Harriot, Thomas, Mss. 6785

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31
31 (16)
32
32 (16v)
33
33 (17)
34
34 (17v)
35
35 (18)
36
36 (18v)
37
37 (19)
38
38 (19v)
39
39 (20)
40
40 (20v)
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16583
[Commentary:
A generalization of Pascal’s triangle,showing the results of multiplication by a and by 3 (see also Add MS 6782 f. ).
Note that in the third table, the entry 34,a12 on the diagonal, for example, is to be read as 3×4a1×2 and similarly for the other entries.
In the lower part of the page are general formulae for the rows, similar to those that Harriot derived elsewhere for the standard version of Pascal's triangle.
See also page 2 of the 'Magisteria' (Add MS f. ).
]
Æquipollentia ex utraque
parte diagonalis perse

[Translation: Equality (or symmetry) on either side of the diagonal is shown by ]

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