Complete Extant Works of Hero of Alexandria, Vol. 3

...it seems, with the calculations laid out, it can be defined in such a way that it is scarcely permitted to doubt. For since the other parts of this codex are completed in quaternions, and by far the greatest part of the dioptric commentary itself is written out in quaternions, it is, if not certain, then highly likely that its first part was also once written in an entire, complete quaternion. Now, since it is sufficiently demonstrated by the continuity of the argument that nothing is missing either between fols. 63 and 64 or between fols. 64 and 65, it is consistent to posit that two pairs of membranes fell out between fols. 62 and 63. Thus, the form of that gathering is restored as follows:

A diagram depicts the structure of a manuscript gathering (quaternion). It shows nested U-shaped lines representing folded parchment sheets. The outermost sheet is labeled 'a' on the left and 'e' on the right. The next sheet is labeled '62' on the left and '63' on the right. The third sheet is labeled 'b' on the left and '64' on the right. The innermost sheet is labeled 'c' on the left and 'd' on the right. The labels 'a', 'b', 'c', 'd', and 'e' represent missing leaves, while '62', '63', and '64' represent existing folios.

That all other copies of Hero's booklet known thus far have been derived from this truncated Parisian codex, either directly or through transcripts, is indicated by the fact that the gap—which I have demonstrated to have arisen from the loss of four sheets of that book—is reported by all of them alike.1) The superscript 1 refers to the footnote below. It is scarcely worth exploring the steps of succession and corruption by which they follow one another; for there is no reason for any of these to have authority, since access to their common source lies open to this day. They are these:

1) For what is written as "stē" on p. 196, 2 in cod. Paris. no. 607 is "stēmatia" in the others; this single word could certainly have been restored by any scribe through conjecture drawn from a similar passage on p. 194, 25. And indeed, it happened so. For if another, more complete example of this commentary had been at hand to that scribe, he would certainly have copied out that whole part of the argument which is now missing from it. But he did not copy it out: therefore, he did not even take those three syllables from another book, but added them from his own. I pass over other evidence; I add this: the more recent codices differ from the Parisian no. 607 in such a way that the dissimilarity could have arisen from the errors of the copyists and also from some attempt at correction.