## 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

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**straight lines**that contain the angle meet one another , is put ' between the other two letters , and one of these two is some- ' where upon one of those**straight lines**, and the other upon ' the other line ...**AB**, CB is named the angle ABC ... Page 13

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**straight line**. Let**AB**be the given**straight line**; it is required to describe an equilateral triangle upon it . From the centre A , at the distance**AB**, describe ( 3. Postulate . ) the cir- cle BCD , and from the centre B , at the ... Page 15

... angle DEF , and the angle ACB to DFE . B CE D F For , if the triangle ABC be applied to DEF , so that the point A may be on D , and the

... angle DEF , and the angle ACB to DFE . B CE D F For , if the triangle ABC be applied to DEF , so that the point A may be on D , and the

**straight line AB**upon DE ; the point B shall coincide with the point E , because AB is equal to DE ; and ... Page 20

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**straight line AB**is divided into two equal parts in the point D. Which was to be done . C A D B PROP . XI . PROB . To draw a straight line at right angles to a given straight line , from a given point in the same . Let AB be a given ... Page 21

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**straight lines**can- A not have a common**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**...### 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