## The Elements of Euclid |

### From inside the book

Results 1-5 of 75

Page 11

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 : ور XVI . Page 67

III from the centres of which the straight lines to the

III from the centres of which the straight lines to the

**circumferences**are equal . ' not a definition but a theorem , the truth of which is evident ' ; for , if the circles be applied to one another , so that “ their centres coincide ... 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

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 . C > Let ABC be a circle , and A , B any two points in the**circumference**; the straight line drawn from A to ... Page 70

In the same manner it may be demonstrated that it does not fall upon the

In the same manner it may be demonstrated that it does not fall upon the

**circumference**; it falls therefore within it . Wherefore , if any two points , & c . Q. E. D. 33 PROP . III . THEOR . IF a straight line drawn through the centre ...### What people are saying - Write a review

We haven't found any reviews in the usual places.

### 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