I was almost driven to madness in considering and calculating the matter. I could not find out why the planet [Mars] would rather go on an ellipitical orbit. Oh ridiculous me! As if the libration on the diameter could not also be the way to the ellipse. So this notion brought me up short, that the ellipse exists because of the libration. With reasoning derived from physical principles agreeing with experience, there is no figure left for the orbit of the planet except for a perfect ellipse.…

Why should I mince my words? The truth of Nature, which I had rejected and chased away, returned by stealth through the back door, disguising itself to be accepted. That is to say, I laid [the original equation] aside, and fell back on ellipses, believing that this was a quite different hypothesis, whereas the two, as I shall prove in the next chapter, are one and the same… I thought and searched, until I went nearly mad, for a reason why the planet preferred an elliptical orbit… Ah, what a foolish bird I have been!

Therefore, during the whole time of their appearance, comets fall within the sphere of activity of the circumsolar force, and hence are acted upon by its impulse and therefore (by Corollary 1. Proposition XII) describe conic sections that have their foci in the center of the sun, and by radii drawn from the sun describe areas proportional to the times. For that force propagated to an immense distance, will govern the motions of the bodies far beyond the orbit of Saturn.

(Natural) philosophy is written in this enormous book, which is continuously open before our eyes (I mean the universe) but it cannot be understood without first learning to understand the language, and to recognize the characters in which it is written. It is written in a mathematical language …

How I came to dare to conceive such motion of the Earth, contrary to the received opinion of the Mathematicians and indeed contrary to the impression of the senses, is what your Holiness [the Pope] will rather expect to hear. So I should like your Holiness to know that I was induced to think of a method of computing the motions of the spheres by nothing else than the knowledge that the Mathematicians are inconsistent in these investigations. …

Taking advantage of this I too began to think of the mobility of the Earth; and though the opinion seemed absurd, yet knowing now that others before me had been granted freedom to imagine such circles as they chose to explain the phenomena of the stars, I considered that I also might easily be allowed to try whether by assuming some motion of the earth, sounder explanations than theirs for the revolution of the celestial spheres might so be discovered.

We now bring forth a brand new science about an ancient subject. There is perhaps nothing older than the study of motion, and books, neither few nor small have been written about it by philosophers; nevertheless, I have found among its properties many that, although well worth knowing, have never before been observed, much less demonstrated. They point out a few of the more obvious ones, for example that the natural motion of falling bodies accelerates continuously; but in what proportions that acceleration occurs has not been shown. No one, as far as I know, has demonstrated that a body falling from rest traverses, in equal times, distances that have between them the same proportions as the successive odd numbers starting from one. It has been observed that missiles, that is to say, projectiles follow some kind of curved path, but that it is a parabola no one has shown. I will show that it is, together with other things, neither few in number nor less worth knowing, and what I hold to be even more important, they open the doors to a vast and crucial science of which these our researches will constitute the elements; other geniuses more acute than mine will penetrate its hidden recesses.

From your remarks on the moon, I infer that your telescope is of such an inferior effectiveness, that perhaps it is not suitable for observing the planets. Since July 5, I have seen and noted these planets in the east with Jupiter in the morning….

Therefore, let it lie concealed in hell and likewise let us make nothing of the insults of the entire crowd. For not even the Giants, much less the pygmies, stood against Jupiter. Let Jupiter stand in the heavens, and let the slanderers bark away as much as they wish….

What must be done? Must we stand with Democritus and Heraclitus? I wish, Kepler, that we could laugh at the extraordinary foolishness of the public. What do you say about the foremost philosophers of this university, who filled with the stubborness of vipers have never wished to see the planets, the moon or the telescope, although I have willingly offered a thousand times.

But as a man stops up his ears, so those men have stopped up their eyes against the light of truth….

Why am I not able to laugh with you long since? What a laugh you would have Kepler, if you could hear what things have been put forward against me in the presence of the Grand Duke at Pisa by a distinguished philosopher of this university, while he tried with logical arguments, as though with magical incantations, to tear away and remove from the sky the nine planets.

For the present I will limit myself to quoting the following result: if we imagine the same quantity, which in the case of a single body I have called its entropy, formed in a consistent manner for the whoie universe (taking into account all the conditions), and if at the same time we use the other notion, energy, with its simpler meaning, we can formulate the fundamental laws of the universe corresponding to the laws of the mechanical theory of heat in the following simple form:

1. The energy of the universe is constant.

2. The entropy of the universe tends to a maximum.

There are however innumerable other local motions which on account of the minuteness of the moving particles cannot be detected, such as the motions of the particles in hot bodies, in fermenting bodies, in putrescent bodies, in growing bodies, in the organs of sensation and so forth. If any one shall have the good fortune to discover all these, 1 might almost say that he will have laid bare the whole nature of bodies so far as the mechanical causes of things are concerned.

It is most useful that the true origins of memorable inventions be known, especially of those which were conceived not by accident but by an effort of meditation … One of the noblest inventions of our time has been a new kind of mathematical analysis, known as the differential calculus.

If I wished to attract the student of any of these sciences to an algebra for vectors, I should tell him that the fundamental notions of this algebra were exactly those with which he was daily conversant … In fact, I should tell him that the notions which we use in vector analysis are those which he who reads between the lines will meet on every page of the great masters of analysis, or of those who have probed the deepest secrets of nature.

I do not consider these principles to be certain mysterious qualities feigned as arising from characteristic forms of things, but as universal laws of Nature, by the influence of which these very things have been created. For the phenomena of Nature show that these principles do indeed exist, although their nature has not yet been elucidated. To assert that each and every species is endowed with a mysterious property characteristic to it, due to which it has a definite mode in action, is really equivalent to saying nothing at all. On the other hand, to derive from the phenomena of Nature two or three general principles, and then to explain how the properties and actions of all corporate things follow from those principles, this would indeed be a mighty advance in philosophy, even if the causes of those principles had not at the time been discovered.