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kepler

kepler

kepler Sentence Examples

  • "It appears like the mystical ratios of Kepler which Newton so happily elucidated."

  • It banished the spirits and genii, to which even Kepler had assigned the guardianship of the planetary movements; and, if it supposes the globular particles of the envelope to be the active force in carrying the earth round the sun, we may remember that Newton himself assumed an aether for somewhat similar purposes.

  • Attempts have been made, principally founded on some remarks of Huygens, to show that Descartes had learned the principles of refraction from the manuscript of a treatise by Willebrord Snell, but the facts are uncertain; and, so far as Descartes founds his optics on any one, it is probably on the researches of Kepler.

  • The different editions of the Descriptio and Constructio, as well as the reception of logarithms on the continent of Europe, and especially by Kepler, whose admiration of the invention almost equalled that of Briggs, belong to the history of logarithms (q.v.).

  • When Napier published the Canonis Descriptio England had taken no part in the advance of science, and there is no British author of the time except Napier whose name can be placed in the same rank as those of Copernicus, Tycho Brahe, Kepler, Galileo, or Stevinus.

  • Like Kepler and all his contemporaries he believed in astrology, and he certainly also had some faith in the power of magic, for there is extant a deed written in his own handwriting containing a contract between himself and Robert Logan of Restalrig, a turbulent baron of desperate character, by which Napier undertakes "to serche and sik out, and be al craft and ingyne that he dow, to tempt, trye, and find out" some buried treasure supposed to be hidden in Logan's fortress at Fastcastle, in consideration of receiving one-third part of the treasure found by his aid.

  • In some of these we see a return to Greek theories, though the influence of physical discoveries, more especially those of Copernicus, Kepler and Galileo, is distinctly traceable.

  • In addition to the various works of Brewster already noticed, the following may be mentioned: - Notes and Introduction to Carlyle's translation of Legendre's Elements of Geometry (1824); Treatise on Optics (1831); Letters on Natural Magic, addressed to Sir Walter Scott (1831); The Martyrs of Science, or the Lives of Galileo, Tycho Brake, and Kepler (1841); More Worlds than One (1854).

  • Kepler's Problem, namely, that of finding the co-ordinates of a planet at a given time, which is equivalent - given the mean anomaly - to that of determining the true anomaly, was solved approximately by Kepler, and more completely by Wallis, Newton and others.

  • For the mathematics of Kepler's problem see E.

  • By Kepler's second law the radius vector, FP, sweeps over equal areas in equal times.

  • Another curious theorem proposed by Bouilland in 1625 as a substitute for Kepler's second law is that the angular motion of the body as measured around the empty focus F' is (approximately) uniform.

  • It was only after the publication of Kepler's Rudolphine Table (1626) that more exact results could be obtained.

  • Kepler (1596).

  • The discoveries of Johann Kepler and Bonaventura Cavalieri were the foundation upon which Sir Isaac Newton and Gottfried Wilhelm Leibnitz erected that wonderful edifice, the Infinitesimal Calculus.

  • John Kepler inferred that the planets move in their orbits under some influence or force exerted by the sun; but the laws of motion were not then sufficiently developed, nor were Kepler's ideas of force sufficiently clear, to admit of a precise statement of the nature of the force.

  • Hooke, contemporaries of Newton, saw that Kepler's third law implied a force tending toward the sun which, acting on the several planets, varied inversely as the square of the distance.

  • One was to show that the law of the inverse square not only represented Kepler's third law, but his first two laws also.

  • Moestlin and his pupil Kepler - the latter applying it in 1607 to the observation of a transit of Mercury - also by Johann Fabricius, in 1611, for the first observations of sun-spots.

  • The first to take up the camera obscura after Porta was Kepler, who used it in the old way for solar observations in 1600, and in his Ad Vitellionem Paralipomena (1604) discusses the early problems of the passages of light through small apertures, and the rationale of the simple dark chamber.

  • Wotton written to Lord Bacon in 1620 we learn that Kepler had made himself a portable dark tent fitted with a telescope lens and used for sketching landscapes.

  • They do not seem to have used a lens, or thought of using the telescope for projecting an enlarged image on Kepler's principle.

  • Various writers on optics in the 17th century discussed the principle of the simple dark chamber alone and with single or compound lenses, among them Jean Tarde (Les Astres de Borbon, 1623); Descartes, the pupil of Kepler (Dioptrique, 1637); Bettinus (Apiaria, 1645); A.

  • Wotton's letter of 1620, already noted, was not published till 1651 (Reliquiae Wottonianae, p. 141), but in 1658 a description of Kepler's portable tent camera for sketching, taken from it, was published in a work called Graphite, or the most excellent Art of Painting, but no mention is made of Kepler.

  • The house is also shown where Kepler died in 1630.

  • Suffice it to say that in spite of its spiritualistic starting-point its general result was to give a stimulus to the prevailing scientific tendency as represented by Galileo, Kepler and Harvey to the principle of mechanical explanations of the phenomena of the universe.

  • Rudolph was a clever and cultured man, greatly interested in chemistry, alchemy, astronomy and astrology; he was a patron of Tycho Brahe and Kepler, and was himself something of a scholar and an artist.

  • He extended the "law of continuity" as stated by Johannes Kepler; regarded the denominators of fractions as powers with negative exponents; and deduced from the quadrature of the parabola y=xm, where m is a positive integer, the area of the curves when m is negative or fractional.

