## 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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**Parallel**straight lines , are such as are in the same plane , and which being produced ever so far both ways , do not meet . POSTULATES . I. Let it be granted that a straight line may be drawn from any one point to any other point . II ... Page 32

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**parallel**. Let the straight line EF , which falls upon the two straight lines AB , CD make the alternate angles AEF , EFD equal to one another ; AB is**parallel**to CD . E For , if it be not**parallel**, AB and CD being produced shall meet ... Page 33

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**parallel**to CD . Wherefore , if a straight line , & c . Q. E. D. PROP . XXIX . THEOR . IF a straight line fall upon two**parallel**straight lines , it makes the alternate angles equal to one another ; and the exterior angle equal to the ... Page 34

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**parallel**to the same straight line are**parallel**to one another . Let AB , CD , be each of them**parallel**to EF , AB is also**parallel**to CD . B K F K C- D E Let the straight line GHK cut AB , EF , CD ; and because GHK cuts the**parallel**... Page 35

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**parallel**to the given straight line BC . Which was to be done . PROP . XXXII . THEOR . Ir a side of any triangle be ...**parallel**( 31. 1. ) to the straight line AB ; and be- cause AB is**parallel**to CE and AC meets them , the al- ternate ...### 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