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The Life of Galileo Galilei, with Illustrations of the Advancement of Experimental Philosophy / Life of Kepler cover

The Life of Galileo Galilei, with Illustrations of the Advancement of Experimental Philosophy / Life of Kepler

Chapter 44: FOOTNOTES:
By John Elliot Drinkwater Bethune
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About This Book

The text chronicles Galileo Galilei's life and scientific work while tracing the wider shift toward experimental philosophy. It emphasizes his insistence on observation, measurement, and controlled experiment as corrective to scholastic reasoning, outlines his mathematical and astronomical contributions including the application of optical instruments, and contrasts his methods with those of contemporaries such as Bacon. Biographical narrative is combined with analysis of method, descriptions of instruments and discoveries, and discussion of contemporary reception, together illustrating the practical development and influence of inductive, experiment-based natural philosophy.

List of Kepler's published Works.

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.

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