Boulliau:  Planetary Theory: Boulliau's Conical Hypothesis (1645), Primary Documents:  Borelli's response to Boulliau; Boulliau's response to Borelli to Prince Leopold of Tuscany
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Astronomia  Philolaïca   (Paris 1645)
Bk I - Chpt xii - Whether the Sun Moves the Planets

The solution to this problem cannot be achieved by Geometrical demonstration.  Nevertheless, from reasons adduced in our Philolaus Book 4, Chapter 2, that which corresponds to reality seems more apt and congruent--that which appears probable--is that the planets and other heavenly bodies are moved by their own nature rather than by an external force.  Because planets have a form through which they exist and proceed, they are directed by that form to the end for which they came into existence, indeed, we see they were born to move and hence move by nature.  I offer another reason, given the fact of planetary motion, which is more obvious, that since a planet has position and is moved, moving renders it a planet as a necessary action, an action stemming from its foundation, indeed, it is a given.  Thus, the origin of a necessary action is in the agent itself, just as the power of combustion is in fire and illustration is in light, so motion is in being movable. On this account, because planets are unavoidably moved, the effort is not from an external mover which moves them but from some unspecified capacity.  Internal form will thus suffice to constitute the nature of planets as well as their attained end.  Nevertheless, while self-moved, the effort is not like that of living organisms, [it is not] in the same manner as illustrating with light, consuming with fire, or soaking with water.  The labor is not by living organisms, rather, the capacity of moving, emanating from its form, is sufficient. 

The most ingenious Kepler wanted the planets to be at rest of their own accord because of their natural inertia, but he believed they should be seized by solar light, as though by an agent of motive power, and thereby led round about the Sun, as he described in chapter XXXIII of his Commentaria de Motibus Stellae Martis, and in other terms in Book IV of the Epitome Astronomiae Copernicanae, Part iii, Question 5:  'The Sun, in order to carry the planets around, makes use, as though they were arms, of the power of its body emitted in straight lines throughout the whole extent of the world'.  In defense of this proposition he puts forward the following reasons: 

    The first of these reasons is that the planet is subject to a retardation during one part of its revolution, where it is, in fact, slower, while in another part of its orbit it is faster.  Now, it is slower where it is most distant from the Sun, faster where it is nearest the Sun.  However these retardations and accelerations must not be ascribed to the motive power of the planet, for in that case, it would tire and weaken with time. 

    The second adds a consideration drawn from the motion of planets compared among themselves:  They complete their orbit more slowly when they are more distant from the Sun, and more quickly when closer. 

    The third rests on the dignity and aptitude of this body which is the source of life and heat, and from which all vegetative life originates.  In such manner heat, as well as light, may be regarded to some extent as the agents of its action. 

    The fourth is drawn from the rotation of the Sun on its axis, which takes place in the same direction as all the others. 

    He would furthermore endow the Sun with a soul which subdues and enflames this great mass of matter, producing therein diverse changes subject to mutations.  From this it appears there is no continuous, perpetual, and uniform power in the body of the Sun.  Kepler proves the animation of the Sun from the very existence of light which he claims is related to the soul.  As for the power with which the Sun seizes the planets, it is corporeal, not animal or mental, for this reason, namely, it is an immaterial kind of body:  The virtue turns together with the Sun in the manner of a very rapid whirlpool, it covers the whole extent of the path which it fills with the same speed with which the Sun turns on its center in its own small space. 

    He also puts forward the analogy of the magnet which attracts iron.  He compares its action to the magnetic virtue of the Sun in the following way:  The magnet, according to the position of its poles, attracts on one side only, and repels on the other side only.  But the Sun possesses throughout its parts the active and energetic faculty to attract, repel, and retain the planet. 

    He maintains that one pole of the planets is friendly to the Sun, the other hostile.  Consequently the Sun attracts them by one part and repels them by the other.  And if there were no rotation, it would have attracted and united them to itself. But because the Sun turns on its axis, its species therefore turns with it, together with the motive power that moves the planets.

