The technical concept of “mass” is traced from its medieval origins in theology up to, but not including, Newton's Principia. Building on the advances of the Middle Ages, Kepler conceived, albeit in rudimentary form, the fundamental physical ideas of mass, “inertia,” and gravitational “mutual attraction.” These splendid concepts were later developed and carried forward into Newton's era by several 17th-century natural philosophers. Unlike his three planetary laws, Kepler's physics has long gone unappreciated by the scientific community. Nonetheless, it formed the conceptual foundation for much of classical dynamics.

1.
Eugene
Hecht
, “
There is no really good definition of mass
,”
Phys. Teach.
44
,
40
45
(
2006
).
2.
John
Freely
,
Before Galileo
(
Overlook Duckworth
,
New York, NY
,
2012
), p.
42
.
3.
Edward
Grant
,
The Foundations of Modern Science in the Middle Ages
(
Cambridge U.P.
,
Cambridge
,
1996
), p.
163
.
4.
Max
Jammer
,
Concepts of Mass in Classical and Modern Physics
(
Dover Publication
,
Mineola, NY
,
1997
), pp.
37
48
.
See for instance,
S.
Donati
, “
La dottrina delle dimensioni indeterminate in Egidio Romano
,”
Medioevo
XIV
,
149
233
(
1988
). See also The Stanford Encyclopedia of Philosophy, can be determined at <http://plato.stanford.edu/archives/fall2009/entries/giles/#4>.
5.
Marshall
Clagett
,
The Science of Mechanics in the Middle Ages
(
University of Wisconsin Press
,
Madison
,
1959
), p.
94
.
6.

Conservation of quantity-of-matter led in turn to conservation of mass, conservation of impetus, conservation of quantity of motion, conservation of momentum, conservation of vis viva, conservation of energy, conservation of charge, and so on. As we will see, Buridan's impetus was a conserved quantity—unless diminished by some external agency, impetus was preserved. Buridan posited that God had given the celestial bodies their initial impetus and the unimpeded circular motion of each orb was therefore forever conserved.

7.
Ernest A.
Moody
, “
Laws of motion in medieval physics
,” in
Toward Modern Science
, edited by
Robert M.
Palter
(
The Noonday Press
,
New York
,
1961
), Vol.
1
, p.
220
.
8.
Edward
Grant
,
The Foundations of Modern Science in the Middle Ages
(
Cambridge U.P.
,
Cambridge
,
1996
), p.
95
.
9.
Marshall
Clagett
,
The Science of Mechanics in the Middle Ages
(
University of Wisconsin Press
,
Madison
,
1959
), p.
522
. See also Buridan and the theory of impetus, can be determined at <http://faculty.fordham.edu/klima/Blackwell-proofs/MP_C23.pdf>.
10.

See The Stanford Encyclopedia of Philosophy, can be determined at <http://plato.stanford.edu/entries/albert-saxony/#3>.

11.
Herbert
Butterfield
,
The Origins of Modern Science
(
The Free Press
,
New York
,
1957
). On p.
24
he asserts that in the Middle Ages “mass was used as the measure of the impetus” when in fact it was “quantity-of-matter” that was used and the technical term mass did not yet exist.
12.
Johannes
Kepler
,
Epitome of Copernican Astronomy & Harmonies of the World (1618–1621)
, translated by Charles Wallis (
Prometheus Books
,
Amherst, NY
,
1995
), p.
65
.
13.
Reference 11, p. 90.
14.
Edward
Rosen
,
Kepler's Somnium
(
University of Wisconsin Press
,
Madison
,
1967
). The complete Latin original can be determined at <https://archive.org/stream/joanniskepleria00frisgoog#page/n8/mode/2up>.
15.
Johannes
Kepler
,
Gesammelte Werke
, edited by
Walther
von Dyck
,
Max
Casper
, and
Franz
Hammer
(
C. H. Beck
,
München
,
1938
), p.
145
; in a 1605 letter to Herwart von Hohenburg.
See also
James R.
Voelkel
,
The Composition of Kepler's Astronomia Nova
(
Princeton U.P.
,
Princeton
,
2001
).
16.
Eugene
Hecht
, “
Origins of Newton's first law
,”
Phys. Teach.
53
,
80
83
(
2015
).
17.
William
Gilbert
, On the Magnet, translated by Silvanus Thompson (
1900
) can be determined at <http://www.gutenberg.org/files/33810/33810-h/33810-h.htm>.
18.

