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" To wit, when we seek to subject them to numeration ... we find that they flee away perpetually, so that not one of them can be apprehended precisely in itself. . . . Now that cannot be called a true number which is of such a nature that it lacks precision.... "
The Teaching of Algebra (including Trigonometry) - 378. lappuse
autors: Sir Thomas Percy Nunn, Thomas Percy Nunn - 1914 - 616 lapas
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The Teaching of Algebra (including Trigonometry)

Sir Thomas Percy Nunn - 1914 - 616 lapas
...only if neither the lengths of the lines nor the areas of the squares upon them are commensurable. 3 The table of binomial coefficients given on p. 213...is easily seen that each irrational falls between APBX FIG. 92. two consecutive integers. Also they are not fractions with definite numerators and denominators,...
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The Teaching of Algebra (including Trigonometry)

Sir Thomas Percy Nunn - 1919 - 616 lapas
...commensurable. 2 The table of binomial coefficients given on p. 213 appears in Book I of this work (folio 45). one hand, argues Stifel, " since, in proving geometrical...is easily seen that each irrational falls between APBX o ~ ; " ? l FIG. 92. two consecutive integers. Also they are not fractions with definite numerators...
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Mathematics: The Loss of Certainty

Morris Kline - 1982 - 366 lapas
...irrational numbers are numbers at all. To wit, when we seek to subject them to numeration [decimal form] ... we find that they flee away perpetually so that not...number, but lies hidden in a kind of cloud of infinity. Then Stifel added that real numbers are either whole numbers or fractions, and, obviously, irrationals...
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Mathematical Thought from Ancient to Modern Times: Volume 1

Morris Kline - 1990 - 428 lapas
...are numbers at all. To wit, when we seek to subject them to numeration [decimal representation] ... we find that they flee away perpetually, so that not...number, but lies hidden in a kind of cloud of infinity, He then argues that real numbers are either whole numbers or fractions; obviously irrationals are neither,...
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Understanding the Infinite

Shaughan LAVINE - 1994 - 372 lapas
...irrational numbers are numbers at all. To wit, when we seek [to give them a decimal representation] ... we find that they flee away perpetually, so that not...number, but lies hidden in a kind of cloud of infinity. [KH72, p. 251] As we shall see, Stifel's remarks were prescient: the basis of the irrational numbers...
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Famous Problems and Their Mathematicians

Art Johnson - 1999 - 179 lapas
...example, AAAA to represent AA. He did not, however, have a grasp of irrational numbers, writing that "an irrational number is not a true number, but lies hidden in some sort of cloud of infinity." Although Stifel solved quadratic equations with negative roots, he...
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The Logic of Thermostatistical Physics

Gerard G. Emch, Chuang Liu - 2002 - 703 lapas
...[2,2,2,2,2,2,2,2, ...] e =2+ [1,2,1, 1,4,1, 1,6,...] \ (5.4.7) TT =3+ [7,15,1,292,1,1,1,2, . . .] J an irrational number is not a true number but lies hidden in a kind of cloud of infinity. |Stifel, 1544] Euler [1744a] proved in 1737/44 that the simple continued fraction expansion of every...
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Everything and More: A Compact History of Infinity

David Foster Wallace - 2003 - 319 lapas
...irrational numbers are numbers at all. To wit, when we seek to subject them to [decimal representation], we find that they flee away perpetually, so that not...number, but lies hidden in a kind of cloud of infinity. §2d. "UNAVOIDABLE BUT ULTIMATELY IYI-GRADE INTERPOLATION Skip the following few pages if you like,...
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