The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh and Twelfth |
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Page 28
... four right angles . There- fore all the angles of the figure , together with four right angles , are equal to twice as many right angles as the figure has sides . COR . 2. All the exterior angles of any rectilineal figure are together ...
... four right angles . There- fore all the angles of the figure , together with four right angles , are equal to twice as many right angles as the figure has sides . COR . 2. All the exterior angles of any rectilineal figure are together ...
Page 29
... four right angles ; therefore all the exterior angles are equal to four right angles . PROP . XXXIII . THEOR . The straight lines which join the extremities of two equal and parallel straight lines towards the same parts , are also ...
... four right angles ; therefore all the exterior angles are equal to four right angles . PROP . XXXIII . THEOR . The straight lines which join the extremities of two equal and parallel straight lines towards the same parts , are also ...
Page 37
... four straight lines BA , AD , DE , EB , are equal to one another , and the paralle- logram ADEB is equilateral : likewise all its angles are right angles ; for , since the straight line AD meets the parallels AB , DE , the angles BAD ...
... four straight lines BA , AD , DE , EB , are equal to one another , and the paralle- logram ADEB is equilateral : likewise all its angles are right angles ; for , since the straight line AD meets the parallels AB , DE , the angles BAD ...
Page 43
... four figures HF , CK , AG , GE are equal to the squares of AC , CB , and to twice the rect- angle AC , CB : but HF , CK , AG , GE make up the whole figure ADEB , which is the square of AB : there- fore the square of AB is equal † to the ...
... four figures HF , CK , AG , GE are equal to the squares of AC , CB , and to twice the rect- angle AC , CB : but HF , CK , AG , GE make up the whole figure ADEB , which is the square of AB : there- fore the square of AB is equal † to the ...
Page 46
... four times the rectangle contained by the whole line , and one of the parts , together with the square of the other part , is equal to the square of the straight line which is made up of the whole and that part . Let the straight line ...
... four times the rectangle contained by the whole line , and one of the parts , together with the square of the other part , is equal to the square of the straight line which is made up of the whole and that part . Let the straight line ...
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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