The Project Gutenberg eBook of The life of Galileo Galilei, with illustrations of the advancement of experimental philosophy and Life of Kepler, by John Elliot Drinkwater Bethune.

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[200] This was the objection originally made to Newton's "Fluxions," and in fact, Napier's idea of logarithms is identical with that method of conceiving quantities.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:

success very inadeqnate to the zeal
success very inadequate to the zeal

p. 20:

"New method of Guaging,
"New method of Gauging,

p. 23:

the knowlege, if it existed
the knowledge, if it existed

p. 30, note:

to represent terrestial objects correctly.
to represent terrestrial objects correctly.

p. 64:

the palace of the Archishop Piccolomini
the palace of the Archbishop Piccolomini

p. 68:

that ladies ringlets
that ladies' ringlets

p. 69:

For hitherto I have never happened to see the terrestial earth
For hitherto I have never happened to see the terrestrial earth

p. 106:

80 1 50, for any read an indefinitely small.
80 2 44, for any read an indefinitely small.

Life of Kepler

p. 6:

the Earth an icosaedron, the circle inscribed in it will be Venus.
the Earth an icosahedron, the circle inscribed in it will be Venus.

Inscribe an octaedron in Venus, the circle inscribed in it will be Mercury.
Inscribe an octahedron in Venus, the circle inscribed in it will be Mercury.

p. 32:

Butthere are no such means
But there are no such means

p. 48:

the compound ratio of the rectangle of the axes directly, and subduplicatly
the compound ratio of the rectangle of the axes directly, and subduplicately

p. 52:

and was in-intended to illustrate the appearances
and was intended to illustrate the appearances

Ein Calender	Gratz,	1594
Prodromus Dissertat. Cosmograph.	Tubingæ,	1596, 4to.
De fundamentis Astrologiæ	Pragæ,	1602, 4to.
Paralipomena ad Vitellionem	Francofurti,	1604, 4to.
Epistola de Solis deliquio		1605
De stellâ novâ	Pragæ,	1606, 4to.
Vom Kometen	Halle,	1608, 4to.
Antwort an Röslin	Pragæ,	1609, 4to.
Astronomia Nova	Pragæ,	1609, fol.
Tertius interveniens	Frankfurt,	1610, 4to.
Dissertatio cum Nuncio Sidereo	Francofurti,	1610, 4to.
Strena, seu De dive sexangulâ	Frankfurt,	1611, 4to.
Dioptrica	Francofurti,	1611, 4to.
Vom Geburts Jahre des Heylandes	Strasburg,	1613, 4to.
Respons. ad epist S. Calvisiii	Francofurti,	1614, 4to.
Eclogæ Chronicæ	Frankfurt,	1615, 4to.
Nova Stereometria	Lincii,	1615, 4to.
Ephemerides 1617-1620	Lincii,	1616, 4to.
Epitomes Astron. Copern. Libri i. ii. iii.	Lentiis,	1618, 8vo.
De Cometis	Aug. Vindelic.	1619, 4to.
Harmonice Mundi	Lincii,	1619, fol.
Kanones Pueriles	Ulmæ,	1620
Epitomes Astron. Copern. Liber iv.	Lentiis,	1622, 8vo.
Epitomes Astron. Copern. Libri v. vi. vii.	Francofurti,	1622, 8vo.
Discurs von der grossen Conjunction	Linz.	1623, 4to.
Chilias Logarithmorum	Marpurgi,	1624, fol.
Supplementum	Lentiis,	1625, 4to.
Hyperaspistes	Francofurti,	1625, 8vo.
Tabulæ Rudolphinæ	Ulmæ,	1627, fol.
Resp. ad epist. J. Bartschii	Sagani,	1629, 4to.
De anni 1631 phænomenis	Lipsæ,	1629, 4to.
Terrentii epistolium cum commentatiunculâ	Sagani,	1630, 4to.
Ephemerides.	Sagani,	1630, 4to.

Somnium	Francofurti,	1634, 4to.
Tabulæ mannales	Argentorati,	1700, 12mo.