Ancient Babylonians Tracked Jupiter With Calculus, page 2

a reply to: SLAYER69

Slayer,
Nice post you have here, thank you for putting it up.

I have found the original paper, and its quite good.

Babylonian astronomers tracked Jupiter

And full of great information.
Here is a bit from the supplemental info,

Materials and Methods
Transliterations, translations and photographs of the cuneiform tablets
Cuneiform Texts A-E were transliterated and translated from the original clay tablets
during several visits to the Study Room of the Middle Eastern department of the British
Museum (London) between 2002 and 2015 and from photographs made on these
occasions. All tablets and fragments are identified by registration numbers assigned by
the British Museum (BM). The transliterations were made in accordance with
Assyriological conventions, i.e. logograms are written in capitals, Akkadian phonetic
signs in italics, [x] indicates a sign broken away, [...] a break of unknown length, and ⸢x⸣
a damaged sign. In the translations, missing text is indicated by [...], untranslatable text
by .... Note that the cuneiform notation for sexagesimal numbers lacks an equivalent of
our decimal point. In the transliterations this feature is maintained by separating all digits
by a period (.). In the translations the absolute value of each number, as inferred from the
context, is indicated by separating the digit pertaining to 600 from the next one pertaining
to 60–1 by a semicolon (
and all other digits by commas. Also note that initial and final
vanishing digits are not written in cuneiform. For instance, in line 1 of Text A the number
written as 12 represents 0;12, which stands for 12/60, 1 represents 1,0 = 60, and 9.30
represents 0;9,30 = 9/60+30/602. All displacements of Jupiter in Texts A-E are measured
in degrees (º), but this unit is, as usual in Babylonian mathematical astronomy, not
mentioned explicitly.
Provenance and date of Texts A-E
The tablets on which Texts A-E are written were excavated unscientifically in Iraq in the
19th century, along with thousands of other tablets (16). Even though their exact findspot
is not documented, there is a consensus that the astronomical tablets from these
excavations originate from Babylon, the main center of Babylonian astronomy during the
first Millennium BCE (2, 16). This is confirmed by occasional references to Babylon's
main temple on some of the astronomical tablets (1, 2).
Due to a combination of factors it is impossible to assign very precise dates to Texts A-E.
First, they lack a colophon that might have mentioned a date of writing or the name of a
datable astronomer. Second, they do not mention datable astronomical phenomena. Third,
since they were excavated unscientifically no information about the archaeological
stratigraphy of the tablets is available. However, the range of possible dates is constrained
by the following considerations. First, the computations in Texts A-E employ ecliptical
coordinates, which implies that they were written after the estimated date of introduction
of these coordinates near the end of the fifth century BCE (3). Second, many of the other
tablets from Babylon that deal with mathematical astronomy have been dated. The dates
of these tablets roughly extend from 350 BCE to 50 BCE, while their distribution peaks
between 180 BCE and 100 BCE (1). Texts A-E therefore very likely date from 350-50
BCE, the range of most probable dates being 180-100 BCE.

Supplementary Materials for
Ancient Babylonian astronomers calculated Jupiter’s position from the area
under a time-velocity graph
Mathieu Ossendrijver*

Fascinating piece, with some interesting implications for the history of mathematics.