## 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 |

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Page 49

... contained by any two of the straight lines which contain one of the right angles . II . E D In every parallelogram , any of the parallelograms about a diame- ter , together ...

... contained by any two of the straight lines which contain one of the right angles . II . E D In every parallelogram , any of the parallelograms about a diame- ter , together ...

**rectangle contained**by G the straight lines A , BC is equal to B. Page 50

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**contained**by A , BD , together with that**contained**by A , DE , and that**contained**by A , EC . G D E C K L H A From ...**rectangle**BH is equal to the**rectangles**BK , DL , EH ; and BH is**contained**by A , BC , for it is**contained**by GB , BC ... Page 51

... contained by AB , BC , for BE is equal to AB ; therefore the

... contained by AB , BC , for BE is equal to AB ; therefore the

**rectangle contained**by AB , AC , together with the rectangle AB , BC , is equal to the square of AB . If therefore a straight line , & c . Q. E. D. PROP . III . THEOR . Ir a ... Page 53

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**rectangle contained**by AD , DB , for DH is equal ( Cor . 4. 2. ) to DB , and E G F DF together with CH is the gnomon CMG ; therefore the gnomon CMG is equal to the rectangle AD , DB : to each of these add LG , which is equal ( 43. 1 ... Page 54

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**rectangle contained**by the whole line thus pro- duced , and the part of it produced , together with the square of half the line bisected , is equal to the square of the straight line which is made up of the half and the part produced ...### 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