## The Elements of Euclid |

### From inside the book

Results 1-5 of 63

Page 11

A

A

**segment**of a circle is the figure contained by a straight « line , and the circumference it cuts off . ” XX . Rectilineal figures are those which are contained by straight lines . XXI . Trilateral figures , or triangles , by three ... Page 22

By help of this problem , it may be demonstrated , that two straight lines cannot have a common

By help of this problem , it may be demonstrated , that two straight lines cannot have a common

**segment**. If it be possible , let the two straight lines ABC , ABD have the**segment**AB common to both of them . From the poirt B draw BE at ... Page 23

... the angle DBE is equal to the angle EBA ; where . fore the angle DBE is equal to the angle CBE , the less to the greater ; which is impossible ; therefore twostraight lines canA not have a common

... the angle DBE is equal to the angle EBA ; where . fore the angle DBE is equal to the angle CBE , the less to the greater ; which is impossible ; therefore twostraight lines canA not have a common

**segment**. PROP . XII . PROB . Page 67

... when the perpendiculars drawn to them from the centre are equal . V. And the straight line on which the greater perpendicular falls , is said to be farther from the centre . C Book III . VI . A

... when the perpendiculars drawn to them from the centre are equal . V. And the straight line on which the greater perpendicular falls , is said to be farther from the centre . C Book III . VI . A

**segment**of a circle 1 ... Page 68

A

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 . An angle in a**segment**...### 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