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tions, with a zeal, firmness, and even alacrity, that bring to mind the best of the cavaliers in the civil wars of England. Of Merchants, we might name many, scattered over the seaboard, who have exerted a noble and enlightened liberality, and who bore an important share in the work of the Revolution, or in that of subsequent legislation. In the West, we discover a large fund of heroic character, romantic and eventful enterprise, and gallant exploit:—the personal annals of Ohio, Kentucky, and Tennessee, are replete with objects and results, which excite curiosity and admiration. In the history of their Indian wars, the reader has, indeed, a repetition of much of what is so minutely told of those of New-England, in her many volumes on that subject; the incidents and characters bear a resemblance; yet the scenes of action, and the actors, are so far different, as to beget a peculiar interest and important variety. It may be hoped that the western states will do justice to themselves, by early embodying their authentic traditions.
We rejoice, that biographical details are acquiring more vogue and importance in the United States; and trust, that this circumstance will animate the citizens, who possess valuable memoirs or documents, to give them to the world. A nation is judged, as much, perhaps, by its single characters and lives, its exalted and striking men, as by the sum of its power, wealth, learning, or civilization. Perhaps, too, the chief interest and consequence of History lie in the virtues or vices, the designs and acts, and the fortunes and adventures, of individuals; rather than in the aggregate of public occurrences, or the mere movements and effects of battles, sieges, state policy and vicissitudes, general felicities or disasters of what kind soever. We Americans should make our Biography as full as possible,—at least the honourable part of it,—for the credit of our political and social institutions, and as a broader standard of comparisonwith Europe; an instrumentality in which, as we have already intimated, we have great reason to be satisfied with it, and shallhave greater, when it shall be enlarged. The study involves many and precious lessons; mementoes, elevating or depressing, lively or serious. It reminds us of life and energy, glory and power; but, as constantly, of misfortune and death.
Optima quaeque dies miseris mortalibus aevi
The records of the venerable dead, in books, are like the monuments in Westminster Abbey, which, if they warmed and excited the authors who visited them, have occasioned, and justly, much solemn moralizing,—very sober conclusions on the end of all human prowess and strife. We need not state the impression, which is felt in thinking of the multitude of names, in Bayle's Dictionary, for example, which were once so celebrated, and deemed so important in the annals of policy, religion, war, literature, philosophy, and which are now utterly forgotten, or generally unknown. Well might Marcus Antoninus exclaim,—even in his time—•" How many men of high renown, with whose praises the world once rang, are now consigned to oblivion; and how many bards and panegyrists, who promised immortality to their names, have, themselves, long since disappeared in the gulf of time!".
Art. II.—Elements of Analytic Trigonometry, Plane and Spherical. By F. R. Hassler, F. A. P. S. New-York: published by the Author. James Bloomfield, printer. 1826. 8vo. pp. 192.
Trigonometry, in its several branches, and in the number of its practicalapplications, forms, perhaps, the most important department of mathematical science. Whether we view it as applied to the simpler business of the land surveyor, and the elementary problems of practical navigation, or extended to the mensuration of the spheroidal surface of the earth, and of the angular positions of those great and distant bodies, that are spread throughout the regions of unbounded space, we feel, in every case, sensible of its value. But it is in the efficient and indispensableaid that it affords to the calculus of modern mathematicians, that we find the highest and most marked instances of its usefulness.
We derive the basis of Trigonometry, like that of almost every branch of our knowledge, from the ancient Greeks; it has, indeed, received from time to time, improvements of the most important character; but we must consider ourselves, even at the present moment, under the deepest obligation to that remarkable people, as well in this instance, as in nearly all the sciences we at present cultivate. Whether it took its rise among them, or whether their Trigonometry was derived from some more early nation, it is impossible, at this day, to determine. The Greeks have been accused of arrogating to themselves, the discoveries and the science of others, and of carefully hiding from posterity the sources whence they obtained them. The Egyptians are frequently considered as the precursors and instructors of the Greeks. Laboured arguments and eloquent treatises have been drawn up, to maintain the early civilization and advance in knowledge, of this mysterious people. More close investigation of their monuments and remains, seems, however, to lead us daily to the conclusion, that much of this superiority and intelligence is entirely imaginary, and that those of their works, on which the record of their remote progress in science has been supposed to be inscribed, are the productions of a later period—the imperfect reflections, instead of the faint dawnings of the light that blazed in Greece.
The eloquent Bailly, abandoning the idea that Egypt was the cradle of European science, has sought it in a nation residing in central Asia, whose name, whose monuments, and whose language, are long forgotten^and of which no trace remains but the imperfect fragments of their astronomic science, preserved, but not understood, by the Chaldeans of the age of Alexander, the Chinese, and the Hindoos of our own times. A late most able and competent judge, Delambre, has stripped this fabled nation of its honours, and shown most conclusively, that the writings of the later Greeks, are, in truth, the basis of all the boasted learning of Hindostan and China, which countries probably received them through the intervention of the Arabs, who preserved, cultivated, and even improved some of the branches in which the Greeks made so marked and rapid a progress.
Wherever we may seek for the origin of the Mathematics, it is to be confessed, that we are to look to the writings of the Grecian geometers for its earliest and most authentic records— for its most elegant and accurate methods. If the progress of the moderns has rendered many of their writings obsolete; pointed out shorter and more advantageous roads to the common end; and finally extended the applications of the science to objects that might, at first sight, appear beyond the reach of human investigation; we may, notwithstanding, consult them with advantage, as the finest models of close and accurate argument, and as the best exercise that has ever been discovered for the improvement of the reasoning faculty.
The time of the origin of trigonometry among the Greeks, is extremely well defined, and marked by circumstances and facts so pointed, as to leave no doubt as to its exact era. Archimedes was born in the year 287 before Christ . He is said to have travelled in his youth into Egypt, to acquire the knowledge taught by the priests of that country. However this may be, he was certainly not only acquainted with all the science of his own country, but made to it many additions. His -flrr