Dicks, D. R._solstices, Equinoxes, & the Presocratics_JHS, 86_1966!26!40

8/9/2019 Dicks, D. R._solstices, Equinoxes, & the Presocratics_JHS, 86_1966!26!40

1/16

Solstices, Equinoxes, &the PresocraticsAuthor(s): D. R. DicksSource: The Journal of Hellenic Studies, Vol. 86 (1966), pp. 26-40Published by: The Society for the Promotion of Hellenic Studies

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2/16

SOLSTICES,

EQUINOXES,

&

THE

PRESOCRATICS

Diog.

Laert.ii

I

(DK

12AI),

['Avac44iav3por]

1pEV

SE

Kat

yV&LOVa

TpWOTO&

c'

EcTT7)TEV

r

e

M

it6aV

KLOn7oPf

oV

ErVeAaKESa&locs

Kaao

th

iniafwpvos

v

HacvTmo&nts

sTopl,

TofThe

TE

Kcr

atic•LEpasa

aratlvovTa, KalWpO

sKOs

aEt

KaTEoKEvaTaE.

Eusebius,

E x

14.I11

DK

12A4),

ohrog

'Ava

'Ptavypos]

7TpcTo

yvmo

ovae

KaCoraKEvaer

TrpOS

LyrVWUcV

pOTiW

tE

n

CuV

Kart

Xdy•oV

Kat

•;pV

Kat

"t'lrEpxase.

Suda,

s.v.

(DK

12A2),

rpjros

SE

['Ava4'lav3pos]]

gLEpt'av

PE

Ka1

oTraO

Ka%

opoAoyE^Za,

Kal

T77V

yrjv

Ev

rLEOtTaTKW

KE•cTaGLC.

VWLOvarE

E•Uc?7yayE

Kal

OAw

yE•wolETpiaS

oTzroTVITWaw'

Etev.

The

literature

s

now

full

of

references o the

scientific

achievements

so-called)

of

the

Presocratics,

nd

the

earlier

the

figure

(and

consequently

he less

information f

reliable

authenticity

we

have

of

him)

the more

enthusiastically

o scholars

enlarge

his

scientific

knowledge-a

proceedingwhich,

of

course,

has

plenty

of

precedent

mong

he

doxographers

and

commentatorsf

antiquity.

The classic

xample

s

Thales,

whomI have discussed

n

an

earlierarticle;' t is chastening buthardlysurprising)o findthattheviewsthereexpressed

have

had

very

ittle

influence n

the

traditional,

astly

exaggerated

stimate f

Thales

as

the

founder

of

Greek

mathematics nd

astronomy

nd

the

transmitter

f

ancient

Egyptian

and

Babylonian

wisdom.

Professor

Guthrie,

n a

work

obviously

destined o be

the

standard

English

textbook

on

early

Greek

philosophy

or decades

to

come,2

can still

say

(p.

58)

'.

.

according

o

an

unchallenged

radition,

Thales]

had himself

visited

Egypt'

(my

italics),

despite

my

demonstration

hat

nowhere

n

the

primary

group

of sources

s

Thales'

name

linked with

Egypt,

and

that

the

whole

story

of his

introducing

Egyptian

mathematical

knowledge

o

the

Greeks

s a

mere

invention

(probably

by

Eudemus)

based

on

separate,

unrelated

tatements

by

Herodotus.3

One

must,

however,

be thankful

hat

the

uncritical

acceptance

f

Thales'

alleged

prediction

f a

solar

eclipse

s

now discountenanced.4

Thales is

not

the

only Presocratic hilosopheror whomextravagant laims

are made

concerning

cientific

knowledge

which can

belong

only

to the

post-Platonic eriod.

One

of the chief

difficulties

which

should

by

now

be

well

known,

but which still

needs

empha-

sising)

n

attempting

o

reconstruct nd

evaluate he ideas of

the earlier

Presocratics

ies,

of

course,

n

the

unsatisfactory

ature

of the

ancient

evidence;

I

have

already

expatiated

on

this

point

n

the

article

mentioned

above,

and mostof

the

standard

extbooks

nclude

ntro-

ductory

discussions

f the

doxographical

ources,5

ased

ultimately

on Diels'

monumental

Doxographi

raeci.

Unfortunately,

ecauseof

the

numerous,

rbitrary scriptions

f

various

elementary

cientific

doctrines

such

as

the

spherical

universe,

he central

position

of the

earth,

ts

sphericity,

he

obliquity

of the

ecliptic,

the

division

of the

zodiac,

etc.)

to

many

different

hinkers

anging

ndiscriminately

romThalesto

Anaxagoras,

hat are

to be

found

in

the

sources,

nd

the

garbled

and

often

contradictory

ccounts

given,

it remains

rue

that

by

a

judicious

selection

and

the

omissionof

inconvenient vidence

practically

any

doctrine

can

be

attributed

o

any

of the

Presocratics n

some

ncient

'authority',

o

suit

a

particular

scholar's

wn

favoured

heory.6

Thuswe

have

Cleostratusrom

time to time resurrected

s

the

first

allegedly

o

introduce

he zodiac

and

the

zodiacal

signs

nto

Greece,

and

the first

1

CQ ix

(1959)

294-309.

2

W.

K.

C.

Guthrie,

A

History of

Greek

Philosophy--

Vol.

i,

C.U.P.

1962.

3

CQ

ix

(1959)

304.

4

Guthrie,

op.

cit.

47-9.

5

E.g.

Heath

(Aristarchus

of

Samos),

Burnet,

Kirk &

Raven, Guthrie-cf. 299 f. of my article.

6

In

this

connexion,

Kirk and

Raven's

sensible

remark

deserves

to

be

quoted

(The

Presocratic

Philosophers, p.

7),

'Thus

it is

legitimate

to feel

com-

plete

confidence in our

understanding

of a

Presocratic

thinker

only

when

the Aristotelean

or

Theophrastean

interpretation,

even

if

it

can

be

accurately

recon-

structed,

is confirmed

by

relevant

and

well-authenti-

cated extracts from

the

philosopher

himself'-a

counsel of perfection which one can hardly expect to

be

exemplified

in their

own

book.

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3/16


4/16

28

D.

R.

DICKS

or

astronomical

text,

and

the

method

commonly

used

to denote

the size of

an

angle

was

to

express

it as the

fraction of

a

right-angle

or of

a

whole

circle or of

a

zodiacal

signl5-thus

Aristarchus

in his

On

the

Sizes

and

Distances

of

the Sun

and

Moon"6

ives

as one of

his

hypotheses

that

'the

moon subtends

I/i

5th

part

of a

zodiacal

sign',

and Archimedes

in the

Sand-Reckoner

states

that he

found that

the

angle

subtended

by

the

diameter of

the

sun was less

than

i/i64th

part

and

greater

than

I/2ooth

part

of a

right-angle."7

Not

only

is the

36o0

division

not found before

the

second

century

B.c.,

but we are

explicitly

told

of other

divisions of

the

circle

which were in

use-e.g.

Strabo

( 13-14)

tells

us

that Eratosthenes

(who

died about

the

time that

Hipparchus

was

born)

divided the

equator

into

sixty

parts,

and

Cleomedes

(cycl.

theor.

Io ?50--p.

92,

ed.

