Harriot, Thomas - Mss. 6782

552276

[Commentary:

Powers of

(b + c)

up to

(b + c)^{5}

. Each power is calculated from the previous one by multiplication.
Note the use of cossist

r

for a first power,

z

for a square,

c

for a cube,

z z

for a square-suare or fourth power,

ßß

for a sursolid or fifth power.
Below the main table is a list of the final sums, including the sixth power (

z c

), which has not been calculated on this page but which can be deduced from the pattern for the previous cases.
For a similar table see Add MS f. . ]

Forma generationis continuegenerandi figurata
proportionalium ab unitatein binomia radice
per logisticen speciosam:
ad demonstrandum pro parte alium
in numeris analysin.
[Translation: A method of generating figurate numbers from binomial roots in ]

Nota: pro
[Translation: Note: for the ]

Species partium
unius cuisque potentiæ
sunt continue proportionales
ut

c

b

[Translation: The case of a single part where the powers are in continued proportion as

c

b

. Et in numeris, sunt
termini minimi si

c

b

sunt primi &c.
et non in
ratione

[Translation: And in numbers, these are the lowest terms, if

b

and

c

are the first,
and they are not multiplied by some ]

511 (256)	512 (256v)
513 (257)	514 (257v)
515 (258)	516 (258v)
517 (259)	518 (259v)
519 (260)	520 (260v)

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