Medieval and Early Modern Science, Vol. 2: Science in the Later Middle Ages and Early Modern Times, XIII–XVII Centuries [2, Revised 2nd Ed]

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REVOLUTION

174

IN

SCIENTIFIC THOUGHT

with the centre of the earth, describe

among

planets a great orbit round the sun which

is

the other

the centre of

the world; and that what appears to be a motion of the

sun is in truth a motion of the earth; but that the size of the world is so great, that the distance of the earth from the sun, though appreciable in comparison to the orbits of the other planets, is as nothing when compared to the sphere of the fixed stars. And I hold it to be easier to concede this than to let the mind be distracted by an al-

most endless multitude of circles, which those are obliged to do who detain the earth in the centre of the world. The wisdom of nature is such that it produces nothing superfluous or useless but often produces many effects from one cause. If all this is difficult and almost incomprehensible or against the opinion of

God, make

it

many

people,

we

shall, please

clearer than the sun, at least to those

know something

of mathematics.

The

first

who

principle there-

fore remains undisputed, that the size of the orbits is measured by the period of revolution, and the order of the

spheres

is

The

then

as follows,

commencing with the upper-

and highest sphere is that of the fixed stars, containing itself and everything and therefore immovable, being the place of the universe to which the motion and places of all other stars are referred. For while some think that it also changes somewhat [this refers to precession], we shall, when deducing the motion of the earth, assign another cause for this phenomenon. Next follows the first planet Saturn, which completes its circuit in thirty years, then Jupiter with a twelve years' period, then Mars, which moves round in two years. The fourth place in the order is that of the annual revolution, in which we have said that the earth is contained with the lunar orbit as an epicycle. In the fifth place Venus goes round in nine months, in the sixth Mercury with a period of eighty days. But in the midst of all stands the sun. For who could in this most beautiful temple place this lamp in another or better place than that from which it can at the same time illuminate most.

first

the whole? Which some not unsuitably call the light of the world, others the soul or the ruler. Trismegistus calls it the visible God, the Electra of Sophocles the all-seeing.

IN THE l6TH AND 17TH So indeed the sun,

sitting

CENTURIES

175

on the royal throne,

steers the

revolving family of stars/

The consequences

of Copernicus' postulates were of two and geometrical. The daily rotation of the earth encountered the Aristotelian and Ptolemaic physical objections, based on the theory of natural motions, concerning 'detached bodies/ an arrow or a stone sent into the air, and the strong east wind (see above, p. 78 et seq.). To these Copernicus replied in the same way as Oresme, making circular movement natural and saying that kinds, physical

the

air

shared that of the earth because of their

nature and also perhaps because of friction.

He

common held that

falling and rising bodies had a double motion, a circular motion when in their natural place, and a rectilinear mo-

tion of displacement from, or return to, that place.

objection to this argument was that

movement

if

The

bodies had a natural

one direction they should have a remotion in the other. The answer to this, like that to the argument that the earth would be disrupted by what is now sometimes called 'centrifugal' force, which Copernicus merely said would be worse for the enormous celestial sphere if it rotated, had to await the mechanics of Galileo. To the annual motion of the earth in an eccentric circle round the sun Copernicus' critics objected on three scientific grounds. First, it conflicted with the Aristotelian theory of natural movements, which depended on the centre of the earth being at the centre of the universe. To this Copernicus replied, with Oresme and Nicholas of Cusa, though abandoning Cusa's theory of balancing heavy and light elements, that gravity was a local phenomenon representing the tendency of the matter of any astronomical body to form spherical masses. The second objection arose from the absence of observable annual stellar parallaxes, or differences in position of the stars. Copernicus attributed this to the enormous distance of the stellar sphere from the earth compared with the dimensions of the earth's orbit. The third objection continued to be a stumbling-block till Galileo changed the whole conception of motion, when it ceased to be relevant. The Aristotelians maintained that circular

