grana, paucis momentis, alia metalla in aurum vertere valeant per activitatem ejusdem Elixiris, quæ naturam scilicet perficere et omni impedimento liberare possit. Similiter senectutis retardatio, aut gradus alicujus juventutis instauratio, non facile fidem reperiat; attamen longe verisimilius est, ab homine qui naturam Arefactionis et spirituum super solida corporis deprædationes bene norit ; quique naturam Assimilationis atque Alimentationis, vel perfectioris vel pravioris, perspexerit ; naturam etiam spirituum et quasi flammæ corporis, alias ad consumendum appositæ alias ad reparandum, notarit; posse per diætas, balnea, unctiones, medicinas proprias, accommodata etiam exercitia, et similia, vitam prolongari aut vigorem juventutis aliqua ex parte renovari; quam quod hoc fieri possit per guttas pauculas, aut scrupulos alicujus pretiosi liquoris aut quintessentiæ. Rursus, ex astris fata elici posse non statim aut facile homines consenserint; illa vero, quod Hora Nativitatis (quæ sæpissime ex pluribus accidentibus naturalibus vel acceleratur vel differtur) vitæ totius fortunam regat; aut quod Hora Quæstionis sit cum re ipsa quæ quæritur confatalis; meras nugas dixeris. Attamen tanta exercet humanum genus impotentia et intemperies, ut non solum quæ fieri non possunt sibi spondeant, sed etiam maxime ardua sine molestia aut sudore, tanquam feriantes, se adipisci posse confidant. Verum de Magia hactenus; cujus et vocabulum ipsum ab infamia vindicavimus, et speciem veram a falsa et ignobili segregavimus.

Hujus vero partis, Operative scilicet de Natura, duæ sunt Appendices, magni utraque pretii. Prima est, ut fiat Inventarium Opum Humanarum, quo excipiantur et breviter enumerentur omnia hominum bona et for

tunæ (sive sint ex fructibus et proventibus naturæ, sive artis) quæ jam habentur, et quibus homines fruuntur; adjectis iis quæ olim innotuisse constat, nunc autem perierunt; ad hunc finem, ut qui ad nova inventa accingitur, de jam inventis et extantibus negotium sibi non facessat. Hoc vero Inventarium magis erit artificiosum magisque etiam utile, si quæ communi hominum opinione Impossibilia reputantur in unoquoque genere adjunxeris; atque una Proxima Impossibilibus, quæ tamen habentur, copules; ut alterum humanam inventionem acuat, alterum quadantenus dirigat; utque ex his Optativis et Potentialibus, Activa promptius deducantur. Secunda est, ut fiat Kalendarium eorum Experimentorum, quæ maxime Polychresta sunt, et ad aliorum inventionem faciunt et ducunt. Exempli gratia; experimentum artificialis conglaciationis aquæ per glaciem cum sale nigro, ad infinita pertinet;1 hoc enim modum condensationis secretum revelat, quo homini nihil est fructuosius. Præsto enim est ignis ad rarefactiones; verum in condensationibus laboratur. Plurimum autem facit ad inveniendi compendium, si hujusmodi Polychresta proprio Catalogo excipiantur.

1 The artificial congelation of water by snow and salt Bacon has elsewhere spoken of as a recent discovery. I have not been able to ascertain by whom it was made. In Boyle's New Experiments of Cold, it is said to be familiarly made use of in Italy, though scarcely known in England; and in the collection of experiments published by the Florentine Academicians in 1667 (in which collection the celebrated "Florentine experiment," which is in reality due to Bacon, is contained), artificial congelations are spoken of, but (probably because the subject was commonly known) without any reference to the history of the invention. "Sal nigrum," it may be well to mention, is saltpetre.

CAPUT VI.

De magna Philosophic Naturalis, tam Speculative quam Operative, Appendice Mathematica; quodque inter Appendices potius poni debet, quam inter Scientias Substantivas. Partitio Mathematica, in Puram et Mixtam.

