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طلبة وطالبات وانشطة تربوية يهتم بجميع شؤون المعلمين والطلاب وبجميع أنواع النشاط الذي يتناسب مع قدرات الطالب وميوله واهتماماته داخل المدرسة (الكلية) وخارجها

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  #4  
قديم 16/11/2005, 01:15 PM
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اسحق نيوتن ولد في إنجلترا سنة 1642م في نفس السنة التي توفي فيها العالم جاليليو، ولقد توفي والده قبل يوم ولادته بشهرين، وتزوجت أمه بعد سنتين من مولده وتركت ابنها ليعيش مع جدته في أحد المزارع. وبعد دراسة لمدة أربع سنوات في المدرسة الملكية، أخرجته أمه من المدرسة وقرّرت أن تجعله مزارعا، ولكن نيوتن كان محبا للألعاب الآلية "الميكانيكية" في طفولته، فاستطاع أن يصنع طاحونة هوائية وساعة مائية ومزولة. ولقد تنبّه لفطنته في تلك الفترة زوج أمه، مما جعله يقنع والدته بإعادته للمدرسة وبخاصة أن نيوتن كان ضعيف البنية مما جعله غير صالح لأعمال الزراعة. وكان نيوتن طالبا صبورا يثق بنفسه وفي قدراته العقلية مما جعل النجاح حليفه. وفي الثامنة عشرة من عمره التحق بكلية ترينتي Trinity في جامعة كامبردج Cambridge لإكمال دراسته، وكانت المصاريف الجامعية تشكل عبئا ماليا عليه، مما جعله يقوم بأداء بعض الأعمال لمساعدة مدرسيه لقاء أجر بسيط يدفعونه له. ولقد بقي نيوتن مغمورا إلى أن تنبه لفطنته وذكائه أستاذ الرياضيات في الكلية، الذي بدأ يوجهه ويرشده إلى الاهتمام بالرياضيات، ولقد تحققت ثقته بنيوتن عندما وضع في سنة 1665 نظرية في الرياضيات تسمى بنظرية ذات الحدين، وهذه كانت أول مشكلة رياضية استطاع نيوتن أن يجد لها حلا.





لقد حصل نيوتن على درجة الماجستير من كلية "ترينتي Trinity" في سنة 1665م أي السنة نفسها التي وضع فيها نظرية ذات الحدين، وفي تلك السنة انتشر مرض الطاعون مما أدى بالجامعة إلى قفل أبوابها لمدة سنتين وبذلك عاد نيوتن إلى بلدته "والزثورب" حيث تعيش جدته، وكان يمكن لهذا الانقطاع عن الجامعة "وبخاصة الابتعاد عن مكتبتها" أن يؤدي إلى نهاية نيوتن العلمية، ولكنه اعتكف في المنزل وأمضى معظم وقته في القراءة والكتابة والتفكير، والتأمل في هذا الكون وإجراء بعض التجارب، ولقد أدت هذه الأعمال إلى اكتشافه مكونات الضوء الأبيض وإدراكه لفكرة الجاذبية في الكون، وعندما بلغ السابعة والعشرين من عمره عين أستاذا للرياضيات في كامبردج، وبعد فترة أصبح رئيسـا للقسـم بدلا من أستاذه، وكان أول عمل عظيم قام به في تلك الفترة هو بناء المقراب (التلسكوب) العاكس الذي أهـداه إلى الجمعية العلمية الملكية التي منحته لقب الزمالة وطلبت إليه أن يكتب شـرحا مفصّلا عن عمل هذا المقراب.



ولقد ذاعت شهرة نيوتن بآرائه وأفكاره وأبحاثه، ولذلك كان يكتب إليه الكثير من علماء عصره يسألونه عن بعض تلك الأفكار والأبحاث العلمية، إلى أن أقنعه أحد العلماء بأن يجمع أبحاثه وآراءه وجميع أعماله في كتاب يبعث به للجمعية الملكية، وبالفعل نشر في سنة 1687م جميع أعماله في علم الميكانيكا في كتابه الأول برنسيبيا (المبادىء Principia) ويعتبر هذا الكتاب أحد الآثار العظيمة للفكر البشري، لقد عرض فيه أسس علم الميكانيكا والتطورات المنتظرة في المستقبل، وطبق هذه الأسس على حركات الأجرام السماوية مستخدما قانون الجاذبية العام. وفي سنة 1703م وضع كتابه الثاني البصريات (Optics) الذي أظهر نيوتن كأحد العلماء الفيزيائيين التجريبيين كما كان فيلسوفا رياضيا عظيما. ولقد اختير نيوتن رئيسا للجمعية العلمية الملكية ومنحته الملكة آن لقب سير (Sir) في سنة 1705م. وتظهر عظمة هذا الرجل المتواضع من عبارة قالها وهو على فراش الموت "إذا كنت قد رأيت أكثر من غيري فذلك يرجع إلى وقوفي على أكتاف العمالقة الذين سبقوني" وكان يخص بالذكر من أولئك العمالقة العالم جاليليو.



