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

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Page 3

A circle is a plane figure contained by one line , which is called the

A circle is a plane figure contained by one line , which is called the

**circumference**, and is such that all straight lines drawn from a certain point within the figure to the**circumference**, are equal to one another . XVI . Page 54

1 I. EQUAL circles are those of which the diameters are equal , or from the centres of which the straight lines to the

1 I. EQUAL circles are those of which the diameters are equal , or from the centres of which the straight lines to the

**circumferences**are equal . “ This is not a definition , but a theorem , the truth of which is evident ; for , if the ... Page 55

A segment of a circle is the figure contained by a straight line and the

A segment of a circle is the figure contained by a straight line and the

**circumference**it cuts off . VII . “ The angle of a segment is that which is contained by the straight line and the**circumference**. " VIII . Page 56

If any two points be taken in the

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 in the**circumference**; the straight line drawn from A to B ... 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 circle ABC ; and join DA , DB ; in 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 ...### 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