The Elements of EuclidJohnson and Warner, 1811 - 518 σελίδες |
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Σελίδα 51
... contained Book II . by any two of the straight lines which contain one of the right angles . II . In every ... rectangle con- tained by the two straight lines , is equal to the rect- angles contained by the undivided line , and the ...
... contained Book II . by any two of the straight lines which contain one of the right angles . II . In every ... rectangle con- tained by the two straight lines , is equal to the rect- angles contained by the undivided line , and the ...
Σελίδα 52
... rectangle contained by the straight lines A , BC is equal B to the rectangle contained by A , BD , together with that contain- ed by A , DE , and that contain- ed by A , EC . From the point B draw a BF at right angles to BC , and make G ...
... rectangle contained by the straight lines A , BC is equal B to the rectangle contained by A , BD , together with that contain- ed by A , DE , and that contain- ed by A , EC . From the point B draw a BF at right angles to BC , and make G ...
Σελίδα 53
... rectangle contained by AB , AC , together with the rectangle AB , BC , is equal to the square of AB . If there- fore a straight line , & c . Q. E. D. PROP . III . THEOR . IF a straight line be divided into any two parts , the rectangle ...
... rectangle contained by AB , AC , together with the rectangle AB , BC , is equal to the square of AB . If there- fore a straight line , & c . Q. E. D. PROP . III . THEOR . IF a straight line be divided into any two parts , the rectangle ...
Σελίδα 54
... rectangle contained by AC , CB , for GC is equal to CB ; therefore GE is also equal to the rectangle AC , CB ; wherefore AG , GE are equal to twice the rectangle AC , CB : and HF , CK are the squares of AC , CB : wherefore the four ...
... rectangle contained by AC , CB , for GC is equal to CB ; therefore GE is also equal to the rectangle AC , CB ; wherefore AG , GE are equal to twice the rectangle AC , CB : and HF , CK are the squares of AC , CB : wherefore the four ...
Σελίδα 55
... rectangle contained by AD , DB , for DH , is equale to DB ; e Cor . 4 . and DF together with CH is the gnomon CMG ; therefore the gnomon CMG is equal to the rectangle AD , DB : to each of these add LG , which is equal to the square of ...
... rectangle contained by AD , DB , for DH , is equale to DB ; e Cor . 4 . and DF together with CH is the gnomon CMG ; therefore the gnomon CMG is equal to the rectangle AD , DB : to each of these add LG , which is equal to the square of ...
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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