What is the source of the quote attributed to Origen, that "the soul has neither beginning nor end"? Related answer: Is there any substance to the claim that Origen supported reincarnation?

The following quote is widely attributed to Origen in books and on the internet  (e.g., here and here):


  The soul has neither beginning nor end. [They] come into this world strengthened by the victories or weakened by the defeats of their previous lives.


It's sometimes attributed to Origen's De Principiis, but a simple text search of that work does not reveal this quote.

From the answer linked above, it's pretty clear that Origen taught at least some doctrine of preexistence of souls, but this quote is often used to say that Origen believed in full-blown reincarnation.  

Where does this quote come from?  Is it actually in the writings of Origen? If not, when/where did it originate?



Note: Some might argue that the quote in this question is a fair summary of Origen's teaching.  That's irrelevant.  I'm interested in the origin of the quote itself, accounting for the possibility of minor differences due to translation into English from the original language. None of the "real" Origen quotes listed in the linked answer are anywhere close enough, in my opinion, to be considered the source of the quote in this question.
I believe the second part of this quote is original to Hatch, Edwin, and A M. Fairbairn. The Influence of Greek Ideas and Usages Upon the Christian Church. London: Williams and Norgate, 1891, as follows:

Every soul has existed from the beginning; it has therefore passed
through some worlds already, and will pass through others before it
reaches final consummation. It comes into this world strengthened by
its victories or weakened by the defeats of its previous life. Its
place in this world as a vessel appointed to honor or to dishonour is
determined by its previous merits or demerits. Its work in this world
determines its place in the world which is to follow. (page 235f)

Hatch and Fairbairn were presenting a summary and pastiche of various Origen texts in such a way that it was not apparent to readers that it was not entirely a direct quote. In this passage, I believe they refer at least to the following passages from Origen's own work, De Principiis:

there were certain causes of prior existence, in consequence of which
the souls, before their birth in the body, contracted a certain amount
of guilt in their sensitive nature, or in their movements, on account
of which they have been judged worthy by Divine Providence of being
placed in this condition. ... And it is probable that these movements
furnish grounds for merit even before they do anything in this world.
(De Principiis III.iii.5)
the cause of each one's actions is a pre-existing one; and then every
one, according to his deserts, is made by God either a vessel unto
honour or dishonour. (De Principiis III.i.20)
we are of opinion that, seeing the soul, as we have frequently said,
is immortal and eternal, it is possible that, in the many and endless
periods of duration in the immeasurable and different worlds, it may
descend from the highest good to the lowest evil, or be restored from
the lowest evil to the highest good. (De Principiis III.i.21)
I am, indeed, of opinion that, as the end and consummation of the
saints will be in those (ages) which are not seen, and are eternal, we
must conclude (as frequently pointed out in the preceding pages), from
a contemplation of that very end, that rational creatures had also a
similar beginning. And if they had a beginning such as the end for
which they hope, they existed undoubtedly from the very beginning in
those (ages) which are not seen, and are eternal. (De Principiis
III.v.4)
we are to suppose that at the consummation and restoration of all
things, those who make a gradual advance, and who ascend (in the scale
of improvement), will arrive in due measure and order at that land.
(De Principiis III.vi.9)

Regarding the editorial practices of Hatch and Fairbairn, Cruttwell writes regarding this section:

Dr. Hatch has ably pieced it together from several of Origen's works
in his own words.
Cruttwell, Charles Thomas. The heretical sects: Volume 2 of A Literary History of Early Christianity. Scribner, 1893, p. 505

The first part of this quote (&quot;The soul has neither beginning nor end.&quot;) is known from Eastern philosophy. (eg. The Brahmavâdin. Madras: Brahmavadin Press, 1895, page 8), but I don't know when or how it became attributed to Origen.