Learn Farsi: به اینکه این پیش‌فرض، زیربنای نظریه‌ی جدید است، توجه کنید. - Pay attention to the fact that this presupposition is the foundation of the new theory.

The prefix pish- means "pre-" or "before". When added to the noun farz (which means "assumption" or "supposition"), it creates pish-farz, literally meaning "pre-assumption" or "presupposition".

What is the literal meaning of zir-banâ, and how does the prefix zir- function here?

The prefix zir- means "under", "sub-", or "infra-". The root noun banâ means "building" or "structure". Put together, zir-banâ literally means "substructure", which we translate naturally in this context as "foundation".

Why does the sentence start with "be inke" instead of just "inke"?

The verb phrase at the very end of the sentence is tavajoh konid (pay attention), which requires the preposition be (to). Because you are paying attention to a whole phrase rather than a simple noun, Farsi uses inke (the fact that) to introduce the clause. The preposition be attaches to it, forming be inke (to the fact that).

Why is there an extra ی (ye) attached to nazariye in "nazariye-ye jadid"?

The word nazariye (theory) ends with a silent heh that acts as the vowel "e". To link it to the adjective jadid (new) using the ezâfe connector (which is an "e" sound), you need a bridge to stop the two vowels from clashing. The consonant "y" bridges the gap, written here as ی to make nazariye-ye.