## 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

Results 6-10 of 54

Page 55

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**rectangle**AB , BC is double of AK , for BK is equal ( Cor . 4. 2. ) to BC ...**contained**by the whole line , and one of the parts , together with the ...**rectangle**AB , BC , together with the square of AC , is equal to the square of the ... Page 56

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**rectangle**CK is equal ( 36. 1. ) to BN , and GR to RN ; but CK is equal ( 43. 1. ) to RN , because they are the ...**contained**by AB , BC , for BK is equal to BC , four times the**rectangle**AB , BC is quadruple of AK but the gnomon AOH was ... Page 60

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**rectangle contained**by the whole and one of the parts shall be equal to the square of the other part . Let AB be the given straight line it is required to divide it into two parts , so that the**rectangle contained**by the whole and one ... Page 61

... containing the obtuse angle , by twice the

... containing the obtuse angle , by twice the

**rectangle contained**by the side upon which , when produced , the perpendicular falls , and the straight line intercepted without the trian- gle between the perpendicular and the obtuse angle ... Page 62

... containing that angle , by twice the

... containing that angle , by twice the

**rectangle contained**by either of these sides , and the straight line intercepted between the perpendicular let fall upon it from the oppo- site angle , and the acute angle . * Let ABC be any triangle ...### 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