Table arithmétique – Fragment

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Notes on the numerical tables of Table arithmétique (Fragment), Latin 9377, f. 113<ref>Note that both "9377" and "113" are prime. Coincidence?</ref> in the Bibliothèque nationale de France (Paris).

Description of Fragment

The fragment consists of a single sheet of parchment, folded in half, with numerical tables written on both the left and right sides of the inside (flesh-side) of the parchment.


A fascimile of the pages can be viewed at [1]:

outside (reverse of left side)

left side

right side

outside (reverse of right side)

On the left side are 2 columns, each with 3 tables (and each with a cut off table at the bottom. On the right side are 2 columns each with 1 continuous table.


Aspices

0123456789


The Tables

Left Side, Column 1, Table 1

Multiples of 9n (n from 0 to 7) and 17n (n from 8 to 1). Note that exponents of the two factors add up to 8.

1 2 3 4 5 6 7 8 9 transcription factors note
9 7 5 7 5 7 4 4 1 975757441 178 error: missing leading 6, should be 6975757441
6 9 3 _ 4 8 _ 5 7 693048057 9 x 177 error: missing leading 3, should be 3693048057
9 5 5 1 4 3 _ 8 9 955143089 92 x 176 error: missing leading 1, should be 1955143089
1 3 5 _ 7 5 7 5 3 135075753 93 x 175 error: missing a zero, should be 1035075753
5 4 7 9 8 1 2 8 1 547981281 94 x 174
2 9 _ 1 _ 7 7 3 7 290107737 95 x 173
1 5 3 5 8 6 4 4 9 153586449 96 x 172
_ 8 1 3 1 _ 4 7 3 081310473 97 x 17 SUE OCTO PARTIENT


Left Side, Column 1, Table 2

First two roles unsolved. Then, multiples of 16n (n from 0 to 5) and 3n (n from 6 to 1). Note that exponents add up to 6.

1 2 3 4 5 6 7 8 9 transcription factors note
5 6 2 8 9 _ 6 2 5 562890625 58 x 11 x 131
3 6 6 8 7 5 . . . 366875 54 x 587
7 2 9 . . . . . . 729 36
3 8 8 8 . . . . . 3888 16 x 35
2 _ 7 3 6 . . . . 20735 162 x 34
1 1 _ 5 9 2 . . . 110592 163 x 33
. 5 8 9 8 2 4 . . 589824 164 x 32
. 3 1 4 5 7 2 8 . 3145728 165 x 3 SUE 7 PARTIENTES

Left Side. Column 1, Table 3

Then, multiples of 7n (n from 0 to 7) and 13n (n from 8 to 1). Note that exponents add up to 6.

1 2 3 4 5 6 7 8 9 transcription factors note
8 1 5 7 3 0 7 2 1 815730721 138
4 3 9 2 3 9 6 1 9 439239619 7 x 137
2 3 6 5 1 3 6 4 1 236513641 72 x 136
1 2 7 3 5 3 4 9 9 127353499 73 x 135
6 8 5 7 4 9 6 1 68574961 74 x 134
3 6 9 2 4 9 7 9 36924979 75 x 133
1 9 8 8 2 6 8 1 19882681 76 x 132
1 0 ? 0 6 0 5 9 10?06059 77 x 13 4th cell obscures “7”, should be10706059

Background

The numbers are "apices" of early Arabic numbers.

in a table from "Histoire de la Mathematique" by J.E. Montucla, published in 1757

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