## The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh and Twelfth. The Errors, by which Theon, Or Others, Have Long Ago Vitiated These Books, are Corrected, and Some of Euclid's Demonstrations are Restored. Also, the Book of Euclid's Data, in Like Manner Corrected |

### From inside the book

Results 1-5 of 62

Page 11

...

...

**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 20

...

...

**segment**. If it be possible , let the two straight lines ABC , ABD have the**segment**AB common to both of them . From the point B draw BE at right angles to AB ; and because ABC is a straight * See Note . line , the angle CBE is equal ... Page 21

...

...

**segment**. PROP . XII . PROB . E D B C C To draw a straight line perpendicular to a given straight line of an unlimited length , from a given point without it . Let AB be the given straight line , which may be produced to any length both ... Page 65

... a circle , when the per- pendiculars drawn to them from the cen- tre are equal . V. And the straight line on which the greater perpendicular falls , is said to be farther from the centre . VI . A

... a circle , when the per- pendiculars drawn to them from the cen- tre are equal . V. And the straight line on which the greater perpendicular falls , is said to be farther from the centre . VI . A

**segment**of a circle is the figure I. Page 66

...

...

**segment**of a circle is the figure con- tained by a straight line and the circum- ference 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**...### Other editions - View all

The Elements of Euclid: Viz, the First Six Books, Together with the Eleventh ... Robert Simson,Euclid Euclid No preview available - 2018 |

### Common terms and phrases

altitude angle ABC angle BAC base BC BC is equal BC is given bisected centre circle ABCD circumference cone cylinder demonstrated described diameter draw drawn equal angles equiangular equimultiples Euclid ex æquali excess fore given angle given in magnitude given in position given in species given magnitude given ratio given straight line gnomon greater join less Let ABC meet multiple parallel parallelogram parallelogram AC perpendicular point F polygon prism proportionals proposition Q. E. D. PROP radius ratio of AE rectangle CB rectangle contained rectilineal figure remaining angle right angles segment sides BA similar sine solid angle solid parallelopipeds square of AC straight line AB straight line BC tangent THEOR third triangle ABC triplicate ratio vertex wherefore