Gilbert used the word moles frequently. These entries are usually translated as mass though “chunk,” “body,” “portion,” “quantity,” or “size” would have been less ambiguous. Thus, we find such phrases as “a mass of iron,” “a flaw in the mass,” “a large and long mass,” “a glowing mass,” “the mass was many pounds,” and so on. The Latin version of De Magnete can be determined at <http://www.scribd.com/doc/299316581/Gilbert-De-Magnete-Latino>.

19.
Reference 14, p. 71.
20.
Betty Jo Teeter
Dobbs
,
The Janus Faces of Genius
(
Cambridge U.P.
,
Cambridge
,
1991
), p.
106
.
21.
William
Donahue
,
Selections From Kepler's Astronomia Nova
(
Green Cat Books
,
Santa Fe, NM
,
2008
), p.
45
.
Alternatively see
Johannes
Kepler
,
Astronomia Nova
, translated by William Donahue (
Green Lion Press
,
Santa Fe, NM
,
2015
), p.
3
.
22.
Reference 21, Selections, p. 68.
23.
Alexandre
Koyré
,
Newtonian Studies
(
Harvard U.P.
,
Cambridge, MA
,
1965
), p.
174
.
24.
Bruce
Stephenson
,
Kepler's Physical Astronomy
(
Princeton U.P.
,
Princeton, NJ
,
1994
). This is an exhaustive account of Keplerian planetary mechanics, most of which involved fictitious forces that Kepler was led to concoct, and most of that would prove to be wrong. All of this aside, Stephenson is not much interested in Kepler's contributions to classical physics, and though he mentions several of those insights (e.g., mass) he glosses over them, often dismissively (as on page 6).
25.
Reference 14, p. 218.
26.
Reference 14, p. 71.
27.
Reference 4, Jammer, p. 54, or Ref. 21, Selections, p. 13.
28.

The majority of authors agree with this translation wherein moles are rendered as mass. However, Donahue, Ref. 21, translates it as bulk, as does Alexandre Koyré on page 174 of Ref. 23, though a few lines later he writes “the mass (moles) of the Earth.” And lower down on that page he simply leaves it “to the moles of the body” implying that he is ambivalent. Rosen, Ref. 14, pp. 220 and 221, translates moles as size.

29.
Reference 21, Selections, p. 56: “And this is true, both of the steelyard or lever, and of the motion of the planets: that the weakening of power is in the ratio of the distances.”
30.
Reference 23, p. 175.
31.
Reference 14, note 66, p. 71.
32.
Reference 21, Selections, p. 16.
33.
Reference 14, note 76, p. 73.
34.
Reference 4, Jammer, p. 56.
35.
Reference 15, Vol. III, p. 242.
36.
Rene
Dugas
,
A History of Mechanics
(
Dover Publications
,
Mineola, NY
,
1988
), pp.
108
119
.
37.
Reference 4, Jammer, p. 55.
38.
Reference 14, note 9, p. 161.
39.
Reference 4, Jammer, p. 57.
40.
Benjamin
Worster
,
Compendious and Methodical Account of the Principles of Natural Philosophy
, 1st/2nd ed. (
Stephen Austen
,
St Paul's Church-Yard
,
1722/1730
), p.
ix
. Writing in English the author provides us with “The true Doctrine of Gravity,” as per Kepler. Worster essentially paraphrased nine of Kepler's various brilliant insights concerning gravity. The book provides a detailed presentation of Kepler's physics of gravity as if it were common knowledge, this at a time when Sir Isaac was still alive. If a reader of this essay had doubts about the influence of Kepler's physics this should go some way to assuage them. Interestingly, Worster translated the Latin moles as Quantity of Matter and did not use the word mass anywhere in the book. That was common for several decades after the Principia, probably because Newton himself favored the term quantitas materiæ.
41.
See Hooke's published lectures of 1679, can be determined at <https://archive.org/details/LectionesCutler00Hook>.
42.
Klaas
Van Berkel
,
Isaac Beeckman on Matter and Motion
(
Johns Hopkins U.P.
,
Baltimore
,
2013
), p.
127
.
43.
Reference 42, p. 128.
44.
Rene
Descartes
,
Principles of Philosophy
(1644), translated by V. R. Miller and R. P. Miller (
Kluwer Academic Publishers
,
Dordrecht
,
1991
), p.
41
. For an earlier exposition of some of this material, see Descartes's The World or Treatise on Light (1629–1633), can be determined at <http://www.princeton.edu/~hos/mike/texts/descartes/world/worldfr.htm>.
45.

