Consider first the terminology of mathematics. Almost all the standard terms are Greek or Latin translations from the Greek, and, although the mathematician may be taught their meaning without knowing Greek, he will certainly grasp their significance better if he knows them as they arise and as part of the living language of the men who invented them. Take the word _isosceles_; a schoolboy can be shown what an isosceles triangle is, but, if he knows nothing of the derivation, he will wonder why such an apparently outlandish term should be necessary to express so simple an idea. But if the mere appearance of the word shows him that it means a thing _with equal legs_, being compounded of ισος {isos}, equal, and σκελος {skelos}, a leg, he will understand its appropriateness and will have no difficulty in remembering it. _Equilateral_, on the other hand, is borrowed from the Latin, but it is merely the Latin translation of the Greek ισοπλευρος {isopleuros}, _equal-sided_. _Parallelogram_ again can be explained to a Greekless person, but it will be far better understood by one who sees in it the two words παραλληλος {parallêlos} and γραμμη {grammê} and realizes that it is a short way of expressing that the figure in question is contained by parallel lines; and we shall best understand the word _parallel_ itself if we see in it the statement of the fact that the two straight lines so described go _alongside one another_, παρ' αλληλας {par' allêlas}, all the way. Similarly a mathematician should know that a _rhombus_ is so called from its resemblance to a form of spinning-top (ῥομβος {rhombos} from ῥεμβω {rhembô}, to spin) and that, just as a parallelogram is a figure formed by two pairs of parallel straight lines, so a _parallelepiped_ is a solid figure bounded by three pairs of parallel planes (παραλληλος {parallêlos}, parallel, and επιπεδος {epipedos}, plane); incidentally, in the latter case, he will be saved from writing 'parallel_o_piped', a monstrosity which has disfigured not a few textbooks of geometry. Another good example is the word _hypotenuse_; it comes from the verb ὑποτεινειν {hypoteinein} (c. ὑπο {hypo} and acc. or simple acc.), to _stretch under_, or, in its Latin form, to _subtend_, which term is used quite generally for 'to be opposite to'; in our phraseology the word _hypotenuse_ is restricted to that side of a right-angled triangle which is opposite to the right angle, being short for the expression used in Eucl. i. 47, ἡ την ορθην γωνιαν ὑποτεινουσα πλευρα {hê tên orthên gônian hypoteinousa pleura}, 'the side subtending the right angle', which accounts for the feminine participial form ὑποτεινουσα {hypoteinousa}, _hypotenuse_. If mathematicians had had more Greek, perhaps the misspelt form 'hypot_h_enuse' would not have survived so long.