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116 [183] DESCARTES DESCARTES
medium of the pineal gland, a small structure attached to the brain, which Galen [65] had thought served as a channel and valve to regulate the flow of thought.
Descartes may have been influenced by this, but he also chose the pineal gland because he believed it to be the one organ found only in man and not in the lower animals, which, without the pineal gland, lacked mind and soul and were merely living machines. (In this re spect he was shown to be wrong. A few decades later Steno [225] discovered the pineal gland in lower animals, and now we know that there is a species of very primitive reptile in which the pineal gland is far better developed than in man.)
Descartes’s most important contri butions to science, however, were in mathematics. For one thing, he was the first to use the letters near the beginning of the alphabet for constants and those near the end for variables. This modification of Vieta’s [153] system stuck and it is to Descartes therefore that we owe the familiar x’s and y’s of algebra. He also introduced the use of exponents and the square root sign. Descartes had grown interested in mathematics while in the army, where his military inactivity gave him time to think. His great discovery came to him in bed, according to one story, while he was watching a fly hovering in the air. It occurred to him that the fly’s position could be described at every moment by locating the three mutually perpendicular planes that intersected at the position oc cupied by the fly. On a two-dimensional surface, such as a piece of paper, every point could be located by means of two mutually perpendicular lines intersecting at that point. In itself this was not original. All points on the earth’s surface can be (and are) located by latitude and longitude, which are analogous, on a sphere’s sur face, to the Cartesian coordinates on a plane surface. What was world-shaking, though, was that Descartes saw that through the use of his coordinate system every point in a plane could be represented by an or dered system of two numbers, such as 2, 5, or —3, —6, which can be interpreted as “two units east and five units north from the starting point” or “three units west and six units south from the start ing point.” For points in space an or dered system of three numbers is re quired, the third number representing the units up or down. In any algebraic equation in which one variable y is made to depend on the fluctuations of a second variable x ac cording to some fixed scheme, as, for in stance, y — 2x2 — 5, then for every value of x there is some fixed value of y. If x is set equal to 1, y becomes —3; if x is 2, y is 3; if x is 3, y is 13, and so on. If the points represented by the x, y combinations (1, —3; 2, 3; 3, 13; etc.) are converted into points on a plane ac cording to the Cartesian system, a smooth curve is obtained. In this case it is a parabola. Every curve represents a particular equation by this system; every equation represents a particular curve. Descartes advanced this concept in an appendix of about a hundred pages which was attached to his book (pub lished in 1637) on vortices and the structure of the solar system. It is not the only time in the history of science that a casual appendix proved to be ines timably more important than the book to which it was attached. Another exam ple, two centuries later, involved Bolyai [530].
The value of Descartes’s concept was that it combined algebra and geometry to the great enrichment of both. The combination of the two could be used to solve problems more easily than either could be used separately. It was this ap plication of algebra to geometry that was to pave the way for the development of the calculus by Newton, which is essen tially the application of algebra to smoothly changing phenomena (such as accelerated motion), which can be repre sented geometrically by curves of various sorts.
