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By George Salmon
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Extra info for A treatise on the analytic geometry of three dimensions
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2 Fihrist (tr. Suter), p. zz. Mhnoires presentes a I'academie des sciences, 1856, XIV. pp. 658-719' , Woepcke read the name of the author, in the title of the first book as B . los (the dot representing a missing vowel). He quotes also from other MSS. g. of the Ta'rikh aIIfukama and of the Fihrist) where he reads the name of the commentator as B . lis, B. n . 1. s. Woepcke takes this auth'or to be Valens, and thinks it possible that he may be the same as the astrologer Vettius Valens. This Heiberg (Euklid-Studien, pp.
Again Eutocius, in his note on Archimedes, On the Sphere and Cylinder I. , just as the problem is solved in the second scholium on Eucl. XII. I. " The actual references to Pappus in Proclus are as follows: (r) On the Postulate (4) that all right angles are equal, Pappus is quoted as saying that the converse, viz. that all angles equal to a right angle are right, is not true 6, since the angle included between the arcs of two semicircles which are equal, and have their diameters . at right angles and terminating at one point, is equal to a right angle, but is not a right angle.
This is further confirmed by the fact that the Fihrist gives this author and Valens as the subjects of two separate paragraphs, attributing to the latter astrological works only. 5 Heiberg, Euklid-Studien, p. 173; ·Euclid's Data, ed. Menge, pp. 256, Iii. 6 Proclus, pp. 189, 190. 7 ibid. p. 197, 6-10. 8 ibid. p. 198, 3-15. 1 3 INTRODUCTION [CR. III (3) Pappus gave a pretty proof of 1. 5· This proof has, I think, been wrongly understood; on this point see my note on the proposition. (4) On 1. " We shall see what Heron's addition consisted of; what Pappus may have added we do not know, unless it was something on the lines of his extension of 1.