The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh and Twelfth |
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Page 7
... is equal to DG ; and † DA , DB , parts of them , are equal ; there- fore the remainder AL is equal to the remainder BG : but it has been shewn , * 15 Def . H D + Constr . B * S Ax . 1 Ax . * 2.1 . * 3 Post . BOOK I. PROP . I. II . 7.
... is equal to DG ; and † DA , DB , parts of them , are equal ; there- fore the remainder AL is equal to the remainder BG : but it has been shewn , * 15 Def . H D + Constr . B * S Ax . 1 Ax . * 2.1 . * 3 Post . BOOK I. PROP . I. II . 7.
Page 20
... shewn that BA , AC are greater than BE , EC ; much more then are BA , AC , greater than BD , DC . Again , because the exterior angle of a triangle * is greater than the interior and opposite angle , the exte- rior angle BDC of the ...
... shewn that BA , AC are greater than BE , EC ; much more then are BA , AC , greater than BD , DC . Again , because the exterior angle of a triangle * is greater than the interior and opposite angle , the exte- rior angle BDC of the ...
Page 23
... shewn that it is not equal to it ; therefore the an- gle BAC is greater than the angle EDF . Wherefore , if two triangles , & c . Q. E. D. PROP . XXVI . THEOR . If two triangles have two angles of the one equal to two angles of the ...
... shewn that it is not equal to it ; therefore the an- gle BAC is greater than the angle EDF . Wherefore , if two triangles , & c . Q. E. D. PROP . XXVI . THEOR . If two triangles have two angles of the one equal to two angles of the ...
Page 27
... shewn that the angle AGK is equal to the angle GHF ; A C- *** B F * 29. 1 . -D * 29. 1 . therefore also AGK is equal to GKD : and they are +1 Ax . alternate angles ; therefore AB is parallel to . CD . Wherefore , straight lines , & c ...
... shewn that the angle AGK is equal to the angle GHF ; A C- *** B F * 29. 1 . -D * 29. 1 . therefore also AGK is equal to GKD : and they are +1 Ax . alternate angles ; therefore AB is parallel to . CD . Wherefore , straight lines , & c ...
Page 28
... shewn to be equal to the angle BAC ; therefore the whole exterior angle ACD is equal to the two interior and opposite angles CAB , ABC : to each of these equals add the angle ACB , and the angles ACD , ACB are equal to the three angles ...
... shewn to be equal to the angle BAC ; therefore the whole exterior angle ACD is equal to the two interior and opposite angles CAB , ABC : to each of these equals add the angle ACB , and the angles ACD , ACB are equal to the three angles ...
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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