  • These functions are named after Friedrich Wilhelm Bessel, who in 1817 introduced them in an investigation on Kepler's Problem.

  • What is thus shown to be possible would, of course, be necessary if we went on, with the astronomer Kepler, to identify the star of the Magi with the conjunction of the planets Jupiter and Saturn which occurred, in the constellation Pisces, in May, October and December of 7 B.C.'

  • The first contemporary mention of Byrgius's table occurs on page 11 of the " Praecepta " prefixed to Kepler's Tabulae Radolphinae (1627); his words are: " apices logistici J.

  • Frisch thinks Bramer possibly relied on Kepler's statement quoted in the text (" Quibus forte confisus Kepleri verbis Benj.

  • There is indirect evidence that Napier was occupied with logarithms as early as 3594, for in a letter to P. Criigerus from Kepler, dated September 9, 1624 (Frisch's Kepler, vi.

  • It is here distinctly stated that some Scotsman in the year 1594, in a letter to Tycho Brahe, gave him some hope of the logarithms; and as Kepler joined Tycho after his expulsion from the island of Huen, and had been so closely associated with him in his work, he would be likely to be correct in any assertion of this kind.

  • In connexion with Kepler's statement the following story, told by Anthony Wood in the Athenae Oxonienses, is of some importance: " It must be now known, that one Dr Craig, a Scotchman..

  • John Kepler, who has been already quoted in connexion with Craig's visit to Tycho Brahe, received the invention of logarithms almost as enthusiastically as Briggs.

  • This erroneous estimate was formed when he had seen the Descriptio but had not read it; and his opinion was very different when he became acquainted with the nature of logarithms. The dedication of his Ephemeris for 1620 consists of a letter to Napier dated the 28th of July 1619, and he there congratulates him warmly on his invention and on the benefit he has conferred upon astronomy generally and upon Kepler's own Rudolphine tables.

  • This letter was written two years after Napier's death (of which Kepler was unaware), and in the same year as that in which the Constructio was published.

  • In the same year (1624) Kepler published at Marburg a table of Napierian logarithms of sines with certain additional columns to facilitate special calculations.

  • .," which contains reprints of Napier's Descriptio of 1614, Kepler's writings on logarithms (1624-1625), &c. In 1889 a translation of Napier's Constructio of 1619 was published by Walter Rae Macdonald.

  • The first table of this kind appeared in Kepler's work of 1624 which has been already referred to.

  • Besides Napier and Briggs, special reference should be made to Kepler (Chilias, 1624) and Mercator (Logarithmotechnia, 1668), whose methods were arithmetical, and to Newton, Gregory, Halley and Cotes, who employed series.

  • Kepler, Uber Gnosis and altbabylonische Religion, a lecture delivered at the Congress of Orientalists (Berlin, 1881); A.

  • JOHANN KEPLER (1571-1630), German astronomer, was born on the 27th of December 1571, at Weil, in the duchy of Wurttemberg, of which town his grandfather was burgomaster.

  • His father, Henry Kepler, was a reckless soldier of fortune; his mother, Catherine Guldenmann, the daughter of the burgomaster of Eltingen, was undisciplined and ill-educated.

  • The misfortune and misconduct of his parents were not the only troubles of Kepler's childhood.

  • Soon after his arrival at Gratz, Kepler contracted an engagement with Barbara von Miihleck, a wealthy Styrian heiress, who, at the age of twenty-three, had already survived one husband and been divorced from another.

  • Before her relatives could be brought to countenance his pretensions, Kepler was obliged to undertake a journey to Wurttemberg to obtain documentary evidence of the somewhat obscure nobility of his family, and it was thus not until the 27th of April 1597 that the marriage was celebrated.

  • Kepler immediately fled to the Hungarian frontier, but, by the favour of the Jesuits, was recalled and reinstated in his post.

  • 24, 1601) a brilliant career seemed to be thrown open to Kepler.

  • Having been provided, in August 1610, by Ernest, archbishop of Cologne, with one of the new Galilean instruments, Kepler began, with unspeakable delight, to observe the wonders revealed by it.

  • The year 1611 was marked by Kepler as the most disastrous of his life.

  • Kepler's fidelity in remaining with him to the last did not deprive him of the favour of his successor.

  • Kepler's second courtship forms the subject of a highly characteristic letter addressed by him to Baron Stralendorf, in which he reviews the qualifications of eleven candidates for his hand, and explains the reasons which decided his choice in favour of a portionless orphan girl named Susanna Reutlinger.

  • The restless disposition and unbridled tongue of Catherine Kepler, his mother, created for her numerous enemies in the little town of Leonberg; while her unguarded conduct exposed her to a species of calumny at that time readily circulated and believed.

  • Kepler immediately hastened to Wurttemberg, and owing to his indefatigable exertions she was acquitted after having suffered thirteen month's imprisonment, and endured with undaunted courage the formidable ordeal of "territion," or examination under the imminent threat of torture.

  • Kepler's whole attention was now devoted to the production of the new tables.

  • Appended were tables of logarithms and of refraction, together with Tycho's catalogue of 777 stars, enlarged by Kepler to 1005.

  • Kepler's claims upon the insolvent imperial exchequer amounted by this time to 12,000 florins.

  • The emperor Ferdinand II., too happy to transfer the burden, countenanced an arrangement by which Kepler entered the service of the duke of Friedland (Wallenstein), who assumed the full responsibility of the debt.

