## 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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Page 46

... right angle BAC ; the

... right angle BAC ; the

**square**described upon the side BC is equal to the**squares**described upon BA ,**AC**. On BC describe ( 46. 1. ) the**square**BDEC , and on BA ,**AC**the F B G 1 D L E H K**squares**46 BOOK I. THE ELEMENTS OF EUCLID . Page 47

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**squares**GB , HC : and through A draw ( 31. 1. ) AL parallel to BD or CE , and join AD , FC : then , because each of the angles BAC , BAG , is a right angle , ( 30. def . ) the two straight lines**AC**, AG upon the opposite sides of AB ... Page 48

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**squares**upon the other sides BA ,**AC**, the angle BAC is a right angle . A D From the point A draw ( 11. 1. ) AD at right angles to**AC**, and make AD equal to BA , and join DC : then because DA is equal to AB , the**square**of DA is equal to ... Page 50

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**square**of the whole line . Let the straight line AB be divided into A any two parts in the point C ; the rectangle contained by AB , BC , together with the rectangle AB ,**AC**, shall be equal to the**square**of AB . Upon AB describe ( 46 ... Page 51

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**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**of BC . B Upon BC describe ( 46. 1. ) the**A C square**CDEB ...### 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