Ziegler)

says

that

Posidonius

divided the

ecliptic

into

forty-

eight

parts.18

For

his

measurement of the

obliquity

of

the

ecliptic,

Eratosthenes

seems

even

(on

one

interpretation

of the

evidence)

to

have

used an instrument

graduated

into

83rds.1"

Thus

the

attempt

to

backdate

the

36o0

division of the circle to

the sixth

century

B.c.

not

only

ignores

the

historical

origin

of the

concept,

but also

disregards

the

scanty

evidence

we

have

from Greek

sources.

The

second of

the

two

pitfalls

mentioned

above

is

a

much

less

obvious

one

and

much

15

This

holds

good

for'all

the

extant

works

of

e.g.

Autolycus, Euclid,

Aristarchus,

and

Archimedes.

There

is,

however,

one

piece

of evidence

which

might

seem at

first

sight

to

suggest

that the

use

of

degrees

was

known

in

the

third

century

B.C. in

Alexandria;

in

Almag.

vii

3

Ptolemy

lists

the

declinations of a

number

of stars

as

observed

by

himself,

by

Hipparchus,

and

by

Timocharis and

Aristyllus,

two

Alexandrian astrono-

mers who

were

active

between

295

and

280

B.C.,

and

in

each

case

Ptolemy

gives

the

data

in

degrees

north

or south

of

the

celestial

equator.

This

appears

to

contradict

our

other

evidence

(cf.

A.

Pannekoek,

A

History of Astronomy, i96i,

124

ad fin.) which all

points

to the

late

introduction of

the

36o0

division of

the

circle,

not

before the

second

century

B.c.

Yet,

if

degrees

were in

use

at

the

time

of

Timocharis

and

Aristyllus,

why

did

not

Aristarchus

and Archimedes

use them

instead of

clumsy

circumlocutions

involving

fractions of

a

certain

segment

?

The

latter at least had

close

connexions

with

Alexandrian

scientists

including

Eratosthenes

(cf.

Heath,

The

Works

of

Archimedes

xvi),

who

likewise

did

not

use

degrees

(see below).

It is

hardly

conceivable

that

Aristarchus,

for

example,

would

have

chosen

to

say

that at

quadrature

the

moon's

distance

from

the

sun is

'less than

a

quadrant

by

one-thirtieth of

a

quadrant' (giaaarov

TeapTr~Uoptov

tx

OTOi

TeTapTffyoptov

tptaKooaCT)

if

he

could have

expressed

exactly

the

same

meaning

by

'870'

(,oitpa;

:T7).

Either

we

must

assume

that

Timocharis and

Aristyllus

knew and

used

the

circle

graduated

into

360o

but that

this

was

not

taken

up by

scientists

again

until

Ioo

years

later-which in

view of the

obvious

convenience

of

the

usage

seems

incredible;

or

(and

this

is

the

most

likely

explanation)

it

was

Ptolemy

who

tacitly

converted the

observations of

Timocharis and

Aristyllus

(originally

given

in

the

customary

fractions

of a

segment)

into

degree

figures

in

order to make

clearer

the

comparison

with his

own and

Hipparchus'

results. It

is

noteworthy

that

Ptolemy emphasises

the inaccuracy of these earlier observations, which he

characterises

as

oi'Te

d6iaTaGKTot

ix"'

i'~:EEtpyaaqtdvat

(Almag.

vii

I-ed.

Heiberg,

ii

3,

4)

and nadvv

6A2oaepci

eAni/i

vat

(id.

vii

3-18,

3).

16

Ed.

Heath,

Aristarchus

of

Samos

352.

17

?I6,

ed.

Heiberg,

ii

226.

18

Cf. Bouch&-Leclercq,

L'astrologie

grecque,

1899,

6o

n.

2;

of the other divisions

he

mentions,

that

into.

144

parts

(Sext.

Emp.,

adv. astrol.

?9

=

adv. math. v

?9)

is

simply

a

variant

used

by

some

of the

Chaldaean

astrologers,

most of whom Sextus makes

clear used

the

360'

division

(i.e.

12 zodiacal

signs

of

30o

each),

for

a

particular

astrological

doctrine.

A division

into

eight parts,

cited

by

Bouch&-Leclercq

(279

n.

2)

from

Hyginus, astron. iv

2,

is merely a method of avoiding

fractions to

express

the

ratio

of

the

longest

day

to

the

shortest

night

at the summer

solstice,

i.e.

5:3

(equivalent

to

a

latitude

of

36'52',

where

at

the

summer

solstice five

parts

of

the sun's diurnal

circuit

would

be above the horizon

and three

parts

below),

instead

of

71:41

on

a

division

of

the circle into

twelve

parts;

it cannot

be taken as evidence

for a

commonly-

used division

of the circle into

eight.

Bouch&-

Leclercq

also cites

(475

n.

2)

a

division of the

zodiac

into

365

parts

from

Censorinus,

frg.

2

(not 3,

as

in

the

citation),

5

(p.

57,

ed.

Hultsch);

but

Censorinus'

account

(which,

anyway,

mentions

the

360o

division)

is

very garbled-he evidently

confuses zodiacal

signs,

which

are

equal

segments

of

300

each,

with

zodiacal

constellations,

which

are

of

unequal

size,

since

he

talks

of

'signa

.

.

quorum

quaedam

minora,

quaedam

ampliora',

and

then

goes

on

to

say

'sed

conpensatio

in

quinque partes

creditur

adplicari,

ut sint

omnes

signiferi

partes

CCCLXV',

apparently

a

muddled

reference to the

fact

that the

sun

takes

365

days

and

a

little

more to

traverse the full

circle. It should

be

noted that

Bouch&-Leclercq

was

writing

before our

understanding

of the

methods

of

Babylonian

mathe-

matics

and

astronomy

and their historical

interaction

with Greek

knowledge

had reached its

present

(still

imperfect)

stage.

19

For a full discussion, see my GeographicalFrag-

ments

of Hipparchus

167-8.




5/16

SOLSTICES,

EQUINOXES,

AND THE PRESOCRATICS

29

easier to

fall

into. It consists of a failure

to

recognise

the tacit

assumptions,

based on

the

scientific

theory

of late

antiquity

or even

(sometimes)

of our own

times,

that underlie so

much

of the

writing

about

early

Greek

science-assumptions

for which there

is no

evidence,

but

which

are

almost

unconsciously

made from our

inability

to dissociate our views on

the

thought

of this

early

period

from more modern

concepts.

It

requires

a considerable effort

of

imagination

to

try

to

envisage

a world without clocks and

watches,

with no universal

standards of

measurement,

where the

only

sources of

power

in

use

were

bodily

muscles

and

the

wind,

and where no

systematic

attempt

was ever made to

exploit

and control

the

forces

of

nature.

Conditioned as we are

by

over

300

years

of scientific

discovery,

by

which

the

circumstances

and

habits of

human

life and

thought

have

been ever more

radically

in-

fluenced,

we

find it

very

difficult to

understand a

world where

science

played

in

effect

a

very

insignificant

part.

This

is,

of

course,

one of

the

perennial

fascinations

of

the

study

of

ancient

civilisations-but it

has

its

dangers.