in

sistance, analogous to weight, to

REVOLUTION

176

IN SCIENTIFIC

THOUGHT

each elementary body had a single natural movement, but Copernicus gave the earth three motions: the two mentioned above which accounted, respectively, for the rising

and

setting of the heavenly bodies

and

for the passage of

the sun along the ecliptic and the retrogradations and tions of the planets,

and

a third

sta-

which was intended to

account for the fact that the axis of the earth, notwithstanding the annual motion, always pointed to the same spot on the celestial sphere. This third motion was also made to account for the precession of the equinoxes and their illusory 'trepidations/

With the

the sun and the celestial sphere, the boundary of

finite universe, at rest,

Copernicus proceeded to pro-

vide the usual eccentrics, deferents and epicycles to ac-

count for the observed movements of the moon, sun and means of perfect uniform circular motion. On the mathematical aspects of the result, Neugebauer in his Exact Sciences in Antiquity (1957, p. 204) comments as follows: 'The popular belief that Copernicus' heliocentric system constitutes a significant simplification of the Ptolemaic system is obviously wrong. The choice of the reference system has no effect whatever on the structure of the model, and the Copernican models themselves require about twice as many circles as the Ptolemaic models and are far less elegant and adaptable/ Copernicus' main mathematical planets by

contributions, according to Neugebauer, were three in

He

num-

the steps from observations to parameters, thus making a methodological improvement. He introduced with his system a criterion for assigning relative dis-

ber.

clarified

tances to the planets.

And he

of the problem of latitudes.

suggested the proper solution

But

his belief in the imaginary

trepidations of the equinoxes led to unnecessary complications and, by taking the centre of the earth's orbit as the centre of all the planets' motions, his treatment of Mars had considerable errors. Further, he relied on ancient

and inaccurate data. This last defect was remedied by Tycho Brahe (1546-1601), who showed that the trepidations were due solely to errors in observation; and Johann Kepler

(1571-1630), while considering Tycho's was to build his system from the orbit of Mars.

results,

IN THE l6TH

AND I7TH CENTURIES

177

Copernicus had produced a mathematical system at least with both mathematical advan-

as accurate as Ptolemy's,

tages and disadvantages. Theoretically and qualitatively it was certainly simpler, in that he could give a unified ex-

planation of a

motion which connected.

He

number

of different features of planetary

in Ptolemy's system

stations of the planets as

movement

were arbitrary and

dis-

could account for the retrogradations and

of the earth,

mere appearances due to a single and could give a simple explana-

tion of various motions peculiar to individual planets. In

the 16th century it was also counted in his favour that he had reduced the number of circles required; he used 34. Copernicus had also argued that the postulated movements of the earth did not conflict with physics, that

is,

with

These arguments in favour of the heliostatic system were negative, and moreover in order to effect the reconciliation he had to interpret Aristotle's physics, just as Oresme had done, in a sense different from that accepted by most of his contemporaries. It is not surprising that many of them remained unconvinced. How then did Copernicus justify his innovation, both to himself and publicly, and why did it make so strong and so emotional an appeal later to Kepler and Galileo? A large part of the answer certainly lies in the Neoplatonism they all shared. In the passage already quoted from De Revolutionibus, book 1, chapter 10, Copernicus justifies the new system he sets out by an appeal to its simplicity (qualitative, not quantitative) and to the special position it gives to the sun. The intellectual biographies of Kepler and Galileo, and the manner in which they used these and similar arguments, show that they too had committed themselves Aristotle's physics.

to the heliocentric system because of their metaphysical beliefs,

before they had

found arguments

to

justify

it

physically.

The Copernican system appealed The Alfonsine Tables had

first

to three types of

caused dissatisfaction both because they were out of date and no longer corresponded to the observed positions of stars and planets, and because they differed from Ptolemy on the precession of the equinoxes and added other spheres beyond his 9th, deinterest.

