Harriot, Thomas - Mss. 6787

11458

[Commentary:

On the left is a table of 'pretend' sines with constant third difference 81.
The final row of the tables is 7240, 600, 405, 81.
The task is to interpolate the table with two new entries between each existing entry, using the formulae calculated in the previous sheets.

n = 3

by hypothesis.
Thus the constant difference in the interpolated table will be

\frac{81}{27} = 3

.
Further calculations give

p = 45

and

p^{2}

for the first new entries after the row beginning 6640. ]

[Translation: ]

n = 3

per hypothesi numero dividendum

[Translation:

n = 3

by hypothesis, the number of parts to be divided.

81 (41)	82 (41v)
83 (42)	84 (42v)
85 (43)	86 (43v)
87 (44)	88 (44v)
89 (45)	90 (45v)

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