Not the least of these is

the

temptation

to

try

to

reason

backwards

from

a

later

standpoint

in

our

efforts to

trace

the

early development

of

scientific

ideas,

for this

process

almost

inevitably

involves the

making

of

tacit

assumptions

that

are

in

reality

completely

foreign

to the

early

stage

in

question, according

to the

available

evidence,

but are not recognisedas such. The classic example is, of course, Aristotle's account of the

opinions

of the

Presocratic

thinkers;20

another

example,

I

believe

to

have

shown,21

is

Eudemus' account of the

beginnings

of

geometry.

Modern

examples

are

too

numerous to

cite

in

detail;

no

dispassionate

reader can fail

to admire

the

ingenuity

of

the

gallant attempts

to

make

some sort of

scientific

sense out

of

the

confused,

and often

primitive,

astronomical

notions of the

Presocratics,

but

he

should also

notice

the

ominous

frequency

in these recon-

structions

of

such

expressions

as

'must have

been',

'it must be

assumed

that',

'this

implies

that

.

.

.' and

the

like,

which indicate

that

the

writer is

making

tacit

assumptions

that

can

nearly always

be

shown

to

be

unfounded for the

particular

period.

Two

examples,

both

pertinent

to

my

main

theme,

must suffice.

Commenting

on

the words

dpouKorTEta

and

dpoAoyEZa

n

the

quotations

from

Diogenes

Laertius

and the

Suda

that

I

have

placed

at

the

head of this article, Kirk and Raven (op. cit.

102-3)

say that these words 'imply that the

ground

near

the

gnomon

was calibrated

so

as

to

give

the

time

of

day,

as well

as the

position

of

the

sun on the

ecliptic

and

so

the

season

of

the

year'.

Such

assumptions

are

totally

inadmissible.

Observations

of the

shadow of

a

gnomon

can

give

only

the

roughest

indica-

tions of the

time

of

day,

unless the

gnomon

s

so

placed

that

its

axis

is

parallel

to the

axis

of

the

earth,

i.e. unless

the

latitude

of the

place

is

known;

and

the

concept

of latitude

necessarily

pre-

supposes

knowledge

of

the

spherical

earth

set

in

the middle

of the celestial

sphere

(see

below).

In

fact,

such

observations can be

expected

to

give

only

the

times

of

noon

(shortest

daily

shadow)

and

of the

solstices

(longest

and

shortest

noon

shadows

in the course

of

a

year),

the

latter

probably

to

an

accuracy

of

at best some five or

six

days.

There can

be

no

question

of

the

calibration

of

'the

ground

near

the

gnomon

.

.

.

to

give

the time

of

day',

because, owing to the fact that the altitude and azimuth of the sun are continually altering,

no one

set

of

markings

applicable

all

the

year

round can be formulated

to

indicate

the

division

of the

day

into

parts;

only

the

midday

shadow

will be

constant

in direction

at all

seasons of

the

year,

though

not,

of

course,

in

length.

Not

until

the

concept

of latitude

was

understood,

and

mathematicians

began

to tackle

the

problem

of

projection

on

to

a

plane

surface,

could the

sun's

course be

traced in this

way

so

as to

give meaningful

results,

and this

did

not

begin

to

happen

until

the fourth

century

B.c.

(cf.

Vitruvius ix

8.I).

Furthermore,

despite

Herodotus'

mention that

the Greeks

learnt of the division of the

day

into twelve

parts

from

the

Babylonians

(ii

Io9-only

partially

correct,

as

it was

the

twenty-four-hour period

20

See

H.

Cherniss,

Aristotle's

Criticism

of

Presocratic

Philosophy,

1935,

some

of the

results

of which he

summarised in Journal of theHistory of Ideas xii

(I95

I)

;

for the

inevitable

reaction

against

the

criticism

of

Aristotle's merits as

an

historian of

thought,

see

W.

K.

C. Guthrie

in

JHS

lxxvii

pt.

I

(I957)

and

his

History of GreekPhilosophy, vol. i 41-3-

21

CQix

(

959)

301

ff.




6/16

30

D. R. DICKS

that the

Babylonians

divided into

12),

such a division did not come into use in

Greece,

even

in scientific

writings,

until the

end of the fourth

century;

instead,

the time of

day

was

roughly

indicated

by

such

phrases

as

rrpwoas-

Ptol. Synt.

iii

I,

p.

205,

21 ed.

Heib.-citing

an

observa-

tion

made

by

Meton

and

Euctemon)

and

TEpt'rA'6ovuav

dyop4v

or

rplv dyopyv

Av6eOva

(Hippocr.

Epid.

vii

25

and

3

-Littr6

v

396

and

400),

or

by

noting

the

length

of a

man's

own shadow

(Aristoph.

Eccl.

652; Menanderfr. 364 K.).

In

fact,

the

gnomon

was not used

to tell the time

(except

perhaps

midday)

until the Hellenistic

period,

when

astronomical

theory

had advanced

sufficiently

to enable the latitude of the

place

of observation to

be

taken

into

account;

all

surviving

examples

of

sundials are from the Hellenistic or

Graeco-Roman

periods

or

later.

Still

less,

in

the

primitive

stage

of

astronomical

thought

in

the

sixth

century

B.C.,

could the

gnomon give

'the

position

of the sun

on the

ecliptic'-a concept

that

was

anyway

not introduced

until

nearly

200

years

later-other than

by marking approxi-

mately

the

days

of

the

solstices

as

isolated

phenomena

whose

true

meaning

was not

yet

understood.22

Similar

assumptions

of Anaximander's

knowledge

of

phenomena

which

could

only

have

become

significant

at

a

much later

stage

of Greek

astronomy

are

evident

in Kirk

and

Raven's

statement

(op.

cit.

137),

'The movement of the sun on the

ecliptic,

the declination of the moon,

and the

wanderings

of the

planets

were

probably explained

as

due

to

wind'.

Knowledge

of

the

moon's

declination

necessarily

assumes

knowledge

of

the

mathematical

ecliptic;

in

Babylonian

astronomy

this

does

not

appear

until

the end

of

the

fifth

century

B.C.,

and it

is

undoubtedly

from this

source

that

the

concept

reached

Greece,

hardly

before the

fourth

century B.C.;

in

Greek

astronomy

the first

attempt

to take

into account

the moon's

movement

in

latitude

is

made in

Eudoxus'

system

of concentric

spheres

(c.

370

B.C.).

As for

the

planets,

it is doubtful whether

they

were

recognised

as

such before

the

fifth

century

B.C.;

careful

observation

over an

extended

period

would

be

necessary

to differentiate

them

from

the

stars

(compare

Venus,

the

brightest

planet,

as

the

Morning

and

Evening

Star

separately

in

Homer),

and

it

would

seem

that

this

knowledge

also came

from

the

Babylonians (cf.

Cumont

in

L'AntiquiteClassique,

iv

(1935) 7). Certainly, the word

7rTAdv?7rE

(in this sense)

is

not

attested until the

fourth

century

B.C.

(Gundel

in RE

s.v.

'Planeten'),

although,

for what

it is

worth,

we are

told

by Diogenes

ix

46

=DK

68A33

that

Democritus wrote

a

book

7rEpt

^-6v

7TAav

7wv.

A

passage

in

Simplicius

(de

caelo

471.1

=DK

12AI9)

repeating

Eudemus' attri-

bution of

the

investigation

of

planetary

sizes

and distances to Anaximander is

regarded

as

'confusing'

by

Guthrie

(p.

