 . . r Let

... 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 . . r Let

**ABCD**be a**circle**, and AD its diameter , in which let any point F be taken which is ...### 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