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

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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 67

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

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 68

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 69

In FIG D I N. B. - Whenever the expression “ straight lines from the centre , " or drawn “ from the centre , " occurs , it is to bo understood that they are drawn to the

In FIG D I N. B. - Whenever the expression “ straight lines from the centre , " or drawn “ from the centre , " occurs , it is to bo understood that they are drawn to the

**circumference**. the same manner it can be shown that no other BOOK ... Page 70

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 ...### 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 equimultiples 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 Q. E. D. PROP ratio reason 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