Mathematische Keilschrift-Texte by O. NeugebauerReview by: R. C. ArchibaldIsis, Vol. 28, No. 2 (May, 1938), pp. 490-491Published by: The University of Chicago Press on behalf of The History of Science SocietyStable URL: http://www.jstor.org/stable/225715 .

Accessed: 14/06/2014 22:59

Your use of the JSTOR archive indicates your acceptance of the Terms & Conditions of Use, available at .http://www.jstor.org/page/info/about/policies/terms.jsp

.JSTOR is a not-for-profit service that helps scholars, researchers, and students discover, use, and build upon a wide range ofcontent in a trusted digital archive. We use information technology and tools to increase productivity and facilitate new formsof scholarship. For more information about JSTOR, please contact support@jstor.org.

.

The University of Chicago Press and The History of Science Society are collaborating with JSTOR to digitize,preserve and extend access to Isis.

http://www.jstor.org

This content downloaded from 185.44.79.191 on Sat, 14 Jun 2014 22:59:38 PMAll use subject to JSTOR Terms and Conditions

490 ISIS, XXVIII, z

FOREL was responsible for devising the first workable microtome with a hollow-ground blade, and claimed to have been the originator of the neuron theory. His early work on the anatomy of the brain, his studies in general neurology and psychology, in hypnotism and suggestion, in myrmecology, and his splendid work in the organisation of the alcoholic abstinence movement (The International Order of Good Templars), and in paving the way for the organisation of the League of Nations, are achievements which will assure his name a lasting fame, for those achievements are among the foundation stones of the Twentieth Century, and above them is the spirit of AUGUST FOREL.

New York University. M. F. ASHLEY-MONTAGU.

Mathematische Keilschrift-Texte herausgegeben von 0. NEUGEBAUER.

Erster Teil, Texte, royal 8vo, '935; Zweiter Teil Register, Glossar, Nachtrdge, Tafeln, mit Io Textfiguren und 69 Tafeln, 4to, 1935 Dritter Teil, Ergdnzungsheft, mit einer Textfigur und 6 Tafeln, 4to, 1937. Berlin, SPRINGER, xii, 5I6 p.; iv + 66 p. + plates; viii + 86 p. + plates. This very extraordinary work lists every known mathematical text,

and dates, and transcribes and translates and interprets, all those ne- cessary for getting a comprehensive idea of the mathematical achieve- ments of the Sumerians, Akkadians and Babylonians, in the light of most recent discoveries. The three volumes form three parts of Band 3, of Quellen und Studien zur Geschichte der Mathematik, Astronomie und Physik, Abteilung A, Quellen. The texts date from 2500 to 2oo B. C. while the work of many other scholars in the field has been important, credit for a very large part of the final results is due to the discoveries of NEUGEBAUER during the past decade. In recent years F. THUREAU-

DANGIN, a learned editor of Revue d'Assyriologie et d'Archdologie Orientale, has also published notable material in connection with mathematical texts.

An article surveying many results in Babylonian mathematics, includ- ing some set forth in the first two parts of Mathematische Keilschrnft- Texte (MKT), has been already published in Isis (v. 26, Dec. 1936). MKT III contains complete discussions (p. 1-48) of eleven texts, two in the British Museum and nine in the Yale Collection. Eight of the latter are series-texts and had already received tentative treatment in MKT I and II. New material on table-texts on pages 49-5I is followed (p. 5z-66, 73-75) by very valuable "Nachtrage und Berichtigungen zu MKT I and II." Chapter V is devoted to a glossary of Akkadian words, and of idiograms and Sumerian words, in MKT III as xell as to correc- tions of a similar glossary in the first two parts. Chapter VI (p. 76-80)

This content downloaded from 185.44.79.191 on Sat, 14 Jun 2014 22:59:38 PMAll use subject to JSTOR Terms and Conditions

REVIEWS 49I

is a "Riickblick". NEUGEBAUER finds in Greek mathematics many influences of Babylonian work, and also remarkable underlying methods and theory which arise also in astronomical texts.

As an example of the valuable new material in Chapter IV we may recall the problem in the Louvre tablet (Ao6770) of about 2ooo B. C. (MKT II, p. 40-4I), to find how long it would take for a sum of money to double itself at compound interest, interest being computed at 20 % per annum. The problem is, then, to find x in the exponential equation

(I + 0; 20)X = 2.

The correct result is approximately 3; 48 years; but it was at first believed that the text gave as an answer x = 4-0;2,23,20 3;57,26,40 years. MKT III shows, however, that the text arrives at an accurate result. The reasoning may have been as follows: I ; I 23 < 2 < I ; I24. Hence the portion of a year which must be subtracted from 4 to give the correct result would be

I; I124 - 2 =--- 0; I2,46,40.

I; I24 - I; I23

But the number of months in this portion of a year would be got by multiplying O;I2,46,4o by I2, which gives 2;33,20 months. Hence the error in the first interpretation of the problem was in assuming 0;2,23,20 to be a portion of a year, instead of 2;33,2o as the number of months, to be subtracted from 4 to give the correct answer. This accurate solution of an exponential equation four thousand years ago is surely very extraordinary.

No earnest student of ancient mathematics can afford to be unfamiliar with the material in these remarkable volumes of NEUGEBAUER. Scholars will eagerly await his volumes dealing with Babylonian astronomy, that they may not only have the complete picture of Babylonian mathematics, but also see more clearly what Greek indebtedness to this mathematics may have been. In certain directions it would seem to have been not inconsiderable.

R. C. ARCHIBALD

William Arthur Heidel. - The Frame of the Ancient Greek Maps, 141 pp. American Geographical Society, New York, 1937.

This book discusses the margins of Greek maps, which represented the outer regions of the known world. Early geography was chiefly empirical and covered only a small portion of the earth's surface. The margins of the maps then coincided even in theory with the limits of travel and commerce. But when this primitive geography was con-

This content downloaded from 185.44.79.191 on Sat, 14 Jun 2014 22:59:38 PMAll use subject to JSTOR Terms and Conditions