Johannes Kepler quotes - page 3
It is not known so generally that Kepler was... a geometrician and algebraist of considerable power, and that he, Desargues, and perhaps Galileo, may be considered as forming a connecting link between the mathematicians of the renaissance and those of modern times. Kepler's work in geometry consists rather in certain general principles enunciated, and illustrated by a few cases, than in any systematic exposition of the subject. In a short chapter on conics inserted in his Paralipomena, published in 1604, he lays down what has been called the principle of continuity, and gives as an example the statement that a parabola is at once the limiting case of an ellipse and of a hyperbola; he illustrates the same doctrine by reference to the foci of conics (the word focus was introduced by him); and he also explains that parallel lines should be regarded as meeting at infinity. He introduced the use of the eccentric angle in discussing properties of the ellipse.
Johannes Kepler
In his curious tract on Stereometry, published in 1615, Kepler made some advances in the doctrine of infinitesimals. Prompted to the task by a dispute with the seller of some casks of wine, he studied the measurement of solids formed by the revolution of a curve round any line whatever. In solving some of the simplest of these problems, he conceived a circle to be formed of an infinite number of triangles having all their vertices in the centre, and their infinitely small bases in the circumference of the circle, and by thus rendering familiar the idea of quantities infinitely great and infinitely small, he gave an impulse to this branch of mathematics. The failure of Kepler, too, in solving some of the more difficult of the problems which he himself proposed roused the attention of geometers, and seems particularly to have attracted the notice of Cavaleri.
Johannes Kepler
The effective inventor of the telescope and compound microscope was Galileo... Galileo's account of the path of the rays through the concave eye-piece and convex objective which he used was not satisfactory and was considerably improved by Kepler, who suggested the use of two convex lenses which became the basis of later instruments. Kepler had already written an important optical treatise in the form of a commentary on Witelo's Perspectiva... His improvements to the telescope may be regarded as what he had learned from the thirteenth-century writer.
Johannes Kepler
When he discovered the polyhedral hypothesis soon after being sent to teach mathematics in Graz, he changed his mind [about becoming a Lutheran minister], indicating... that he now saw his work in astronomy as an exercise of a priestly vocation. ...he claimed that, in the Harmonice mundi, he offered to the world nothing less than the plan of creation, which God himself had waited six thousand years for someone to comprehend.
Johannes Kepler
I esteem myself happy to have as great an ally as you in my search for truth. I will read your work ... all the more willingly because I have for many years been a partisan of the Copernican view because it reveals to me the causes of many natural phenomena that are entirely incomprehensible in the light of the generally accepted hypothesis. To refute the latter I have collected many proofs, but I do not publish them, because I am deterred by the fate of our teacher Copernicus who, although he had won immortal fame with a few, was ridiculed and condemned by countless people (for very great is the number of the stupid).
Johannes Kepler
A law explains a set of observations; a theory explains a set of laws. The quintessential illustration of this jump in level is the way in which Newton's theory of mechanics explained Kepler's law of planetary motion. Basically, a law applies to observed phenomena in one domain (e.g., planetary bodies and their movements), while a theory is intended to unify phenomena in many domains. Thus, Newton's theory of mechanics explained not only Kepler's laws, but also Galileo's findings about the motion of balls rolling down an inclined plane, as well as the pattern of oceanic tides. Unlike laws, theories often postulate unobservable objects as part of their explanatory mechanism. So, for instance, Freud's theory of mind relies upon the unobservable ego, superego, and id, and in modern physics we have theories of elementary particles that postulate various types of quarks, all of which have yet to be observed.
Johannes Kepler
To say... that the motion of the Earth meeting with the motion of the Lunar Orb, the concurrence of them occasioneth the Ebbing and Flowing [of the seas], is an absolute vanity, not onely because it is not exprest, nor seen how it should so happen, but the falsity is obvious, for that the Revolution of the Earth is not contrary to the motion of the Moon, but is towards the same way. So that all that hath been hitherto said, and imagined by others, is, in my judgment, altogether invalid. But amongst all the famous men that have philosophated upon this admirable effect of Nature, I more wonder at Kepler than any of the rest, who being of a free and piercing wit, and having the motion ascribed to the Earth, before him, hath for all that given his ear and assent to the Moons predominancy over the Water, and to occult properties, and such like trifles.
Johannes Kepler
Galileo argued that nature, God's second book, is written in mathematical letters... Kepler is even more explicit in his work on world harmony; he says: God created the world in accordance with his ideas of creation. These ideas are the pure archetypal forms which Plato termed Ideas, and they can be understood by man as mathematical constructs. They can be understood by Man, because Man was created in the spiritual image of God. Physics is reflection on the divine Ideas of Creation, therefore physics is divine service.
Johannes Kepler
The Harmony of the World is the continuation of the Cosmic Mystery, and the climax of his lifelong obsession. What Kepler attempted here is, simply, to bare the ultimate secret of the universe in an all-embracing synthesis of geometry, music, astrology, astronomy and epistemology. It was the first attempt of this kind since Plato, and it is the last to our day. After Kepler, fragmentation of experience sets in again, science is divorced from religion, religion from art, substance from form, matter from wind.
Johannes Kepler