وتوفي نيوتن في 20 مارس سنة 1727م عن عمر يناهز الخامسة والثمانين عاما. ومن هذه الخلاصة نجد أن نيوتن عان الكثير والكثير في سبيل التحصيل العلمي مما انتفعت البشرية من بعده. ونحن هنا لدينا كل سبل الدعم سواء كانت من الدولة أو الأهل فكم نويتن سيكون منا لتنتفع منه الدول العربية؟؟؟؟؟



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  #5  
قديم 16/11/2005, 09:09 PM
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Sir Isaac Newton (1642 - 1727)

From `A Short Account of the History of Mathematics' (4th edition, 1908) by W. W. Rouse Ball.

The mathematicians considered in the last chapter commenced the creation of those processes which distinguish modern mathematics. The extraordinary abilities of Newton enabled him within a few years to perfect the more elementary of those processes, and to distinctly advance every branch of mathematical science then studied, as well as to create some new subjects. Newton was the contemporary and friend of Wallis, Huygens, and others of those mentioned in the last chapter, but though most of his mathematical work was done between the years 1665 and 1686, the bulk of it was not printed - at any rate in book-form - till some years later.

I propose to discuss the works of Newton more fully than those of other mathematicians, partly because of the intrinsic importance of his discoveries, and partly because this book is mainly intended for English readers, and the development of mathematics in Great Britain was for a century entirely in the hands of the Newtonian school.

Isaac Newton was born in Lincolnshire, near Grantham, on December 25, 1642, and died at Kensington, London, on March 20, 1727. He was educated at Trinity College, Cambridge, and lived there from 1661 till 1696, during which time he produced the bulk of his work in mathematics; in 1696 he was appointed to a valuable Government office, and moved to London, where he resided till his death.

His father, who had died shortly before Newton was born, was a yeoman farmer, and it was intended that Newton should carry on the paternal farm. He was sent to school at Grantham, where his learning and mechanical proficiency excited some attention. In 1656 he returned home to learn the business of a farmer, but spent most of his time solving problems, making experiments, or devising mechanical models; his mother noticing this, sensibly resolved to find some more congenial occupation for him, and his uncle, having been himself educated at Trinity College, Cambridge, recommended that he should be sent there.

In 1661 Newton accordingly entered as a student at Cambridge, where for the first time he found himself among surroundings which were likely to develop his powers. He seems, however, to have had but little interest for general society or for any pursuits save science and mathematics. Luckily he kept a diary, and we can thus form a fair idea of the course of education of the most advanced students at an English university at that time. He had not read any mathematics before coming into residence, but was acquainted with Sanderson's Logic, which was then frequently read as preliminary to mathematics. At the beginning of his first October term he happened to stroll down to Stourbridge Fair, and there picked up a book on astrology, but could not understand it on account of the geometry and trigonometry. He therefore bought a Euclid, and was surprised to find how obvious the propositions seemed. He thereupon read Oughtred's Clavis and Descartes's Géométrie, the latter of which he managed to master by himself, though with some difficulty. The interest he felt in the subject led him to take up mathematics rather than chemistry as a serious study. His subsequent mathematical reading as an undergraduate was founded on Kepler's Optics, the works of Vieta, van Schooten's Miscellanies, Descartes's Géométrie, and Wallis's Arithmetica Infinitorum: he also attended Barrow's lectures. At a later time, on reading Euclid more carefully, he formed a high opinion of it as an instrument of education, and he used to express his regret that he had not applied himself to geometry before proceeding to algebraic analysis.

