FOOTNOTES:

[199] The meaning of this passage is not very clear: Kepler evidently had seen and used logarithms at the time of writing this letter; yet there is nothing in the method to justify this expression,—"At tamen opus est ipsi Tangentium canone."

[200] This was the objection originally made to Newton's "Fluxions," and in fact, Napier's idea of logarithms is identical with that method of conceiving quantities. This may be seen at once from a few of his definitions,

1 Def. A line is said to increase uniformly, when the point by which it is described passes through equal intervals, in equal times.

2 Def. A line is said to diminish to a shorter one proportionally, when the point passing along it cuts off in equal times segments proportional to the remainder.

6 Def. The logarithm of any sine is the number most nearly denoting the line, which has increased uniformly, whilst the radius has diminished to that sine proportionally, the initial velocity being the same in both motions. (Mirifici logarithmorum canonis descriptio, Edinburgi 1614.)

This last definition contains what we should now call the differential equation between a number and the logarithm of its reciprocal.

[201] Histoire del'Astronomie Moderne, Paris, 1821.

[Corrections.]

The first line indicates the original, the second the correction.

Life of Galileo Galilei

p. [20]:

p. [20]:

p. [23]:

p. [30], note:

p. [64]:

p. [68]:

p. [69]:

p. [106]:

Life of Kepler

p. [6]:

p. [32]:

p. [48]:

p. [52]: