The Elements of Euclid |
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Page 38
... four right angles , Therefore all the angics of the figure , together with four right angles are equal to twice as many right angles as the figure has sides . a 2 Cor . 15. 1 . b 13. 1 . COR . 2. All the exterior angles of any ...
... four right angles , Therefore all the angics of the figure , together with four right angles are equal to twice as many right angles as the figure has sides . a 2 Cor . 15. 1 . b 13. 1 . COR . 2. All the exterior angles of any ...
Page 39
... four sided figure , of which the opposite sides are parallel ; and the diameter is the straight line joining two of its opposite angles . Let ACDB be a parallelogram , of which BC is a diameter ; the opposite sides and angles of the ...
... four sided figure , of which the opposite sides are parallel ; and the diameter is the straight line joining two of its opposite angles . Let ACDB be a parallelogram , of which BC is a diameter ; the opposite sides and angles of the ...
Page 48
... four straight lines ba , ad , de , EB are equal to one another , and the parallelogram ADEB is equilateral , likewise all its angles are right angles ; because the straight D line AD meeting the parallels AB , DE , the angles BAD , ADE ...
... four straight lines ba , ad , de , EB are equal to one another , and the parallelogram ADEB is equilateral , likewise all its angles are right angles ; because the straight D line AD meeting the parallels AB , DE , the angles BAD , ADE ...
Page 54
... four figures HF , CK , AG , GE are equal to the squares of AC , CB , and to twice the rectangle . AC , CB ; but HF , CK , AG , GE make up the whole figure ADEB , which is the square of AB : therefore 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 rectangle . AC , CB ; but HF , CK , AG , GE make up the whole figure ADEB , which is the square of AB : therefore the square of AB is equal to the ...
Page 57
... 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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Common terms and phrases
altitude angle ABC angle BAC base BC BC is equal BC is given bisected Book XI centre circle ABCD circumference cone cylinder demonstrated described diameter draw drawn equal angles equiangular equimultiples Euclid 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 meet multiple parallel parallelogram parallelogram AC perpendicular point F polygon prism proportionals proposition pyramid Q. E. D. PROP radius ratio of AE rectangle CB rectangle contained rectilineal figure remaining angle right angles segment sides BA similar solid angle solid parallelopiped square of AC straight line AB straight line BC tangent THEOR third triangle ABC triplicate ratio vertex wherefore