The confusion regarding Descartes and quantity of motion is remarkably commonplace; see P. Damerow, G. Freudenthal, P. McLaughlin; J. Renn, Exploring the Limits of Preclassical Mechanics (Springer-Verlag, New York, 1991). This is a fine erudite discussion of pre-Newtonian mechanics, but their treatment of mass (which does not even appear in the index) is superficial. On page 76, they say that they can equate Descartes's volume-based quantity-of-matter with mass and then they write “∣mv∣, is explicitly stated and argued by Descartes…” who, in all fairness, never stated it, nor argued it. See also Gerald Holton, Thematic Origins of Scientific Thought Kepler to Einstein (Harvard U.P., Cambridge, 1973), p. 59. Holton quotes Dijksterhuis who also wrongly takes Descartes's “quantity of motion” as “the product of mass and velocity.” Reference 4, Jammer, p. 10, also mistakenly says that Descartes's term “force” is “mass times velocity.” Descartes simply didn't use the word mass; for him “The Universe is a machine in which there is nothing at all to consider except the shapes and motions of its parts.”

46.
Reference 42, p. 79.
47.
N. R.
Hanson
,
Patterns of Discovery
(
Cambridge U.P.
,
London
,
1961
), pp.
45
and
188
.
48.
Pierre
de Fermat
,
Oeuvres
, edited by
P.
Tannery
and
C.
Henry
(
Gauthier-Villars
,
Paris
,
1894
), Vol.
2
, p.
36
. See also Ref. 4, Jammer, p. 92.
49.
Max
Casper
,
Kepler
(
Collier Books
,
New York
,
1962
), p.
142
.
50.
Reference 45, Holton, p. 88, note 12.
51.
Reference 45, Holton, p. 89, note 13.
52.
Reference 4, Jammer, p. 62.
53.
Isaac
Newton
,
The Principia
, translated by I. Bernard Cohen and Anne Whitman (
University of California Press
,
Berkley, CA
,
1999
).
54.
Reference 23, p. 177.
55.
The Latin original of Theoricae mediceorum planetarum ex causis physicis deductae can be found at <https://archive.org/details/bub_gb_-a1tAxwj5lcC>.
56.
Reference 4, Jammer, p. 63. An English translation of De vi centrifuga can be determined at <https://www.princeton.edu/~hos/mike/texts/huygens/centriforce/huyforce.htm>.
57.
Richard
Westfall
,
Never at Rest
(
Cambridge U.P.
,
Cambridge
,
1987
), p.
94
.
58.
Thomas
Streete
,
Astronomia Carolina
(
Gale ECCO
,
London, England
).
59.
Reference 45, Holton, p. 89.
60.
A.
Rupert Hall
,
From Galileo to Newton
(
Dover Publications
,
New York, NY
,
1981
), p.
282
.
61.
Reference 53, p. 100.
62.
Reference 23, p. 69.
63.
Reference 23, p. 70.
64.
William F.
Magie
,
A Source Book in Physics
(
Harvard U.P.
,
Cambridge, MA
,
1963
), pp.
52
55
. Also see Ernst Mach, The Science of Mechanics (Open Court Publication, Co., La Salle, IL, 1974), p. 365.
65.

Colin Maclaurin (1698–1746), who was a protégé of Newton, wrote “An Account of Sir Isaac Newton's Physical Discoveries,” which was likely started while Newton was still alive. After a discussion of the history of astronomy he went on: “But to return to Kepler, his great sagacity: continual meditation on the planetary motions, suggested to him some views of the true principles from which these motions flow.” Maclaurin then outlined Kepler's physics and respectfully corrected it where appropriate. Extending Kepler's concept of inertia, Maclaurin wrote about the “passive nature or inertia” of a “body” resisting changes in its state. Matter was seen to be inherently “passive,” resisting all change, in rest and in motion. Maclaurin maintained that inertia “being always proportional to the quantity of matter in the body; insomuch that it is by this inertia only we are able to judge of the quantity of matter.” Recall Kepler's words, “Inertia or opposition to motion is a characteristic of matter; it is stronger, the greater the amount of matter…” Maclaurin leaves little doubt that Kepler's ideas on mass (quantity-of-matter), gravity, and inertia, reverberated across the 17th century.

66.
Eugene
Hecht
, “
On defining mass
,”
Phys. Teach.
49
,
40
44
(
2011
).
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