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OF THE

CAMBRIDGE PROBLEMS,

FROM 1800 TO 1820.

BY I. M. F. WRIGHT, B. A.,

LATE SCHOLAR OF TRINITY COLLEGE, CAMBRIDGE.

IN TWO VOLUMES.

VOL. I.

STOR LIBRART

NEW-YORK

LONDON:

PRINTED FOR BLACK, YOUNG, AND YOUNG,

TAVISTOCK-STREET, COVENT-GARDEN.

MDCCCXXV.

LONDON:

Printed by WILLIAM CLOWES,

Northumberland-court.

PREFACE..

WHEN first these volumes went forth to the public, their Author, being on the wing for a distant province of the empire, on business deeply affecting the interests of science, had barely sufficient leisure to announce to his readers, by way of preface, that he had laboured long and hard for their benefit, and anticipated a proportionate reward in the consequences of their approbation. In neither more nor less than two sentences, was all this expressed, "together with" a complimentary inuendo, that to those for whose use or entertainment the book was designed, a long head was a thing quite superfluous. Such was the sum and substance of this very brief and pithy preface-brief demonstratively, and as pithy to the full as are the sigus along the road, which invite you to refect and recreate the body. Like these, it intimated that no pains had been spared to afford good entertainment. But quitting the land of tropes and metaphors, which we resign to the wise of the east, who so adroitly associate Euclid with the Eumenides, Pappus with the Peris, or Minerva with the Muses, we shall indulge at parting, by stating the pleasing fact, that the invitations thus held out have not been unaccepted. Mathematicians of every pretension to that appellative have honoured us with a perusal, the consequence of which is, that we have carefully revised the whole work, and adopted such corrections, emendations, and additions, as have either suggested themselves to us, or been haply pointed out by our good friends the critics; and at the same time we acknowledge and confess these obli

VOL. I.

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gations in a preface comprehensive enough also to detail other matters.

The hints found available for improvement, have almost in every instance, been such as a revisal of the work itself suggested, and it is but reasonable to suppose an author to be most conversant with his own works. The remarks of others, however, have not been disregarded. The work has been commented on freely both by private individuals, and by the public press. In the correspondence of the former, many flattering encomiums have been received, and are here gratefully acknowledged. It is hoped that if in some instances the proposed alterations, which served to qualify this approbation, are not adopted, a reconsideration will produce conviction on the part of the proposer of their futility. The same remark applies to the (narox) critics. The Westminster Reviewer, spite of the general praise he bestows, must not be offended when he finds the recommendation not taken, as to entering into the details of bookwork connected with the higher subjects-nor were his remarks as to problem 718, vol. ii. anywise convincingnor does his solution of the sections of greatest and least curvature of the surface being at right angles, appear a good sample of his own skill. Although a senior wrangler, he is not infallible, and must therefore excuse any refractoriness we may have exhibited, and fairly balance it with the opposite symptoms.

The Reviewer in the Quarterly Mag.-now defunct (not the man that I wot of,) although no S. W., has nevertheless not been unheeded or treated with contempt. Intemperate and fearless as his censures are, there is withal a sort of painstaking about him which makes him pry into every the minutest error, and so eager is he in the pursuit, that excellencies which catch the eye of every one else, are by him either overlooked or trodden under foot. So comprehensive are his views, that to make sure of catching one

error, he grasps along with it all the surrounding truths, as though these innocents were aiding and abetting the false one. He will allow no merit, but must palpably, against common sense and common honesty, lay level all pretensions to it, as when he makes practical hypotheses about letting the gas escape, in the problem upon balloons, (see p. 548, vol. ii.) to defend Playfair, which hypotheses, if the reader will consult the words of that writer, will nowhere be found-as when he departs from the subject under immediate consideration, to inveigh against a work lauded by every other writer, and by its extensive sale proved incontestably valuable, &c. &c. Some would conclude nothing from this hyper-criticism, but they would judge inconsiderately. From amongst a mass of his own confusion, there may be something extricated. After a careful sifting, I have adopted a full half dozen of his ideas, and am grateful for the benefit. But although I thus make him useful, let him be reminded of a truth, the contemplation of which may teach him some degree of modesty, that in detecting these errors, he himself has committed at least two for one, thereby forcibly reminding us of a certain fraternity of travellers, yclept tinkers. But again are we transgressing the bounds of mathematical decorum.

Resuming the gravity so appropriate to the subject matter of these volumes, I (we will be egotists now if you please) may express a hope that the corrected edition now offered to the public, will be found more worthy of their approbation than its predecessor. In the original execution of a work so multifarious and diversified, embracing questions of every degree of difficulty in the several branches of abstract and applied science, I may be reasonably allowed to draw liberally upon the candour and indulgence of all competent judges. The practised mathematician will at once perceive the disadvantage with regard to mental energy in a work of this ever-deviating and desultory nature. There being

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