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HISTORICAL VIEW OP THE

to many other subjects, on which we cannot here enter.In his mechanical speculations he was less fortunate:he applies geometry with considerable effect to manyquestions in this science ; but, in the investigation of theinclined plane, betrays an erroneous notion of the reso-lution of forces, which renders defective his estimate ofthe force necessary to sustain a body on the plane : thisdefect in the knowledge of so essential a principle marksa point beyond which the ancient mechanics did not ex-tend, and which must have precluded a further advance.

Theon and Proclus , about the same period, or ratherlater, were known chiefly as commentators on Euclid .To the former we are little indebted for his attempts toimprove upon his author ; the latter wrote also a trea-tise on Motion.

Diodes, who lived before a. d. 500, is known as theinventor of an elegant curve, called the cissoid, towhich he was led by a previous construction of Pappusfor finding two mean proportionals between given ex-tremes. This curve is the locus traced out by the in-tersection of a chord from one end of the diameter of asemicircle drawn to the summit of an ordinate, with an-other ordinate equidistant from the centre. A perpen-dicular at the other end of the diameter becomes anasymptote to the curve ; which was named the cissoid *,from a fancied resemblance to a sprig of ivy mountingup a wall, as the curve does up its asymptote.

On alluding to these abstract topics, these elegantfictions, as it were, of a geometrical imagination inwhich the ancient mathematicians loved to indulge,the question of utility will doubtless be raised ; a ques-tion which, of course, can only be answered when theobjector states to what class of objects he will extendthe character of utility. For any practical resultsthese methods are no longer of use, because we nowpossess easier and shorter processes. But that mat-ters of abstract contemplation, as such, are not useful, isan assertion which surely betrays the most confined* ivy.