The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh and Twelfth |
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Page 7
... fore equilateral , and it is described upon the given straight line AB . Which was required to be done . PROP . II . PROB . From a given point to draw a straight line equal to a given straight line . Let A be the given point , and BC ...
... fore equilateral , and it is described upon the given straight line AB . Which was required to be done . PROP . II . PROB . From a given point to draw a straight line equal to a given straight line . Let A be the given point , and BC ...
Page 9
... fore the base BC coincides with the base EF , and there- fore is equal to it . Wherefore the whole triangle ABC † 8 Ax . coincides with the whole triangle DEF , and is equal to it ; and the other angles of the one coincide with the ...
... fore the base BC coincides with the base EF , and there- fore is equal to it . Wherefore the whole triangle ABC † 8 Ax . coincides with the whole triangle DEF , and is equal to it ; and the other angles of the one coincide with the ...
Page 15
... fore , from the given point C , a perpendicular CH has been drawn to the given straight line AB . Which was to be done . PROP . XIII . THEOR . The angles which one straight line makes with another upon one side of it , are either two ...
... fore , from the given point C , a perpendicular CH has been drawn to the given straight line AB . Which was to be done . PROP . XIII . THEOR . The angles which one straight line makes with another upon one side of it , are either two ...
Page 22
... fore much more is the angle EFG greater than the angle EGF and because the angle EFG of the trian- gle EFG is greater than its angle EGF , and that the greater * angle is subtended by the greater side ; there- fore the side EG is ...
... fore much more is the angle EFG greater than the angle EGF and because the angle EFG of the trian- gle EFG is greater than its angle EGF , and that the greater * angle is subtended by the greater side ; there- fore the side EG is ...
Page 24
... fore , if two triangles , & c . Q. E , D. PROP . XXVII . THEOR . If a straight line falling upon two other straight lines make the alternate angles equal to one another , these two straight lines shall be parallel . Let the straight ...
... fore , if two triangles , & c . Q. E , D. PROP . XXVII . THEOR . If a straight line falling upon two other straight lines make the alternate angles equal to one another , these two straight lines shall be parallel . Let the straight ...
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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