The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh and Twelfth |
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Page 8
... 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 AL has been ...
... 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 AL has been ...
Page 9
... wherefore also the + Hyp . point C shall coincide with the point F , because the straight line AC + is equal to DF : but the point B was † Hyp . proved to coincide with the point E : wherefore the base BC shall coincide with the base EF ...
... wherefore also the + Hyp . point C shall coincide with the point F , because the straight line AC + is equal to DF : but the point B was † Hyp . proved to coincide with the point E : wherefore the base BC shall coincide with the base EF ...
Page 14
... Wherefore , from the given point C , in the given straight line AB , FC has been drawn at right angles to AB . Which was to be done . * COR . - By help of this problem , it may be demon- strated , that two straight lines cannot have a ...
... Wherefore , from the given point C , in the given straight line AB , FC has been drawn at right angles to AB . Which was to be done . * COR . - By help of this problem , it may be demon- strated , that two straight lines cannot have a ...
Page 17
... wherefore the angles * A * 13. 1 . CEA , AED are equal to the angles AED , DEB . +1 Ax . Take away the common angle AED , and the remain- ing angle CEA is equal to the remaining angle DEB . * 3 Ax . In the same manner it can be ...
... wherefore the angles * A * 13. 1 . CEA , AED are equal to the angles AED , DEB . +1 Ax . Take away the common angle AED , and the remain- ing angle CEA is equal to the remaining angle DEB . * 3 Ax . In the same manner it can be ...
Page 23
... 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 other , each to each ; and one side equal to one side , viz . either the sides adjacent to the ...
... 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 other , each to each ; and one side equal to one side , viz . either the sides adjacent to 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