The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh and Twelfth |
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Page 9
... equal sides are opposite , shall be equal each to each , viz . the angle ABC to the angle DEF , and the angle ACB to DFE . For , if the triangle ABC be applied to DEF , so that the point A may be on D , and the straight line AB upon DE ...
... equal sides are opposite , shall be equal each to each , viz . the angle ABC to the angle DEF , and the angle ACB to DFE . For , if the triangle ABC be applied to DEF , so that the point A may be on D , and the straight line AB upon DE ...
Page 10
... 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 is equal ...
... 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 is equal ...
Page 13
... angle , that is , to divide it into two equal angles . Let BAC be the given rectilineal angle ; it is re- quired to bisect it . Take any point D in AB , and from AC cut off AE * 3. 1 . equal to AD ; join DE , and upon it describe * an ...
... angle , that is , to divide it into two equal angles . Let BAC be the given rectilineal angle ; it is re- quired to bisect it . Take any point D in AB , and from AC cut off AE * 3. 1 . equal to AD ; join DE , and upon it describe * an ...
Page 15
... angles : but when a straight line , standing on another straight line , makes the adjacent angles equal to one another , each of them is a right angle , and the straight line which stands upon the other , is called a perpendicular + to ...
... angles : but when a straight line , standing on another straight line , makes the adjacent angles equal to one another , each of them is a right angle , and the straight line which stands upon the other , is called a perpendicular + to ...
Page 16
... equal to one another ; therefore the angles CBE , EBD are equal to the angles DBA , ABC : but CBE , EBD are two right angles ; therefore , DBA , ABC are together equal † to two right angles . Wherefore , when a straight line , & c ...
... equal to one another ; therefore the angles CBE , EBD are equal to the angles DBA , ABC : but CBE , EBD are two right angles ; therefore , DBA , ABC are together equal † to two right angles . Wherefore , when a straight line , & c ...
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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