And thus much for the definitions placed before the first of Euclid’s Elements. Before the third of his Elements is this definition: “_In circulo æqualiter distare a centro rectæ lineæ dicuntur, cum perpendiculares quæ a centro in ipsas ducuntur sunt æquales_.” _In a circle two straight lines are said to be equally distant from the centre, upon which the perpendiculars drawn from the centre are equal._ This is true; but it is rather an axiom than a definition, as being demonstrable that the perpendicular is the measure of the distance between a point and a straight or a crooked line. Before the fifth Element the first definition is of a part: _Pars est magnitudo magnitudinis, minor majoris, cum minor metitur majorem_. _A part is one magnitude of another, the less of the greater, when the less measureth the greater._ From which definition it followeth, that more than a half is not a part of the whole. But because Euclid meaneth here an aliquot part, as a half, a third, or a fourth, &c., it may pass for the definition of a measure under the name of part, as thus: _a measure is a part of the whole, when multiplied it may be equal to the whole_, though properly a measure is external to the thing measured, and not the aliquot part itself, but equal to an aliquot part. But the third definition is intolerable; it is the definition of λόγος, in Latin _ratio_, in English, _proportion_, in this manner, λόγος ἐςὶ δύο μεγεθῶν ὁμογενῶν ῆ κατὰ πηλικότητα προς ἄλληλα ποιὰ σχέσις. “_Ratio est duarum magnitudinum ejusdem generis mutua quædam secundum quantitatem habitudo._” _Proportion is a certain mutual habitude in quantity, of two magnitudes of the same kind, one to another._ First, we have here _ignotum per ignotius_; for every man understandeth better what is meant by _proportion_ than by habitude. But it was the phrase of the Greeks when they named like proportions, to say, the first to the second, οὕτως ἔχει, _id est, ita se habet_, and in English, _is as_, the third to the fourth. As for example, in the proportions of two to four, and three to six, to say two to four, οὕτως ἔχει, _id est, ita se habet, id est_, _is as_, three to six. From which phrase Euclid made this his definition of proportion by ποιὰ σχέσις, which the Latins translate _quædam habitudo_. _Quædam_ in a definition is a most certain note of not understanding the word _defined_; and in Greek, ποιὰ σχέσις is much worse; for to render rightly the Greek definition, we are to say in English, that proportion is a what-shall-I-call-it-_isness_, or _soness_ of two magnitudes, &c.; than which nothing can be more unworthy of Euclid. It is as bad as anything was ever said in geometry by Orontius, or by Dr. Wallis. That proportion is quantity compared, that is to say, little or great in respect of some other quantity, as I have above defined it, is I think intelligible.