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THE mathematical or exact sciences, as they are frequently called, having been reckoned, in all ages, among the most useful and sublime productions of the human mind, it must appear a matter of surprise, that, till within a few years past, no regular or well connected history had ever been given of their origin and progress; or to shew by what steps they had advanced from their first rude beginnings to their present state of improvement. While many other branches of knowledge, both civil and literary, have been traced through all their stages, and elucidated in every possible variety of method and language, this interesting and important subject, which is so well calculated to display the reasoning and inventive powers of man, has been almost wholly neglected.

This defect appears to be owing to various causes, and has long been perceived and lamented by those, who were able to estimate the advantages of such inquiries. Lord Chancellor Bacon accordingly remarked, near

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two centuries ago, that most of the histories, which had then appeared, might be compared to the trunk of a tree, deprived of it's most noble branches. ́ ́And in more ancient times, the elder Pliny, speaking on the same subject, has observed, with regret, that no writer of his time had undertaken to transmit to posterity the names and labours of those eminent men, who by their meditations and researches had enlarged the boundaries of science, and dignified and solaced life by their inventions and discoveries.


It is, indeed, obvious, that a good history of Mathematics might be considered as a register of experiments, to ascertain the strength of the human understanding, in some of it's highest attainments; which would also serve, as far as they have been successful, to guide and encourage our future researches. And, even in those cases where they have failed, they might prove of nearly equal importance, in preventing the repetition of useless trials, and unprofitable labour, How many, for instance, have wasted a great part of their lives in attempts to square the circle, to discover the perpetual motion, &c., who, if they had only read an account of what had been done by others in that way, would probably have been, deterred

deterred from entering upon these hopeless and illfated speculations.

But among the advantages which may be expected from a comparison of the early state of these sciences, with their present extension and improvement, one of the most consider able is, that it will lead to the full discovery of the origin of many theories and practices, which though, at first, defective and insufficient, have given birth to others more correct and commodious in their application. Such, for example, has been the case of the Fluxional and Differential Calculi, which may be traced through the methods of Slusius, Bar row, and the Indivisibles of Cavallerius, to their present improved form.

The young mathematician, in reading a work of this kind, will, also, be highly gratified, in following the accounts which have been given of the contention of rival talents, in the attempts that have been made to excel in the solution of some new and difficult problems; many ; many of which are now become comparatively easy; but which, at the time they were first published, required the utmost exertions of the most vigorous understanding, to complete their investigation. This he will find to be particularly the case with many of the questions

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questions proposed by Leibnitz, the Ber noullis and several british and french mathematicians; which being but little known to the generality of english students, cannot fail of proving extremely entertaining and


Another advantage which such a work may produce, is that of showing the difficulties. which the learner has to encounter, before he can hope to arrive at any degree of eminence in the pursuits which he has embraced. He will here soon perceive, that it is not an acquaintance with the mere elements of the various branches composing the great body of these sciences, which can entitle him to rank among mathematicians; but that he must look to the example of Newton, Euler, Lagrange, and other eminent men, who have risen to a height so far above that of their predecessors.

M. de Monmort, a celebrated french mathematician, being impressed with the utility of such an undertaking, observes, in one of his letters to Bernoulli, that "it is much to be wished some person would take the pains to inform us, how and in what order mathematical discoveries succeeded each other, and to whom we owe the obligation. We have histories

histories of painting, music and medicine; but a good history of geometry would be a work much more curious and useful. What pleasure would it afford us to perceive the connection of methods, and the chain of new theories, proceeding from the earliest periods to our own time! Such a work, well executed, might be considered as a history of the human mind; because it is in this science, more than in any other, that man shows the excellence and intelligence which God has given him, for the purpose of elevating him above all other creatures."

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It may, also, be added, that M. de Monmort did not content himself with mere wishes, but undertook to perform the task, which he had recommended to others; and no one could have been better qualified to execute a work of this kind, than this learned geometer; who, to a profound knowledge of the subject, joined the advantage of an extensive correspondence and connection with most of the ablest mathematicians in Europe. But after having made considerable advances in the undertaking, as we learn from a fragment of one of his letters, which has been preserved in the Leipsic Acts, he was prevented, by death, from finishing the work. And from A 4 the

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