Lastly you object against the corollary of art. 28; which you make absurd enough by rehearsing it thus: _Si quantitas aliqua divisa supponatur in partes aliquot æquales numero infinitas_, &c. Do you think that of _partes aliquot_, or of _partes aliquotæ_, it can be said without absurdity, that they are _numero infinitæ_? And then you say I seem to mean, that if of the quantity A B, there be supposed a part C B, infinitely little; and that between A C and A B be taken two means, one arithmetical, A E, the other geometrical, A D, the difference between A D and A E, will be infinitely little. My meaning is, and is sufficiently expressed, that the said means taken everywhere (not in one place only) will be the same throughout: and you that say there needed not so much pains to prove it, and think you do it shorter, prove it not at all. For why may not I pretend against your demonstration, that B E, the arithmetical difference, is greater than B D, the geometrical difference. You bring nothing to prove it; and if you suppose it, you suppose the thing you are to prove. Hitherto you have proceeded in such manner with your _Elenchus_, as that so many objections as you have made, so many false propositions you have advanced. Which is a peculiar excellence of yours, that for so great a stipend as you receive, you will give place to no man living for the number and grossness of errors you teach your scholars. At the fourteenth chapter your first exception is to the second article; where I define a plane in this manner: _A plane superficies is that which is described by a straight line so moved, as that every point thereof describe a several straight line_. In which you require, first, that instead of _describe_, I should have said _can describe_. Why do you not require of Euclid, in the definition of a cone, instead of _continetur_, _is contained_, he say _contineri potest_, _can be contained_ ? If I tell you how one plane is generated, cannot you apply the same generation to any other plane? But you object, that the plane of a circle may be generated by the motion of the _radius_, whose every point describeth, not a straight, but a crooked line, wherein you are deceived; for you cannot draw a circle (though you can draw the perimeter of a circle) but in a plane already generated. For the motion of a straight line, whose one point resting, describeth with the other points several perimeters of circles, may as well describe a conic superficies, as a plane. The question, therefore, is, how you will, in your definition, take in the plane which must be generated before you begin to describe your circle, and before you know what point to make your centre. This objection, therefore, is to no purpose; and besides, that it reflecteth upon the perfect definitions of Euclid before the eleventh Element, it cannot make good his definition (which is nothing worth) of a plane superficies, before his first Element.