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Click on the phrases to see them in context. The original texts by Immanuel Kant and David Hume are available from the Gutenberg Projet.

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Mathematics, too, treats of the difference of lines and surfaces--as spaces of different quality, of the continuity of extension--as a quality thereof.

 In our experiences it is easy to observe that it is only the continuous influences in all parts of space that can conduct our senses from one object to another; that the light which plays between our eyes and the heavenly bodies produces a mediating community between them and us, and thereby evidences their coexistence with us; that we cannot empirically change our position (perceive this change), unless the existence of matter throughout the whole of space rendered possible the perception of the positions we occupy; and that this perception can prove the contemporaneous existence of these places only through their reciprocal influence, and thereby also the coexistence of even the most remote objects--although in this case the proof is only mediate. For as conditions of all existence in general, space and time must be conditions of the existence of the Supreme Being also. Space and time, therefore, do not consist of simple parts. But the matter of phenomena, by which things are given in space and time, can be presented only in perception, a posteriorI. The only conception which represents a priori this empirical content of phenomena is the conception of a thing in general; and the a priori synthetical cognition of this conception can give us nothing more than the rule for the synthesis of that which may be contained in the corresponding a posteriori perception; it is utterly inadequate to present an a priori intuition of the real object, which must necessarily be empirical. For, if they decide for the first view, and make space and time into substances, this being the side taken by mathematical natural philosophers, they must admit two self-subsisting nonentities, infinite and eternal, which exist (yet without there being anything real) for the purpose of containing in themselves everything that is real. 
  • Speculative reason has thus, at least, made room for such an extension of our knowledge; and, if it must leave this space vacant, still it does not rob us of the liberty to fill it up, if we can, by means of practical data--nay, it even challenges us to make the attempt.*
 And the world is termed nature,* when it is regarded as a dynamical whole--when our attention is not directed to the aggregation in space and time, for the purpose of cogitating it as a quantity, but to the unity in the existence of phenomena. Thus the conception of pure and merely intelligible objects is completely void of all principles of its application, because we cannot imagine any mode in which they might be given, and the problematical thought which leaves a place open for them serves only, like a void space, to limit the use of empirical principles, without containing at the same time any other object of cognition beyond their sphere.