## 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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**ABCD**be a**circle**, and AC , BD two straight lines in it which cut one another in the point E , and do not both pass ...**circle**, & c . Q. E. D. B E C PROP . V. THEOR . If two**circles**cut one another , they shall not have the same centre ... Page 71

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**ABCD**be a**circle**, and AD its diameter , in which let any point F be taken which is not the centre ; let the centre be E ; of all the straight lines FB , FC , FG , & c . that can be drawn from F to the**circumference**, FA is the greatest ... Page 78

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**circle**; and , of all others , that which is nearer to the centre is always greater than one more remote ; and the greater is nearer to the centre than the less . * Let**ABCD**be a**circle**, of which the di- ameter is AD , and the centre E ... Page 83

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**circle**be within the angle BAC , and join AE , and produce it to F ; because EA is equal to EB , the angle EAB is ...**ABCD**be a**circle**, and BAD , BED angles in the same segment BAED : the angles BAD , BED are equal to one another . Take ... Page 84

... ABCD be a quadrilateral figure in the

... ABCD be a quadrilateral figure in the

**circle ABCD**; any two of its opposite angles are together equal to two right angles . D C Join AC , BD ; and because the three angles of every triangle are equal ( 32. 1. ) to two right angles , the ...### 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