In reply to these premises, I say concerning the first that it does not demonstrate that the planets are moved by the Sun, although it states a truth, namely, that the planets move more quickly near perihelion and more slowly further away.  Indeed, the Sun does not cause this speed and state of motion, instead, the planets depend entirely on the very system of planetary motion itself and the manner in which it has been ordered, as we shall soon show. 

To the second, I reply it is true that the superior planets complete their revolutions more slowly due to the distance covered as well as to their form.  It would seem that in order to provide an explanation the two causes must be combined.  But it is not the distance from the Sun nor the attenuation of the motive power that causes this retardation.  For the greater distance of the planet from the Sun only makes its revolution more extended, and for that reason it requires a longer period to cover the orbit. 

As for the third, I say it merely proves that the rays from the Sun, as well as its motive power, act on the planet through light and heat, not by causing it to move, but by producing changes, and should that be its nature, producing generations and corruptions such as those on Earth. 

The fourth, in my opinion, proves nothing, unless it be that it is fitting for all bodies in the world to move, either locally, or by orbiting.  I willingly grant this. 

However, I should like to ask Kepler why he would endow the Sun with a motive soul and a corporeal life while the planets remain so stupid and inert that they resist motion.  Is it because changes such as we see on the Sun are never produced in the planets?  For if sunspots and other things that show changes, mutations, and activity in parts of the Sun persuade us that it is endowed with the semblance of life, is not Earth, the planet we inhabit, perhaps not subject to still more frequent and even graver changes?  Our planet emits flames, vapors, waters; it causes trees to fall from great heights and sends clouds into the air. This proves the activity and changes in generation and corruption in various parts of the Earth.  What then prevents it from being animated by a motive soul and hence moving of its own accord? 

Finally, how could the following propositions also be true, that which asserts the Sun moves the Earth which, like the other planets, possesses a certain inertia and resistance to motion.   And this other, on page 175 of the Commentaria de Motibus Stellae Martis, which states the motion of the chief, monthly Moon [derives] entirely from the Earth as its source; and further on, To be sure, such is the strength of the Earth's immaterial species, and doubtless, too, the rarity of the lunar body is equally great, and the dislike of this body for motion is equally feeble.  If the Sun moves the Earth by means of its immaterial species, and if the Earth is inert with respect to motion like the other planets, how is it able to impress a monthly motion on the Moon?  This is absurd and impossible.  Perhaps Kepler means the Earth, impelled in the first place by the Sun, moves the Moon in a subordinate manner-- but it is not difficult to close off this avenue of escape.  If planets are seized and carried on their path by the light of the Sun in the guise of an instrument of motive power, then the Earth, in the grip of this motive power, would not be able to seize the Moon and carry it along except by a repercussion [a secondary effect] of the solar light, in so far as the Earth reflects light from the Sun to the Moon.  In this case, the Earth would cease to do so at the time of Full Moon, and indeed the power of the Earth would increase from Full Moon up to New Moon, at which time the Earth would move the Moon very rapidly.  But nothing of the kind is revealed by the phenomena. 

As for the power by which the Sun seizes or grips the planets, and which, being corporeal, functions in the manner of hands, it is emitted in straight lines throughout the whole extent of the world, and like the species of the Sun, it turns with the body of the Sun.  Now, given that it is corporeal, it becomes weaker and attenuates at a greater distance or interval, and the ratio of its decrease in strength is the same as in the case of light, namely, the duplicate proportion, but inversely, of the distances [that is, as the inverse squared, 1/d squared]. Kepler does not deny this, yet he claims the motive power decreases only in direct proportion to the distance [that is, 1/d].  Furthermore, Kepler claims this attenuation in the motive power produces a weakening of the power only in longitude, because local motion impressed by the Sun on the planets (which motion similarly animates the corporeal parts of the Sun itself) occurs only in longitude, not in latitude.  In response to this Kepler offsets the inadequacy of this analogy by increasing the quantity matter in the slower planets. 

