8744r
[Commentary:
The reference to Bernardus Tornius Florentinus is to his commentary De motu locali of William Heytesbury (c. 1313–1372/3). The text of Tornius is found as the seventh treatise in William Heytesbury, De sensu composito et diviso
(Tornius , 73v–77v.
The reference to Alvarus Thomas is to his Liber de triplici motu (Thomas .
The texts of both Alvarus and Tornius are verbal, expressed in terms of repeated proportions. Harriot converts their results into arithmetic notation, and in doing so shows how to find sums of some infinite series that are not simple geometric progressions.
His first example (from Tornius) . Harriot shows how this can be treated as the sum of infinitely many other series, each of which is a simple geometric progression, namely:
,
,
,
. The sums of these series form a new geometric progression .
The other two series on the page (from Alvarus) are summed in the same ]
The reference to Alvarus Thomas is to his Liber de triplici motu (Thomas .
The texts of both Alvarus and Tornius are verbal, expressed in terms of repeated proportions. Harriot converts their results into arithmetic notation, and in doing so shows how to find sums of some infinite series that are not simple geometric progressions.
His first example (from Tornius) . Harriot shows how this can be treated as the sum of infinitely many other series, each of which is a simple geometric progression, namely:
,
,
,
. The sums of these series form a new geometric progression .
The other two series on the page (from Alvarus) are summed in the same ]
Bernardus Tornius Florentinus
in doctrinam Heytisberi de
motu locali. pag. 77
conclusio
[Translation: Bernard Tornius Florentinus, in his teaching on Heytesbury's De motu locali, page 77, third ]
in doctrinam Heytisberi de
motu locali. pag. 77
conclusio
[Translation: Bernard Tornius Florentinus, in his teaching on Heytesbury's De motu locali, page 77, third ]
Alvarus Thomas.
2 conclusio. pag.
[Translation: Alvarus Thomas, Conclusion 2, page ]
2 conclusio. pag.
[Translation: Alvarus Thomas, Conclusion 2, page ]