## 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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**rectangle**contained by the two parts , together with the**square**of the foresaid part . Let the straight line AB be divided into two parts in the point C ; the**rectangle**AB , BC is equal to the**rectangle**AC ,**CB**together with the**square**... Page 52

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**rectangular**; for CG is parallel to BK , and**CB**meets them ; the angles KBC , GCB are therefore D equal to two right angles ; and KBC is a right angle ; wherefore GCB is a right angle : and therefore also the angles ( 34. 1. ) CGK , GKB ... Page 53

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**rectangle**contained by the unequal parts , together with the**square**of the line be- tween the points of section , is ...**CB**. A B C D L Η M Upon**CB**describe ( 46. 1. ) the**square**CEFB , join BE , and through D draw ( 31. 1. ) DHG ... Page 54

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**rectangle**AD , DB , together with the**square**of**CB**, is equal to the**square**of CD . A C B D Ꮮ H K M Upon CD describe ( 46. 1. ) the**square**of CEFD , join DE , and through B draw ( 31. 1. ) BHG parallel to CE or DF , and through H draw ... Page 55

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**rectangle**AB , BC is double of AK , for BK is equal ( Cor . 4. 2. ) to BC therefore the gnomon AKF , to- gether with ...**CB**, and upon AD describe the**square**ÁEFD ; and construct two figures such as in the preceding . Because**CB**is equal ...### 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