2. Four books of ' Conic Sections,' afterwards amplified and appro priated by Apollonius, who added four others. So says Pappus, as already mentioned in APOLLONIUS That Euclid did not write these books, appears to us more than probable from the silence of Proclue the Platonist, who, eulogising Euclid the Platooiat, and stating that lie wrote on the regular solids (a part of geometry culti vated by the Platonists), being led thereto by Platonism, never mentions his writing on the still more Platonic subject of the conic sections. But that Aristaus had written on the subject is known, and that Euclid taught it cannot be doubted, any more than that Apollonius, like other writers, prefixed to his own discoveries all that he judged fit out of what was previously known on the subject.
3. fly( Aim/Army, on 'Divisions.' This work is mentioned by Proclus in two words. John Dee imagined the book of Mohammed of Bagdad (which is annexed to the English edition of Euclid herein after cited) on the division of surfaces to be that of Euclid now under consideration ; but there seems to be no ground for this notion. The Latin of this work (from the Arabic) is given at the end of Gregory's Euclid, together with a fragment 'De Levi et Ponderoso,' attributed, without any foundation, to Euclid.
4. Mid nopicrgarwr, on Porisms,' in three books. This is men tioned both by Pappus and Proclus, the former of whom gives the enunciations of various propositions in it, but the text is so corrupt that they can hardly be understood.
5. Waxer wpbs irichtivelav, Locorum ad Superficiem,' which we cannot translate. It is mentioned by Pappua, but has not come down to us.
The preceding works are either lost or doubtful; those which follow all exist, and are contained in Gregory's edition, in the order inverse to that in which they are here mentioned.
6. 'Orr era sal warowrpisci, on Optics and Catoptrics.' These books are attributed to Euclid by Proclus, and by Marinus in the preface to the 'Data,' or rather books on these subjects. Savile, Gregory, and others doubt that the books which have oome down to ua are those of Euclid, and Gregory gives his reasons in the preface, which are—that Pappus, though he demonstrates propositions in optics and also iu astronomy, and mentions the 'Plimnomena ' of Euclid with reference to the latter, does not mention the Optics' with reference to the former; and that there are many errors in the works in question, such as it is not likely Euclid would have made. Proceeding on the sup
position that rays of light are carried front the eye to the object, the first of these hooka demonstrates some relations of apparent magni tude, and shows how to measure an unknown height by the well-known law of reflected light. In the second an imperfect theory of convex and concave mirrors is given.
7. on ' Astronomical Appearances,' mentioned by Pappus and Philoponus (cited by Gregory). It contains a geometrical doctrine of the sphere, and, though probably much corrupted by time, is undoubtedly Euclid's.
8. Kavaron4 saybor and Elcrayoryb appLovish, the Division of the Scale' and Introduction to Harmony.' Proclus mentions that Euclid wrote on harmony, but the first of these treatises is a distinct gee metrical refutation of the principles laid down in the second, which renders it unlikely that Euclid should have written both. The second treatise is Ariatoxenian [Asuman:sus], while the first proceeds on principles of which Gregory states he never found a vestige in any other writer who was reputed anterior to Ptolemnus (to whom he attri hutea it). The second treatiao is not geometrical, but is purely a description of the system mentioned, and as this treatise is not alluded to by Ptolernacua nor by any previous writer on the subject, it is very probable that Euclid did not write it.
9. Adonba, a 'Book of Data.' This is the most valuable specimen which we have left of the rudiments of the geometrical analysis of the Greeks. Before a result can bo found, it should be known whether the given hypotheses are sufficient to determine it. The application of algebra settles both points ; that is, ascertains whether one or more definite results cau be determined, and determines them. But in geometry it is possible to propose a question which is really inde terminate, and in a determinate form, while at the same time the methods of geometry which give one answer may not give the means of ascertaining whether the answer thus obtained is the only one. Thus the two following questions seem equally to require one specific answer, to one not versed in geometry :— Given, the area of a parallelogram, and the ratio of its sides; required, the lengths of those sides : and Given, the area of a parallelogram, the ratio of its sides and one of its angles; required, the lengths of the sides.