The Sleepwalkers (282 page)

5

Ca.,
p. 119.

6

"Tycho
to
Jessenius,
8.4.1600",
G.
W.
,
Vol.
XIV,
p.
112
seq
.

7

April,
1600,
G.
W.
,
Vol.
XIV,
p.
114
seq
.

7a

He
had
signed,
however,
a
written
undertaking
to
keep
all
information
he
obtained
from
Tycho
"in
highest
secrecy",
i.e.
he
could
publish
nothing
without
Tycho's
consent.

8

9.9.
1600,
G.
W.
,
Vol.
XIV,
p.
150
seq
.

9

9.10.
1600,
G.
W.
,
Vol.
XIV,
p.
155
seq
.

10

28.8.
1600,
G.
W
.,
Vol.
XIV,
p.
145
seq
.

11

F.
Morison, op. cit.

12

Dreyer,
op. cit., p. 386 f.

13

Quoted
by
Kepler
in
Astronomia
Nova,
I
,
Cap.
6.

Part
IV
Chapter
VI.
THE
GIVING
OF
THE
LAWS

1

ASTRONOMIA
NOVA
AITIO
Λ
O
Γ
HTO
Σ
,
sev
PHYSICA
COELESTIS,
tradita
commentariis
DE
MOTIBUS
STELLÆ
MARTIS,
Ex
observationibus,
G.
V.
TYCHONIS
BRAHE.

1a

Astronomia
Nova,
G.
W.,
Vol.
III,
Preamble
to
the
Table
of
Contents.

2

Ibid.,
II, Cap. 7.

3

Ibid.,
Dedication.

4

"It
is inconceivable that a non-material force should be present in a
non-body and should move through space and time," Ibid, I, Cap.
2.

5

Ibid.,
II, Cap. 14.

6

Ibid.,
II, Cap. 14.

7

At
a later stage, however, he reverted to the Ptolemaic position.

8

Altogether,
Tycho
had
observed
ten
oppositions,
and
Kepler
himself
two
(
1602
and
1604).
The
Tychonic
data
which
he
used
were
those
for
1587,
'91,
'93,
and
'95.

8a

"Letter
to
Herwart,
12.7.1600",
G.
W.
,
Vol.
XIV,
p.
132
f.

9

Astronomia
Nova,
II
,
Cap.
18.

10

Ibid.,
II, Cap. 19.

11

Science
and
the
Modern
World
,
Cambridge,
1953
(reprint),
p.
3.

12

Astronomia
Nova,
II
,
Cap.
20,
III,
Cap.
24.

13

Ibid.,
III, Cap. 22.

14

Loc.
cit.

15

The
observer
on
Mars
went
into
action
each
time
Mars
returned
to
a
given
position
in
its
orbit,
i.e.
had
the
same
heliocentric
longitude.
Since
the
sidereal
period
of
Mars
was
known,
the
times
when
this
occurred
could
be
determined,
and
the
different
positions
which
the
earth
occupied
at
these
times
could
also
be
determined.
The
method
yielded
a
series
of
triangles
Mars-Sun-Earth:
MSE
₁
,
MSE
₂
,
MSE
₃
,
where
the
angles
at
S
and
E
were
known
(from
Tycho's
data
and/or
from
Kepler's
previously
established
method
of
approximation).
These
yielded
the
ratios
SE
₁
/SM,
SE
₂
/SM,
SE
₃
/SM;
and
it
was
now
a
simple
problem
in
geometry
to
determine
the
earth's
orbit,
(still
assumed
to
be
circular),
its
eccentricity,
and
the
position
of
the
punctum
equans
.
The
same
method
enabled
him
later
on
to
determine
the
relative
distances
Mars-Sun
for
any
observed
geocentric
longitude
of
Mars.

16

At
the beginning of III, Cap. 33.

17

Table
of Contents, summary of Cap. 32.

18

"At
other
places
[not
in
the
vicinity
of
aphelion
and
perihelion]
there
is
a
very
small
deviation..."
The
passage
implies
that
the
deviation
is
negligible.
This
is
true
of
the
earth's
orbit,
because
of
its
small
eccentricity,
but
not
at
all
true
of
Mars,
with
its
large
eccentricity.

19

That
Descartes
derived
his
theory
of
vortices
from
Kepler
is
probable,
but
unproven.

20

Astronomia
Nova,
III
,
Cap.
40.

21

Loc.
cit.

22

Loc.
cit.

23

To
sum
up,
the
three
incorrect
assumptions
are:
(a)
that
the
planet's
velocity
varies
in
inverse
ratio
with
its
distance
from
the
sun;
(b)
the
circular
orbit;
(c)
that
the
sum
of
eccentric
radii
vectors
equals
the
area.
The
erroneous
physical
hypotheses
played
only
an
indirect
part
in
the
process.

24