Part 9

“Le lettere trasposte sono queste:

“Haec immatura a me jam frustra leguntur, o.y.”

Which may be translated thus:—

“I am anxiously looking for an answer to my last two letters, that I may learn what Kepler says about the marvels of Saturn’s orb. In the meantime I send him a riddle concerning a certain new and splendid observation which tends to decide great controversies in astronomy; and especially contains a fine argument in favour of the Pythagorean and Copernican system of the universe. At the proper time I will publish the solution of the riddle, and some other particulars. I hope that I have found a method of determining the periodic times of the four Medicean planets, which Kepler, not without very good reason, thought inexplicable, etc.

“The letters turned into an anagram, are these:

“Haec immatura a me jam frustra leguntur, o.y.”

So far Galileo. But if, reader, this letter has filled you with a desire to know the meaning contained in those letters, then you must read another letter of Galileo which follows.

E the Earth (centre of universe). S the Sun. C centre of eccentric. D centre of planet’s epicycle. VV' stationary points. s v v' projections of SVV' on the ecliptic of which E is the centre.]

S the Sun, centre of solar system. v e positions of planet and Earth at conjunction. VV' stationary points of planet. EE' corresponding positions of the Earth.]

But before you do so, I should like you to notice, by the way, what Galileo says about the Pythagorean and Copernican system of the universe. For he points to my Mystery of the Universe, published fourteen years ago, in which I took the dimensions of the Planetary orbits according to the astronomy of Copernicus, who makes the sun immovable in the centre, and the earth movable both round the sun and upon its own axis; and I showed that the differences of their orbits corresponded to the five regular Pythagorean figures, which had been already distributed by their author among the elements of the world, though the attempt was admirable rather than happy or legitimate, and for which figures’ sake Euclid wrote the whole of his Geometry. Now, in that Mystery you may find a sort of combination of Astronomy and Euclid’s Geometry, and through this combination a most thorough completion and finishing of them both; and this was the reason why I waited with intense longing to see what sort of an argument Galileo would produce in favour of the Pythagorean system of the universe. After this explanation, Galileo’s letter about this argument was as follows:—

Kepler, in his Mystery of the Universe, endeavoured to connect the orbits of the planets with the five regular solids, thus: If in a sphere (i.) a cube be inscribed, and in the cube a sphere (ii.); and in that sphere a tetrahedron, and in the tetrahedron a sphere (iii.); and in that sphere a dodecahedron, and in the dodecahedron a sphere (iv.); and in that sphere an icosahedron, and in the icosahedron a sphere (v.); and in that sphere an octahedron, and in the octahedron a sphere (vi.), the diameters of these six spheres will be proportional to the diameters of the orbits of Saturn, Jupiter, Mars, the Earth, Venus, and Mercury respectively; or, as Kepler expresses it, the common centre of these spheres represents the position of the Sun, and the six spheres represent the spheres of the planets.

By these considerations, however, Kepler was led to enunciate his third law, that the squares of the periodic times of planets are proportional to the cubes of their mean distances from the sun.—KEPLER, Prodromus Dissertationum Mathematicarum continens Mysterium Cosmographicum, etc. (Tübingen, 1596.)

“Illustrissimo e Reverendissimo Signore mio colendissimo.

“È tempo che io deciferi a Vostra Signoria Illustrissima e Reverendissima e per lei al Sig. Keplero le lettere trasposte le quali alcune settimane sono le inviai; è tempo dico, giacchè sono interamente chiaro della verità del fatto, sicchè non ci resta un minimo scrupolo, o dubbio. Sapranno dunque come circa a tre mesi fa vedendosi Venere vespertina la cominciai ad osservar diligentemente coll’occhiale, per veder col senso stesso quello di che non dubitava punto l’intelletto. La vidi dunque sul principio di figura rotonda, pulita e terminata, ma molto picciola; di tal figura si mantenne sino che cominciò ad avvicinarsi alla sua massima digressione, ma tra tanto andò crescendo in mole. Cominciò poi a mancare dalla rotondità nella sua parte orientale ed avversa al Sole, e in pochi giorni si ridusse ad esser un mezzo cerchio perfettissimo, e tale si mantenne, senza punto alterarsi, finchè incominciò à ritirarsi verso il Sole, allontanandosi dalla tangente. Ora va calando dal mezzo cerchio, e si mostra cornicolata, e anderà assottigliandosi sino all’occultazione, riducendosi allora con corna sottilissime. Quindi passando all’ apparizione mattutina, la vedremo pur falcata, e sottilissima e colle corna avverse al Sole; anderà poi crescendo fino alla massima digressione, dove apparirà semicircolare, e tale senza alterarsi si manterrà molti giorni, e poi dal mezzo cerchio passerà presto al tutto tondo, e così rotonda si conserverà poi per molti mesi. Il suo diametro adesso è circa cinque volte maggiore di quello, che si mostrava nella sua prima apparizione vespertina; dalla quale mirabile esperienza abbiamo sensata, e certa dimostrazione di due gran questioni state fin qui dubbie trà i maggiori ingegni del Mondo. L’una è, che i Pianeti tutti son di lor natura tenebrosi (accadendo anco a Mercurio l’istesso, che a Venere). L’altra, che Venere necessarissimamente si volge intorno al Sole, come anco Mercurio, cosa, che degli altri Pianeti, fu creduta da’ Pitagorici, dal Copernico, dal Keplero e da’ loro seguaci, ma non sensatamente provata, come ora in Venere, ed in Mercurio.

