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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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On this successive synthesis of the productive imagination, in the generation of figures, is founded the mathematics of extension, or geometry, with its axioms, which express the conditions of sensuous intuition a priori, under which alone the schema of a pure conception of external intuition can exist; for example, "be tween two points only one straight line is possible," "two straight lines cannot enclose a space," etc.

 We never can imagine or make a representation to ourselves of the non-existence of space, though we may easily enough think that no objects are found in it. 
It is a matter of indifference, whether I say, "I may in the progress of experience discover stars, at a hundred times greater distance than the most distant of those now visible," or, "Stars at this distance may be met in space, although no one has, or ever will discover them." For, if they are given as things in themselves, without any relation to possible experience, they are for me non-existent, consequently, are not objects, for they are not contained in the regressive series of experience.
 For since, according to their hypothesis, the least as well as greatest figures contain an infinite number of parts; and since infinite numbers, properly speaking, can neither be equal nor unequal with respect to each other; the equality or inequality of any portions of space can never depend on any proportion in the number of their parts. The questions; whether the world has a beginning and a limit to its extension in space; whether there exists anywhere, or perhaps, in my own thinking Self, an indivisible and indestructible unity--or whether nothing but what is divisible and transitory exists; whether I am a free agent, or, like other beings, am bound in the chains of nature and fate; whether, finally, there is a supreme cause of the world, or all our thought and speculation must end with nature and the order of external things--are questions for the solution of which the mathematician would willingly exchange his whole science; for in it there is no satisfaction for the highest aspirations and most ardent desires of humanity.