95)-'nonsensical'

would be

a

truer

epithet-and apart

from

this,

the

only

evidence

for

any

knowledge

of the

planets

in the

sixth

century

B.C.

is

provided by

one dubious

statement

ofAetius

(ii 15.6

=DK

I2AI8,

mentioning

Anaximander in

company

with

Metrodorus of

Chios

and

Crates-cf.

Kahn

61)

and

some

very

unconvincing

inferences

drawn

by

Heath

(Arist. 42

f.)

regarding

Anaximenes.

The

purpose

of the

present

article is to

discuss one

aspect

of

the

astronomical

knowledge

commonly ascribed to the Presocratics, and to Anaximander in particular (see the quotations

at the

beginning), namely,

that

of

the

solstices and

equinoxes,

and

to

show

that,

whereas

knowledge

of

the

solstices

does not

presuppose anything

other

than

(relatively)

simple

observations,

the

concept

of

equinoxes

is a

much more

sophisticated

one,

involving

neces-

sarily

the

complete picture

of

the

spherical

earth

and the celestial

sphere

with

equator

and

tropics

and the

ecliptic

as a

great

circle traversed

by

the

sun-a

picture

for the existence of

which

before the

time of

Philolaus

there is not a shred

of

good

evidence,

which first

appears

as

22

On

the

whole

subject

of

sundials and

ancient

time-measurement,

see

G.

Bilfinger,

Die

Zeitmesser

der

antiken

V6lker,

1886;

Daremberg

and

Saglio,

s.v.

'Horologium',

iii

256-264-which

contains

a

re-

grettable number of wrong references; RE, s.v.

'Horologium',

viii

2416

f.;

H.

Diels,

Antike

Technik,

3rd

ed.

1924,

ch.

7;

E.

v.

Basserman-Jordan,

Die

Geschichte der

Zeitmessung

und der

Uhren,

Bd.

i,

Lief.

E

byJ.

Drecker,

Die

Theorie

der

Sonnenuhren,

925;

W. K.

Kubitschek,

Grundriss der antiken

Zeitrechnung,

1928:

references to Anaximander's advanced astronomical

knowledge

should

be

discounted in all the

above.




7/16

SOLSTICES,

EQUINOXES,

AND

THE

PRESOCRATICS

31

a

mathematically

developed

system

in

Eudoxus,

and which

is

entirely

anachronistic

for

the

sixth

century

B.C.

In

the course

of the

discussion,

critical references

will

be made to

C.

H.

Kahn's

book,

Anaximander nd the

Origins of

Greek

Cosmology Columbia

University

Press,

I96o0)

which it

seems to me

gives

a

highly imaginative

and

very

misleading

account

of

Anaxi-

mander's

thought

and,

by

exaggerating

his

alleged

mathematical

insight,

seriously

impairs

our

understanding

of the

development

of Greek

science;

it is all the

more

necessary

to enter

a

caveat

against

Kahn's

opinions,

since

his book

is

constantly

cited

with

approval

in

Guthrie's

chapter

on

Anaximander

(op.

cit.

72-I

5).

Now the

solstices

represent

the

northernmost

and

southernmost

points

of

the

sun's

annual

path

round

the

earth,23

occurring

in

June

and December

respectively;

that is

to

say,

if

observations are

made

of the

point

on the

horizon

where

the

sun rises

(or

sets)

it will

be

found

that

these

points

gradually

shift

northwards

during

early

summer,

until

a time

is

reached

when

the

sun

seems

to rise

(or set)

at the same

point

of

the

horizon

for several

days

in

succession,

and

after

this the

rising

and

setting

points

shift

slowly

southwards until

they

reach

a

southern

limit on the

horizon,

when

again

there is no

perceptible

change

for

several

days-and

the

sun

seems

to oscillate

between these

two

limits,

six months

apart.

It

is

important

to realise that

knowledge

of these

phenomena requires

only

simple

observation

and a

clear

horizon with

recognisable

landmarks

by

which to

gauge

the

position

of

the

sun's

rising

or

setting-it

implies

no

astronomical

heory

whatsoever.24

The

earth

and the

universe

can

be

any

shape

and

size,

the

sun, moon,

and

stars can be

arranged

in

any

order

one cares

to

imagine,

and the sun can

even be

supposed

to

be

extinguished

every night25-it

makes

no

difference

to

the

observed

phenomena.

Hence it is

not

surprising

that

knowledge

of

these

'turnings

of

the

sun'

(Tpora'

Aglov) long

antedates

any

theoretical

astronomical

speculation.

It

is

doubtful

whether

the

single

occurrence

of

the

words in

Homer

means

anything

more

than

a

vague

reference to

the

far

west,

26but

Hesiod uses

them

in

the sense of

solstices,27

and from

this

time

on,

in

conjunction

with

the

rising

and

setting

of

certain

prominent

stars and

star-

groups,

such as

Sirius and

the

Pleiades,

the

solstices

play

an

important

part

in

helping

to

determine the season of the

year

for

agricultural

operations28

and act as fixed reference

points

for

dating

historical

events.29

Thus there

is

no

reason

to

doubt

that

the

phenomena

of the

solstices

(as

distinct

from the

true

understanding

of

them)

were

known to Anaxi-

mander;

but

it

must be

emphasised

that

such

knowledge

belongs

still to

a

pre-scientific

stage

of

astronomical

thought.

The

case

is far

otherwise

with

the

equinoxes.

These

are the

two

points

when the

sun's

annual

course

coincides

with

the

celestial

equator

(in

other

words where

the

ecliptic

intersects

the

equator),

so

that at

the

equinoxes

days

and

nights

are of

equal

lengths

all

over the

globe

as

they

are

at all

times of

the

year

for

observers

on

the

equator

itself;

after the

vernal

equinox

23

In

what

follows,

a

geocentric

universe

is

assumed

and

the

observer

is

supposed

to

be

situated

north of

the

equator

between

the

tropic

of Cancer

(231'N.

latitude)

and

the

arctic

circle

(661'N.

latitude)-for

a

general

description

of Greek

astronomical

theory

in

its

developed

form,

see

my

paper

in

BICS

xi

(1964)

43-53.

24

Another

method

of

recognising

the two

limits

of

the

sun's

movement

would

be

to

note that

the

shadow

of a

fixed

object

on

the

ground

is

shortest at the

northern

limit

and

longest

at

the

southern at

the

same

hour

of the

day

in

each

case;

but

this

already

involves

the

assumption

that the

time of

day

is

determinable

on

a

theoretical

division

of

it

into

equal

parts,

which

is

highly

improbable

for

the

early stages

of

Greek

astronomy-cf.

O.

Neugebauer,

'The

Egyptian

"Decans" ' in Vistas in Astronomy,i

(1955,

dedicated

to

F.

J.

M.

Stratton)

5

I,

'It

is

only

within

theoretical

astronomy

of the

Hellenistic

period

that the

Babylon-

ian time-reckoning, with its strictly sexagesimal

division,

combined

with

the

Egyptian

norm

of

2

X

12

hours,

led

to the

24 "equinoctial

hours"

of

6o

minutes

each

and of constant

length.'

25

As we are

told was the

opinion

of

Xenophanes

and

Heraclitus.