“Averanno dunque il Sig. Keplero, e gli altri Copernicani da gloriarsi di aver creduto e filosofato bene, sebbene ci è toccato, e ci è per toccare ancora ad esser reputati dall’ università dei Filosofi in libris, per poco intendenti, e poco meno che stolti.

“Le parole dunque, che mandai trasposte, e che dicevano,

Haec immatura a me jam frustra leguntur, o.y.

dicono ordinate

Cynthiae figuras aemulatur mater amorum.

“Cioè, che Venere imita le figure della Luna. Osservai tre notti sono l’ecclisse, nella quale non vi è cosa notabile, solo si vede il taglio dell’ombra indistinto, confuso e come annebbiato, e questo per derivare essa ombra dalla Terra lontanissima da essa Luna. Voleva scrivere altri particolari, ma essendo stato trattenuto molto da alcuni gentiluomini, ed essendo l’ora tardissima, son forzato a finire. Favoriscami salutare in mio nome i SS. Keplero, Asdale e Segheti, ed a Vostra Signoria Illustrissima con ogni reverenza bacio le mani, e dal Signore Dio gli prego felicità. Di Firenze il primo di Gennaio 1610. Ab Incarnatione.

“Di Vostra Signoria Illustrissima e Reverendissima Servidore obbligatissimo.

Galileo Galilei.”

Such is Galileo’s letter; but let me give you the substance of it:—

“It is time for me to disclose the method of reading the letters which some weeks since I sent you as an anagram. It is time now, I mean, after I have become quite certain about the matter, so much so that I have no longer even a shadow of doubt. You must know then that about three months ago, when the star of Venus could be seen, I began to look at it through a telescope with great attention, so that I might grasp with my physical senses an idea which I was entertaining as certain. At first then you must know the planet Venus appeared of a perfectly circular form, accurately so, and bounded by a distinct edge, but very small; this figure Venus kept until it began to approach its greatest distance from the sun, and meanwhile the apparent size of its orb kept on increasing. From that time it began to lose its roundness on the eastern side, which was turned away from the sun, and in a few days it contracted its visible portion into an exact semicircle; that figure lasted without the smallest alteration until it began to return towards the sun where it leaves the tangent drawn to its epicycle. At this time it loses the semicircular form more and more, and keeps on diminishing that figure until its conjunction, when it will wane to a very thin crescent. After completing its passage past the sun, it will appear to us, at its appearance as a morning star, as only sickle-shaped, turning a very thin crescent away from the sun; afterwards the crescent will fill up more and more until the planet reaches its greatest distance from the sun, in which position it will appear semicircular, and that figure will last for many days without appreciable variation. Then by degrees, from being semicircular it will change to a full orb, and will keep that perfectly circular figure for several months; but at this instant the diameter of the orb of Venus is about five times as large as that which it showed at its first appearance as an evening star.

“From the observation of these wonderful phenomena we are supplied with a determination most conclusive, and appealing to the evidence of our senses, of two very important problems, which up to this day were discussed by the greatest intellects with different conclusions. One is that the planets are bodies not self-luminous (if we may entertain the same views about Mercury as we do about Venus). The second is that we are absolutely compelled to say that Venus (and Mercury also) revolves round the sun, as do also all the rest of the planets. A truth believed indeed by the Pythagorean school, by Copernicus, and by Kepler, but never proved by the evidence of our senses, as it is now proved in the case of Venus and Mercury. Kepler therefore and the rest of the school of Copernicus have good reason for boasting that they have shown themselves good philosophers, and that their belief was not devoid of foundation; however much it has been their lot, and may even hereafter be their lot, to be regarded by the philosophers of our times, who philosophise on paper, with an universal agreement, as men of no intellect, and little better than absolute fools.

“The words which I sent with their letters transposed, and which said,

Haec immatura a me jam frustra leguntur, o.y.

when reduced to their proper order, read thus,