## 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**. Let AB , CD be equal and**parallel**straight lines , and joined towards the same parts by the straight lines AC , BD ; AC , BD are also equal and**parallel**. A C B D Join BC ; and because AB is**parallel**to CD ; and BC meets them ... Page 37

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**parallel**; and the diameter is the straight line joining two of its opposite angles . Let ACDB be a parallelogram ...**parallel**to CD , and A BC meets them , the alternate angles ABC , BCD are equal ( 29. 1. ) to one another ; and because ... Page 39

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**parallel**straight lines to- wards the same parts , are themselves equal and**parallel**; ( 33. 1. ) therefore EB , CH are both equal and**parallel**, and EBCH is a parallelogram ; and it is equal ( 35. 1. ) to ABCD , because it is upon the ... Page 40

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**parallels**. Let the equal triangles ABC , DBC be upon the same base BC , and upon the same side of it ; they are between the same**parallels**. Join AD ; AD is**parallel**to BC : for , if it is not , through the point A draw ( 31. 1. ) AE ... Page 41

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**parallel**to BC . In the same manner , it can be demonstrated that no other line but AD is**parallel**to BC ; AD is therefore**parallel**to it . Wherefore equal triangles upon , & c . Q. E. D. B C PROP . XL . THEOR . EQUAL triangles upon ...### 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