topics: |  history | science | china

Cambridge University Press, 1977, 434 pages

European mechanics

	p. 56-59 gives a succinct history of European developments
	   to contrast it with the Mohist positions of 3d-4th c.

Aristotle: motion was either
    - "natural" - seeking its natural place;
        - local (i.e. terrestrial) motion took place in a linear manner
      		towards the 'natural place' of the object concerned.
	- celestial motions were 'naturally' circular.
    - "violent" motion - compelled by some external force to move in some
	other manner.  Velocity was proportional to the motive power and
	inversely to the resistance of the medium.

antiperistasis (ἀντιπερίστασις): The medium was necessary for the
    continuation of the motion - air rushed in owing to 'horror vacui' behind
    the projectile and sent it further on its way.

Medieval Science

[the antiperistasis theory was subjected to strong crticism from +6th c,
onwards:
Simplicius: impetus or inertia, a special quality, was present in them moving
    body from the outset [Sarton v.1 p.422]
Joannes Philoponus of Byzantine (d. c. 560] also considered that the
    disturbed medium could not possibly be a cause of the projectile's
    flight; it must have a motive virtue which travelled with it.
Ibn bAjjah (fl. 1118 to 1138) perpetuated the views of Philoponus [Avempace
    of the Latins, see Hitti (1) p. 58 Mieli  p. 188, Moody]
John Buridan: impetus gradually fades out; the heavier the body the more
    impetus it could receive.  It would last in perpetuity if it were not
    diminished by the resistance of the medium.
Nicolas d'Oresme (fl. 1348, d.1382) : everything was a continuously varying
    quantity.  anticipated Descartes in the idea of coordinates : longitudo
    and altitudo (or intensio).  ascending st line on graph = uniformiter
    difformis; ascending curve = difformiter difformis.  p.56-57

But it was upto galileo to separate horizontal motion (uniform) from vertical
motion (based on falling body).  Trajectory of a projectile must follow a
parabola, gravity beginning to act as soon as the path is commenced. p.58

 
medieval european concept of projectile motion: 
modus violentus (straight line) modus mixtus (curved) followed by
modus naturalis_ (vertical free fall).  Fig. following Nicholas
Tartaglia (1537) from Renn: Galileo in context, p. 48; see also,
Rene Dugas, A history of mechanics, 1950

by the 15th c. (Leonardo's time), path of a projectile had come to be
imagined as first a violent motion in a straight line (modus violentus),
which after a time, since 'nullum violentum potest esse perpetuum', gave way
to a composite motion (modus mixtus), and finally to a vertical free fall
in accordance with gravity (modus naturalis).  The discovery of parabolic
trajectory by Galileo and gunners was one of the great advances of the early
phase of modern science.  [FN: this conception probably derived from a simple
optical illusion (Ronchi p.3)]

Newton was not the first to state his First Law of Motion: "every body
continues in its state of rest, or of uniform motion in a right line, unless
it is compelled to change that state by forces impressed upo it."  Huygens
and Descartes had said practically the same thing and Galileo had used the
principle though not applying it apart from projectiles.  It is also claimed
that Ibn al-Haitham (965 to 1039) stated the law too.

very similar: Mo Ching - 4th (or 3d) c. :

Cessation of motion (chih) is due to the opposing force of a 'supporting
pillar' (chu)

=> motion is due to the absence of an opposing force ["supporting pillar"]

Propagation of Indian trigonometric concepts to China

The notion of sines and versed sines appears for the first time in the
paulisa sidhAnta shortly after 400.  AryabhaTa (c. +510) was the first to
give a special name to the function and to draw up a table of sines for each
degree.  His contemporary Varahamihira, in the Panca-siddhAntikA (c.+505)
gave formulae which in modern terms would comprise both sines and cosines.

The Indian work was taken over by the Arabs and transmitted to Europe, while
in the other direction Indian monks or lay mathematicians who took service
with the Chinese bureau of astronomy spread the new development farther
east.  Books on Indian astronomical methods were circulating in Chinese well
before +600.  One of these men. e.g. Chiayeh (Kashyapa) Hisao-Wei, assisted
Li Shun-Feng in his calendrical calculations of +665.

By far their greatest representative was the astronomer and mathematician
Chhuthan His-Ta (Gautama SiddhArtha) at the height of his powers when I-Hsing
and Nankung Yueh were busied with their meridian arc.  In +729 he finished
his Khai-Yuan Chan Ching (treatise of the Khai-Yuan reign-period on astronomy
and astrology), a work which still constitutes are greatest surviving
thesaurus of ancient chinese astronomical quotations and fragments.  chapter
104 consists of a translation into Chinese under than name Chiu Chih of the
+6th c. navagraha (nine upholders) calendar system of Varahamihira.  This was
the first occasion in which a zero symbol appeared in a chinese text
[FN. this has been studied by Yabuuchi], but more relevant is the fact that
the chapter also contains a table of sines.  It is typically Indian in that
it tabulates at intervals of 3 deg 45 min, a value derived by repeated
bisection of 60 degrees, the cosine of which was known to be ½.  A half
dozen years latter in the great geodetic survey tables with much smaller
intervals were computed... - p.48-50

see also:
  * The Buddhist Route for Transmission of Days of the Week :
	http://www.cjvlang.com/Dow/BuKong.html
  * Kiyoshi Yabuuchi: THe development of the sciences in China : 4th-12th c.
    	http://www.medievalists.net/files/09012347.pdf