There is a manuscript of his, dated May 28, 1665, written in the same year as that in which he took is B.A. degree, which is the earliest documentary proof of his invention of fluxions. It was about the same time that he discovered the binomial theorem.

On account of the plague the College was sent down during parts of the year 1665 and 1666, and for several months at this time Newton lived at home. This period was crowded with brilliant discoveries. He thought out the fundamental principles of his theory of gravitation, namely, that every particle of matter attracts every other particle, and he suspected that the attraction varied as the product of their masses and inversely as the square of the distance between them. He also worked out the fluxional calculus tolerably completely: this in a manuscript dated November 13, 1665, he used fluxions to find the tangent and the radius of curvature at any point on a curve, and in October 1666 he applied them to several problems in the theory of equations. Newton communicated these results to his friends and pupils from and after 1669, but they were not published in print till many years later. It was also whilst staying at home at this time that he devised some instruments for grinding lenses to particular forms other than spherical, and perhaps he decomposed solar light into different colours.

Leaving out details and taking round numbers only, his reasoning at this time on the theory of gravitation seems to have been as follows. He suspected that the force which retained the moon in its orbit about the earth was the same as terrestial gravity, and to verify this hypothesis he proceeded thus. He knew that, if a stone were allowed to fall near the surface of the earth, the attraction of the earth (that is, the weight of the stone) caused it to move through 16 feet in one second. The moon's orbit relative to the earth is nearly a circle; and as a rough approximation, taking it to be so, he knew the distance of the moon, and therefore the length of its path; he also knew that time the moon took to go once round it, namely, a month.



Hence he could easily find its velocity at any point such as M. He could therefore find the distance MT through which it would move in the next second if it were not pulled by the earth's attraction. At the end of that second it was however at M', and therefore the earth E must have pulled it through the distance TM' in one second (assuming the direction of the earth's pull to be constant). Now he and several physicists of the time had conjectured from Kepler's third law that the attraction of the earth on a body would be found to decrease as the body was removed farther away from the earth inversely as the square of the distance from the centre of the earth; if this were the actual law, and if gravity were the sole force which retained the moon in its orbit, then TM' should be to 16 feet inversely as the square of the distance of the moon from the centre of the earth to the square of the radius of the earth. In 1679, when he repeated the investigation, TM' was found to have the value which was required by the hypothesis, and the verification was complete; but in 1666 his estimate of the distance of the moon was inaccurate, and when he made the calculation he found that TM' was about one-eighth less than it ought to have been on his hypothesis.



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This discrepancy does not seem to have shaken his faith in the belief that gravity extended as far as the moon and varied inversely as the square of the distance; but from Whiston's notes of a conversation with Newton, it would seem that Newton inferred that some other force - probably Descartes's vortices - acted on the moon as well as gravity. This statement is confirmed by Pemberton's account of the investigation. It seems, moreover, that Newton already believed firmly in the principle of universal gravitation, that is, that every particle of matter attracts every other particle, and suspected that the attraction varied as the product of their masses and inversely as the square of the distance between them; but it is certain that he did not then know what the attraction of a spherical mass on any external point would be, and did not think it likely that a particle would be attracted by the earth as if the latter were concentrated into a single particle at its centre.

On his return to Cambridge in 1667 Newton was elected to a fellowship at his college, and permanently took up his residence there. In the early part of 1669, or perhaps in 1668, he revised Barrow's lectures for him. The end of the fourteenth lecture is known to have been written by Newton, but how much of the rest is due to his suggestions cannot now be determined. As soon as this was finished he was asked by Barrow and Collins to edit and add notes to a translation of Kinckhuysen's Algebra; he consented to do this, but on condition that his name should not appear in the matter. In 1670 he also began a systematic exposition of his analysis by infinite series, the object of which was to express the ordinate of a curve in an infinite algebraical series every term of which can be integrated by Wallis's rule; his results on this subject had been communicated to Barrow, Collins, and others in 1669. This was never finished: the fragment was published in 1711, but the substance of it had been printed as an appendix to the Optics in 1704. These works were only the fruit of Newton's leisure, most of his time during these two years being given up to optical researches.