REVOLUTION

178

IN SCIENTIFIC

viations offensive to humanists

who

THOUGHT

believed that the per-

knowledge was to be found in the classical writAll practical astronomers, whatever their views on the

fection of ings.

hypothesis of the earth's rotation, thus turned to the 16th-

century Prussian Tables calculated on Copernicus' system, fact, these were scarcely more accurate. Some humanists regarded Copernicus as the restorer of the classical purity of Ptolemy. Another group of writers, such as the physicist Benedetti, Bruno, and Pierre de la Ramee, or, as he was called, Petrus Ramus (1515-72), saw in the Copernican system a stick with which to beat Aristotle.

though, in

scientists like Tycho Brahe, William Gilbert (1540-1603), Kepler and Galileo, came to face the full meaning of De Revolutionibus and attempted to unify observations, geometrical descriptions and physical theory. It was because of the absence of such a unity that until the end of the 16th century, while everyone used the Prussian Tables, no one advanced astronomical theory. Tycho Brahe's contribution was to realise that such an advance demanded careful observation, and to make that observation. Tycho's main work was done at Uraniborg, the observatory built for him in Denmark by the king. His first task was to improve the instruments then in use. He greatly increased their size, constructing a quadrant with a 19-foot radius and a celestial globe 5 feet in diameter, and he improved methods of sighting and graduation. He also determined the errors in his instruments, gave the limits of accuracy of his observations, and took account of the effect of atmospheric refraction on the apparent positions of heavenly bodies. It had been customary before Tycho to make observations in a somewhat haphazard manner, so that there had been no radical reform of the ancient data. Tycho made regular and systematic observations of known error, which revealed problems hitherto hidden in the pre-

Finally,

vious inaccuracies.

Tycho's

first

problem arose when

a

new

star

appeared in

the constellation Cassiopeia on 11 November, 1572, and remained until early in 1574. Scientific opinion received a

marked shock from this object. Tycho attempted to determine its parallax and showed that this was so small that the

IN THE star

l6TH AND I7TH CENTURIES

must be beyond the planets and adjacent

Way. Although he

179

Milky

to the

himself never fully accepted

the

it,

mutability of celestial substance had thus been definitely

demonstrated. Also, though comets had been regularly observed since the days of Regiomontanus, Tycho was able to show, with his superior instruments, that the comet of 1577 was beyond the sun and that its orbit must have passed through the solid celestial spheres, if these existed. He also departed from the Platonic ideal and suggested that the

comets were not circular but oval. Further, Ariscomets were manifestations in the air. It is significant that, although it would have been possible with instruments available from antiquity to show that comets penetrated the unchanging world beyond the moon, such observations were not in fact made until the 16th century. In 1557 Jean Pena, royal mathematician at Paris, had maintained on optical reasoning that some comets were beyond the moon and hence had rejected the spheres of fire and of the planets. He held that air extended to the fixed stars. Tycho went further and abandoned both orbits of

totelian theory held that

the Aristotelian theory of comets and the solid spheres.

the same time, the discovery of land scattered

all

At

over the

globe led other natural philosophers, such as Cardano, to

abandon the theory of concentric spheres of earth and water based on the Aristotelian doctrine of natural place and motion. Land and sea they held to form one single sphere. While Tycho provided the observations on which to base an accurate geometrical description of heavenly motions, he was led by physical as well as by Biblical difficulties to

He did not consider that Copernicus had answered the Aristotelian physical objections. Further, before the invention of the telescope had revealed the fact that the fixed stars, unlike the planets, appear as mere luminous points and not as discs, it was usually held that they shone by reflected light, and their brightness was taken as a measure of their magnitude. Tycho therefore deduced, from the absence of observable annual stellar parallax, that the Copernican system would reject the rotation of the earth.

involve the conclusion that the stars had diameters of incredible dimensions.

