APPENDIX I.

CONTAINING

A SELECTION OF PROPOSITIONS

DEDUCIBLE FROM

THE FIRST SIX BOOKS

OF

Euclid's Elements.

Censemus, autem, nihil utilius ad Geometriam penitius cognoscendam haberi posse, quam hujusmodi contentio tyronis, in, deducendis theorematis, vel solvendis problematis: qua fit, ut Geometria ipsa ejus animo multo altius insideat, et investigationis fontes aperiantur.

BOSCOVICH.

a

DEDUCTIONS

FROM THE FIRST SIX BOOKS

OF

Euclid's Elements.

GEOMETRICAL EXERCISES are peculiarly adapted to the improvement of the chief powers of the mind; and the sole motive which has prompted the publication of the following selection of Questions, is a desire to engage the Academical Student in that employment, from which he is likely to be most benefited in the beginning of his course. It is by no means intended to recommend to him the cultivation of this department of Science, to the neglect of all others; but he is advised to make it the ground-work of his future acquirements in the Mathematics, and never to advance until he has laid that foundation well; because it is the firmest upon which the superstructure of solid mathematical knowledge can be built.

No credit whatever is expected by the author to accrue to him from the execution of this design,

unless it be of that very humble, but surely not dishonourable, kind, which belongs to an useful performance. Although some of the questions, which he has here published, are original, he is far from thinking it probable that even these have not occurred to others, at least as early as they did to himself.

His materials are, for the most part, taken from works of established reputation, both ancient and modern. Well known, as they must be to the learned, they may, however, be useful, as a collection, to the student in Geometry. They have been chosen, either as exhibiting some remarkable property of lines or figures, omitted by Euclid, or as furnishing a mere exercise of ingenuity. Some Propositions, that are very obvious, and very easy of demonstration, are purposely inserted, as best suited to the ability of beginners; and, perhaps, it may not be improper to add, that many others are the Geometrical Solutions of Problems belonging to the several branches of Natural Philosophy.

8

Such an arrangement has been given to the deductions, as will, in many cases, lead to at least one method, it would be presumption to say the best method, of solution. They are distributed according to the same order as the several Books of Euclid, which are most studied; and further, they are placed, each under the last of the propositions upon which it may be made to depend, or which need be quoted in its proof. They are not always, therefore, although they are often,