## 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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**circumference**, and is such that all straight lines drawn from a certain point within the figure to the**circumference**, are equal to one another : XVI . And this point is called the centre of the circle . XVII . A diameter of a circle ... Page 66

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**circumference**. " VIII . An angle in a segment is the angle con- tained by two straight lines drawn from any point in the**circumference**of the segment , to the extremities of the straight line which is the base of the segment . IX . And ... Page 67

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**circumference**of a circle , the straight line which joins them shall fall within the circle . Let ABC be a circle , and A , B any two points in the circum- ference ; the straight line drawn from A to B shall fall within the circle . For ... Page 68

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**circumference**; it falls therefore within it . Wherefore , if any two points , & c . Q. E. D. PROP . III . THEOR . Ir a straight line drawn through the centre of a circle bisect a straight line in it which does not pass through the ... Page 71

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**circumference**, the greatest is that in which the centre is , and the other part of that diameter is the least ; and , of any others , that which is nearer to the line which passes through the centre is always greater than one more ...### 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