9749
[Commentary:
The tables on this folio appear to have been begun at the top left
but then re-started and continued along the right-hand edge.
The tables are calculated in turn for 1, 2, 3, 4, 5, 6 throws of a die.
Take, for example, the fourth table, for four throws of a die.
The first row indicates that the combination 1111 can occur in only one way.
The next two rows indicate how many ways only 1 and 2 can occur, distributed as either 3 + 1 (thus, 1112, 1121, 1211, 2111, 2221, 2212, 2122, 1222), that is, ways in total, or as 2 + 2 (thus, 1122, 1212, 1221, 2112, 2121, 2211), that is, 3 + 3 = 6 ways in total. These two calculations are shown in full on Add MS 6782 f. .
The fourth row indicates how many ways only 1, 2, and 3 can occur, with any one of them appearing twice (thus 1123, 1132, 1212, 3112, ...), that is, ways in total. Further details of the calculation are shown on Add MS 6782 f. .
The fifth and final row indicates how many ways 1, 2, 3, 4 can appear, that ways in total.
All the other tables are calculated in a similar way. Several of the calculations can be seen on Add MS 6782 f. .
Below the line (still reading the page sideways) are two further tables; for the continuation of these, see Add MS 6782 f. .
Harriot also includes some brief notes to explain how the tables have been ]
The tables are calculated in turn for 1, 2, 3, 4, 5, 6 throws of a die.
Take, for example, the fourth table, for four throws of a die.
The first row indicates that the combination 1111 can occur in only one way.
The next two rows indicate how many ways only 1 and 2 can occur, distributed as either 3 + 1 (thus, 1112, 1121, 1211, 2111, 2221, 2212, 2122, 1222), that is, ways in total, or as 2 + 2 (thus, 1122, 1212, 1221, 2112, 2121, 2211), that is, 3 + 3 = 6 ways in total. These two calculations are shown in full on Add MS 6782 f. .
The fourth row indicates how many ways only 1, 2, and 3 can occur, with any one of them appearing twice (thus 1123, 1132, 1212, 3112, ...), that is, ways in total. Further details of the calculation are shown on Add MS 6782 f. .
The fifth and final row indicates how many ways 1, 2, 3, 4 can appear, that ways in total.
All the other tables are calculated in a similar way. Several of the calculations can be seen on Add MS 6782 f. .
Below the line (still reading the page sideways) are two further tables; for the continuation of these, see Add MS 6782 f. .
Harriot also includes some brief notes to explain how the tables have been ]
11112 variatur
[Translation: 11112 may be varied ]
[Translation: 11112 may be varied ]
conversionem, 22221.
[Translation: conversion, as ]
[Translation: conversion, as ]
transpositionem,
11112,
11121,
11211,
12111,
[Translation: transposition,
11112,
11121,
11211,
12111,
]
11112,
11121,
11211,
12111,
[Translation: transposition,
11112,
11121,
11211,
12111,
]
coniugationum ut supra
sunt 2 ex 6; sunt 15ies
[Translation: conjugation, as there are 2 out of 6, there are 15 ]
sunt 2 ex 6; sunt 15ies
[Translation: conjugation, as there are 2 out of 6, there are 15 ]
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