  • In July 1628 Kepler accordingly arrived with his family at Sagan in Silesia, where he applied himself to the printing of his ephemerides up to the year 1636, and whence he issued, in 1629, a Notice to the Curious in Things Celestial, warning astronomers of approaching transits.

  • Wallenstein's promises to Kepler were but imperfectly fulfilled.

  • In lieu of the sums due, he offered him a professorship at Rostock, which Kepler declined.

  • The character of Kepler's genius is especially difficult to estimate.

  • It is impossible to consider without surprise the colossal amount of work accomplished by Kepler under numerous disadvantages.

  • Kepler's extensive literary remains, purchased by the empress Catherine II.

  • Reuschle, Kepler and die Astronomie (Frankfort, 1871); Karl Goebel, Ober Keplers astronomische Anschauungen (Halle, 1871); E.

  • Forster, Johann Kepler and die Harmonie der Sphdren (Berlin, 1862); R.

  • Kepler in Prag (1872); H.

  • Brocard, Essai sur la Mete'orologie de Kepler (Grenoble, 1 879, 1881); Siegmund Gunther, Johannes Kepler and der tellurischkosmische Magnetismus (Wien, 1888); N.

  • He now set himself to the revision of the Rudolphine Tables (published by Kepler in 1627), and in the progress of his task became convinced that a transit of Venus overlooked by Kepler would nevertheless occur on the 24th of November (O.S.) 1639.

  • This transit of Venus is remarkable as the first ever observed, that of 1631 predicted by Kepler having been invisible in western Europe.

  • He first brought the revolutions of our satellite within the domain of Kepler's laws, pointing out that her apparent irregularities could be completely accounted for by supposing her to move in an ellipse with a variable eccentricity and directly rotatory major axis, of which the earth occupied one focus.

  • He also reduced the solar parallax to 14" (less than a quarter of Kepler's estimate), corrected the sun's semi-diameter to 15' 45", recommended decimal notation, and was the first to make tidal observations.

  • As early as 1530 the Lutheran doctrine was preached in Graz by Seifried and Jacob von Eggenberg, and in 1540 Eggenberg founded the Paradies or Lutheran school, in which Kepler afterwards taught.

  • The Copernican theory of the solar system - that the earth revolved annually about the sun - had received confirmation by the observations of Galileo and Tycho Brahe, and the mathematical investigations of Kepler and Newton.

  • He quotes as an instance that Newton in this way added to the planetary appearances contained in Kepler's laws the gravitation of the planets to the sun, as a notion of causality not contained in the appearances, and thus discovered that gravitation is the cause of the appearances.

  • Kepler (1571-1630) was led by his study of the planetary motions to reject this method of statement as inadequate, and it is in fact incapable of giving a complete representation of the motions in question.

  • In 1609 and 1619 Kepler published his new laws of planetary motion, which were subsequently shown by Newton to agree with the results obtained by experiment for the motion of terrestrial bodies.

  • As a law of acceleration of the planets relatively to the sun, its approximate agreement with Kepler's third law of planetary motion follows readily from a consideration of the character of the acceleration of a point moving uniformly in a circle.

  • Some years later he succeeded in showing that Kepler's elliptic orbit for planetary motion agreed with the assumed law of attraction; he also completed the co-ordination with terrestrial gravity by his investigation of the attractions of homogeneous spherical bodies.

  • His astronomical vocation, like that of Kepler, came from without.

  • During this journey, the duration of which cannot be precisely stated, Hobbes acquired some knowledge of French and Italian, and also made the important discovery that the scholastic philosophy which he had learned in Oxford was almost universally neglected in favour of the scientific and critical methods of Galileo, Kepler and Montaigne.

  • 112), makes two incidental references to Bacon's writings, but never mentions Bacon as he mentions Galileo, Kepler, Harvey, and others (De corpore, ep. ded.), among the lights of the century.

  • In astronomy he depreciates the merits of Newton and elevates Kepler, accusing Newton particularly, a propos of the distinction of centrifugal and centripetal forces, of leading to a confusion between what is mathematically to be distinguished and what is physically separate.

  • Kepler, who examined Porta's account of his concave and convex lenses by desire of his patron the emperor Rudolph, declared that it was perfectly unintelligible.

  • Kepler first explained the theory and some of the practical advantages of a telescope constructed of two convex lenses in his Catoptrics (1611).

  • William Gascoigne was the first who practically appreciated the chief advantages of the form of telescope suggested by Kepler, viz., the visibility of the image of a distant object simultaneously with that of a small material object placed in the common focus of the two lenses.

  • But it was not till about the middle of the 17th century that Kepler's telescope came into general use, and then, not so much because of the advantages pointed out by Gascoigne, but because its field of view was much larger than in the Galilean telescope.

  • The sharpness of image in Kepler's telescope is very inferior to that of the Galilean instrument, so that when a high magnifying power is required it becomes essential to increase the focal length.

  • The former represents Kepler's, the latter Lippershey's or the Galilean telescope.

  • " Kepler's " nova in Ophiuchus broke out in 1604 and attained a brightness greater than that of Jupiter; it likewise gradually waned, and disappeared after about fifteen months.

  • Much of the Principia consists of synthetical deductions from definitions and axioms. But the discovery of the centripetal force of the planets to the sun is an analytic deduction from the facts of their motion discovered by Kepler to their real ground, and is so stated by Newton in the first regressive order of Aristotle - P-M, S-P, S-M.