OPTIME Aristoteles, Physicam et Mathematicam generare Practicam sive Mechanicam. Quare, cum jam tam Speculativam quam Operativam partem doctrinæ de Natura tractaverimus, locus est ut de Mathematica dicamus, quæ ad utramque est scientia auxiliaris. Hæc siquidem, in Philosophia recepta, Physicæ et Metaphysicæ pars tertia adjungitur; at nobis ista retractantibus et recolentibus, si eam ut scientiam substantivam et principalem designare in animo esset, magis consentaneum videretur et rei ipsius naturæ et ordinis perspicuitati, ut constitueretur tanquam portio Metaphysicæ. Quantitas enim (quæ subjectum est Mathematica) Materia applicata veluti Dosis Naturæ est, et plurimorum effectuum in rebus naturalibus causativa; ideoque inter Formas Essentiales numeranda est. Figure autem et Numerorum potentia in tantum apud antiquos valere visa est, ut Democritus principia varietatis rerum in figuris atomorum præcipue collocaverit; ac Pythagoras naturam rerum ex numeris constitui asseruerit. Illud interim verum est, Quantitatem inter Formas Naturales (quales nos eas intelligimus) omnium maxime esse abstractam, et a materia separabilem; quod ipsum in causa fuit, cur et diligentius exculta et acrius inquisita ab hominibus fuerit quam aliæ quæcunque

1 Arist. Præf. ad Quæst. Mechan.

Formæ, quæ omnes in materia magis sunt immersæ. Cum enim id hominum animis plane insitum sit (plurimo certe cum scientiarum detrimento) ut Generalium quasi campis liberis magis quam Particularium silvis et septis delectentur, nil repertum est Mathematicis gratius et jucundius, quo appetitus iste expatiandi et meditandi expleretur. Etsi autem hæc vera sint, nobis tamen qui non tantum veritati et ordini, verum etiam usui et commodis hominum consulimus, satius demum visum est Mathematicas, cum et in Physicis et in Metaphysicis et in Mechanicis et in Magicis plurimum polleant, ut omnium Appendices et copias auxiliares designare. Quod etiam quodammodo facere compellimus, propter delicias et fastum Mathematicorum, qui hanc scientiam Physicæ fere imperare discupiant. Nescio enim quo fato fiat ut Mathematica et Logica, quæ ancillarum loco erga Physicam se gerere debeant, nihilominus certitudinem suam præ ea jactantes, dominatum contra exercere præsumant. Verum de loco et dignitate hujus scientiæ minus curandum, de re ipsa videamus.

Mathematica aut Pura est, aut Mixta. Ad Puram referuntur Scientiæ, quæ circa Quantitatem occupatæ sunt, a Materia et Axiomatibus physicis penitus abstractam. Eæ duæ sunt, Geometria et Arithmetica ; Quantitatem altera Continuam, altera Discretam tractans. Quæ duæ artes magno certe cum acumine et industria inquisitæ et tractatæ sunt; veruntamen et Euclidis laboribus in Geometricis nihil additum est a sequentibus, quod intervallo tot sæculorum dignum sit; et doctrina de Solidis nec a veteribus nec a modernis pro rei usu et excellentia instructa et aucta est.1 In

1 We might here expect to find some mention of Archimedes and of Apollonius, whose labours contributed more to the progress of geometry

Arithmeticis autem, nec satis varia et commoda inventa sunt Supputationum compendia, præsertim circa Progressiones, quarum in Physicis usus est non mediocris, nec Algebra bene consummata est; atque Arithmetica illa Pythagorica et Mystica, quæ ex Proclo et reliquiis quibusdam Euclidis cœpit instaurari, expatiatio quædam speculationis est. Hoc enim habet ingenium humanum, ut cum ad solida non sufficiat, in supervacaneis se atterat. Mixta habet pro subjecto Axiomata et portiones physicas; Quantitatem autem considerat, quatenus est ad ea elucidanda et demonstranda et actuanda auxiliaris. Multæ siquidem na

than those of Euclid, who was rather a systematiser than an original discoverer, and whose Elements do not embrace 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 Aperçu Historique des Méthodes de la Géométrie of M. Chasles, himself one of those who have contributed the most to its recent progress.

1 One would certainly not infer from this remark, to which there is nothing corresponding 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 published 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 succeeding 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.