In October 1669, Barrow resigned the Lucasian chair in favour of Newton. During his tenure of the professorship, it was Newton's practice to lecture publicly once a week, for from half-an-hour to an hour at a time, in one term of each year, probably dictating his lectures as rapidly as they could be taken down; and in the week following the lecture to devote four hours to appointments which he gave to students who wished to come to his rooms to discuss the results of the previous lecture. He never repeated a course, which usually consisted of nine or ten lectures, and generally the lectures of one course began from the point at which the preceding course had ended. The manuscripts of his lectures for seventeen out of the first eighteen years of his tenure are extant.

When first appointed Newton chose optics for the subject of his lectures and researches, and before the end of 1669 he had worked out the details of his discovery of the decomposition of a ray of white light into rays of different colours by means of a prism. The complete explanation of the theory of the rainbow followed from this discovery. These discoveries formed the subject-matter of the lectures which he delivered as Lucasian professor in the years 1669, 1670 and 1671. The chief new results were embodied in a paper communicated to the Royal Society in February, 1672, and subsequently published in the Philosophical Transactions. The manuscript of his original lectures was printed in 1729 under the title Lectiones Opticae. This work is divided into two books, the first of which contains four sections and the second five. The first section of the first book deals with the decomposition of solar light by a prism in consequence of the unequal refrangibility of the rays that compose it, and a description of his experiments is added. The second section contains an account of the method which Newton invented for determining the coefficients of refraction of different bodies. This is done by making a ray pass through a prism of the material so that the deviation is a minimum; and he proves that, if the angle of the prism be i and the deviation of the ray be , the refractive index will be sin ½ (i + ) cosec ½ i. The third section is on refractions at plane surfaces; he here shews that if a ray pass through a prism with minimum deviation, the angle of incidence is equal to the angle of emergence; most of this section is devoted to geometrical solutions of different problems. The fourth section contains a discussion of refractions at curved surfaces. The second book treats of his theory of colours and of the rainbow.

By a curious chapter of accidents Newton failed to correct the chromatic aberration of two colours by means of a couple of prisms. He therefore abandoned the hope of making a refracting telescope which should be achromatic, and instead designed a reflecting telescope, probably on the modal of a small one which he had made in 1668. The form he used is that still known by his name; the idea of it was naturally suggested by Gregory's telescope. In 1672 he invented a reflecting microscope, and some years later he invented the sextant which was rediscovered by J. Hadley in 1731.

His professorial lectures from 1673 to 1683 were on algebra and the theory of equations, and are described below; but much of his time during these years was occupied with other investigations, and I may remark that throughout his life Newton must have devoted at least as much attention to chemistry and theology as to mathematics, though his conclusions are not of sufficient interest to require mention here. His theory of colours and his deductions from his optical experiments were at first attacked with considerable vehemence. The correspondence which this entailed on Newton occupied nearly all his leisure in the years 1672 to 1675, and proved extremely distasteful to him. Writing on December 9, 1675, he says, ``I was so persecuted with discussions arising out of my theory of light, that I blamed my own imprudence for parting with so substantial a blessing as my quiet to run after a shadow.'' Again, on November 18, 1676, he observes, ``I see I have made myself a slave to philosophy; but if I get rid of Mr. Linus's business, I will resolutely bid adieu to it eternally, excepting what I do for my private satisfaction, or leave to come out after me; for I see a man must either resolve to put out nothing new, or to become a slave to defend it.'' The unreasonable dislike to have his conclusions doubted or to be involved in any correspondence about them was a prominent trait in Newton's character.



Newton was deeply interested in the question as to how the effects of light were really produced, and by the end of 1675 he had worked out the corpuscular or emission theory, and had shewn how it would account for all the various phenomena of geometrical optics, such as reflexion, refraction, colours, diffraction, etc. To do this, however, he was obliged to add a somewhat artificial rider, that his corpuscules had alternating fits of easy reflexion and easy refraction communicated to them by an ether which filled space. The theory is now known to be untenable, but it should be noted that Newton enunciated it as a hypothesis from which certain results would follow: it would seem that he believed that wave theory to be intrinsically more probable, but it was the difficulty of explaining diffraction on that theory that led him to suggest another hypothesis.

Newton's corpuscular theory was expounded in memoirs communicated to the Royal Society in December 1675, which are substantially reproduced in his Optics, published in 1704. In the latter work he dealt in detail with his theory of fits of easy reflexion and transmission, and the colours of thin plates, to which he added an explanation of the colours of thick plates [bk. II, part 4] and observations on the inflexion of light [bk. III].



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قديم 16/11/2005, 09:33 PM
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