Page:Popular Science Monthly Volume 75.djvu/497

Rh 1.21, $$\textstyle\overline{10^2}$$ as 1.36, $$\textstyle\overline{20^2}$$ as 6.40—naturally all in cuneiform characters. The only possible interpretation of this is that the 1 in the left hand place stands for 60. The table of cubic numbers bears out this interpretation as $$\textstyle\overline{30^3} = 27{,}000$$ is given as 7.30, meaning $$7 \times 3{,}600$$ or $$7 \times \textstyle\overline{60^2} + 30 \times 60 = 25{,}200 + 1{,}800$$ which makes the total of 27,000. Up to date no documents have been found which show the presence of the zero in this system. Even though a zero, and with it thus a full place system, had existed the unwieldiness of the large base would have operated against a universal adoption of the system; a number system must be adapted to child mind.

Our division of the day into 24 hours is probably a heritage from the Babylonians; the division of the hour and minute into sixty parts is certainly a survival from this hoary system. So also the division of the arc of the circle into 360° and the further subdivisions have come to us from this extinct civilization. Greek astronomers and through them all European astronomers borrowed much from the same source, and for over fifteen hundred years of the Christian era sexagesimal fractions were used in all arithmetical computation. The first tables of trigonometric functions were on the basis of a radius of 600,000, later 6,000,000, finally to be discarded by Regiomontanus in 1470 for the base 105, later for 1015, and then by the great Vieta, in 1579, for the base one with decimal values.

It is entirely within the bounds of possibility that the first development of the Hindu, commonly called Arabic, place system was due to some oriental scholar who was familiar with the writings of these ancient Babylonians. Abundant testimony exists tending to prove the communication between Europe and the east. Having special symbols, such as existed in India for 1, 2, 3, 4, 5, 6, 7, 8 and 9 as early as the second century, acquaintance with this advancement of the Babylonians may have suggested the step to a decimal place system and the innovation of a zero. The existence of a Babylonian zero symbol would strengthen this hypothesis; even a blank space may have been the first symbol.

The Egyptians were in possession of a complete decimal system, with separate symbols for 1, 10, 100, 1,000, 10,000 and higher powers of 10. The famous Papyrus Rhind of the British Museum gives us a practically complete Egyptian arithmetic. The striking peculiarity of their arithmetic consisted in the work in fractions which was confined almost entirely to unit fractions. The Ahmes Papyrus of date about 1700 B.C. gives a table for a conversion of fractions from to  into unit fractions. The tremendous inertia of even the clumsiest system once established is seen in the fact that Greek manuscripts of date 700 at least 2,200 years later, contain this same bungling system of fractions. Aside from this malign influence European arithmetic was not affected by the Egyptian.