  • Newton did indeed first show synthetically what kind of motions by mechanical laws have their ground in a centripetal force varying inversely as the square of the distance (all P is M); but his next step was, not to deduce synthetically the planetary motions, but to make a new start from the planetary motions as facts established by Kepler's laws and as examples of the kind of motions in question (all S is P); and then, by combining these two premises, one mechanical and the other astronomical, he analytically deduced that these facts of planetary motion have their ground in a centripetal force varying inversely as the squares of the distances of the planets from the sun (all S is M).

  • Phaenomena, 4-5; prop. 2.) What Newton did, in short, was to prove by analysis that the planets, revolving by Kepler's astronomical laws round the sun, have motions such as by mechanical laws are consequences of a centripetal force to the sun.

  • Thus Whewell mistook Kepler's inference that Mars moves in an ellipse for an induction, though it required the combination of Tycho's and Kepler's observations, as a minor, with the laws of conic sections discovered by the Greeks, as a major, premise.

  • Kepler and Galilei secured it against that disaster.

  • He made some preliminary use of these expressions in 1817, in a paper on Kepler's Problem (Transactions Berlin Academy, 1816-1817, p. 49), and fully developed them seven years later, for the purposes of a research into planetary perturbations (Ibid.

  • Johann Kepler had proved by an elaborate series of measurements that each planet revolves in an elliptical orbit round the sun, whose centre occupies one of the foci of the orbit, that the radius vector of each planet drawn from the sun describes equal areas in equal times, and that the squares of the periodic times of the planets are in the same proportion as the cubes of their mean distances from the sun.

  • Newton, by calculating from Kepler's laws, and supposing the orbits of the planets to be circles round the sun in the centre, had already proved that the force of the sun acting upon the different planets must vary as the inverse square of the distances of the planets from the sun.

  • Many of the letters are lost, but it is clear from one of Newton's, dated the 19th of September 1685, that he had received many useful communications from Flamsteed, and especially regarding Saturn, " whose orbit, as defined by Kepler," Newton " found too little for the sesquialterate proportions."

  • In the other letters written in 1685 and 1686 he applies to Flamsteed for information respecting the orbits of the satellites of Jupiter and Saturn, respecting the rise and fall of the spring and neap tides at the solstices and the equinoxes, respecting the flattening of Jupiter at the poles (which, if certain, he says, would conduce much to the stating the reasons of the precession of the equinoxes), and respecting the difference between the observed places of Saturn and those computed from Kepler's tables about the time of his conjunction with Jupiter.

  • " Your information," he says, " about the errors of Kepler's tables for Jupiter and Saturn has eased me of several scruples.

  • For as Kepler knew the orb to be not circular but oval, and guessed it to be elliptical, so Mr Hooke, without knowing what I have found out since his letters to me, can know no more, but that the proportion was duplicate quam proxime at great distances from the centre, and only guessed it to be so accurately, and guessed amiss in extending that proportion down to the very centre, whereas Kepler guessed right at the ellipsis.

  • And so Mr Hooke found less of the proportion than Kepler of the ellipsis.

  • And so, in stating this business, I do pretend to have done as much for the proportion as for the ellipsis, and to have as much right to the one from Mr Hooke and all men, as to the other from Kepler; and therefore on this account also he must at least moderate his pretences.

  • The doctrine of geometrical continuity and the application of algebra to geometry, developed in the 16th and 17th centuries mainly by Kepler and Descartes, led to the discovery of many properties which gave to the notion of infinity, as a localized space conception, a predominant importance.

  • The science had its origin in the demonstration by Sir Isaac Newton that Kepler's three laws of planetary motion, and the law of gravitation, in the case of two bodies, could be mutually derived from each other.

  • Conversely, assuming this law of attraction, it can be shown that the planets will move according to Kepler's laws.

  • The power and spirit of the analytic method will be appreciated by showing how it expresses the relations of motion as they were conceived geometrically by Newton and Kepler.

  • It is quite evident that Kepler's laws do not in themselves enable us to determine the actual motion of the planets.

  • Having these data, the position of the planet at any other time may be geometrically constructed by Kepler's laws.

  • The problem of constructing successive radii vectores, the angles of which are measured off from the radius vector of the body at the original given position, is then a geometric one, known as Kepler's problem.

  • The periodic time varying inversely as n, this equation expresses Kepler's third law.

  • Kepler's third law therefore expresses the fact that the mass of the sun is the same for all the planets, and deviates from the truth only to the extent that the masses of the latter differ from each other by quantities which are only a small fraction of the mass of the sun.

  • ==Problem of Three Bodies== As soon as the general law of gravitation was fully apprehended, it became evident that, owing to the attraction of each planet upon all the others, the actual motion of the planets must deviate from their motion in an ellipse according to Kepler's laws.

  • This is an extension of Kepler's second law.

  • (2) The motion takes place in accord with Kepler's laws, enunciated elsewhere.

  • (6) The relation between the periodic time of a planet and its mean distance, approximately expressed by Kepler's third law, follows very simply from the laws of centrifugal force.

  • - Kepler's laws do not completely express the motion of a planet around a central body, except when no force but the mutual attraction of the two bodies comes into play.

  • No more congruous arrangement could have been devised than the inheritance by Johann Kepler of the wealth of materials amassed by Tycho Brahe.

  • Kepler, on the contrary, was endowed with unlimited powers of speculation, but had no mechanical faculty.

  • The announcement of the third of " Kepler's Laws " was made ten years later, in De Harmonice Mundi.

