LIBER TERTIUS. 577 



maticorum, qui hanc scientiam Physicae fere imperare dis- 

 cupiant. Nescio enim quo fato fiat ut Mathematica et Lo- 

 gica, quae ancillarum loco erga Physicam se gerere debeant, 

 nihilominus certitudinem suam prae ea jactantes, dominatum 

 contra exercere praesumant. Verum de loco et dignitate hujus 

 scientiae minus curandum, de re ipsa videamus. 



Mathematica aut Pura est, aut Mixta. Ad Puram referun- 

 tur Scientiae, qua3 circa Quantitatem occupata3 sunt, a Materia 

 et Axiomatibus physicis penitus abstractam. Eae duae sunt, 

 Geometria et Arithmetica; Quantitatem altera Continuam, altera 

 Discretam tractans. Quae duae artes magno certe. cum acumine 

 et industria inquisitae et tractatae sunt ; veruntamen et Euclidis 

 laboribus in Geometricis nihil additum est a sequentibus, quod 

 intervallo tot saeculorum dignum sit ; et doctrina de Solidis 

 nee a veteribus nee a modernis pro rei usu et excellentia in- 

 structa et aucta est. 1 In Arithmeticis autem, nee satis varia 

 et commoda inventa sunt Supputationum compendia, praesertim 

 circa Progressiones, quarum in Physicis usus est non me- 

 diocris 2 , nee Algebra bene consummata est ; atque Arithme- 

 tica ilia Pythagorica et Mystica, quae ex Proclo et reliquiis 

 quibusdam Euclidis coepit instaurari, expatiatio quaedam spe- 

 culationis est. Hoc enim habet ingenium humanum, ut cum 



1 We might here expect to find some mention of Archimedes and of Apollonius, 

 whose labours contributed more to the progress of geometry than those of Euclid, who 

 was rather a systematiser than an original discoverer, and whose Elements do not em- 

 brace the whole extent of the geometry of the Greeks. The doctrine of conic sections, 

 which was commenced by Plato, and the method of limits of Archimedes, both most 

 important portions of the Greek geometry, are of course not to be found in Euclid's 

 Elements, not to mention a variety of isolated investigations. It is undoubtedly true 

 that even long after Bacon's time geometry advanced more slowly beyond the limits it 

 had attained in antiquity than other parts of mathematics, though in the present day 

 it may be said to have become a new science. See on this head, the Apergu Historique 

 des Methodes de la Geometrie of M. Chasles, himself one of those who have contributed 

 the most to its recent progress. 



2 One would certainly not infer from this remark, to which there is nothing corre- 

 sponding in the Advancement of Learning, that Bacon was aware that in the interval 

 which had elapsed since its publication, the greatest of all inventions for facilitating 

 arithmetical computations had been made known. Napier's Logarithms were pub- 

 lished in 1614, and reprinted on the continent in 1620; in which year Gunter's Canon 

 of Triangles was also published. In 1618 Robert Napier's account of his father's 

 method and Briggs's first, table of Logarithms were both published. In the year suc- 

 ceeding that of the publication of the De Augmentis his larger tables, and probably 

 those of Wingate, made their appearance. 



These dates are sufficient to show how much the attention of mathematicians was 

 given to the subject. It would almost seem as if some one, possibly Savile, had told 

 Bacon what was no doubt true that the application of the doctrine of series to 

 arithmetical computation was not as yet brought to perfection, and that he had adopted 

 the remark without understanding the importance of the discovery to which it referred, 

 and perhaps without being aware that any such discovery had been made. 



VOL. I. P P 



