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" ... ratio between two whole numbers the impossibility of the problem of rectification is not inferable. The quadrature of the circle stands and falls with the problem of rectification. This is based upon the truth above mentioned, that a circle is equal... "
Sir Isaac Newton's Two Treatises: Of the Quadrature of Curves, and Analysis ... - Page 347
by Isaac Newton - 1745 - 479 pages
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The Monist, Volume 1

Paul Carus - Electronic journals - 1891 - 734 pages
...truth above mentioned, that a circle is equal in area to a right-angled triangle, in which one side is equal to the radius of the circle and the other to the circumference. Supposing, accordingly, that the circumference of the circle were rectified, then...
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Mathematical Essays and Recreations

Hermann Schubert - Circle-squaring - 1899 - 163 pages
...truth above mentioned, that a circle is equal in area to a right-angled triangle, in which one side is equal to the radius of the circle and the other to the circumference. Supposing, accordingly, that the circumference of the circle had been rectified,...
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Annual Report of the Board of Regents of the Smithsonian Institution

Smithsonian Institution. Board of Regents - Discoveries in science - 1891 - 898 pages
...truth above mentioned, that a circle is equal in area to a right-angle triangle, in which one side is equal to the radius of the circle and the other to the circumference. Supposing, accordingly, that the circumference of the circle were rectified, then...
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A Source Book in Medieval Science

Edward Grant - History - 1974 - 890 pages
...there follows this conclusion : [HI.] EVERY CIRCLE is EQUAL то A RIGHT TRIANGLE ONE OF WHOSE TWO SIDES INCLUDING THE RIGHT ANGLE IS EQUAL TO THE RADIUS OF THE CIRCLE AND THE OTHER OF THESE TO THE CIRCUMFERENCE OF THE CIRCLE. Let there be a circle Z, whose center is Z [Fig. 3]. Fig....
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