  • Kepler's ineradicable belief in the existence of some such congruity was derived from the Pythagorean idea of an underlying harmony in nature; but his arduous efforts for its realization took a devious and fantastic course which seemed to give little promise of their surprising ultimate success.

  • The formal astronomy of the ancients left Kepler unsatisfied.

  • Galileo Galilei, Kepler's most eminent contemporary, took a foremost part in dissipating the obscurity that still hung over the very foundations of mechanical science.

  • Yet they were never assimilated by Kepler; while, on the other hand, the laws of planetary circulation he had enounced were strangely ignored by Galileo.

  • Galileo's contributions to astronomy were of a different quality from Kepler's.

  • The true foundations of a mechanical theory of the heavens were laid by Kepler's discoveries, and by Galileo's dynamical demonstrations; its construction was facilitated by the development of mathematical methods.

  • At the same time, however, he followed with interest the discoveries of Galileo and Kepler, and became more and more dissatisfied with the Peripatetic system.

  • the Platonic solids, while the four polyhedra in which the centre is multiply enclosed are referred to as the Kepler-Poinsot solids, Kepler having discovered three, while Poinsot discovered the fourth.

  • [iv.] 1810), three of them having been previously considered by Kepler.

  • Galileo seems, at an early period of his life, to have adopted the Copernican theory of the solar system, and was deterred from avowing his opinions - as is proved by his letter to Kepler of August 4, 1 597 - b y the fear of ridicule rather than of persecution.

  • To this notion, which took its rise in a confusion of thought, he attached capital importance, and he treated with scorn Kepler's suggestion that a certain occult attraction of the moon was in some way concerned in the phenomenon.

  • Kepler's first and second laws were published in 1609, and his third ten years later.

  • Kepler was more cautious in his opinion; he spoke of astronomy as the wise mother, and astrology as the foolish daughter, but he added that the existence of the daughter was necessary to the life of the mother.

  • We may here notice one very remarkable prediction of the master of Kepler.

  • Kepler explained the double movement of the earth by the rotation of the sun.

  • Kepler, who in his youth made almanacs, and once prophesied a hard winter, which came to pass, could not help putting an astrological interpretation on the disappearance of the brilliant star of 1572, which Tycho had observed.

  • The constancy of this velocity in the case of the sun and a single planet is formulated in Kepler's second law.

  • Johann Kepler (1571-1630) made many important discoveries in the geometry of conics.

  • We may also notice Kepler's approximate value for the circumference of an ellipse (if the semi-axes be a and b, the approximate circumference is ir(a+b)).

  • The mechanics of the Copernican astronomy of Galileo attracted him and he also studied Kepler ' s Optics.

  • He wrote to Kepler suggesting a mechanical means to calculate ephemerides.

  • In the case of the Kepler Mission about 1000 of our target stars should have giant inner planets.

  • "It appears like the mystical ratios of Kepler which Newton so happily elucidated."

  • It is beyond doubt that Huygens independently discovered that an object placed in the common focus of the two lenses of a Kepler telescope appears as distinct and well-defined as the 3 Delambre, Hist.

  • These doctrines of inertia, and of the composite character of curvilinear motion, were scarcely apprehended even by Kepler or Galileo; but they follow naturally from the geometrical analysis of Descartes.

  • It banished the spirits and genii, to which even Kepler had assigned the guardianship of the planetary movements; and, if it supposes the globular particles of the envelope to be the active force in carrying the earth round the sun, we may remember that Newton himself assumed an aether for somewhat similar purposes.

  • Attempts have been made, principally founded on some remarks of Huygens, to show that Descartes had learned the principles of refraction from the manuscript of a treatise by Willebrord Snell, but the facts are uncertain; and, so far as Descartes founds his optics on any one, it is probably on the researches of Kepler.

  • The different editions of the Descriptio and Constructio, as well as the reception of logarithms on the continent of Europe, and especially by Kepler, whose admiration of the invention almost equalled that of Briggs, belong to the history of logarithms (q.v.).

  • When Napier published the Canonis Descriptio England had taken no part in the advance of science, and there is no British author of the time except Napier whose name can be placed in the same rank as those of Copernicus, Tycho Brahe, Kepler, Galileo, or Stevinus.

  • Like Kepler and all his contemporaries he believed in astrology, and he certainly also had some faith in the power of magic, for there is extant a deed written in his own handwriting containing a contract between himself and Robert Logan of Restalrig, a turbulent baron of desperate character, by which Napier undertakes "to serche and sik out, and be al craft and ingyne that he dow, to tempt, trye, and find out" some buried treasure supposed to be hidden in Logan's fortress at Fastcastle, in consideration of receiving one-third part of the treasure found by his aid.

  • Considering the time in which he lived, Napier is singularly free from superstition: his Plaine Discovery relates to a method of interpretation which belongs to a later age; he shows no trace of the extravagances which occur everywhere in the works of Kepler; and none of his writings contain allusions to astrology or magic.

  • In some of these we see a return to Greek theories, though the influence of physical discoveries, more especially those of Copernicus, Kepler and Galileo, is distinctly traceable.

  • In addition to the various works of Brewster already noticed, the following may be mentioned: - Notes and Introduction to Carlyle's translation of Legendre's Elements of Geometry (1824); Treatise on Optics (1831); Letters on Natural Magic, addressed to Sir Walter Scott (1831); The Martyrs of Science, or the Lives of Galileo, Tycho Brake, and Kepler (1841); More Worlds than One (1854).