Yet Kepler's efforts carry little weight.  For if he considers the quantity of this motive power with respect to area, he must necessarily decrease it according to the duplicate proportion of the distance.  On the other hand, if he regards it merely as lines [that is, simply as a geometrical representation] he contradicts the previous proposition, which states that this motive power is indeed corporeal.  For if it were corporeal it could not arise from lines alone.  Furthermore, this power acts by contact with the Sun's species which emanates from the Sun together with the motive power.  Now, this species touches the body of the planet in the same manner that one surface makes contact with another surface.  Consequently, the power touches it in the same manner, given that it emanates from the Sun in the same fashion.  It follows that the power must decrease in the duplicate proportion of the distance as does the species.   But if we were to accept this argument, Saturn would make but one revolution while Jupiter, in the same period, would make three revolutions and part of the next, Mars 39, Venus 173, and Mercury nearly 557.  As for the Earth, it would make 90. This is clearly contrary to the phenomena.  In order to show agreement among the ratios between revolutions, Kepler appeals in vain to the quantity of matter by compensating [balancing] the distance of one by the moles of the other.  For example, Jupiter at its mean distance from the Sun is three and one-eighth times further away from the Sun than is Mars.  For this reason, if the proportion between the periods of revolution were as the lines of distance, Mars would complete only three and one-eighth revolutions while Jupiter completed its revolution.  Consequently, Kepler either had to increase the corporeal moles of Jupiter, or else decrease that of Mars, so that the moles of Mars being less, the species would show less resistance to move Mars, and therefore this planet would be accelerated to such a degree that Mars would complete nearly seven revolutions.  But observations show Mars is less than one-thousandth the size of Jupiter.  Where then is the proportion between motions?  For the motion of Mars should have exceeded that of Jupiter beyond all measure.  Hence, no compensation between the matter and moles of the planet and the distances is permissible.  Moreover, Kepler cannot avoid objections by saying: all the fibers of the globe taken together are moved by all the circles of the motive power taken together in simple proportion, in the same manner as the individual lines, or that the fibers of two isolated planetary bodies would be moved by the individual circles of the motive power in the simple proportion of the distances, as if corporeal power could arise from geometrical lines.  When diminution founders on these reefs, the astronomy of fibers is included in the shipwreck. 

Comparison with the magnet, as proposed by Kepler, does not agree very well with the Sun's virtues as postulated by him.  For a magnet attracts with only one of its poles and repels, as it were, with the other.  But these effects result from the nature of its parts, which cannot be changed.  Now the Sun has no distinct parts, as are found in the planets, though Kepler says so without proof.  A magnet attracts those parts of iron which are cognate to it, and does not make them turn [round about it], indeed, a magnet attracts them by one part while it repels with the other.  When the planet's fibers are in equilibrium, then the Sun either attracts the planet at aphelion or it repels the planet at perihelion.  On the other hand, a magnet never repels but only tends to cause cognate parts to unite with it, thereby aligning them in the direction of its poles.  If the fibers, when at the apsides, attract and repel uniformly, should the Sun not propel the planet by the one, and attract it by the other, because the power and the body which is moved are in equilibrium?  On this account, the planet ought to remain stationary.  Yet it clearly continues to move.  Finally I ask, how can Kepler prove the Sun would draw all the planets toward itself, if it did not turn on its axis, and why, given that it indeed turns, does it not attract them but rather makes them turn round about itself?  I fear Kepler's devices are mere fantasies engendered by his extremely lively and most ingenious mind, a mind which imagines the cause of things where the real cause lay hidden. 

In the end, the question resolved, I say the Sun is moved by its own form around its axis, by which form it was ignited and made bright, I say no kind of motion presses upon the remaining planets, which [kind of motion] carries them along, indeed, individual planets are driven round by individual forms with which they were provided, as we indicated sufficiently in the Philolaus, Book 4, chapter 2.  And now, in the following books, we will show more adequately and completely than Kepler the cause of the real acceleration and retardation of the planets, first in some, and then in other parts of their orbit.


Translation after R.E.W Maddison, Appendix III, in Alexandre Koyré,
The Astronomical Revolution, Copernicus, Kepler, Borelli, pp. 37 1-375, modified and expanded by Robert A. Hatch©.