I would like to translate "knowledge builds upon knowledge" into Latin. Google Translate is obviously not good as it gives very different words depending on the structure of the English version, so I can't really tell what is correct. How should it be translated?
A very basic, apothegmatic translation would be something like this:
scientia ē scientiā fit / ē scientiā fit scientia
'Knowledge is produced from/arises out of/is the result of knowledge.'
For something extra-pithy, fit could be omitted and left understood:
scientia ē scientiā / ē scientiā scientia
Or, in a comment, tony suggested using the verb crescere ('to grow,' but also 'to come into existence' or 'to arise'), which should also work. This would yield, for example:
scientia (ā) scientiā crescit
'Knowledge grows/arises from knowledge.'
(The ā is optional; or it can be replaced with dē.)
Some other possibilities
Depending on the use that this translation will be put to, something more elaborate or poetic/less succinct or literal may be desired. Here are a couple of alternatives – though, if you really don't care about succinctness, the translation that brianpck gives in his answer is (in my opinion) best of all.
Since the notion is one of cumulative knowledge, you could also, conveniently, use the verb cumulare ('to pile up,' 'accumulate,' and, in the passive, also 'to be made up of') – for example:
scientia scientiā cumulātur / scientia aliā scientiā cumulātur / scientia alia aliā cumulātur
'Knowledge is piled up/increased with/made up of (other) knowledge.'
scientia super scientiam cumulātur / scientia alia super aliam cumulātur / alia super aliam cumulātur scientia
'Knowledge is piled on top of (other) knowledge.'
For comparison, there are (somewhat incongruously) these sentence:
Cicero, In Catilinam 1.14:
nuper cum morte superioris uxoris novis nuptiis locum vacuefecisses, nonne etiam alio incredibili scelere hoc scelus cumulavisti?
'...did you not heap up this crime with another unbelievable crime too?'
Livy, Ab urbe condita 26.41.8:
aduersae pugnae in Hispania nullius in animo quam meo minus oblitterari possunt, quippe cui pater et patruus intra triginta dierum spatium ut aliud super aliud cumularetur familiae nostrae funus interfecti sunt;
'...so that one death in our household was piled up on top of another...'
Or, you could combine crescere and cumulare, and do something like this:
scientiā cumulāta crescit scientia
'Knowledge grows heaped up from knowledge.'
This is adapted (also somewhat incongruously) from Silius Italicus, Punica 1.418:
et iam corporibus cumulatus creverat agger
'And now the rampart had grown heaped up with bodies'
Finally, speaking of heaps, there's a lovely bit in Lucretius, De rerum natura (6.185–186), where the verb ex(s)truere is used to describe clouds heaped (literally, built) up on top of other clouds:
scilicet hoc densis fit nubibus et simul alte
extructis aliis alias super impete miro.
'This [sc. lightning and thunder], you should know, happens in dense and high
Heaped-up clouds, heaped up one on another, a fabulous bulwark' [Trans. Anthony M. Esolen]
This could be adapted to produce:
scientia exstruitur alia aliam super / scientia exstruitur scientiam super / exstruitur scientia scientiam super
'Knowledge is built up on top of other knowledge.'
Note: super is the preposition, here used as a postposition. Among the other possible word arrangements would be scientia super scientiam exstruitur, where super is used in its normal function as a preposition, not as a postposition.
Here's an answer that is probably far more philosophical than you are looking for.
This principle actually was formally stated by Aristotle, in the first line of the Posterior Analytics:
Πᾶσα διδασκαλία καὶ πᾶσα μάθησις διανοητικὴ ἐκ προϋπαρχούσης γίνεται γνώσεως (71a1-2)
A common Medieval Latin translation (such as that commented on by St. Thomas Aquinas) runs as follows:
Omnis doctrina et omnis disciplina intellectiva ex praeexistenti cognitione fit.
Here's Barnes' translation:
All teaching and all learning of an intellectual kind proceed from pre-existent knowledge.
("Knowledge" in this translation is meant to stand in for the generic case as well, including non-intellectual knowledge.)
It certainly doesn't have the raw power of aphorism, but it is far more precise than "knowledge comes from knowledge": if all knowledge comes from prior knowledge, where would the first knowledge come from? And how can we explain the fact that our intellectual knowledge seems to spring from lower kinds of cognition, e.g. sensation? Aristotle gives us a robust account that is able to meet these objections.
If "knowledge builds" is understood reflexively, I could suggest:
Scientia de scientiā conficitur
"Science is built from/about science". This rendering exploits two senses of de, viz. "from" and "about".
Scientia supra scientiam conficitur
"Science is built upon science".
(Note that fit, "is made", instead of conficitur, "is built/constructed", may also do the trick).
Medieval Latin would allow this genitive construction:
Scientia scientiae fit
(as in Carmina Burana, 1: fit iuris confusio).
But if "knowledge builds" is read transitively, not reflexively, I would suggest:
Omnia supra scientiam / de scientiā scientia conficit
"Science builds everything upon/from/about science".
I would try
Scientia astruit scientiam.
to put it literally.