The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh and Twelfth |
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Page 9
... remaining angles of the other , and are equal to them , viz . the angle ABC to the angle DEF , and the angle ACB to DFE . Therefore , if two triangles have two sides of the one equal to two sides of the other , each to each , and have ...
... remaining angles of the other , and are equal to them , viz . the angle ABC to the angle DEF , and the angle ACB to DFE . Therefore , if two triangles have two sides of the one equal to two sides of the other , each to each , and have ...
Page 10
... remaining angles of the one are 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 ...
... remaining angles of the one are 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 ...
Page 16
... remaining angle ABE is equal to the remaining angle ABD , the less to the greater , which is impossible ; therefore BE is not in the same straight line with BC . And , in like manner , it may be demonstrated , that no other can be in ...
... remaining angle ABE is equal to the remaining angle ABD , the less to the greater , which is impossible ; therefore BE is not in the same straight line with BC . And , in like manner , it may be demonstrated , that no other can be in ...
Page 17
... remaining angle DEB . * 3 Ax . In the same manner it can be demonstrated , that the angles CEB , AED are equal . Therefore , if two straight lines , & c . Q. E. D. COR . 1. From this it is manifest , that , if two straight lines cut one ...
... remaining angle DEB . * 3 Ax . In the same manner it can be demonstrated , that the angles CEB , AED are equal . Therefore , if two straight lines , & c . Q. E. D. COR . 1. From this it is manifest , that , if two straight lines cut one ...
Page 25
... remaining angle † 3 Ax . GHD : and they are alternate angles ; therefore AB is parallelt to CD . Wherefore , if a straight line , & c . † 27. 1 . Q. E. D. 4 ( aby prop 17 ) because any 2 Lr of a A are 17 ) 2rh Ls the cause " BG H + L ...
... remaining angle † 3 Ax . GHD : and they are alternate angles ; therefore AB is parallelt to CD . Wherefore , if a straight line , & c . † 27. 1 . Q. E. D. 4 ( aby prop 17 ) because any 2 Lr of a A are 17 ) 2rh Ls the cause " BG H + L ...
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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