The Thirteen Books of Euclid's Elements ; The Works of Archimedes, Including the Method ; Introduction to Arithmetic |
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Page 255
... straight line and the irrational straight lines after it are neither the same with the medial nor with one another . For the square on a medial , if applied to a rational straight line , produces as breadth a straight line rational and ...
... straight line and the irrational straight lines after it are neither the same with the medial nor with one another . For the square on a medial , if applied to a rational straight line , produces as breadth a straight line rational and ...
Page 295
Euclid. Therefore the apotome is not the same with the binomial straight line . Q. E. D. The apotome and the irrational straight lines following it are neither the same with the medial ... a rational straight line applied ELEMENTS X 295.
Euclid. Therefore the apotome is not the same with the binomial straight line . Q. E. D. The apotome and the irrational straight lines following it are neither the same with the medial ... a rational straight line applied ELEMENTS X 295.
Page 297
Euclid. But KE is rational ; therefore FK is also rational . Therefore FK , KE are rational straight lines ... line commensurable with CD or by the square on a straight line incommensurable with it . If then the square on CD is greater ...
Euclid. But KE is rational ; therefore FK is also rational . Therefore FK , KE are rational straight lines ... line commensurable with CD or by the square on a straight line incommensurable with it . If then the square on CD is greater ...
Common terms and phrases
added apotome applied axis base called centre of gravity circle circle ABCD circumference circumscribed commensurable in length commensurable in square common cone constructed continued cube cylinder described diameter difference divided double draw drawn equal extremes fall figure fluid follows four fourth given greater half height Hence incommensurable inscribed joined least less magnitudes mean measure medial meet multiplying namely parallel parallelogram perpendicular placed plane polygon portion possible prime prism produced Prop proportional PROPOSITION proved pyramid ratio rational straight line reason rectangle remaining respectively right angles segment side similar Similarly solid sphere square number squares on AC straight lines commensurable surface taken third touch triangle twice the rectangle unit vertex whole