By Pierre de la Harpe
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In the second and third columns, where he wrote denominators at all, Warner wrote them as 10 and 1 where we might expect them all to be 100, probably because they were intended to be values of f D 10a and g D 100e, respectively. Most of the time, however, he simply omitted them. 10 10 11 10 12 10 13 10 ::: DD DD DD DD 700 100 781 100 864 100 949 100 79 10 81 2 1 2 83 2 85 2 1600 100 99 10 2 1 ::: ::: 20 10 DD Table 31. Warner’s interpolation of Table 30. 36 Thomas Harriot’s ‘Magisteria magna’ 9 Once again Warner has given an easy rule (add 10 to the leading first difference) but without explanation, suggesting that he, or perhaps Harriot, had already worked a number of examples of this kind.
BL Add MS 4395, f. 166. 2 2 2 2 34 Thomas Harriot’s ‘Magisteria magna’ Clearly this is very similar in construction to Harriot’s table for 1C C3R (see Table 13). It is followed in Warner’s manuscript by a similar table for a cubic equation, aaa C 2aa C 3a D 1230; see Table 29. This example was also given by Harriot (see the second row of Table 16). Continued far enough, the table would show that a D 10 is a root of the given equation. aD1 aD2 aD3 aD4 aD5 == == == == == DD 6 DD 22 DD 54 DD 108 DD 190 6 16 32 54 82 4 10 16 22 28 6 6 6 6 6 &c.
As we saw in discussing Harriot’s tables, this first row together with the constant difference in the final column makes it easy to continue such tables as far as required. It is possible to find the first row by extrapolating upwards from the first few calculated values, as Harriot seems to have done in some of his early explorations (see Tables 13 and 15), but Warner also gave rules for writing it down immediately:70 The primes [first terms] of these progressions are given thus first of the squares, the first is the summe of the coefficients, the second is the same, the third the characteristic 2.
Algebres d'Operateurs by Pierre de la Harpe