  • Kepler's Problem, namely, that of finding the co-ordinates of a planet at a given time, which is equivalent - given the mean anomaly - to that of determining the true anomaly, was solved approximately by Kepler, and more completely by Wallis, Newton and others.

  • For the mathematics of Kepler's problem see E.

  • If the law of attraction is that of gravitation, the orbit is a conic section - ellipse, parabola or hyperbola - having the centre of attraction in one of its foci; and the motion takes place in accordance with Kepler's laws (see Astronomy).

  • By Kepler's second law the radius vector, FP, sweeps over equal areas in equal times.

  • Another curious theorem proposed by Bouilland in 1625 as a substitute for Kepler's second law is that the angular motion of the body as measured around the empty focus F' is (approximately) uniform.

  • It is shown in the article Astronomy (Celestial Mechanics) that the mean distance and mean motion or time of revolution of a planet are so related by Kepler's third law that, when one of these elements is given, the other can be found.

  • The problem of determining a heliocentric orbit first presented itself to Kepler, who actually determined that of Mars.

  • It was only after the publication of Kepler's Rudolphine Table (1626) that more exact results could be obtained.

  • Kepler (1596).

  • The discoveries of Johann Kepler and Bonaventura Cavalieri were the foundation upon which Sir Isaac Newton and Gottfried Wilhelm Leibnitz erected that wonderful edifice, the Infinitesimal Calculus.

  • John Kepler inferred that the planets move in their orbits under some influence or force exerted by the sun; but the laws of motion were not then sufficiently developed, nor were Kepler's ideas of force sufficiently clear, to admit of a precise statement of the nature of the force.

  • Hooke, contemporaries of Newton, saw that Kepler's third law implied a force tending toward the sun which, acting on the several planets, varied inversely as the square of the distance.

  • One was to show that the law of the inverse square not only represented Kepler's third law, but his first two laws also.

  • Moestlin and his pupil Kepler - the latter applying it in 1607 to the observation of a transit of Mercury - also by Johann Fabricius, in 1611, for the first observations of sun-spots.

  • The first to take up the camera obscura after Porta was Kepler, who used it in the old way for solar observations in 1600, and in his Ad Vitellionem Paralipomena (1604) discusses the early problems of the passages of light through small apertures, and the rationale of the simple dark chamber.

  • Wotton written to Lord Bacon in 1620 we learn that Kepler had made himself a portable dark tent fitted with a telescope lens and used for sketching landscapes.

  • They do not seem to have used a lens, or thought of using the telescope for projecting an enlarged image on Kepler's principle.

  • Various writers on optics in the 17th century discussed the principle of the simple dark chamber alone and with single or compound lenses, among them Jean Tarde (Les Astres de Borbon, 1623); Descartes, the pupil of Kepler (Dioptrique, 1637); Bettinus (Apiaria, 1645); A.

  • Wotton's letter of 1620, already noted, was not published till 1651 (Reliquiae Wottonianae, p. 141), but in 1658 a description of Kepler's portable tent camera for sketching, taken from it, was published in a work called Graphite, or the most excellent Art of Painting, but no mention is made of Kepler.

  • The house is also shown where Kepler died in 1630.

  • Suffice it to say that in spite of its spiritualistic starting-point its general result was to give a stimulus to the prevailing scientific tendency as represented by Galileo, Kepler and Harvey to the principle of mechanical explanations of the phenomena of the universe.

  • Rudolph was a clever and cultured man, greatly interested in chemistry, alchemy, astronomy and astrology; he was a patron of Tycho Brahe and Kepler, and was himself something of a scholar and an artist.

  • He extended the "law of continuity" as stated by Johannes Kepler; regarded the denominators of fractions as powers with negative exponents; and deduced from the quadrature of the parabola y=xm, where m is a positive integer, the area of the curves when m is negative or fractional.

  • These functions are named after Friedrich Wilhelm Bessel, who in 1817 introduced them in an investigation on Kepler's Problem.

  • What is thus shown to be possible would, of course, be necessary if we went on, with the astronomer Kepler, to identify the star of the Magi with the conjunction of the planets Jupiter and Saturn which occurred, in the constellation Pisces, in May, October and December of 7 B.C.'

  • The first contemporary mention of Byrgius's table occurs on page 11 of the " Praecepta " prefixed to Kepler's Tabulae Radolphinae (1627); his words are: " apices logistici J.

  • Frisch thinks Bramer possibly relied on Kepler's statement quoted in the text (" Quibus forte confisus Kepleri verbis Benj.

  • There is indirect evidence that Napier was occupied with logarithms as early as 3594, for in a letter to P. Criigerus from Kepler, dated September 9, 1624 (Frisch's Kepler, vi.

  • It is here distinctly stated that some Scotsman in the year 1594, in a letter to Tycho Brahe, gave him some hope of the logarithms; and as Kepler joined Tycho after his expulsion from the island of Huen, and had been so closely associated with him in his work, he would be likely to be correct in any assertion of this kind.

  • In connexion with Kepler's statement the following story, told by Anthony Wood in the Athenae Oxonienses, is of some importance: " It must be now known, that one Dr Craig, a Scotchman..

  • John Kepler, who has been already quoted in connexion with Craig's visit to Tycho Brahe, received the invention of logarithms almost as enthusiastically as Briggs.

