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Of St John's College, Cambridge.

“They are all good, and each volume adds to the value of the rest” — . “Perspicuous language, vigorous investigations, scrutiny of difficulties, and methodical treatment, characterise Mr. Todhunter's works.” —.

No method of overcoming the difficulties experienced by young students of Euclid appears to be so useful as that of breaking up the demonstrations into their constituent parts; a plan strongly recommended by Professor ''De Morgan. In the present Edition each distinct assertion in the argu&shy;ment'' begins a new line; and at the ends of the lines are placed the necessary references to the preceding principles on which the assertions ''depend. The longer propositions are distributed into subordinate parts,'' ''which are distinguished by breaks at the beginning of the lines. Notes,'' Appendix, and a collection of Exercises are added.

The subjects included in the present work are those which have usually ''found a place in Elementary Treatises on Mensuration. The mode of'' treatment has been determined by the fact that the work is intended for the ''use of beginners. Accordingly it is divided into short independent chapters,'' ''which are followed by appropriate examples. A knowledge of the elements'' of Arithmetic is all that is assumed; and in connection with most of the Rules of Mensuration it has been found practicable to give such explana&shy;tions and illustrations as will supply the place of formal mathematical demonstrations, which would have been unsuitable to the character of the work, “For simplicity and clearness of arrangement it is unsurpassed by any text-book on the subject which has come under our notice.” — .