The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh and Twelfth |
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Page 7
... equal to AB ; and because the point B is the * 15 Defi- centre of the circle ACE , BC is equal to BA : but it has nition . been proved that CA is equal to AB ; therefore CA , CB , are each of them equal to AB : but things which are equal ...
... equal to AB ; and because the point B is the * 15 Defi- centre of the circle ACE , BC is equal to BA : but it has nition . been proved that CA is equal to AB ; therefore CA , CB , are each of them equal to AB : but things which are equal ...
Page 8
... equal to BG ; wherefore AL and BC are each of them equal to BG : and things that are equal to the same thing are equal + to one another ; therefore the straight line AL is equal to BC . Wherefore from the given point A a straight line ...
... equal to BG ; wherefore AL and BC are each of them equal to BG : and things that are equal to the same thing are equal + to one another ; therefore the straight line AL is equal to BC . Wherefore from the given point A a straight line ...
Page 9
... equal † to DE : and AB coinciding with Hyp . DE , AC shall coincide with DF , because the angle BAC is equal to the angle EDF ; wherefore also the + Hyp . point C shall coincide with the point F , because the straight line AC + is equal ...
... equal † to DE : and AB coinciding with Hyp . DE , AC shall coincide with DF , because the angle BAC is equal to the angle EDF ; wherefore also the + Hyp . point C shall coincide with the point F , because the straight line AC + is equal ...
Page 10
... equal * to the remaining angles of the other , each to each , to which the equal sides are opposite ; viz . the angle ACF to the angle ABG , and the angle AFC to the an- gle AGB : and because the whole AF is equal to the whole AG , of ...
... equal * to the remaining angles of the other , each to each , to which the equal sides are opposite ; viz . the angle ACF to the angle ABG , and the angle AFC to the an- gle AGB : and because the whole AF is equal to the whole AG , of ...
Page 12
... equal to the angle BCD ; but BDC has been proved to be greater than the same BCD ; which is impossible . The case in ... equal to another , and likewise those which are terminated in the other extremity . Q. E. D. PROP . VIII . THEOR ...
... equal to the angle BCD ; but BDC has been proved to be greater than the same BCD ; which is impossible . The case in ... equal to another , and likewise those which are terminated in the other extremity . Q. E. D. PROP . VIII . THEOR ...
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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