Curated texts / Math
Math
School and working mathematics from the 3rd to 1st millennium BCE: multiplication and reciprocal tables, squares, field and canal computations, and a gold-alloy problem. Numbers survive machine translation better than words, but the connecting English is an unedited machine draft.
Machine drafts. Every English quotation here is unedited output of an ATF-to-English model, not a scholarly translation. Each card names its source; cards marked machine English only come from sources (eBL) whose transliterations we do not republish.
Reading Babylonian numbers
Mesopotamian scribes counted in base 60 (sexagesimal). Each place is worth 60 times the place to its right, just as each decimal place is worth 10 times. So “1 15” means 1×60 + 15 = 75, and “8.00” (as written in the English below) means 8×60 = 480. The same notation is used for fractions: “30” after the units place means 30/60 = ½. Scribes usually did not mark where the units place was, so “1 15” could also mean 1¼ (1 + 15/60); the reader works it out from context. Base 60 survives in our 60 minutes and 360 degrees. A reciprocal table lists, for each number, the number that multiplies with it to make 60 (or 1): “reciprocal 4 and 15” means 4 × 15 = 60. Numbers such as 7 or 59 have no finite reciprocal in base 60, and the tables mark them as missing.
8 tablets
Canal excavation volumes, dated (UET 5, 856)
UET 5, 0856 · Ur (mod. Tell Muqayyar) · Old Babylonian“37 1/2 ninda, the length, 1/2 ninda, 2 cubits, the height”line 4
Old Babylonian problem text from Ur computing earthwork for a canal, dated by a year name.
Read the tablet →Early Dynastic table of squares (SF 082)
SF 082 · Shuruppak (mod. Fara) · ED IIIa“8.00 (480) (ninda) squared:”line 3.b
One of the oldest known mathematical tables, from Šuruppak (Fara).
Read the tablet →Earth moved for the Takirum canal (UET 5, 855)
UET 5, 0855 · Ur (mod. Tell Muqayyar) · Old Babylonian“soil of the Takirum canal”line 6
Old Babylonian canal problem from Ur, a companion to UET 5, 856.
Read the tablet →Gold alloy computations (RA 78, 41–45 no. 8)
RA 078, 041-045, no. 08 · Mari (mod. Tell Hariri) · Old Babylonian“with 1 1/3 mina 9 (sila3) of gold, 1 5/6 (sila3) of reddish gold”line 11
Old Babylonian calculations from Mari weighing gold and reddish gold.
Read the tablet →Reciprocal table (TMN Ist Ni 374)
TMN Ist Ni 00374 · Nippur (mod. Nuffar) · Old Babylonian“reciprocal 4 and 15”line 4
Old Babylonian school table of reciprocals from Nippur, including numbers that have none.
Read the tablet →A Syrian times table (KTT 069)
KTT 069 · Tuttul (mod. Tell Bi'a) · Old Babylonian“the 30th (time) 9 times”line 10
Old Babylonian multiplication table from Tuttul on the Euphrates.
Read the tablet →Early field and bread arithmetic (AoF 39, 222)
AoF 39, 222 · Zabalam (mod. Tall Ibzaīykh) · ED IIIb“10 top quality ninda breads”line 1.a1
Early Dynastic IIIb computations from Zabalam.
Read the tablet →Barley capacity table (TMN Ist Ni 3741)
TMN p. 338, Ist Ni 03741 · Nippur (mod. Nuffar) · Old Babylonian“3 barig 4 ban2 barley”line 10'
Old Babylonian table of grain capacities from Nippur.
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