The question Translation: that which was to have been made deals with grammatical aspects of the expression quod erat demonstrandum, but I am interested in a detailed break-down of the meaning attributed to each word. Generally this is translated as which was (necessary) to be demonstrated, but how is this meaning broken down according to each of the three individual words? More specifically, is the "necessity" aspect inherent in the gerundive "demonstrandum" or in "erat" ? Since "erat" is just past tense of "to be", it seems likely that the meaning of "necessity", if any, would be in the gerundive. Do gerundives generally carry such a connotation of necessity?
Yes. In Quod erat demonstrandum the sense of necessity can be attributed completely to the gerundive. As in our case, often the gerundive is coupled with the verb esse (to be) - most famously in Censeo Carthaginem esse delendam ("I think Carthage must be destroyed").
However, the gerundive can bear a similar sense of necessity without being coupled with the verb esse, as it can be used adjectively.
So it seems that saying that the "necessity" aspect is inherent in the gerundive is a fair statement - and that usage is general indeed. This does not mean, however, that a gerundive forces a necessity as there are some other constructions in Latin where gerundive do not necessarily bear the "necessity" sense.
As for the word-breakdown. Quod=what, erat=was, demostrandum=to be demonstrated.