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

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Page 69

Similar segments of

Similar segments of

**circles**are those in which the angles are equal , or which contain equal angles . PROP . I. PROB . # * 10.1 . * 11.1 . To find the centre of a given**circle**. Let**ABC**be the given**circle**; it is required to find its ... Page 70

If any two points be taken in the circumference of a

If any two points be taken in the circumference of a

**circle**, the straight line which joins them shall fall within the**circle**. Let**ABC**be a**circle**, and A , B any two points B in the circumference ; the straight line drawn from A to B ... Page 72

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 euch other . Let**ABCD**be a**circle**, and AC , BD two straight lines in it which cut one another in the point E , and do ... Page 73

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 † to EF ... Page 74

impossible : therefore F is not the centre of the

impossible : therefore F is not the centre of the

**circles ABC**, CDE . ... 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 ...### 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

altitude angle ABC angle BAC base base BC BC is equal centre circle ABCD circumference common cone Const contained cylinder demonstrated described diameter divided double draw drawn equal angles equiangular equilateral equimultiples extremities fall figure fore four fourth given given straight line greater half inscribed join less Let ABC likewise magnitudes manner meet multiple opposite parallel parallelogram pass perpendicular plane polygon prism PROB produced PROP proportionals proved pyramid ratio reason rectangle contained rectilineal figure remaining angle right angles segment shown sides similar solid solid angle solid parallelopiped sphere square taken THEOR third touches triangle ABC vertex wherefore whole