Since a synonym for algebra ever since the days of Vieta is “analysis,” Des cartes’s system of fusing the two
[184] GELLIBRAND RICCIOLI
branches of mathematics into one has come to be called analytic geometry. [184] GELLIBRAND, Henry (gell'uh- brand) English astronomer and mathe matician Born: London, November 17, 1597
Died: London, February 16, 1636 Gellibrand was educated at Oxford, obtaining his master’s degree in 1623. He became professor of astronomy at Gresham College in 1627. He was a friend of Briggs [164] and finished some of the latter’s unfinished manuscripts after Briggs’s death. His strongly Puritan tendencies got him into trouble with the Anglican authorities in 1631, but he was acquitted. Gellibrand noted that the recorded di rection of the compass needle in London changed slowly despite Gilbert’s [155] contention, and had shifted by more than seven degrees in the previous half century. In 1635 he published his findings. This was the first indication that the earth’s magnetic field slowly changes and, indeed, not only the hori zontal angle of the needle changes, but also the angle of magnetic dip. The very strength of the field changes and, to the present day, no clear explanation for this has been given. [185] RICCIOLI, Giovanni Battista (reet-chohlee) Italian astronomer Born: Ferrara, April 17, 1598 Died: Bologna, June 25, 1671 Riccioli, a Jesuit from the age of six teen, did not accept the views of Coper nicus [127], To arguments that the Ptole maic system was impossibly complicated, he countered with the argument that the more complicated the system, the better the evidence for the greatness of God. He mentioned the ellipses of Kepler [169] but dismissed them out of hand. It seems natural, therefore, that he should have concentrated on a study of the moon. The moon revolved about the earth in the Copernican system as well as in the older system of Ptolemy [64], and its investigation could raise no em barrassing problems. In connection with the moon, he could produce some useful results. He was the first to maintain there was no water on the moon. In 1651 Riccioli published a book called New Almagest in Ptolemy’s honor in which he accepted Tycho Brahe’s [156] system and in which he included his own maps of the lunar surface, four years after Hevelius’ [194] pioneer effort. On his maps Riccioli named the lunar craters in honor of the astronomers of the past, giving due weight to his anti- Copemican views. Hipparchus [50], Ptol emy, and Tycho Brahe received better craters than Copernicus and Aristarchus [41]. These names are still used today. Some of those honored now are Alba- tegnius [83], Anaxagoras [14], Apol lonius [49], Arago [446], Archimedes [47], Aristotle [29], Bessel [439], Biot [404], Bond [660], Cassini [209], Clavius [152], De la Rue [589], Eudoxus [27], Fabricius [167], Flammarion [756], Flamsteed [234], Gassendi [182], Gauss [350], Geber [76], Guericke [189], Her- schel, Caroline [352], Kepler [169], Lalande [309], Messier [305], Meton [23], Olbers [372], Picard [204], Picker ing [784], Plato [24], Pliny [61], Poseido- nius [52], Rheticus [145], Roemer [232], Stevinus [158], and Riccioli himself. A mountain has been named for Huygens [215] and a mountain range for Leibniz [233]. The basic system has even been extended by astronomers to the other side of the moon. In 1650 Riccioli had used a telescope to view the star Mizar (the middle star of the handle of the Big Dipper) and found it to be two stars very close to gether. This was the first observation of a double star and it gave another proof that the telescope could reveal features of the heavens not visible to the naked eye.
He also tried to measure the parallax of the sun and decided it was twenty- four million miles from the earth, a value soon to be more than tripled by Cassini.
[186] CAVALIERI FERMAT
He noticed colored bands on Jupiter parallel to its equator and, along with Grimaldi [199], improved the theory of the pendulum and made clearer the con ditions under which it would mark time accurately. [186] CAVALIERI, Bonaventura (kah'- vah-lyeh'ree) Italian mathematician Born: Milan, 1598 Died: Bologna, November 30, 1647
Cavalieri joined the Jesuit order in 1615, where he was introduced to a thorough study of the Greek mathe maticians. He also met Galileo [166], corresponded with him and considered himself a disciple of that man. His vari ous church offices did not prevent him from working at his mathematics and from teaching. Archimedes [47] had done some of his work in measuring geometric areas by supposing such areas to be made up of very small components. Cavalieri fol lowed that line of reasoning to produce the notion that volumes were made up components that were not exactly lines but thin areas so small as to be no fur ther divisible. Making use of such “indi visibles” he could work out a number of theories involving areas and volumes. The importance of this is that it was a stepping-stone toward the notion of infinitesimals and the development of the calculus by Newton [231], which is the dividing line between classical and mod em mathematics. [187] KIRCHER, Athanasius (kirTcher) German scholar Born: Fulda, Hesse-Nassau, May 2, 1601
