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collected works, Oxford, 1699, folio. The subject of this fragment is the mode of multiplying large numbers ; from which it has been suspected that the first two books treated of arithmetic only. 8. Part of the preface of the seventh book is given (Gr. Lat.) by Gregory in the introduction to the Oxford Euclid [eucleides]. 4. The complete preface of the seventh book, with the lemmas given by Pappus, as introductory to the subject of analysis of loci (rod OiVahvo^evov t^ttou), are given by Halley (Gr. Lat.), in the preface to his version of Apollonius, de Lectione Rationis, Oxford, 1706, 8vo. So far Fabricius, verified by ourselves in every case except the part in [ ] : we may add that Dr. Trail gave (op. cit., p. 182) two pas­sages (Gr. Lat.) on the classification of lines, which had been much alluded to by Robert Simson: and that Dr. Trail also states, that in the preface of an edition of Vieta's Apollonius Gallus, 1795, J. G. Camerer gave the Greek of the preface and lemmas relating to Tactions (jrepl eTratyoov). Hoffman and Sehweiger mention the second part of the fifth book as published (Gr.) by H. J. Eisenmann, Paris, 1824, folio.

There are two Latin editions of Pappus. The first, by Commandine, and published by his repre­sentatives, was made apparently from one manu­script only. Its description is " Pappi Alexandrini Mathematicae Collectiones a Federico Commandino .... commentariis illustratae," Pisauri, 1588 (folio size, quarto signatures). This edition shows, m various copies, three distinct title pages, the one above, another Venetiis, 1589, a third Pisauri, 1602. It is remarkably erroneous in the paging and the catch-words ; but it does happen, we find, that one or the other is correct in every case. There is a cancel which is not found in some copies. The second edition, by Charles Manolessius, has the same title, augmented, Bo-noniae, 1660 (larger folio, quarto signatures). It professes to be cleared ,from innumerable errors. We cannot find any appearance of the use of any additional manuscripts, or any thing except what is usual, namely, correction of obvious misprints and commission of others. And we find that Dr. Trail formed the same judgment. The first edition is the more clearly printed. What Mersenne gives, sometimes called an edition, is a mere synopsis of enunciations. An intended edition by John Gal-laesius, mentioned by Fabricius, never appeared.

The third book of Pappus treats on the dupli­cation of the cube, geometrical constructions con­nected with the three kinds of means, the placing in a triangle two lines' having a sum together greater than that of the two sides (which was regarded as a sort of wonder), and the inscrip­tion of the regular solids in a sphere. The fourth book treats of various subjects of pure geo­metry, as also of several extra-geometrical curves, as that called the quadratrix, &c. The fifth book treats of the properties of plane and solid figures, with reference to the greatest content under given boundaries, &c., at great length. The sixth book is on the geometry of the sphere. The seventh book is on geometrical analysis, and is preceded by the curious preface, which, mutilated as it is in parts, is the principal source of information we have on the history and progress of the Greek analysis. The eighth book is on mechanics, or rather on machines. A great deal might be written on Pappus, with reference to the effect his work has


produced on modern geometry by the spirit of in­quiry and conjecture which its appearance at once excited. But, unless a full account were given of the contents of the Collections, any such digression would be useless. (Suidas ; Fabric. Bibl. Gr. vol. ix ; Trail, Life of Simson, &c.) [A. De M.]

PAPUS, the name of a family of the patrician Aemilia Gens.

1. M. aemilius papus, was created dictator in b. c. 321, in which year the Romans received their memorable defeat from the Samnites near Caudium. (Liv. ix. 7.)

2. Q. aemilius papus, twice consul, first in b. c. 282, and again in 278, and censor in 275. In both his consulships and in his censorship he had as colleague C. Fabricius Luscinus. In his former consulship he was employed against the Etruscans and Boians, while Fabricius was engaged in South­ern Italy. He completely defeated the allied forces, and the chastisement which the Boians re­ceived was so severe, that Cisalpine Gaul remained quiet for upwards of fifty years (Dionys. xviii. 5 ; comp. Polyb. ii. 20). The passage in Frontinus (i, 2. § 7) which speaks of the defeat of the Boii by Aemilius Paullus (an error for Papus), is rightly referred by Niebuhr (Hist, of Rome, vol. iii. p. 430) to the above mentioned victory, though most modern writers make it relate to the conquest of the Gauls by the consul of b. c. 225 [see below, No. 3]. In b. c. 280 he accompanied Fabricius, as one of the three ambassadors who were sent to Pyrrhus. The history of this embassy, as well as of his second consulship and censorship, is given in the life of his colleague. [LusciNUS, No. 1.]

3. L. aemilius Q. p. cn. n. papus, grand­son apparently of No. *2, was consul b. c. 225, with C. Atilius Regulus. This was the year of the great war in Cisalpine Gaul. The Cisalpine Gauls, who had for the last few years shown symptoms of hostility, were now joined by their brethren from the other side of the Alps, and prepared to invade Italy. The conduct of this war was assigned to Aemilius, while his colleague Regulus was sent againt Sardinia, which had lately revolted. Aemi­lius stationed himself near Ariminum, on the road leading into Italy by Umbria, and another Roman army was posted in Etruria, under the command of a praetor. The Gauls skilfully marched between the two armies into the heart of Etruria, which they ravaged in every direction. They defeated the Roman praetor when he overtook them, and would have entirely destroyed his army, but for the timely arrival of Aemilius. The Gauls slowly re­treated before the consul towards their own country; but, in the course of their march along the coast into Liguria, they fell in with the army of the other consul, who had just landed at Pisa, having been lately recalled from Sardinia. Thus placed between two consular armies, they were obliged to fight, and thoug-h they had every disadvantage on their side, the battle was long contested. One of the consuls, Regulus, fell in the engagement ; but the Gauls were at length totally defeated with great slaughter. Forty thousand of the enemy are said to have perished and ten thousand to have been taken prisoners, among whom was one of their kings, Concolitanus. Aemilius followed up his victory by marching through Liguria and invading the country of the Boii, which he laid waste in every direction. After remaining there a few days he returned to Rome and triumphed. (Polyb. ii»

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