It begins thus: "Mathematics carries with it thoroughly apodeictic certainty, that is, absolute necessity, and, therefore, rests on no empirical grounds, and consequently is a pure product of reason, and, besides, is thoroughly synthetical. How, then, is it possible for human reason to accomplish such knowledge entirely _a priori_?... But we find that all mathematical knowledge has this peculiarity, that it must represent its conception previously in _perception_, and indeed _a priori_, consequently in a perception which is not empirical but pure, and that otherwise it cannot take a single step. Hence its judgements are always _intuitive_.... This observation on the nature of mathematics at once gives us a clue to the first and highest condition of its possibility, viz. that there must underlie it _a pure perception_ in which it can exhibit or, as we say, _construct_ all its conceptions in the concrete and yet _a priori_. If we can discover this pure perception and its possibility, we may thence easily explain how _a priori_ synthetical propositions in pure mathematics are possible, and consequently also how the science itself is possible. For just as empirical perception enables us without difficulty to enlarge synthetically in experience the conception which we frame of an object of perception through new predicates which perception itself offers us, so pure perception also will do the same, only with the difference that in this case the synthetical judgement will be _a priori_ certain and apodeictic, while in the former case it will be only _a posteriori_ and empirically certain; for the latter [i. e. the empirical perception on which the _a posteriori_ synthetic judgement is based] contains only that which is to be found in contingent empirical perception, while the former [i. e. the pure perception on which the _a priori_ synthetic judgement is based] contains that which is bound to be found in pure perception, since, as _a priori_ perception, it is inseparably connected with the conception _before all experience_ or individual sense-perception." This passage is evidently based upon the account which Kant gives in the _Doctrine of Method_ of the method of geometry.[35] According to this account, in order to apprehend, for instance, that a three-sided figure must have three angles, we must draw in imagination or on paper an individual figure corresponding to the conception of a three-sided figure. We then see that the very nature of the act of construction involves that the figure constructed must possess three angles as well as three sides. Hence, perception being that by which we apprehend the individual, a perception is involved in the act by which we form a geometrical judgement, and the perception can be called _a priori_, in that it is guided by our _a priori_ apprehension of the necessary nature of the act of construction, and therefore of the figure constructed.