26

Od. xv

404-see

Stanford

ad

loc.

27 Works

and

Days

564

and

663-even

here there

is

a

slight

element

of

uncertainty,

since

both these

lines

occur

immediately

after

passages

bracketed

in

Rzach's

text as

having

been

proscribed

by

Plutarch.

28

E.g.

Hesiod

tells

us

(WD 564 ff.)

that

when

Arcturus

rises in the

evening,

6o

days

after

the

winter

solstice,

and

is visible all

night,

the

vines

must

be

pruned.

29

E.g.

Thuc. vii

16;

viii

39.




8/16

32

D. R.

DICKS

(March),

for

observers

in

the

north

temperate

zone,

the

days

continue

to

lengthen

until

the

longest day

at

the

summer

solstice,

and

after

the autumnal

equinox (September)

they

continue

to

shorten

until

the

shortest

day

at the

winter solstice.

How

are the

equinoxes

to

be determined

?

They

are

not

conveniently

marked

by

an

apparent

halt in the

shifting

to-and-fro

of the

points

on

the horizon

where

the

sun

rises and

sets;

in

fact,

the sun's

declina-

tion is

altering

comparatively rapidly

at the time of the

equinoxes,

compared

with the

change

at the

solstices,30

and

there is

nothing

to

show

that one

day

rather than

another

should

be

marked

as

the

day

of the

equinox.

Similarly,

there is no obvious

way

of

differentiating

the

equinoctial

shadow

from

those cast

by

the

sun on other

days-it

is

neither

the

longest

(as

at

the

winter

solstice)

nor

the shortest

(as

at the

summer

solstice),

but

inter-

mediate

between

the

two.31

Direct

measurement

of

the

length

of

day

and

night

can

be

entirely

discounted;

a

glance

at tables of sunrise

and sunset for

Greece

will

show that over

the

ten

days

spanning

the

equinox

there

is a total

change

of some

eighteen

minutes

in the

length

of

the

day,

i.e.

less

than

two

minutes

a

day,

and

this standard

of

accuracy

is

out

of

the

question

for

the

water-clocks and other

devices

of

ancient time-measurement

even

in

late

antiquity.32

In

fact,

the

equinoxes

annot

be determined

y

simple

observation

lone,

as can

the sol-

stices;33 it is a facile error to assume that knowledge of the solstices necessarily implies also

knowledge

of

the

equinoxes.

The times of the

latter have to

be

obtained

by

calculation,

and

such a

calculation

presupposes

considerable

knowledge

of

basic astronomical

theory.

In

particular,

it

presupposes

a

spherical

earth

as the

central

point

of

a

celestial

sphere

with

equator,

tropics,

and

the

ecliptic

as

the

circular

path

of the

sun

round

the

earth

inclined at an

angle

to the

equator;

it

presupposes

also

sufficient

mathematical

understanding

to

envisage

the

plane

of

the

meridian

(the

great

circle

passing

through

the observer's

zenith

and the

celestial

poles)

intersecting

the

plane

of

the

horizon

at

right angles,

and the

plane

of

the

equator

inclined

at an

angle

to

the

horizon34-and,

of

course,

it

presupposes

a

knowledge

of

30 For

example,

in

Ptolemy's obliquity

table

in

Almag. i 15, at the beginning, i.e. near the equinox,

10

on

the

ecliptic

is

equivalent

to

about

o024'

on the

meridian,

while at

the

end,

i.e. near

the

solstice,

10

on

the

ecliptic

is

equivalent

to less

than

ooI'

on the

meridian.

31

See

the

list

of

shadow

lengths

at

different

lati-

tudes

(undoubtedly

taken

from

Hipparchus) given

in

Almag.

ii

6.

32

Ptolemy

mentions

(Almag.

v

o1,

ed.

Heiberg,

i

400,

13)

that

in

lunar

observations

errors of

kth of

an

hour

could

be

expected,

and

this was at the

highest

point

of

Greek

astronomical

development.

For

the

inaccuracies

of

water-clocks,

see

J.

K.

Fothering-

ham

in

CR

xxix

(1915)

and

cf.

A.

Rome,

Annales

de la

Socigte

Scientifique

de Bruxelles

lviii

(1938)

I-12.

33

As

Nilsson

remarks

(Die

Entstehung

und

religidse

Bedeutung

des

griechischen

Kalenders,

(2nd

rev.

ed.

1962)

27-8

n.

3),

'Die

Sonnenwenden

sind

nach den

Wendepunkten

der

Sonne

an

einem

gewissen

Ort

leicht

zu

beobachten,

die

Tag-

und

Nacht-gleichen

konnen,

da

die

Sonnenbahn

kontinuierlich

ist,

erst

durch

Berechnung festgestellt

werden'.

34

This

is

clear

from the

methods used

by

Hippar-

chus

and

Ptolemy

to

determine the

equinoxes

(Almag.

i

12,

with

Theon's

commentary

ad

loc.).

Two of

the

instruments

employed,

the

meridional

armillary

and

the

plinth,

have

to be

accurately aligned

in

the

plane

of the meridian perpendicular to the plane of the

horizon;

readings

were

then

taken of

the

height

of

the

sun

at

midday

at each of the

solstices,

and

the

point

exactly half-way between these two readings repre-

sented the zenithal

distance of the

equator,

which

could therefore be marked on the instrument. The

actual time

of the

equinox

could then

be

determined

roughly by noting

when the

midday

shadow

of

the

pointer

coincided

as

nearly

as

possible

with

the

marked

equator;

for

greater accuracy

(since

the

moment

of intersection of

ecliptic

and

equator

need

not

be at

midday)

several

readings

were taken

on

days

near the

equinox

and

interpolation

carried

out

by

means

of

the

obliquity

table-but

this was

a

refinement

which

was

not

possible

before

Hipparchus.

A third

instrument,

the

equinoctial

or

equatorial

armillary, consisting simply

of a

large

bronze

ring

of

uniform

cross-section,

had to be

placed

exactly

in

the

plane

of the

equator

(previously

determined

by

one

of the other

two

methods),

and would

then mark

the

time of the

equinox directly

by

the moment

when

the shadow of the

upper part

of the

ring

exactly

covered the lower

part;

Ptolemy specifically

draws

attention

to

the

difficulty

of

ensuring

that

the

ring

was

accurately

set in the

plane

of

the

equator,

a

slight

shift

in

position

necessarily

causing

a

large

error

in

the

time

of

the

equinox

(Almag.

iii

I,

ed.

Heiberg

197,

ii

ff.).

For

a

detailed

description

of these and

other

ancient

astronomical

instruments,

see

my paper

in

Journal of

the

British AstronomicalAssociation

lxiv

(1954)

77-85. The important thing to realise is the rela-

tively

advanced nature

of the

theoretical

knowledge




9/16

SOLSTICES,

EQUINOXES,

AND

THE PRESOCRATICS

33

the

length

of the solar

year

and a fixed

calendaric scheme. In

fact,

an

understanding

of

the

phenomena

of the

equinoxes

belongs

without

any

doubt to

a

mathematically

advanced

stage

of

astronomical

thought,

compared

with

the

simple

observational

stage

characterised

by

recognition

of the

solstices.

There

is

not

the

slightest possibility

that

any

of the

above

concepts

were

known in

the sixth

century

B.C.

