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Let any one turn to the Magazines, those reputed barometers of taste, and he will find that, with one exception, the Monthly Magazine, there is not in any of them a single scrap of science, or a single article aiming at a higher or more durable character, than the idle amusement of an idle hour. Chapters of novels and tales, which have been rejected in the shape of volumes; rhymes, in which there is neither poetry nor point, and slender critiques upon matters still more slender, have come in the place of the profound remarks and masterly dissertations of the Johnsons, Hawksworths, Prices, Priestleys, and Thomsons, who once gave vigour and value to our periodical literature. In the regular books it is not much better; we have tales and travels, accounts of ideal beings who never could exist, and of real ones who will not be remembered; and even in the scientific departments, we have the science of skulls and of shells, instead of the dissection of mind, and the display of the grandeur of nature. The whole structure has, in short, become light and frivolous; and though there be no “royal road to Geometry” now, any more than there was in the time of the Grecian sage, we have found out a bye-path to Fame, such as it is, by which Geometry may be avoided. Under these circumstances, every attempt to bring genuine science within the range of a greater number of readers is praiseworthy.

In the following pages, it has been the object of the compiler to reject every thing trivial, and to present a body of mathematical and physical knowledge as substantial and as complete as it is unobtrusive. He has been sedulous to exclude every thing merely ornamental; and by doing this he hopes that he has squeezed into this little volume all the really useful

matter which is to be found in works of far higher price and loftier pretensions. Science is not a thing of fashion, and therefore little novelty can be expected. Discoveries and inventions in pure

Mathematics were never abundant at any period, and latterly they have been exceedingly few.

As the compiler has himself had a good deal of practice in communicating mathematical knowledge, he hopes he may be pardoned if he offers a few words on what to him appears to be the most successful way of pursuing the study of them. Number, and form, and quantity, are the three subjects of all mathematical speculation. Number is the most simple, perhaps the most simple of all subjects of correct and rational enquiry; and therefore it is the one with which to begin. The notation, and common operations are easily understood; and these being once managed, a most beautiful field of speculation is opened up. The doctrine of prime and composite numbers, the doctrines of divisors, of fractions, and of ratios, and the doctrine of roots and powers, are all beautiful in themselves, and prepare the student for entering upon the more general subject of Algebra. That science, as far as relates merely to numbers, should immediately follow the study of Arithmetic; and then the mind is prepared for the elements of Geometry. In the study of these, old Euclid never has been, and probably never can be, equalled; and so the first book of his elements may follow the study of the notation, the common rules, and simple equations in Algebra. Before entering upon the second book of the elements, the student may proceed a little way with quadratics, and these and the second book will mutually assist each other.

When quadratics are well understood, the whole re

maining books of the elements both of Geometry and of Trigonometry are easily mastered; and then may come the higher equations. After this, the elements of the fluxionary or differential calculus may be studied; and then the doctrine of curves; and the more abstruse parts of the calculus. And, when this has been done, the student is ready for the mixed sciences; and, with such preparation, his progress can hardly fail in being both sure and rapid. Before, however, he proceeds too far in the mechanical sciences, it is advisable that he study the elements of Chemistry, just for the purpose of enabling him to decide what phenomena are mechanical and what are not. Such a course of study as we have been sketching, would, if rightly gone about, not occupy more time than most boys waste upon a few idle, or at least superficial, accomplishments, and it would fill society with men of another description than are now found in them.

To contribute to such a result is one of the objects of this Dictionary; and we shall close this preface by mentioning the names of a few of the books which would be found useful as auxiliaries, or which would furnish those details which cannot be looked for in a work so small and so condensed as this :-For a general synopsis, perhaps no book is better than Nicholson; but Bezout, and some others of the French authors, are more systematic. Of Arithmetic, the books: are many; but in English few of them are profound. Barlow's Theory of Numbers is among the best. The practical ones are without number, and many of them without variety. Joyce, Hutton, Bonnycastle, Walkingham, Vyse, and far from the worst, Dr. Hamilton, may be noted. In Algebra, Euler is at once the

most simple and the most profound. Then we have Bridge, Wood, Ludlam, Simson, and a hundred others In Elementary Geometry we have Euclid; Playfair's last edition is decidedly the best. Again, in the practical parts, we have Hutton's Course, Crocker's Surveying, Keith's Mensuration, Moore and Mackay's Navigation, and an endless chain. On Trigonometry, we have Wood, Wodehouse, Keith, and many others. On Fluxions and the differential Calculus, we have Simson, Vince, Stone, La Croix, Boucharlat, and many others. In Mechanical Philosophy, we have Blair's Grammar, Young's Lectures, Bridge's Mechanics, Wood and Vince's Course, Playfair's Outlines, part of the same, by Leslie, and a Course by Millington. In Astronomy, we have Vince, Squire, the Wonders of the Heavens, and a variety of others. In short, if we have relaxed in our mathematical and scientific studies, it is not for want of books; for, though they be of lighter fabric, and fewer in proportion to the whole number of books than at some former periods, they are still numerous; and if we do suffer, it is not through want of books, but want of readers.

Every lover and student of the Sciences will duly estimate the value of a portable Dictionary of the Mathematical and Philosophical Sciences. Other Dictionaries of these subjects are, by their high price, placed beyond the reach of the general mass of purchasers, while by their fullness they tend to supersede elementary works, without supplying their places. The great use of a Dictionary is to aid study by convenient reference to particular points of difficulty, and to assist enquiry by an alphabetical arrangement of subjects.

London, Sept. 10, 1823.





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A table used before of light, and the earth's motion in the introduction of the modern or its orbit. This apparent motion is figurate arithmetic, for facilitat so minute, that it could never have ing the basmess of calculation. been discovered by observations, Originally it appears to have been unless they had been made with nothing more than a smooth piece extreme care and accuracy. Dr. of board, covered with sand, and Bradley, astronomer royal, was served indifferently for arithmeti-l led to it accidentally by the result cal computations, or geometrical | of some careful observations, diagrams. The word calculate is which he made with a view of dederived from the calculi, or small termining the annual parallax of pehbles, which were used along the fixed stars. It Jight be supwith the abacus. These were dis-/ posed to have a progressive motributed in rows, each row having lion, the position of the telescope, a different value, in the same man- through which any celestial object ner as the ranks or places of figures is viewed, must be different from have in the modern scale of num- that which it must have been, if bers. As many rows were regnir-light were instantaneous; and, ed as there were ranks or places therefore, the place ineasured in in the largest number which en- the heavens will be dillerent from tered into the calculation; and one the true place. counter less than the root of the Clairaut explains the aberration, scale of arithmetic was required by supposing drops of rain to fall for each row. For instance, it rapidly after each other from a the root of the scale had been 10, cloud, under which a

person nine counters would have been moves with a very narrow tube ; required in each; and to express in which case it is evident that the any particular number, as many tube must have a certain inclinawould have been required in tion, in order to admit a drop which each row as there were ones in enters at the top, to fall freely the corresponding word or tigure. through the axis of the tube, withThus, 365 would have been ex- out touching the sides of it; and pressed by 5 in the right-hand row, this inclination must be greater or 6 in the second, and 3 in the third less, according to the velocityofthe It is easy to see how, by the help drops in respect to that of the tube. of such an instrument, the com- In ihis case, the angle made by non operations of arithmetic could the direction of the tube, and that be performed.

of the falling drops, is the aberraABERKATION, an apparent motion, arising from the combination tion of the celestial bodies, occa of these two motions. sioned by the progressive motion


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