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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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A beginning is an existence which is preceded by a time in which the thing does not exist.

 I find in the first place, that whatever objects are considered as causes or effects, are contiguous; and that nothing can operate in a time or place, which is ever so little removed from those of its existence. It follows from this that you must accept the absolutely necessary as out of and beyond the world, inasmuch as it is useful only as a principle of the highest possible unity in experience, and you cannot discover any such necessary existence in the would, the second rule requiring you to regard all empirical causes of unity as themselves deduced. Now this completeness of a science cannot be accepted with confidence on the guarantee of a mere estimate of its existence in an aggregate formed only by means of repeated experiments and attempts. Resemblance and contiguity are relations not to be neglected; especially when by an inference from cause and effect, and by the observation of external signs, we are informed of the real existence of the object, which is resembling or contiguous. 

I can consider a given point of time in relation to past time only as conditioned, because this given moment comes into existence only through the past time rather through the passing of the preceding time.

 But I should like very well to know by what means this possibility of non-existence is to be cognized, if we do not represent to ourselves a succession in the series of phenomena, and in this succession an existence which follows a non-existence, or conversely, consequently, change. And, indeed, how should it be possible, merely by the aid of the unity of consciousness--which we cognize only for the reason that it is indispensable to the possibility of experience--to pass the bounds of experience (our existence in this life); and to extend our cognition to the nature of all thinking beings by means of the empirical--but in relation to every sort of intuition, perfectly undetermined--proposition, "I think"? But I cannot admit that this being exists absolutely and in itself, because all of the conceptions by which I can cogitate an object in a determinate manner fall short of assuring me of its existence; nay, the conditions of the objective validity of my conceptions are excluded by the idea--by the very fact of its being an idea. If I take away from an empirical intuition all thought (by means of the categories), there remains no cognition of any object; for by means of mere intuition nothing is cogitated, and, from the existence of such or such an affection of sensibility in me, it does not follow that this affection or representation has any relation to an object without me.