(even

Kahn

does

not

postulate

a

spherical

earth

for Anaximander) or indeed before the latter half of the fifth century

B.c.

(see below); thus

the

doxographical

attributions of

knowledge

of the

equinoxes

to

Anaximander

are

worth-

less.35

Confirmation

of the

truth of this

is

provided

both

by

the late

appearance

of the

word

laorqtcpla

tself

and

also

by

considerations

relating

to

the

Greek

calendar.

Apart

from Aris-

totle36

and the

pseudo-Platonic

Axiochus,37

he earliest attested occurrence

of

lot'"Epla

is

in

the treatise

On

Airs,

Waters,

Places

in

the

Hippocratic

collection;38

it

is

notoriously

difficult

to date these

treatises,

but

certainly

none of

them

can

be earlier than

the last

part

of the

fifth

century.

To the same

period

belongs

the first

scientifically

formulated

intercalation

system

for astronomical

reckoning, namely

the

nineteen-year

cycle

connected

with

the

names of

Meton

and

Euctemon

and

containing

6,94o days

and

235

lunar

months

including

seven intercalary months;39 this gives a figure for the mean lunar month accurate to within

that must underlie

a

problem

such as the determina-

tion

of

the

equinoxes;

without

the fundamental

concepts

of

equator, tropics,

and

ecliptic

on

the

celestial

sphere,

the

equinoxes

are

meaningless.

35

A

minor,

but

instructive,

example

of the

manner

in which the

alleged

scientific achievements

of

the

Presocratics

are

gratuitously augmented by

the

doxo-

graphers

is

provided

by

the

three

citations

at

the

beginning

of this

article.

Diogenes

Laertius

contents

himself

with

saying

that

Anaximander

was the

first

to discover and set

up

a

gnomon (the

word

in

this

context

means

simply

a vertical

marker

casting

a

shadow)

'which

marks

solstices

and

equinoxes',

acrpaivovTa

note

the

present

participle) giving

a

generic description

of

this

instrument,

thus

avoiding

stating

in

so

many

words that Anaximander himself

actually

observed solstices

and

equinoxes.

By

Eusebius,

Anaximander

is credited

with the 'con-

struction' of

more

than one

gnomon

(yv~wdovaq

KavTaKevaae-probably

a

rationalisation

of

the

otiose

addition

Ka

poaKorKda

KaTEaKvacae

in

Diogenes,

which

reads

like

a

gloss)

for the

express purpose

of

distinguishing

(npd6

~

dyvwatv)

the dates and hours

of

solstices

and

(presumably-but why

laqltepiag

in

the singular? Another gloss?) equinoxes. In the

Suda,

finally,

not

only

is

knowledge

of

all

the

above

attributed to

Anaximander,

but

we are

assured that

he

treated

the

whole

subject

on

geometrical

lines It

remains

merely

for

Kahn to

put

the

finishing

touches

to

this

imaginary

edifice

by

assuring

us

(op.

cit.

93)

that '.

..

in

the

cosmos of

Anaximander

the orbits of

the

sun

and

moon

are

represented

by

definite

geo-

metric

(and

probably

mechanical)

structures'-

whatever

this

may

mean-and

by

citing

with

approval

(95)

Diels'

unfortunate

remark

(Archiv

iir

Geschichte der

Philosophie

(1897) 237)

'Anaximander

steht

dem

Kosmos

Kepplers

naher als

Hipparchos

und Ptolemaios'-but see below for some more

sensible

remarks

by

Diels.

36

E.g.

Meteor.

ii

6.364

b

I;

ii

2.371

b

30;

iii

5-377

a

12

and

14-

37

37oc-variously

attributed

to

the

fourth or first

century

B.C.

according

to H.

Leisegang

in RE

s.v.

'Platon'

col.

2366.

38

IHEpI

dipwov

dO'xwv

dnoV

?I

I

(Corpus

Medicorum

Graecorum

,

ed.

Heiberg,

67,

I927)-the

author tells

us that the

following

days

are the most

dangerous:

?/Itov rponatl

dPu20depat

Kai

Odlaov at

e0ptva

Kat

at

larlUeplat volUtLdLevat lvat da~idoepat,

.~

llov

d6

at

peronrwptval.

The words

underlined are

ignored

in

LittrC's

translation

(tom.

ii

(1840)

52)

and in

Adams' The Genuine Works

of

Hippocrates, (1939) 31,

and

rendered

'sogennanten' by

R.

Kapferer,

Die

Werke des

Hippocrates (Teil

6

(1934)

40)

and

'so

reckoned'

by Jones

(Loeb Hippocrates

i

Io5).

There

seems

to be no

parallel

for

voluiteaOat

used in this

last

sense,

and

'sogennanten' hardly

helps

the

meaning;

one is

tempted

to

read

Aoytdoervat,

'calculated',

which

gives

the

right

sense and

might

easily

have

been

misread

by

a

scribe.

At

any

rate,

it is

clear

that

there

is a contrast

between

the

solstices,

which

can

be

mentioned without

any

qualification

as well-known

phenomena,

and the

equinoxes,

which

as a

less

familiar

concept require

an

explanatory description.

39

The locus classicus for

Greek astronomical

calendars

is

Geminus,

Isagoge,

ch.

8;

this is discussed

at

length by

Ginzel,

Handbuch der mathematischenund

technischen

Chronologie,

ii

(1911)

366

ff. and

Heath,

Aristarchus

of

Samos

(1913)

ch.

19,

284-96.

Both

these

scholars

appear

to

accept

a

very

early

date

for

Homer,

and

consequently

tend

to

assign knowledge

of

the

basic

parameters

to an

earlier

period

than is

warranted

by

the evidence as we

can now

interpret

it.

I

have stated

that

the Metonic

cycle

was

'the

first

scientifically

formulated intercalation

system'.

Gem-

inus describes what

purports

to

be

an

earlier

cycle,

the octacteris, consisting of eight years containing

2,922 days

and

ninety-nine

lunar

months

including

VOL.

LXXXVI.

c




10/16

34

D. R.

DICKS

two

minutes,

but

for the solar

year

(6,940

19-=365

5/19 days)

a

figure

about

half an

hour

too

long.

Meton and

Euctemon's date

is

firmly

fixed

to

432

B.C.40

The over-estimate

for

the

solar

year

was

eventually

discovered

and,

almost

exactly

Ioo

years

later,

Callippus put

forward a new

seventy-six-year

cycle

consisting

of

27,759

days (i.e.

four Metonic

cycles

less

one

day)

and

940

lunar

months

including

twenty-eight

intercalary

ones;

this

gives

a

year

of

exactly 3651

days

(in

fact,

the

Julian year,

which is some eleven minutes too

long)

and a

mean lunar

month

only twenty-two

seconds too

long.

Two

hundred

years

later

still,

Hipparchus

decided

that

the correct

figure

for

the

solar

year

was

I/3ooth

of

a

day

less

than

365k

days,41

i.e.