  • This erroneous estimate was formed when he had seen the Descriptio but had not read it; and his opinion was very different when he became acquainted with the nature of logarithms. The dedication of his Ephemeris for 1620 consists of a letter to Napier dated the 28th of July 1619, and he there congratulates him warmly on his invention and on the benefit he has conferred upon astronomy generally and upon Kepler's own Rudolphine tables.

  • This letter was written two years after Napier's death (of which Kepler was unaware), and in the same year as that in which the Constructio was published.

  • In the same year (1624) Kepler published at Marburg a table of Napierian logarithms of sines with certain additional columns to facilitate special calculations.

  • .," which contains reprints of Napier's Descriptio of 1614, Kepler's writings on logarithms (1624-1625), &c. In 1889 a translation of Napier's Constructio of 1619 was published by Walter Rae Macdonald.

  • The first table of this kind appeared in Kepler's work of 1624 which has been already referred to.

  • Besides Napier and Briggs, special reference should be made to Kepler (Chilias, 1624) and Mercator (Logarithmotechnia, 1668), whose methods were arithmetical, and to Newton, Gregory, Halley and Cotes, who employed series.

  • Kepler, Uber Gnosis and altbabylonische Religion, a lecture delivered at the Congress of Orientalists (Berlin, 1881); A.

  • JOHANN KEPLER (1571-1630), German astronomer, was born on the 27th of December 1571, at Weil, in the duchy of Wurttemberg, of which town his grandfather was burgomaster.

  • His father, Henry Kepler, was a reckless soldier of fortune; his mother, Catherine Guldenmann, the daughter of the burgomaster of Eltingen, was undisciplined and ill-educated.

  • The misfortune and misconduct of his parents were not the only troubles of Kepler's childhood.

  • The best recognized function of German astronomers in that day was the construction of prophesying almanacs, greedily bought by a credulous public. Kepler thus found that the first duties required of him were of an astrological nature, and set himself with characteristic alacrity to master the rules of the art as laid down by Ptolemy and Cardan.

  • Soon after his arrival at Gratz, Kepler contracted an engagement with Barbara von Miihleck, a wealthy Styrian heiress, who, at the age of twenty-three, had already survived one husband and been divorced from another.

  • Before her relatives could be brought to countenance his pretensions, Kepler was obliged to undertake a journey to Wurttemberg to obtain documentary evidence of the somewhat obscure nobility of his family, and it was thus not until the 27th of April 1597 that the marriage was celebrated.

  • Kepler immediately fled to the Hungarian frontier, but, by the favour of the Jesuits, was recalled and reinstated in his post.

  • 24, 1601) a brilliant career seemed to be thrown open to Kepler.

  • In this, the most memorable of Kepler's multifarious writings, two of the cardinal principles of modern astronomy - the laws of elliptical orbits and of equal areas - were established (see Astronomy: History); important truths relating to gravity were enunciated, and the tides ascribed to the influence of lunar attraction; while an attempt to explain the planetary revolutions in the then backward condition of mechanical knowledge produced a theory of vortices closely resembling that afterwards adopted by Descartes.

  • Having been provided, in August 1610, by Ernest, archbishop of Cologne, with one of the new Galilean instruments, Kepler began, with unspeakable delight, to observe the wonders revealed by it.

  • The year 1611 was marked by Kepler as the most disastrous of his life.

  • Kepler's fidelity in remaining with him to the last did not deprive him of the favour of his successor.

  • Kepler's second courtship forms the subject of a highly characteristic letter addressed by him to Baron Stralendorf, in which he reviews the qualifications of eleven candidates for his hand, and explains the reasons which decided his choice in favour of a portionless orphan girl named Susanna Reutlinger.

  • The insurmountable difficulties presented by the lunar theory forced Kepler, after an enormous amount of fruitless labour, to abandon his design of comprehending the whole scheme of the heavens in one great work to be called Hipparchus, and he then threw a portion of his materials into the form of a dialogue intended for the instruction of general readers.

  • The restless disposition and unbridled tongue of Catherine Kepler, his mother, created for her numerous enemies in the little town of Leonberg; while her unguarded conduct exposed her to a species of calumny at that time readily circulated and believed.

  • Kepler immediately hastened to Wurttemberg, and owing to his indefatigable exertions she was acquitted after having suffered thirteen month's imprisonment, and endured with undaunted courage the formidable ordeal of "territion," or examination under the imminent threat of torture.

  • Kepler's whole attention was now devoted to the production of the new tables.

  • The pursuit of science needed a more tranquil shelter; and on the raising of the blockade, Kepler obtained permission to transfer his types to Ulm, where, in September 1627, the Rudolphine Tables were at length given to the world.

  • Appended were tables of logarithms and of refraction, together with Tycho's catalogue of 777 stars, enlarged by Kepler to 1005.

  • Kepler's claims upon the insolvent imperial exchequer amounted by this time to 12,000 florins.

  • The emperor Ferdinand II., too happy to transfer the burden, countenanced an arrangement by which Kepler entered the service of the duke of Friedland (Wallenstein), who assumed the full responsibility of the debt.

  • In July 1628 Kepler accordingly arrived with his family at Sagan in Silesia, where he applied himself to the printing of his ephemerides up to the year 1636, and whence he issued, in 1629, a Notice to the Curious in Things Celestial, warning astronomers of approaching transits.

  • Wallenstein's promises to Kepler were but imperfectly fulfilled.

  • In lieu of the sums due, he offered him a professorship at Rostock, which Kepler declined.

  • The character of Kepler's genius is especially difficult to estimate.

