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OXFORD

*

TO STUDENTS.

ÓF the former parts of this work that have been already before the public, a new and much improved edition shall be published in the course of the ensuing year.

There is also in a forward state a collection of Algebraic questions; comprising examples on each rule, in order, but most particularly on the application of Algebra to Geometry, which is certainly a desideratum at the present time.

The Author having completely made himself up in the undergraduate course, intends to devote part of his time, in future, to pupils. His terms shall be found moderate; two or three reading in the same Class will be instructed at proportionately reduced prices. Application to be made to him personally, or by letter directed to him at 16, College.

CORRIGENDA.

Page 16, line 2 from bottom, for that the sides about the right angle, read the three sides of the A

23,

36, 4.5, 47,

52,

53,

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1, for rectage, read rectangle

19, for ratio, their, read ratio of their
5, for occourse read occurse
8, for point, read points

9, for point, read points

31, for 's, read 2
23, for it, read its.

24, for touch each, read touch, each

55,-29, for of sides, (n) read of sides (n),
30, for plain read plane

PREFACE.

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THE general objects of the present treatise being to facilitate the study of the Elements of Geometry, as well as to promote the exercise of it amongst the students as much as possible; it seems advisable to show how far the reader may presume on these objects being attained. The former is attempted by giving the propositions of the Elements general demonstrations, which must more than any other contribute to give the reader clear and comprehensive views on the subject of Geometry, and to cultivate his reasoning powers with respect to all parts of human knowledge.

On the subject of viva voce demonstrations, much has been said against its general use, particularly in the higher orders of Mathematics and Physics, and indeed too much could not be said if any good were likely to result from it. Academical reform is too hopeless a case, and one of too extensive a nature to be worth discussing at any length.

In plane Geometry, however, where analytic artifice has no place, and where the reader is seldom if ever obliged to lose sight of the basis on which his reasoning rests, vivâ voce demonstrations are of powerful effect. They

accustom him to clearness and solidity of reasoning, and enable him to take a view of the whole of a subject at once, the discussion of which would bewilder any person not accustomed to such.

The second object is aimed at, by presenting the reader with a collection of Geometrical Theorems, Loci, Porisms, and Problems, carefully selected from the best Geometrical writings, and some of them perhaps never before published. Mutual dependence has been considered as well as relative importance in the way of difficulty. The Demonstrations are not given, first from the great size and consequent expense it would entail upon the work; and secondly, because it would otherwise completely fail in the effect of exercising the student in reasoning for himself, and only accustom him to get off by rote the reasoning of others.

The best system of Geometry that has lately been presented to the public is that of Professor Leslie, as far as he confines himself to the strict limits of plane Geometry. As for the crude, inadequate and false demonstrations that are huddled together at random in the books of Creswell and Bland, the reader is cautioned to avoid them; unless where he may be occasionally recommended to use them as being the works of some abler hands; for it may be said of these writers, as it has been said by an able critic of one of their cotemporaries, that "their errors only are original."

Perhaps the collection here presented is the most complete and most numerous that has yet appeared; and is by no means to be considered as a mere geometrical exercise it is a collection of truths, and as such a powerful and necessary portion of human knowledge. They have a still greater use, " humana notitia et humana potentia in idem coincident," says Lord Bacon; they put

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