365

days

five hours

fifty-five minutes

twelve seconds,

which is only

about

six and a half

minutes

in

excess

of

the

true

figure;

Censorinus

tells

us42

that

Hipparchus'

cycle

was

304 years

with

I

12

intercalary

months

(i.e.

four

Callippic

cycles

with

I11,035

days

instead

of

I11,036

=4

x

27,759),

but

this

cycle

was never

used

even

by

astronomers

(Geminus

does

not

mention

it),

and

Ptolemy

still

uses

the

Callippic

cycle

in

conjunction

with

the

Egyptian

system

for

dating

purposes.

I mention these

cycles

and

their

dates

to

show

something

of

the

complexity

of

the

problem

of

establishing

a

luni-solar

year,

and

the

long

period

of time

that

elapsed

before

an

accurate

figure

for

the

length

of the

year

was arrived

at.

It was the figurefor the solaryear that caused the chief difficulty (it was easierto arriveat a

reasonable

estimate for

the

lunar

month,

simply

because

it

recurred more

frequently,

and a

lunar

year

of

12

X

29-

=354 days

may

well

have

been known

in

the earliest

stages

of

Greek

astronomy),43

and

this is

precisely

what one

would

expect

from inexact observations of

solstices at a

time

before the

concept

of

equinoxes

and all

that

it entails

was

understood.

In

the

parapegma

texts,

Euctemon

is

the

earliest

astronomerto

whom

equinoctial

observations

are

attributed;44

because

of

the

disorder

of

the Athenian

civil

calendar

in

the

fifth

century,

Thucydides

preferred

to

date

events in

his

history

not

by

the archon's calendar

(where

no

systematic

scheme of

intercalation was

ever

in

use,

but

intercalation

depended

on

the

vagaries

of

officialdom)45

but

by

astronomical reference

points

such

as the

rising

of Arcturus

and the

solstices-not,

be

it

noted,

the

equinoxes,

although

he would

no doubt have used

them had he been familiar with the concept. Another indication of the uncertainties

attending

investigations

of

the

length

of

the

year

is

provided

by

the values

adopted

for the

four

astronomical

seasons,

i.e. the

four

segments

of

the sun's

course

marked

by

the

solstices

and

equinoxes.

According

to

a

papyrus

fragment

called the Ars

Eudoxi,46

Euctemon

made

the

lengths

of

the

seasons

(beginning

from the vernal

equinox)

93, 90,

90

and

92 days

re-

spectively;

Eudoxus,

some

sixty

years

later,

still

operated

on

the

assumption

that

the sun's

motion was

uniform,

since

he

gave

the

lengths

of

the

seasons

as

91,

91,

92

(presumably

in

three

intercalary

ones;

but

there

are several diffi-

culties

in

accepting

his

account at

its face

value

(in

particular,

it

assumes a

figure, 3651

days,

for the

length

of the

year,

which

was not

discovered

until

Callippus-cf.

Heath,

op.

cit.

288-92),

and

according

to

Censorinus

(de

die

natali,

I8,

5)

the

octaiteris

was

usually

ascribed

to

Eudoxus,

although

other

names

(including

Cleostratus)

were

also connected with

it.

40

Cf.

B.

L.

van

der

Waerden,

'Greek

Astronomical

Calendars',

JHS

lxxx

(1960)

170,

'This date

is

given

by

three

independent

witnesses and

accepted

by

all

chronologers'.

41

Ptolemy, Almag.

iii

(ed.

Heiberg

i

207,

I2

ff.).

42

De

die

natali,

18,

9.

43

This

was

in

fact

the

'festival

year'

of

the

Athenian

calendar-cf.

B.

D.

Meritt,

The

Athenian

rear

(1961)

3

f.

44

E.g.

in

the

calendar

that

appears

as

ch.

17

of

Geminus' Isagoge (which Manitius includes in his

Teubner

edition

of

1898,

but

proves-pp.

280-2-

that it

belongs

to

a

period

ioo

years earlier)

p.

216

?3,

6v

iv

oYvr0j d

pip&a

[sc.

roi5

v'yov]

E?icriovT

ta•lnuepia

eZErxonwptv~,

nd

p.

228

?Io,

for the

vernal

equinox.

On the

parapegmata,

see

especially

A.

Rehm,

'Parapegmastudien',

Abh. d.

Bayerischen

Akad.

d.

Wiss.,

Phil.-hist.

Abt.,

Neue

Folge,

Heft

xix

(1941),

and his articles

'Episemasiai'

and

'Parapegma'

in

RE,

Bd. vii

(1940)

cols.

175-98

and Bd.

xviii,

4

(I949)

cols.

1295-366;

cf.

also

my

Geographical

Frag-

ments

of

Hipparchus

I

I

I1-12.

45

See

especially

W. K.

Pritchett,

'Thucydides

v

20o',

Historia,

Bd.

xiii,

Heft

I

(Jan.

1964) 21-36,

with

references to

the

more

recent work

done on

the

Athenian

calendar.

46

Ed. F.

Blass,

1887,

p.

25-the

papyrus (the

text

of

which

shows

many

errors)

was written

between

193

and

165

B.c.

and

is,

of

course,

not

by

Eudoxus

himself;

it

may

be

a

student's exercise with later

information added.




11/16

SOLSTICES,

EQUINOXES,

AND

THE PRESOCRATICS

35

order to

bring

the total

up

to the

required

365)

and

91 days;

and it was not until a

generation

later

that

Callippus

gave

values correct to

the nearest

day,

viz.

94, 92, 89

and

90

days

(the

true

lengths being

94.I,

92.2,

88.6,

90.4 days

to one decimal

point).41

It is

noteworthy

also

that

Hipparchus,

in the second

century

B.C.,

found himself

obliged

to make use of

solstitial

observations

to define the

length

of the solar

year

even

though

he

expressly

states that

there

was a

margin

of error of a

quarter

of a

day

in such

measurements,

and that

equinoctial

observations

would

be

preferable;48

he

gives

a series of

equinoctial

observations

which

he

himself

had

made as

accurately

as

possible

(and

of which

Ptolemy

makes full

use),

but

was

unable

to find

any

earlier ones of a

comparable

standard of

accuracy.49

In

the

light

of

all the

evidence

presented

above,

it

should

by

now be

perfectly

clear

that

even

the

beginnings

of Greek

mathematical

astronomy

cannot

possibly

be

put

back to

earlier

than

the fifth

century

B.C. and

certainly

not

to the sixth

century;

not

only

were the

basic

concepts

lacking,

but

the whole

history

of the later

development

shows that several

centuries

were

required

before

sufficient

observations were

accumulated

to

provide

such

fundamental

data

as the

length

of

the

solar

year

and an

accurate

calendaric scheme.

It is

only by

ridding

ourselves

of

misleading

preconceptions

and

by

an

impartial

examinationof what

knowledge

was

possible

at a

particular

epoch,

that a true

picture

of the

development

of

early

Greek

astronomy

can

be

obtained;

this

will

not be

achieved

by

picking

and

choosing

among

the

tidbits

of miscellaneous

information

(usually

inaccurate

and

frequently

false)

provided

by

the

biographical

tradition.

Yet this

is

just

what

Kahn

does

in the

work

already

mentioned.

In his

misguided

determination to

paint

a

picture

of

Anaximander 'as the earliest known

type

of

a mathematical

physicist'

(p.

