[52] Prol., § 9.
[53] Cf. (Introduction, B. xvii, M. xxix): "But if the object (as object of the senses) conforms to the nature of our faculty of perception, I can quite well represent to myself the possibility of a priori knowledge of it [i. e. mathematical knowledge]."
[54] Cf. Descartes, Princ. Phil. i. § 13, and Medit. v sub fin.
[55] The view that kinds of space other than that with which we are acquainted are possible, though usually held and discussed by mathematicians, belongs to them qua metaphysicians, and not qua mathematicians.
[56] The first sentence shows that 'relative determinations' means, not 'determinations of objects in relation to us', but 'determinations of objects in relation to one another.' Cf. B. 37, M. 23; and B. 66 fin., 67 init., M. 40 (where these meanings are confused).
[57] B. 42, M. 26.
[58] This conclusion is also to be expected because, inconsistently with his real view, Kant is here (B. 41-2, M. 25-6) under the influence of the presupposition of our ordinary consciousness that in perception we are confronted by things in themselves, known to be spatial, and not by appearances produced by unknown things in themselves. Cf. (B. 41, M. 25) "and thereby of obtaining immediate representation of them [i. e. objects];" and (B. 42, M. 26) "the receptivity of the subject to be affected by objects necessarily precedes all perceptions of these objects." These sentences identify things in themselves and bodies in space, and thereby imply that in empirical perception we perceive things in themselves and as they are.
[59] A. reads 'only under'
[60] B. 43, M. 27.