MS 475-476 (1903) - Lowell Lecture VIII

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arithmetic to the Arabians. It was not original with him, but was commonly used in Chorasmia, which is a country north of Aria. There is no evidence at all that the socalled Arabic system was in use even in Aria much before the christian era; but likely enough that it was so. The cipher for naught would probably not then have been in use. For the system was originally only used for calculations made in ruled columns. The figures were not written as a substitute for the name of the number. As long as the use of it was thus restricted to computations, the absence of the cipher would be a matter of no consequence

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If the system was used in Aria for calculations at that early day, we may be tolerably sure that Pythagoras would become acquainted with it. We know that the Pythagorean brethren, who were highly refined, exclusive, gentlemanly, and aristocratic people, supported themselves for centuries by their brains, and that they possessed some secret about numbers,— which was kept as only trade secrets are apt to be kept,— and which secret was of such a nature as to lead them to speak in concealed ways of the number ten. Thus they called it the tetrad, a word which does not naturally suggest ten; but ten

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was called the tetrad because of the figure []

Perhaps the Pythagoreans supported themselves by book-keeping by making computations as many Italians did at a much later day. We only know that in a book of Boethius, who lived about A.D. 500 the Arabic figures are given and are said to be used by the Pythagoreans. It is true that the critics have endeavored to make it probable, or to use their favorite expression to “demonstrate”,— some of them that this chapter of the book is spurious, others that the whole of the second book of the Geometry of Boethius in which this chapter

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occurs is spurious, still others that the entire work is spurious. But it never seems to have occurred to any of them that even if they were to prove it spurious, which they are very far from having done, it would still remain to be explained how this very singular passage ever came to be written at all or ever came to be attributed to Boethius. For my part, having most carefully examined all the evidence and several of the manuscripts, I have no doubt at all that the passage is genuine. I consider the arguments brought against it to be utter rubbish.

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The evidence if we admit the MSS to be genuine is that even to A.D. 500 there was a guild of accountants descended from the old Pythagoreans and calling themselves by that name who used our Arabic notation without the zero for computing in columns.

This guild disappeared during the following dark ages when no accounts were kept, because justice had disappeared.

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