719 



STEVIN, SIMON. 



STEWART, MATTHEW, D.D. 



7-10 



Lighthouse Commission era, he made his first tour of inspection, and 

 afterwards introduced a still greater improvement on the illumination 

 of lighthouses by means of the catoptric principle, and by adopting 

 various means to distinguish one lighthouse from another. In 1807, an 

 Act having been obtained in the previous year, he commenced the con- 

 struction of the Bell Rock Lighthouse, on a rock in the North Sea, a few 

 miles off Arbroath in Forfarshire, on which the light was exhibited for 

 the first time on Feb. 1, 1811. The rock being extremely small, and 

 almost entirely covered, even at low-water, except in spring-tides, 

 offered great obstacles to the construction, but they were successfully 

 overcome, and an account of the details of the erection and structure, 

 illustrated with plates, was published at Edinburgh in 1824. A con- 

 troversy has arisen as to the originality of Mr. Stevenson's plans, into 

 which we cannot enter, but it is certain that much of the merit arises 

 from the mechanical means adopted to secure a firm and enduring 

 foundation, and this was undoubtedly done by Mr. Stevenson. In 

 1814, on another tour of inspection, Sir Walter Scott was a companion 

 of the engineer and commissioners in the voyage, which afforded many 

 materials for descriptions in Scott's poem of ' The Lord of the Isles,' 

 and in the novel of ' The Pirate.' Mr. Stevenson held the situation of 

 engineer till 1842, during which time he erected no fewer than 23 light- 

 houses. He was also employed in numerous engineering works in 

 various parts of the United Kingdom, but chiefly in Scotland, in con- 

 nection with the improvement of rivers and harbours, and the erection 

 of piers and bridges, into which latter class of works he introduced 

 some new principles of 'construction. He likewise surveyed a line of 

 railway between Edinburgh and Glasgow, which, though not adopted, 

 was admitted to be extremely clever. He was employed to report on 

 other lines of railway, and he suggested the use of malleable iron rails 

 instead of the cast-iron rails and tramplates previously in use. In 

 1828 he became a member of the Institution of Civil Engineers, and 

 while he lived was looked upon as an authority of great weight on all 

 questions connected with the improvements of ports, harbours, and 

 rivers. He died on July 12, 1850, when the Commissioners of Northern 

 Lighthouses passed a resolution acknowledging his great services and 

 merits. He left sons, whom he had brought up to his own profession, 

 who worthily sustain the reputation of their father. 



STEVIN, SIMON, a celebrated Flemish mathematician, was born 

 about the middle of the 16th century, at Bruges : it has been ascer- 

 tained tbat he went to reside in Holland, where he obtained the title 

 of mathematician to Prince Maurice of Nassau, and that he was made 

 civil-engineer to the States, the charge of constructing and repairing 

 the dykes being confided to him. It is to be regretted that no other 

 particulars concerning his life have been preserved : even the year of 

 his death is unknown. 



He wrote a treatise on arithmetic, which was printed at Antwerp 

 in 1 585 ; and in the same year he published a collection of geometrical 

 problems in five books. He appears to have studied algebra with 

 great attention, and to have made in that branch of science several 

 improvements. The principal of these consist in the employment of 

 fractional indices, as exponents of the roots of quantities (the use of 

 integers as the exponent of powers had previously been introduced by 

 Stifel [STIFEL, MICHAEL]), and in a general but laborious method of 

 approximating in numbers to the root of any equation. He repre- 

 sented the unknown quantity by a small circle ; and a number, either 

 integral or fractional, contained within the circle, indicated a power or 

 root of that quantity. 



In 1586 Stevin published in quarto, and in the Dutch language, his 

 tract on statics and hydrostatics, in the preface of which he endeavours 

 to prove that the Dutch language is more ancient than any other ; and 

 in the same year he published, also in Dutch, his ' New System of 

 Fortification.' In 1589 he brought out a tract entitled 'De Motu 

 Cceli ;' and ten years afterwards, in Dutch, a treatise on navigation : 

 the latter was translated into Latin by Qrotius, and published at 

 Leyden in 1 624. 



In 1605 W. Snell translated into Latin, and published in two volumes, 

 folio, the greater part of the works of Stevin, but he did not live to 

 complete the undertaking. In 1634 however Albert Qirard "published, 

 at Leyden, the whole of the works in French : this edition contains 

 the treatise on arithmetic ; the six books of the algebra of Diophantus 

 (the first four books were translated from the Greek by Stevin, and 

 the others by Girard), and an explanation of the tenth book of Euclid ; 

 tracts on cosmography, geography, and astronomy, the practice of 

 geometry, statics, optics, castrametation, a new system of fortification, 

 and a method of fortifying places in which manoeuvres of water, by 

 means of sluices, were to contribute to the defence. 



The work on statics contains a simplification of the demonstration 

 of Archimedes relating to the fundamental property of the lever. 

 Stevin represented the two weights at the extremities of the lever by 

 parallelepipeds suspended horizontally by strings applied at their 

 middle points : the breadths and depths of these parallelepipeds were 

 equal, but the length of each was double the distance from the fulcrum 

 of the lever to the point from which the other was suspended. When 

 the parallelepipeds were placed end to end, the middle of the whole 

 was vertically under the fulcrum of the lever, and therefore the Latter 

 was necessarily in cquilibrio, while the weights of the separate 

 parallelepipeds were inversely proportional to the lengths of the arms 

 from whose extremities they were suspended. 