  • It is impossible to consider without surprise the colossal amount of work accomplished by Kepler under numerous disadvantages.

  • Kepler's extensive literary remains, purchased by the empress Catherine II.

  • Reuschle, Kepler and die Astronomie (Frankfort, 1871); Karl Goebel, Ober Keplers astronomische Anschauungen (Halle, 1871); E.

  • Forster, Johann Kepler and die Harmonie der Sphdren (Berlin, 1862); R.

  • Kepler in Prag (1872); H.

  • Brocard, Essai sur la Mete'orologie de Kepler (Grenoble, 1 879, 1881); Siegmund Gunther, Johannes Kepler and der tellurischkosmische Magnetismus (Wien, 1888); N.

  • In 1636 he met with a congenial spirit in William Crabtree, a draper of Broughton, near Manchester; and encouraged by his advice he exchanged the guidance of Philipp von Lansberg, a pretentious but inaccurate Belgian astronomer, for that of Kepler.

  • He now set himself to the revision of the Rudolphine Tables (published by Kepler in 1627), and in the progress of his task became convinced that a transit of Venus overlooked by Kepler would nevertheless occur on the 24th of November (O.S.) 1639.

  • This transit of Venus is remarkable as the first ever observed, that of 1631 predicted by Kepler having been invisible in western Europe.

  • He first brought the revolutions of our satellite within the domain of Kepler's laws, pointing out that her apparent irregularities could be completely accounted for by supposing her to move in an ellipse with a variable eccentricity and directly rotatory major axis, of which the earth occupied one focus.

  • He also reduced the solar parallax to 14" (less than a quarter of Kepler's estimate), corrected the sun's semi-diameter to 15' 45", recommended decimal notation, and was the first to make tidal observations.

  • As early as 1530 the Lutheran doctrine was preached in Graz by Seifried and Jacob von Eggenberg, and in 1540 Eggenberg founded the Paradies or Lutheran school, in which Kepler afterwards taught.

  • The Copernican theory of the solar system - that the earth revolved annually about the sun - had received confirmation by the observations of Galileo and Tycho Brahe, and the mathematical investigations of Kepler and Newton.

  • He quotes as an instance that Newton in this way added to the planetary appearances contained in Kepler's laws the gravitation of the planets to the sun, as a notion of causality not contained in the appearances, and thus discovered that gravitation is the cause of the appearances.

  • Kepler (1571-1630) was led by his study of the planetary motions to reject this method of statement as inadequate, and it is in fact incapable of giving a complete representation of the motions in question.

  • In 1609 and 1619 Kepler published his new laws of planetary motion, which were subsequently shown by Newton to agree with the results obtained by experiment for the motion of terrestrial bodies.

  • As a law of acceleration of the planets relatively to the sun, its approximate agreement with Kepler's third law of planetary motion follows readily from a consideration of the character of the acceleration of a point moving uniformly in a circle.

  • Some years later he succeeded in showing that Kepler's elliptic orbit for planetary motion agreed with the assumed law of attraction; he also completed the co-ordination with terrestrial gravity by his investigation of the attractions of homogeneous spherical bodies.

  • His astronomical vocation, like that of Kepler, came from without.

  • During this journey, the duration of which cannot be precisely stated, Hobbes acquired some knowledge of French and Italian, and also made the important discovery that the scholastic philosophy which he had learned in Oxford was almost universally neglected in favour of the scientific and critical methods of Galileo, Kepler and Montaigne.

  • 112), makes two incidental references to Bacon's writings, but never mentions Bacon as he mentions Galileo, Kepler, Harvey, and others (De corpore, ep. ded.), among the lights of the century.

  • In astronomy he depreciates the merits of Newton and elevates Kepler, accusing Newton particularly, a propos of the distinction of centrifugal and centripetal forces, of leading to a confusion between what is mathematically to be distinguished and what is physically separate.

  • Kepler, who examined Porta's account of his concave and convex lenses by desire of his patron the emperor Rudolph, declared that it was perfectly unintelligible.

  • Kepler first explained the theory and some of the practical advantages of a telescope constructed of two convex lenses in his Catoptrics (1611).

  • William Gascoigne was the first who practically appreciated the chief advantages of the form of telescope suggested by Kepler, viz., the visibility of the image of a distant object simultaneously with that of a small material object placed in the common focus of the two lenses.

  • But it was not till about the middle of the 17th century that Kepler's telescope came into general use, and then, not so much because of the advantages pointed out by Gascoigne, but because its field of view was much larger than in the Galilean telescope.

  • The sharpness of image in Kepler's telescope is very inferior to that of the Galilean instrument, so that when a high magnifying power is required it becomes essential to increase the focal length.

  • The former represents Kepler's, the latter Lippershey's or the Galilean telescope.

  • in diameter when viewing faint objects, we obtain the rule that the minimum magnifying power which can be efficiently employed is five times the diameter of the object-glass expressed in inches.`'- The defects of the Galilean and Kepler telescopes are due to the chromatic and spherical aberration of the simple lenses of which they are composed.

  • " Kepler's " nova in Ophiuchus broke out in 1604 and attained a brightness greater than that of Jupiter; it likewise gradually waned, and disappeared after about fifteen months.

  • Much of the Principia consists of synthetical deductions from definitions and axioms. But the discovery of the centripetal force of the planets to the sun is an analytic deduction from the facts of their motion discovered by Kepler to their real ground, and is so stated by Newton in the first regressive order of Aristotle - P-M, S-P, S-M.

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