Died: Rome, Italy, November 28, 1680
Kircher, the youngest of six sons, re ceived a Jesuit education and was or dained a priest in 1628. Like that other cleric of two centuries before, Nicholas of Cusa [115], Kircher had an uncanny knack of making intu itive guesses that were eventually proved correct. His early work with the micro scope, for instance, caused him to won der if disease and decay might not be brought about by the activities of tiny living creatures, a fact that Pasteur [642] would demonstrate two centuries later. He invented a magic lantern, an Aeo lian harp, and a speaking tube. Inter ested in antiquities, he was one of the very first to make an attempt to decipher the Egyptian hieroglyphics, something that was not carried much further till Young’s [402] time a century and a half later. In 1650 Kircher made use of the new methods of producing a vacuum intro duced by Guericke [189]. His experi ments demonstrated that sound would not be conducted in the absence of air. This supported one of the few theories in physics that Aristotle [29] advanced and that turned out to be correct. [188] FERMAT, Pierre de (fehr-mahO French mathematician
Languedoc, August 20, 1601 Died: Castres, near Toulouse, January 12, 1665 Fermat, the son of a leather merchant, was educated at home and then went on to study law, obtaining his degree in 1631 from the University of Orleans. He was a counselor for the Toulouse parlia ment and devoted his spare time to mathematics. Considering what he ac complished one wonders what he might have done as a full-time mathematician. Fermat had the supremely frustrating habit of not publishing but scribbling hasty notes in margins of books or writ ing casually about his discoveries in let ters to friends. The result is that he loses credit for the discovery of analytic ge ometry, which he made independently of Descartes [183]. In fact, where Des cartes’s formal analysis involves only two dimensions, Fermat takes matters to three dimensions. Fermat also loses credit for the discovery of some features of the calculus that served later to in- 119 [189] GUERICKE
GUERICKE [189] spire Newton [231], (However, he prob ably would not have cared. He engaged in mathematics for his own amusement and that he achieved.) He, together with Pascal [207], founded the theory of probability. He also worked on the properties of whole numbers, being the first to carry this study past the stage where Diophantus [66] had left it. Fermat is thus the founder of the modem “theory of num bers.” In that field he left his greatest mark, for in the margin of a book on Dio phantus he scribbled a note saying he had found that a certain equation (xn + yn = zD, where n is greater than 2) had no solution in whole numbers but that there was no room for the simple proof in the margin. For three centuries math ematicians, including the greatest, have been searching for the proof of what is now called “Fermat’s last theorem” (be cause it is the last that remains un proved) and searching in vain. Modem computers have shown that the equation has no solutions for all values of n up to 2,000, but this is not a general proof. In 1908 a German professor willed a prize of 100,000 marks to anyone who would find a proof, but German inflation in the early 1920s reduced the value of those marks to just about zero. In any case, no one has yet won it. Fermat did not publish his work on the theory of numbers. His son published his notes five years after Fermat’s death. [189] GUERICKE, Otto von (gay'rih- kuh)
German physicist Born: Magdeburg, November 20, 1602
Died: Hamburg, May 11, 1686 Guericke studied law and mathematics as a youth and attended the University of Leiden, where Snell [177] may have been one of his teachers. He then trav eled in France and England, and served as an engineer for the German city of Erfurt. Guericke in 1627 returned to Magdeburg and entered politics there. It was a bad time. The Thirty Years’ War was raging and Magdeburg, a Protestant city, was on the side that was, at the mo ment, losing. In 1631 it was destroyed by the imperial armies in the most savage sack of the war, and Guericke and his family barely managed to escape at the cost of all their possessions. After serv ing for a time in the army of Gustavus II Adolphus of Sweden (who managed to turn the tide of the war), Guericke re turned to a Magdeburg rising again out of mins, serving as an engineer in this rebirth effort, and in 1646 became mayor of the town, retaining that post for thirty-five years, then retiring to Hamburg in his eightieth year. In 1666, he had been ennobled, gaining the right to add “von” to his name. He grew interested in philosophic dis putations concerning the possibility of a vacuum. Numerous arguments denying its existence were advanced. Aristotle [29] had worked out a theory of motion in which a body impelled