In order to exhibit the conditions under which a body is in equi- 

 librio on an inclined plane, Stevin supposes a triangular prism to be 

 placed with one side parallel to the horizon, so that the other sides 

 may form a double inclined plane ; and he imagines a string, on which 

 are placed a number of equal weights, at equal distances from one 

 another, to be laid on those sides across the upper edge of the prism : 

 each part of the string of weights extends from the edge to the base 

 of the prism ; or the two extremities of the string are at equal distances 

 below that base. He concludes that the string so placed would be at 

 rest on the two planes, because if it were to begin to move (the string 

 of weights being of infinite length) it would move for ever, which he 

 supposed to be absurd, so that the tendency of the weights to descend 

 on one side must exactly counterbalance the like tendency of those 

 on the other side; and evidently the sum of the weights lying on one 

 plane is to the sum of the weights lying on the other, in the same 

 proportion as the lengths of those planes respectively, the lengths 

 being measured in directions perpendicular to the edge of the prism. 

 Hence he infers that the same power is required to support different 

 bodies on single inclined planes of equal heights, when the weights of 

 the bodies arc proportional to the lengths of the plane?. If one side 

 of the prism is in a vertical position, the tendency to descend is evi- 

 dently equal to the weight ; and hence, on every inclined plane, the 

 sustaining power, in a direction parallel to the plane, is to the weight 

 of a body, as the height of the plane is to its length. 



From this theory, also, Steviu discovered that an equilibrium 

 between three forces acting at one point in a body, takes place when 

 the forces are parallel and proportional to the three sides of a triangle. 

 His demonstration however extends only to the case in which the 

 directions of two of the forces are at right angles to one another ; for 

 he states that when a body is supported on an inclined plane, and 

 retained by a force acting parallel to the plane, it is in the same cir- 

 cumstances as if it were suspended by two strings, one perpendicular 

 and the other parallel to the plane ; and he concludes that the ratio 

 of the weight of the body, to a force parallel to the plane, is as the 

 hypotenuse to the base of a right-angled triangle formed by three 

 lines, one in a vertical direction, another perpendicular to the plane, 

 and the base or third side being in a horizontal position. 



Stevin is said to have contrived a car which moved by means of 

 sails, on the flats of Holland, with more rapidity than any carriage 

 drawn by horses. 



STEWART, MATTHEW, D.D., a mathematician of North Britain, 

 who attained great distinction by his researches in the higher branches 

 of science, and the success with which he cultivated the ancient geo- 

 metry. He was born at Rothsay, in the Isle of Bute, in 1717; and 

 having received the best education which a grammar school afforded, 

 he prosecuted his studies in philosophy and theology at the Univer- 

 sity of Glasgow, into which he was admitted in 1734. Dr. Sinison, 

 who then occupied the chair of mathematics in that university, is said 

 to have early discerned the predilection of Stewart for mathematical 

 researches ; and his lectures appear to have given his pupil that 

 decided preference for the ancient over the modern analysis, which he 

 retained to his death. 



On going to reside in Edinburgh, Mr. Stewart attended the lectures 

 of Maclaurio, till, having adopted the church as a profession, he was 

 appointed to the living of Roseneath, in the west of Scotland. la 

 1747 however, on the death of that mathematician, he was elected to 

 succeed him ; and he held the post of mathematical professor in the 

 University till 1772, when his health began to decline. His SOD, the 

 late Dugald Stewart, from that time began to assist him by occasionally 

 delivering lectures ; and three years afterwards the young mathema- 

 tician and philosopher was appointed joint professor with his father. 

 In 1775 he retired to an estate in Ayrshire, where he spent nearly 

 all the rest of his life in cultivating science as an amusement. He 

 was elected a Fellow of the Royal Society in 1764; and he died in 

 1785, being then sixty-eight years of age. 



The first efforts of Dr. Stewart in science were to extend the subject 

 of what is called the ' locus ad quatuor rectas ' to the powers of any 

 number of perpendiculars drawn to an equal number of lines. While 

 engaged in this pursuit, after his removal to Roseneath, he discovered 

 most of those propositions which, in 1746, he published under the 

 title of ' Geometrical Theorems.' These, which are mostly porisms, 

 are sixty-nine in number, but five only of them are accompanied by 

 demonstrations. Dr. Stewart is said to have suppressed, for the sake 

 of brevity, the proofs of the others ; but several of the theorems 

 were afterwards demonstrated by Dr. Small, and Mr. Lowry has given, 

 in Leybourne's ' Mathematical Repository,' demonstrations of all 

 those which admit of investigation by the processes of the ancient 

 geometry. 



In the first volume of the ' Essays of the Philosophical Society of 

 Edinburgh,' there is a paper by Stewart containing some propositions 

 founded on a theorem in the fourth book of Pappus ; and, in the 

 second volume of the same work, he gave a solution of ' Kepler's 

 problem,' in accordance with the methods of the ancients. This he 

 accomplished by the application of a property of curves, from which 

 the approximations may be carried to any degree of accuracy in fa 

 series of rapidly converging results. In 1761 he published his 'Four 

 Tracts, Physical and Mathematical/ in which there is an attempt to 

 investigate the higher parts of mixed mathematics in a manner con- 



