Any proofs allowed, the

With regard to Euc. VI. Definition or test of Pro

I. 33.

portion being stated.

N.B. When the Examiner wishes for other proofs than the above, the necessary restrictions and allowable assumptions may be given in the question.

PRELIMINARY NOTICES.

The following symbols will be used simply in lieu of the words to which they are here prefixed.

angle.
▲ triangle.
parallelogram.

O circle.

Oce circumference.

1 perpendicular (to).
Il parallel.

+ together with.

= equal to.

> greater than.

< less than.

... because.

... therefore.

: is to.

The object aimed at is merely to place before the student the various steps of an argument in a more succinct form by curtailing the verbiage, thus enabling him to take in at a glance the outline of a proof. It must however be borne in mind that the words themselves must be substituted in any examinations in which symbols are objected to.

It will be assumed as self-evident that:—

Things which are equal to the same thing are equal to one another.

The whole is equal to the sum of its parts.

If equals be added to equals the wholes are equal.

If equals be taken from equals the remainders are equal.

If equals be added to unequals the wholes are unequal. If equals be taken from unequals the remainders are unequal.

Things which are double of equal things are equal to one another.

Things which are halves of equal things are equal to one

another.

Equimultiples of equal things are equal.

Things, of which the equimultiples are equal, are themselves equal.

If one magnitude be greater than another. any multiple of the former is greater than the same multiple of the latter.

If a multiple of one magnitude be greater than the same multiple of another then the former magnitude is greater than the latter.

ERRATA.

P. 12, 1. 7, for equal circles read Os having equal radii.

24, 1. 10 and p. 27, 1. 20, 22, for has been read is.

38, 1. 4, for FE read FG.

71,,, 13, 16. For definitions, see p. 86.

107,,,

6, for divides read divide.

1, add if possible, let them bisect each other; ,, 131,,, 13, omit to it.

201. In the diagram the diagonal of FB is AC.