The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh and Twelfth |
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Page 35
... passes ; and BK , KD the other parallelograms which make up thewhole figure ABCD , which are therefore called the complements , BK shall be equal to the complement KD . BG K F The complement * Because ABCD is a parallelogram , and AC ...
... passes ; and BK , KD the other parallelograms which make up thewhole figure ABCD , which are therefore called the complements , BK shall be equal to the complement KD . BG K F The complement * Because ABCD is a parallelogram , and AC ...
Page 57
... pass through the centre , it shall cut it at right angles : and if it cut it at right angles , it shall bisect it . Let ABC be a circle ; and let CD , a straight line drawn through the centre , bisect any straight line AB , which does ...
... pass through the centre , it shall cut it at right angles : and if it cut it at right angles , it shall bisect it . Let ABC be a circle ; and let CD , a straight line drawn through the centre , bisect any straight line AB , which does ...
Page 58
... pass through the centre : AC , BD shall not bisect one another . A F B For , if it be possible , let AE be equal to EC , and BE to ED . If one of the lines pass through the centre , it is plain that it cannot be bisected by the other ...
... pass through the centre : AC , BD shall not bisect one another . A F B For , if it be possible , let AE be equal to EC , and BE to ED . If one of the lines pass through the centre , it is plain that it cannot be bisected by the other ...
Page 59
... passes through the centre is al- ways greater than one more remote : and from the same point there can be drawn only two straight lines that are equal to one another , one upon each side of the shortest line . * 20.1 . Let ABCD be a ...
... passes through the centre is al- ways greater than one more remote : and from the same point there can be drawn only two straight lines that are equal to one another , one upon each side of the shortest line . * 20.1 . Let ABCD be a ...
Page 61
... passes through the centre , and of the rest , that which is nearer to the one passing through the centre is always greater than one more remote : but of those which fall upon the convex circumference , the least is that between the ...
... passes through the centre , and of the rest , that which is nearer to the one passing through the centre is always greater than one more remote : but of those which fall upon the convex circumference , the least is that between the ...
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The Elements Of Euclid: Viz. The First Six Books, Together With The Eleventh ... Robert Simson,Euclid,John Davidson No preview available - 2019 |
Common terms and phrases
ABC is given AC is equal altitude angle ABC angle BAC base BC bisected centre circle ABCD circumference common logarithm cone Constr 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 logarithm multiple opposite parallel parallelogram AC perpendicular polygon prism proportionals proposition pyramid Q. E. D. PROP radius ratio of AE rectangle contained rectilineal figure right angles segment shewn 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