He

produced a system of

his

own

REVOLUTION

l8o

IN SCIENTIFIC

THOUGHT

(1588), in which the moon, sun and fixed stars revolved round a stationary earth while all the five planets revolved round the sun. This was geometrically equivalent to the Copernican system, but escaped what he considered to be the latter's physical defects and included the benefits of his own observations. It remained an alternative to Copernicus (or Ptolemy) during the first half of the 17th century, and when Tycho bequeathed his observations to Kepler, who had come to work with him, he asked him to use it

in the interpretation of his data.

Kepler did more than

whom

1631), under

Michael Mastlin

this.

he had

first

also calculated the orbit of the

(1550-

studied, had, like Tycho,

comet of 1577, and he

de-

clared the Copernican system alone capable of accounting for

it.

Kepler persisted in this opinion.

influenced by Pythagoreanism.

mony, according

to

structed, sustained

The

He was

also strongly

vision of abstract har-

which he believed the world to be con-

him through the drudgery

of arithmet-

computation to which he was consigned both by his astronomical researches and by his work as a professional astrologer. Throughout his life he was inspired by the search for a simple mathematical law which would bind together the spatial distribution of the orbits and the motions of the members of the solar system. After numerous trials he ical

arrived at the idea published in his Mysterium Cosmographicum (1596), that the spaces between the planetary orbits each corresponded, from Saturn to Mercury, to one

of the five regular solids or Tlatonic bodies': cube, tetrahedron, dodecahedron, icosahedron and octahedron. His

object was to

only sizes

sun.

show the and of

six planets

necessity of there being six

and

their orbits being of the relative

they are, as calculated from their periods round the tried to show that the five regular solids could be

He

was inscribed about which the next outer orbit was circumscribed. He then went to Tycho Brahe, who had moved to Prague, from whom alone he could get the corfitted

in the

to the six orbits so that each orbit

same

solid

rect values of the

would confirm aside,

mean

and eccentricities that was forced instead to set it

distances

this theory.

He

but his mathematical vision came to perceive in

I i.

Nicole Oresme with an Armillarv sphere. From Le Livre et du Monde, Bibliotheque Nationale, Paris, Ms

du Ciel

frangais 565 (xivcent.).

ii.

The

tude

earliest-known graph; showing the changes in latilongitude

(vertical divisions) of the planets relative to

(horizontal divisions).

From

MS

Munich 14436

(xi cent.).

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A page from Descartes, La Geometric (1637), he discusses the algebraic equation of parabola.

in.

tiplianc in

which

iv.

The mathematical disciplines and philosophy. The is met by Euclid at the outer gate. Inside he finds

dent

stu-

Tar-

surrounded by the mathematical disciplines: ArithmeMusic, Geometry, Astronomy, Astrology, etc. A cannon

taglia tic, is

firing,

showing the trajectory of the projectile. At the far welcome the student into

gate stand Aristotle and Plato, to

the presence of Philosophy. Plato holds a scroll with the no one untrained in geometry enter here' (cf. p. 6, Vol. 1). From N. Taj;taglia, Nova Scientia, Venice,

inscription 'Let

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Diagram of vortices, from Descartes, Piincipia PhilosoAmsterdam, 1644. Planets are carried in the whirlpool of subtle matter round the sun S. A comet, escaped from a vortex, is seen descending by an irregular path from the top right. Descartes thought that it would be impossible to reduce the motion of comets to law. v.

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The Copernican system. From Copernicus, De RevoluOrbium Coelestium, Nuremburg, 1543.

tionibus

Kepler's demonstration of the elliptical orbit of Mars. the sun is at one focus (n) of the ellipse (the curve shown by the broken line) and the planet at m, then according to vii. If

Kepler's second law the radius in equal times.

The

nm

Prague, 1609.

and

epicycle.

is

part of

motion on an ellipse to From Astronomia Nova,

Kepler's proof of the equivalence of

that on a deferent

sweeps out equal areas

small diagram on the right

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