Boulliau:  Planetary Theory: Boulliau's Conical Hypothesis (1645), Primary Documents:  Borelli's response to Boulliau; Boulliau's response to Borelli to Prince Leopold of Tuscan
B  O  U  L  L  I  A  U  -   P  L  A  N  E  T  A  R  Y  -   T  H  E  O  R  Y
Dr Robert A. Hatch  -  University of Florida

B O U L L I A U ' S    C R I T I Q U E   O F   B O R E L L I
Ismaël Boulliau to Prince Leopold [Florence] - Paris 23 July 1666
Original:  Unknown [not BNC Florence]  -  Draft:  BN Paris, 13027, f. 10r-11v
Unpublished Letter Translated from the Latin by R.A. Hatch ©

To the Most Serene and Noble Prince Leopold of Tuscany,
Ismaël Boulliau  S.P.D.

Most Serene Prince

The disturbed state of my affairs, which  has occupied my mind with various concerns for several months, has hindered my activities in so many ways that I have been unable to discharge my duty to your Serene Highness, which has inflicted me with great pain.  I hope you will pardon me in proportion to your kindness and goodwill for whatever faults and transgressions I have admitted in the matter, for the long delay in responding to your kind letters, for books you have sent me, and for so many distinguished observations communicated and imparted to me, for which I have been late in thanking you.  I hope you hold me excused, since this needed to be presented to a more tranquil mind unburdened with cares.

I have read the Theory of the Medicean Planets deduced from the laws of physics by the illustrious M. Jo. Alfonse Borelli.  Anyone knowledgeable in these matters will acknowledge and confess with me from this learned work that he is expert in Geometry and Astronomy; but they will also acknowledge and confess with me that he is fortunate in his speculations from physics. For these conjectures rely heavily on their similarity to truth, not upon proof.  Certainly the idea concerning the motion of the planets, which extends from their appropriate forms, which I adhere to, is no less similar to truth than the other, which states that it is pressed upon them by rays from the Sun.  It is likely that the mean motion around the axis of a cone is thus made; for in truth, the speed of the planet, while it is turned in an Ellipse, is extended through larger circles [rather than being thus] moved closer by the power of the Sun and [thus] proceeding to this speed. Although the learned Borelli presents the fluctuating shifts in length of the funipenduli with the surrounding [circle], which may be applied in some fashion to the fluctuating distances of a given planet from the Sun, nevertheless, no proof follows from this.  But the distances of all the planets from the sun are never different from one another; they can be so applied that the ratios of their accelerations and decelerations answer to the ratios of their revolutions by the unequal interval of time between them. The power of the tendency to be moved by itself towards the sun, and the strength of the revolution repelling the planet from the sun, must be moderated:  Whether by the power of its radii for moving; by the aversion of planetary bodies to motion; or by [actual] resistance of the planetary body to it.  But all of these things subsist as mere suppositions of mind, arising, to be sure, from a mind both subtle and sublime. Yet they do not reveal the truth.  The approach is simpler and more natural, it seems to me, which operates by the simplest means, which assumes the planets are self-moved.

The mind is led to this conclusion, to be sure, by all natural bodies which, as sensitive as they are filled with life, we see are moved by their own form.  In this [case] magnetic principles need not be fashioned, nor other [principles] which, once applied, never agree on all sides.  Nevertheless, I allow anyone to choose as he wishes, since nothing concerning Astronomical Hypotheses can be shown to have been derived from the causes or reasoning of physics.

In the physical hypothesis of the honorable Borelli, a planet is moved more slowly because of its greater distance from the sun and its [corresponding] weaker strength.  In my hypothesis it is due to the smaller circles on which it travels in the Ellipse.

I have stated that an indivisible point, the second focus or axis of the ellipse, is set on the axis of the cone (assuming only indivisibility and length) around which traverse equal motions, which are indeed about the Sun at the other focus, which is the center through which the planes of the planetary ellipses pass and [around which] unequal motion is completed.  The equality of the revolution of the planet is not changed.  Instead, it remains constant around the axis of the cone.  Hence, if the eye were placed at any point along the axis of the cone, through which the plane of the equant circle passes, and in which the planet describes an ellipse, it would always see a uniform motion (with a tiny inequality subtracted) as I have shown in response to the honorable and learned Seth Ward concerning the equinoxes and solstices.  I provide the internal causes of both motions and show they reside in the same system of revolution.  Will the Sun therefore remain an indifferent fount of heat and life, the heart, so to speak, of the entire world? I think not, for its works are more resourceful than can be denied.  But that the sun itself moves the planets (although it does other things on our Earth, by analogy with the other planets, enlivening the forms of living things, in showing the way to be about their work, in assisting the activities of animals, and in illuminating bodies where its perceptible light is able to go) and in moving the planets--which seems to me no closer to the truth than that the planets are moved by their own forms.  Why then do the planes of all the ellipses pass through the center of the Sun, and why is the other point, or focus, found in it by comparison, if the Sun contributes nothing to their motions?  I am able to respond that it is close to the truth that it happens this way:  For the Sun is in the center of the Ellipse, through which all the planets revolve with their planes inclined toward it, so they neither can nor ought to be forced from it.

It is not possible to demonstrate by what means or to what end the planetary paths are moved.  But this much may be close to the truth:  Whole systems of planetary motion ought also to be moved and transferred, since the planets themselves are moved.  These and similar things are based on conjecture and are not confirmed by demonstration.  This distinguished comparison is the product of subtle and skilled reasoning between mechanical laws, either natural motion or the violent motion of projectiles, and consideration of the physical causes of celestial motion.  But no one has asserted that this constitutes proof.  Besides [I recall that the honored M. Borelli is writing much on account of {GK}, without so mentioning]. 

I congratulate the noble artisan Campani, because he has made such exquisite lenses, and also the astronomer Cassini, because he has been so blessed, and has used them there so well, and I proclaim the discipline of Astronomy and its patrons have been overwhelmed by this name.  Up until now there has not arisen in France such fine and accurate instruments.  To your Serene Highness I send attached to this letter an observation of the solar eclipse which I made, and wish greatly that those made in Florence and elsewhere by capable men be shared with me in turn.  Recently a Royal Academy has been established here, and when it convenes in a place fitted with suitable instruments, it will concern itself with such matters more carefully and accurately; for I have learned from certain men in attendance that they have made the observation correctly.  This not withstanding, I have heard that they wish to publish as an example of their work and their industry [a report] agreeing with my observations and those of Agarrat, and adapted to them.

Farewell Serene Prince, and continue to love your Highness' most sincere observer and student who is devoted in proportion to his kindness and generosity. I was writing at Paris on 23 July 1666.