The eighth is of a plane angle, Ἑπὶπεδος γωνία ἑϛὶν ἡ ἐν ἐπιπέδω, &c. “_Angulus planus est duarum linearum in plano se mutuo tangentium, et non in directum jacentium, alterius ad alteram inclinatio._” _A plane angle is the inclination one towards another of two lines that touch one another in the same plane, and lie not in the same straight line._ Besides the faults here observed by Sir Henry Savile, as the clause of not lying in the same straight line, and the obscurity or equivocation of the word _inclination_, there is yet another, which is, that by this definition two right angles together taken, are no angle; which is a fault which you somewhere (asking leave to use the word _angle_, καταχριϛικώς acknowledge, but avoid not. For in geometry, where you confess there is required all possible accurateness, every καταχρῆσις is a fault. Besides you see by this definition, that Euclid is not of your, but of Clavius’s opinion. For it is manifest that the two lines which contain an angle of contact incline one towards another, and come together in a point, and lie not in the same straight line, and consequently make an angle. The thirteenth definition is exact, but makes against your doctrine, that a point is nothing. Examine it. Ὅρος ἐϛὴν ὅ τινός ἐϛῖ πέρας. “_Terminus est quod alicujus extremum est._” _A term or bound is that which is the extreme of anything._ We had before, _the extremes of a line are points_. But what is in a line the extreme, but the first or last _part_, though you may make that part as small as you will? A point is therefore a part, and nothing is no extreme. The fourteenth, Σχῆμα ἐϛὶ τὸ ὑπὸ τινος ἤ τινῶν ὅρων περιεχόμενον. “_Figura est (subaudi quantitas) quæ ab aliquo, vel aliquibus terminis undique continetur sive clauditur._” _A figure is quantity contained within some bound or bounds._ Or shortly thus, _a figure is quantity every way determined_, is in my opinion as exact a definition of a figure as can possibly be given, though it must not be so in yours. For this _determination_ is the same thing with _circumscription_; and whatsoever is anywhere _(ubicunque) definitivè_ is there also _circumscriptivè_; and by this means the distinction is lost, by which theologers, when they deny God to be in any place, save themselves from being accused of saying he is nowhere; for that which is nowhere is nothing. This definition of Euclid cannot therefore possibly be embraced by you that carry double, namely, mathematics and theology. For if you reject it, you will be cast out of all mathematic schools; and if you maintain it, from the society of all school-divines, and lose the thanks of the favour you have shown (you the astronomer) to Bishop Bramhall.