Basic Mathematics

Author(s): L C Jain
Publisher: Rajasthan Prakrit Bharti Sansthan Jaipur

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whose rudimentary forms have already been attested in numerous economic texts (table and problem) from the earliest phases of written documents (about 500,000 cuneiform tablets) found in the ruins of Mesopotamia and Nippur. The table texts on the tablets have vocabularies basic to scribal instructions and indispensable for the mastery of the secrets of cuneiform writing in Akkadian and in Sumerian. The problem texts mixed with those of weights & measures (c.-2500) were needed for routine matters. This is the western region of the Tigris and Euphretes rivers where civilization cropped up since -5700. The people preserved their learning in baked earth found in forms of circular, cylindrical and prismatic tablets. Agriculture was the base of their civilization requiring a calendar, year beginning from vernal equinox. The Babylonians learnt from the Sumerians the measures based on sexagesimal, which also contained the partial decimal system; ten, perhaps from fingers, and six, perhaps from simplicity of manipulating fractions.
From -- 2000, their tables of arithmetic contained not only multiplication but also squares, cubes and square-roots. The tables of n3+n? were needed for n from 1 to 30, proving their tendency towards functionality, with observation and proof. Equations were partially solved in forms of x3 +ax? +b=0, through the tables. They could also solve linear equations in ten unknowns. They could also find out areas of rectangles, rightangled triangles etc., and the value of 77 was denominated as 3. For irrigation purposes the inhabitants could solve the problems for volumes of right circular cylinders and prisms. They knew that the angle in the segment of semicircle is right angle, that in a right angle the hypotenuse square is equal to the sum of squares of its base and perpendicular and that the corresponding sides of right angled triangles are proportional. Arithmetical concept "ratio" had a special term. The value 7 3 does not appear to be attested in the preserved literature of this period. After this no more progress is available here as it seems.
(b) Egypt :
For Neugebaur finds Egyptian34 ancient the most pleasant, without excessive development of Greek heroism, spared from struggles, full of pyramids and agricultural culture. This is the gifted plain of the Nile, with records of archaeology from-4000 to-2781. A calendar (c.-4241) represents 12 months of 30 days each, to be added by five days for completion of a year. The records could be preserved in the desert's climate through papyri. The Egyptians had to wait with their old
34. Cf. ibid., pp. 71 et, seq.
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