And whereas I said that _the ends of all straight lines drawn from a straight line, and passing through one and the same point, if their parts be proportional, shall be in a straight line_; is true and accurate; as also, _if they begin in the circumference of a circle, they shall also be in the circumference of another circle_. And so is this: _if the proportion be duplicate, they shall be in a parabola_. All this I say is true and accurately spoken. But this was no place for the demonstration of it. Others have done it. And I perceive by that you put in by parenthesis (“_Intelligis credo inter duas peripherias concentricas_”) that you understand not what I mean. Hitherto reach your objections to my geometry: for the rest of your book, it containeth nothing but a collection of lies, wherewith you do what you can, to extenuate as vulgar, and disgrace as false, that which followeth, and to which you have made no special objection. I shall therefore only add in this place concerning your _Analytica per Potestates_, that it is no art. For the rule, both in Mr. Ougthred, and in Des Cartes, is this: “_When a problem or question is propounded, suppose the thing required done, and then using a fit ratiocination, put A or some other vowel for the magnitude sought_.” How is a man the better for this rule without another rule, how to know when the ratiocination is fit? There may therefore be in this kind of analysis more or less natural prudence, according as the analyst is more or less wise, or as one man in choosing of the unknown quantity with which he will begin, or in choosing the way of the consequences which he will draw from the hypothesis, may have better luck than another. But this is nothing to art. A man may sometimes spend a whole day in deriving of consequences in vain, and perhaps another time solve the same problem in a few minutes.