97),

Kahn does

not

scruple

to select 'evidence' to bolster his

thesis

from the least

trustworthy

sources while

feeling

free

to

reject

much,

from no other

reason

than

personal preference

apparently.50

Thus he

accepts

knowledge

of the

obliquity

of

the

ecliptic

for Anaximander

on the

authority

of

Pliny (nat.

hist.

ii

31)

and the

words

KE/JLEVOV

A~O6dv

referring

to the

sun's

circle)

in

Aetius

(ii

25.

=DK

I2A22);51

but in

the

same

passage

of

Aftius,

the

explanation

of

eclipses

attributed to Anaximander

is

rejected

as

'corrupt' because, in Kahn's opinion, it does not agree with another

explanation

that

Aetius

gives

a

little

earlier.

Both

explanations

are

equally

fantastic and neither deserves

serious

consideration-why

should

one be

more

'corrupt'

than the

other

?

More

fantasy

is

shown

in

the

explanation

that

the

'turnings

of the sun'

(-rporac'

?~'lov)

are

caused

by

the

vapours

produced

when

the sun

evaporates

the

moist

regions

of

the

earth;

this

theory

is

attributed to Anaximander

and

Diogenes

by

Alexander

commenting

on a

passage

in

Aristotle's

Meteorology

353

b

5

=DK

I2A27)

and,

as

Kahn

points

out

(p. 67),

the remarkable

notion

that

the

sun is

nourished

by

exhalations

from the earth's

surface

was

common

to

several of

the

later

Presocratics.52

Even

Kahn

is

constrained

to

remark

(p. 103

n.

2),

'The

details

are

very

obscure,

and it is

difficult

to see

how such an

interpretation

of

solstices is

compatible

with

the

description

of the

sun's

circle

as

"lying

aslant" the

equator'. Precisely

-the two ideas areentirely incompatible, and it should be obvious that the words

KE41EVOV

47

Cf.

Heath,

Arist.

200

and

215-16; Pannekoek,

op.

cit. III.

4s

Almag.

iii

I

(ed.

Heiberg,

I94-5).

49

Ptolemy

several

times

emphasises

the

approxi-

mate

nature of

Meton's and

Euctemon's

observations

-e.g. Almag.

iii

I

(Heib.

p.

203,

13),

Zdg~

7rn'

KeKdvov

[i.e.

Meton,

Euctemon

and

Aristarchus]

napadedo-

ypvaq (sc. Oeptvdg

ponrig)

6joaXepZaZepov

el.•up

vag,

and

again

(Heib.

p.

205,

I5),

rjv

V'nr6

xv

nrepi

M~xovcid

T

Kat

EO3KT/ncova

sTnpnrLvv

Optv %v

ponxIv,

b•

dkoAXOepCaTepov

vayeypaQppeviv.

50

Cf. his discussion of 'The

Doxography',

28-71,

passim,

and

particularly 59

ff.

51

Cf.

p.

88,

'Since the circles of the sun and moon

are

said

to

"lie aslant"

(Aoldv

KFeaOat),

Anaximander

must

have been familiar with

the inclination

of the

ecliptic

relative to the

diurnal

path

of the

stars.

Pliny

also

attributes

this

knowledge

to

him,

and other

sources

speak

of

his interest

in

solstices,

equinoxes,

and

the

measurement of the

"diurnal hours".'

Needless

to

say,

there

is

not

the

slightest

indication

that

Kahn

has

considered

any

of the

implications

of

Anaxi-

mander's

possession

of

such

knowledge.

52

Typically,

Kahn informs us

(p.

103)

that 'here

the link between

meteorology

and

astronomy

is

dramatically

established'




12/16

36

D. R.

DICKS

Ao6dv

are a

late addition

in

the

doxographical

tradition,

inserted

by

someone who was

so

familiar with the

slanting

ecliptic

of late Greek

astronomy

that

he could not conceive of

its

not

being

a well-known

concept

in this

early

period;

just

as Kahn cannot

envisage

the

ecliptic

without

mentioning

the

equator,

although

there is not

a word about this in

the

original

quotation.

Time and

again

Kahn

emphasises

what

he

alleges

is the

mathematical

content of Anaximander's

thought;

e.g.

p.

77,

'What is most

striking

in this doctrine is its

specifically

mathematical

character

....

Anaximander's

own use of this

geometric

idea

[the

free

position

of the

earth],

as a

general

expression

for the

principle

of

symmetry

or

in-

difference';

p.

78,

'That this

cosmological

application

of

a

geometric

idea was

Anaximander's

personal

achievement,

is

fortunately

beyond

doubt';

p.

8o

(the crowning absurdity

in

this

monstrous

edifice of

exaggeration),

'Anaximander's view

prepared

the

way

for.

a

purely

geometric

approach

to

astronomy,

and

hence,

indirectly,

for the

heliocentric

hypothesis.

This mathematical

insight

was .

.

. refused

by

his

more

empirically

minded successors.'

Examination of the

evidence

on which Kahn bases these

sweeping

statements shows

that,

apart

from

the doctrine

of the

unsupported

earth

in

the centre of the

universe,53

he relies

(a)

on

the

attribution to

Anaximander

of a

cylindrical

earth,

three times

as wide as it is

deep,

and (b) on some conjectural figures for the supposed sizes of Anaximander's tubes of fire

representing

sun

and moon. The

authority

for

(a)

is a

single

passage

in

pseudo-Plutarch

(Strom.

2

=DK

I2AIo);

elsewhere

(p.

59)

in another context Kahn is

very

properly

hesitant

about

accepting

'the

isolated

testimony

of

Aftius'.

As

regards

(b),

the

only figures

to be

found

in

the

doxographical

tradition are contained

in

the statements

that

the

sun's

circle

is

twenty-eight

times

(Aetius

ii

20.I

=-DK

I2A2I)

or

twenty-seven

times

(Aetius

ii

21.1)

the

earth,

while the

moon's circle is

nineteen times the earth

(Aetius

ii

25.1

=DK

I2A22);

but

Tannery54

put

forward

some

ingenious

speculation

purporting

to show

that Anaximander

conceived

his

universe

on

mathematical lines

according

to the series

3

(earth): 9

(stars):

18

(moon): 27

(sun).

Kahn

admits

(p.

62)

that

'there

is

little

documentary

basis for this

attractive

result'

(my

italics),

but

nevertheless states

(p.

88)

'The

inherent

plausibility

of this

conjecture is very great'. In fact, of course, the whole thing is astronomical nonsense;55

no

reliance

whatsoever

can

be

placed

on

the numbers

(only

27

in

the series has

any

textual

authority,

as Kahn

agrees)

which were

in

all

probability

invented

by

the

doxographers.56

There is

not

the

remotest

possibility

that

the numbers are

based on

observational data

(even

Kahn

admits

this,

p.

96),

and

Tannery's

hypothetical

series can

hardly

be taken

seriously

as

evidence for

a

mathematically-based

universe

in

Anaximander's

thought;

even the

assump-

tion that the unit

of

measurement is

the

earth's

diameter5"

is

very

dubious-the

phrase

lTTraKaLEEKOUa7TAta,•a)

"-r

y-g

is

itself

ambiguous-and

it is

unlikely

that the

idea of

taking

as

a

standard the

whole

earth could

have

presented

itself before a

time when

the earth's

sphericity

had

become

a

familiar

concept,

and

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Dicks, D. R._solstices, Equinoxes, & the Presocratics_JHS, 86_1966!26!40

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