The Elements of Euclid |
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Page 55
... divided into two equal parts , and also into two unequal parts ; the rectang ! con- tained by the unequal parts , together with the square of the line between the points of section , is equal to the square of half the line . Let the ...
... divided into two equal parts , and also into two unequal parts ; the rectang ! con- tained by the unequal parts , together with the square of the line between the points of section , is equal to the square of half the line . Let the ...
Page 56
... divided into any two parts , the square of the whole line , and of one of the parts , are equal to twice the rectangle contained by the whole and that part , together with the square of the other part . Let the straight line AB be divided ...
... divided into any two parts , the square of the whole line , and of one of the parts , are equal to twice the rectangle contained by the whole and that part , together with the square of the other part . Let the straight line AB be divided ...
Page 57
... divided into any two parts , 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 ...
... divided into any two parts , 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 ...
Page 59
... divided into two equal , and also into two unequal parts ; the squares of the two unequal parts are together double of the square of half the line , and of the square of the line between the points of section . Let the straight line AB ...
... divided into two equal , and also into two unequal parts ; the squares of the two unequal parts are together double of the square of half the line , and of the square of the line between the points of section . Let the straight line AB ...
Page 62
... divided in H , so that the rectangle AB , BH is equal to the square of AH . F G H B Produce GH to K ; because the straight line AC is bisected in E , and produced to the point F , the rectangle CF , FA , to- gether with the square of AE ...
... divided in H , so that the rectangle AB , BH is equal to the square of AH . F G H B Produce GH to K ; because the straight line AC is bisected in E , and produced to the point F , the rectangle CF , FA , to- gether with the square of AE ...
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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