The Elements of Euclid |
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Page 48
... fore ADEB is a parallelogram : whence AB is equal d to DE , and AD to BE : but BA is equal to C AD ; therefore the four straight lines ba , ad , de , EB are equal to one another , and the parallelogram ADEB is equilateral , likewise all ...
... fore ADEB is a parallelogram : whence AB is equal d to DE , and AD to BE : but BA is equal to C AD ; therefore the four straight lines ba , ad , de , EB are equal to one another , and the parallelogram ADEB is equilateral , likewise all ...
Page 54
... fore the side BC is equal to the side CG : but CB is equalf also to GK , H and CG to BK ; wherefore the figure CGKB is equilateral ; it is likewise rectangular ; for CG is parallel to BK , and CB meets them ; the angles KBC , GCB are ...
... fore the side BC is equal to the side CG : but CB is equalf also to GK , H and CG to BK ; wherefore the figure CGKB is equilateral ; it is likewise rectangular ; for CG is parallel to BK , and CB meets them ; the angles KBC , GCB are ...
Page 57
... fore the squares of AB and BC are equal to twice the rect- angle AB , BC , together with the square of AC . Wherefore , if a straight line , & c . Q. E. D. D PROP . VIII . THEOR . IF a straight line be divided into any two parts , four ...
... fore the squares of AB and BC are equal to twice the rect- angle AB , BC , together with the square of AC . Wherefore , if a straight line , & c . Q. E. D. D PROP . VIII . THEOR . IF a straight line be divided into any two parts , four ...
Page 58
... fore AG is equal also to RF : therefore the four rectangles AG , MP , PL , RF are equal to one another , and so are quadruple of one of them AG . And it was demonstrated , that the four CK , BN , GR , and RN are quadruple of CK ...
... fore AG is equal also to RF : therefore the four rectangles AG , MP , PL , RF are equal to one another , and so are quadruple of one of them AG . And it was demonstrated , that the four CK , BN , GR , and RN are quadruple of CK ...
Page 62
... fore the remaining rectangle CF , FA is equal to the square of AB : and the figure FK is the rectangle contained by CF , FA , for AF is equal to FG ; and AD is the square of AB ; therefore FK is equal to AD : take away the common part ...
... fore the remaining rectangle CF , FA is equal to the square of AB : and the figure FK is the rectangle contained by CF , FA , for AF is equal to FG ; and AD is the square of AB ; therefore FK is equal to AD : take away the common part ...
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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