The second definition is of a line: γραμμὴ δὲ μῆκος ἂπλατες. “_Linea est longitudo latitudinis expers_; _a line is length which hath no breadth_;” and if candidly interpreted, sound enough, though rigorously not so. For to what purpose is it to say _length not broad_, when there is no such thing as a _broad length_. One path may be broader than another path, but not one mile than another mile; and it is not the path but the mile which is the way’s length. If therefore a man have any ingenuity he will understand it thus, _that a line is a body whose length is considered without its breadth_, else we must say absurdly a _broad length_; or untruly, that there be bodies which have length and yet no breadth; and this is the very sense which Apollonius, saith Proclus, makes of this definition; “when we measure,” says he, “the length of a way, we take not in the breadth or depth, but consider only one dimension.” See this of Proclus cited by Sir Henry Savile, where you shall find the very word _consider_. The fourth definition is of a straight line, thus Ἐυθεῖα γραμμή ἐϛιν, &c. “_Recta linea est quæ ex æquo sua ipsius puncta inter jacet._” _A straight line is that which lieth equally (or perhaps evenly) between its own points._ This definition is inexcusable. Between what points of its own can a straight line lie but between its extremes? And how lies it evenly between them, unless it swerve no more from some other line which hath the same extremes, one way than another? And then why are not between the same points both the lines straight? How bitterly, and with what insipid jests would you have reviled Euclid for this, if living now he had written a _Leviathan_ . And yet there is somewhat in this definition to help a man, not only to conceive the nature of a straight line (for who doth not conceive it?) but also to express it. For he meant perhaps to call a straight line that which is all the way from one extreme to another, equally distant from any two or more such lines as being like and equal have the same extremes. So the axis of the earth is all the way equally distant from the circumference of any two or more meridians. But then before he had defined a straight line, he should have defined what lines are _like_, and what are _equal_. But it had been best of all, first to have defined crooked lines, by the possibility of a deduction or setting further asunder of their extremes; and then straight lines, by the impossibility of the same. The seventh definition, which is that of a plain superficies, hath the same faults.