## The Elements of Euclid |

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Page 11

And this point is called the

And this point is called the

**centre**of the circle . XVII . A diameter of circle is a straight line drawn through the**centre**, and terminated both ways by the circumference . XVIII . A semicircle is the figure contained by a diameter and ... Page 13

And that a circle may be described from any

And that a circle may be described from any

**centre**, at any dig . tance from that**centre**. AXIOMS . 1 . THINGS which are equal to the same are equal to one another . II . If equals be added to equals , the wholes are equal . III . Page 15

Let AB be the given straight line ; it is required to describe an equilateral triangle upon it . с From the

Let AB be the given straight line ; it is required to describe an equilateral triangle upon it . с From the

**centre**A , at the distance AB , describe a the circle & 3. PostuBCD , and from the**centre**B , at late . the distance BA ... Page 16

22 th Book I. Because the point B is the

22 th Book I. Because the point B is the

**centre**of the circle CGH , BC is equal e to BG ; and because D is the**centre**of the circle GKL , e 15. Def . DL is equal to DG , and DA , DB , parts of them , are equal ; f 3. Page 23

It is required to draw a straight line с perpendicular to AB from the point C. Take any point D upon the other side of AB , and from the

It is required to draw a straight line с perpendicular to AB from the point C. Take any point D upon the other side of AB , and from the

**centre**C , at the distance H CD , describe b the circle FDG AF b 3. Post .### 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