The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh and Twelfth |
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Page 38
... double * of the triangle ABD , because they are upon the same base BD , and between the same parallels BD , AL ; and the square GB is double of the triangle FBC , because these also are upon the same base FB , and † 11 Ax . 2 Ax . † 30 ...
... double * of the triangle ABD , because they are upon the same base BD , and between the same parallels BD , AL ; and the square GB is double of the triangle FBC , because these also are upon the same base FB , and † 11 Ax . 2 Ax . † 30 ...
Page 39
... doubles of equals are equal to one another ; therefore the 6 Ax . parallelogram BL is equal to the square GB . In the same manner , by joining AE , BK , it can be demon- strated , that the parallelogram CL is equal to the square HC ...
... doubles of equals are equal to one another ; therefore the 6 Ax . parallelogram BL is equal to the square GB . In the same manner , by joining AE , BK , it can be demon- strated , that the parallelogram CL is equal to the square HC ...
Page 45
... double of AK : but twice the rectangle AB , BC is double of AK , D for BK is equal to BC ; therefore the gnomon AKF , together with the square CK , is equal † to twice the rectangle AB , BC : to each of these equals add HF , which is ...
... double of AK : but twice the rectangle AB , BC is double of AK , D for BK is equal to BC ; therefore the gnomon AKF , together with the square CK , is equal † to twice the rectangle AB , BC : to each of these equals add HF , which is ...
Page 47
... 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 be divided into two equal parts at the point C , and into two unequal parts at the point D : the squares of ...
... 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 be divided into two equal parts at the point C , and into two unequal parts at the point D : the squares of ...
Page 48
... double of the square of AC : but the square of AE is equal to the squares of AC , CE because ACE is a right angle ; therefore the square of AE is double of the square of AC : again , because EG is equal to GF , the square of EG is equal ...
... double of the square of AC : but the square of AE is equal to the squares of AC , CE because ACE is a right angle ; therefore the square of AE is double of the square of AC : again , because EG is equal to GF , the square of EG is equal ...
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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