by a certain continuing force would move faster as the surrounding medium grew less dense. In a vacuum it would move with infinite speed. Since Aristotle did not accept the possibility of infinite speed he decided that a vacuum could not exist. This, like almost all of Aristotle’s views, was ac cepted uncritically by later philosophers and was expressed in the catch phrase “Nature abhors a vacuum.” Guericke decided to settle the question by experiment rather than argument and in 1650 constructed the first air pump, a device something like a water pump but with parts sufficiently well fitted to be reasonably airtight. It was run by muscle power and was slow, but it worked and Guericke was able to put it to use for pieces of showmanship of quite Madison Avenue proportions. And he spared no expense, either, for he spent $20,000 on his experiments, a tremendous sum for those days. He began with an evacuated vessel. He showed that a ringing bell within such a vessel could not be heard, thus bearing out Aristotle’s contention that sound would not travel through a vacuum, though it would travel through liquids
[189] GUERICKE
GLAUBER [190] and solids as well as through air. Guericke also showed that candles would not bum and that animals could not live in a vacuum, but the true significance of these observations had to await Lavoisier [334] a century and a quarter later. Guericke grew more dramatic. He affixed a rope to a piston and had fifty men pull on the rope while he slowly drew a vacuum on the other side of the piston within the cylinder. Air pressure inexorably pushed the piston down the cylinder despite the struggles of the fifty men to prevent it. Guericke prepared two metal hemi spheres that fitted together along a greased flange. (They were called the Magdeburg hemispheres, after his town.) In 1657 he used them to demonstrate the power of a vacuum to Emperor Fer dinand III. When the hemispheres were put together and the air within evac uated, air pressure held them together even though teams of horses were at tached to the separate hemispheres and whipped into straining to their utmost in opposite directions. When air was al lowed to reenter the joined hemispheres, they fell apart of themselves. It was about this time that Guericke heard of Torricelli’s [192] experiments, and he saw that the results of his more dramatic demonstrations were due to the fact that air had weight. His demon strations added nothing to what Tor ricelli had established, but they had flair and forced the world of scholarship to understand and accept the basic discov ery. Furthermore, he saw the application of the barometer to weather forecasting and in 1660 he was the first to attempt to use it for this purpose. Guericke also made important ad vances in another field. Gilbert [155] had worked with substances that could be “electrified” by rubbing and made to at tract light objects. Guericke mechanized the act of rubbing and devised the first frictional electric machine. This was a globe of sulfur that could be rotated on a crank-turned shaft. When stroked with the hand as it rotated, it accumulated quite a lot of static electricity. It could be discharged and recharged indefinitely. He produced sizable electric sparks from his charged globe, a fact he reported in a letter to Leibniz [233] in 1672. Guericke’s sulfur globe initiated a full century of experimentation—with other and better frictional devices—which reached its height with the work of Franklin [272]. Guericke was also interested in astron omy and felt that comets were normal members of the solar system and made periodic returns. This notion was to be successfully taken up by Halley [238] some twenty years after Guericke’s death.
[190] GLAUBER, Johann Rudolf (glow'ber) German chemist
conia, 1604 Died: Amsterdam, Netherlands, March 10, 1670 At an early age the self-taught Glauber, the son of a barber, lived in Vienna, then in various places in the Rhine Valley. Some time during this in terval, perhaps about 1625, he noted that hydrochloric acid could be formed by the action of sulfuric acid on ordinary salt (sodium chloride). This was the most convenient method yet found for the manufacture of hydrochloric acid, but what interested Glauber most was the residue (today called sodium sul fate). Glauber fastened on to this substance, studying it intensively and noting its ac tivity as a laxative. Its action is mild and gentle and throughout history there have always been those who place great value on encouraging the bowels. Glauber, en amored of his discovery, labeled it sal mirabile (“wonderful salt”) and adver tised it as a cure-all in later years. He believed its use had once cured him of typhus. (The fact that his only source of income was the sale of his chemical products forced him into a heavy sell, of course.) We don’t consider it a cure-all these days, but the common name of sodium suifate is still “Glauber’s salt.” Download 17.33 Mb. Do'stlaringiz bilan baham: 
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