"The Mss. [of Euclid’s Elements] contain a curious addition to XIII. I-5 in the shape of analyses and syntheses for each proposition prefaced by the heading: "What is analysis and what is synthesis. "Analysis is the assumption of that which is sought as if it were admitted by means of its consequences at something admitted to be true. "Synthesis is an assumption of that which is admitted by means of its consequences at something admitted to be true." There must apparently be some corruption in the text; it does not, in the case of synthesis, give what is wanted. B and V have, instead of "something admitted to be true," the words "the end or attainment of what is sought." ... the addition is altogether alien from the plan and manner of the Elements. The interpolation took place before Theon's time, and the probability is that it was originally in the margin, whence it crept into the text of P after XIII. 5. Heiberg... cited the remark of Pappus at the beginning of his "comparisons of the five [regular solid] figures which have an equal surface," to the effect that he will not use "the so-called analytical investigation by means of which some of the ancients effected their demonstrations." More recently Heiberg conjectures that the author is Heron, on the ground that the sort of analysis and synthesis recalls Heron's remarks on analysis and synthesis in his commentary on the beginning of Book II. and his quasi-algebraical alternative proofs of propositions in that Book."