mth the Geometry o/*Boethius. 531 



There are again other MSS. which do not contain so much as the 

 printed copies. Such are the Harleian, Lansdowne, and Arundel 

 MSS. in the British Museum, none of which have the appendix*. 



The Harleian and Arundel MSS. coincide in their contents with the 

 editions down to the beginning of the Demonstratio.or Appendix, that 

 is, nearly the foot of p. 1536. Immediately after the table in that 

 page, there are a few lines which have never been published in the ori- 

 ginal Latin, and the existence of which was unknown until M. Chasles 

 gave a French translation of a portion, in his ' Aper^u sur I'Histoire de 

 Geometric,' from a MS. belonging to the town of Chartresf . At 

 the end of this passage the Harleian has the words epilogus finitur : 

 and then follows in both this sentence — " Si quis vero de contro- 

 versiis, et de qualitatibus et nominibus agrorum, deque limitibus, et 

 de statibus controversiarum scire desideret, Julium Frontinum necnon 

 Urbicum Agenum lectitet. Nos vero hsec ad praesens dixisse sufficiat." 



Here the Arundel MS. ends, but in the Harleian we find what is 

 a meagre abstract of Balbus, followed by a collection of geometrical 

 and arithmetical problems, which are taken, in part at least, from 

 Nipsus, Epaphroditus and Vitruviusj:. 



Such and so varied are the contents of the different MSS. We 

 have now to inquire whether any and what part is to be attributed 

 to their reputed author. 



The opinion of Niebuhr on the authorship of this treatise is to be 

 found in the appendix to the first edition of the second volume of his 

 ' History.' " It is absolutely certain," says he, " that the section on 

 the art of marking out boundaries in Boethius's Geometry can never 

 have been written by the learned and talented Consular. It is a 

 confused heap of rubbish, almost worse even than the great compi- 

 lation. Boethius's Geometry, until the appearance of Pope Gerbert's, 

 was, with Nipsus, Vitruvius and Epaphroditus, the manual of the 

 land surveyors ; and by one of them has this addition, which dis- 

 honours his name, been surreptitiously introduced ; just as the rude 

 ignorance of the copyist, at least of the MS. from which it was 

 printed, has stript the propositions and diagrams of what was most 

 essential §." 



Blume agrees with Niebuhr in thinking that the Demonstratio is 

 spurious, but differs from him as to the genuineness of the Euclid. 



eleventh century, deserves a closer examination. Five MSS. have been used for 

 the new edition of the Agrimensors, two of which (a and m) apparently do not 

 contain the Euclid, and one {z) has only the two books without the appendix. 



* These MSS. are respectively numbered 3595, 842, and 339. 



t Memoires Couronnees de 1' Academic de Bruxelles, t. xi. p. 471. The contents 

 of this MS. are fully given by M. Chasles in his 'Catalogue des Manuscrits de la 

 Biblioth6que de Chartres,' No. 142. According to Bethman it is not older than 

 the end of the twelfth century. 



X Only a part of these problems are published in Lachman's edition (p. 297-301). 

 Some of them were also published from the Arcerian MS. by Hase, in Bredow's 

 ' Epistolai Parisinas,' p. 201 seqq., and the whole of them by Schott in his ' Tabulae 

 Rei Nummariaellom. etGrasc. (Ant. 1615),' from a MS. in the Cistercian Monastery 

 at Duyn, which had also the ' Musica et Arithmetica' of Boethius. Is the MS. in 

 the public library of Cambridge (Moore 74) similar to this? 



§ Hist, of Rome, translated by Walters, vol. ii. p. 557. 



