ADVANCEMENT OF LEARNING 173 



to the labors of Euclid, though he lived many ages since. 

 The doctrine of solids has not been prosecuted and extended 

 equal to its use and excellency, neither by the ancients nor 

 the moderns; and in arithmetic there is still wanting a suf 

 ficient variety of short and commodious methods of calcu 

 lation, especially with regard to progressions, whose use in 

 physics is very considerable. 4 Neither is algebra brought 

 to perfection. As for the Pythagorical and mystical arith 

 metic, which began to be recovered from Proclus, 6 and cer 

 tain remains of Euclid, it is a speculative excursion, the 

 mind having this misfortune, that when it proves unequal 

 to solid and useful things, it spends itself upon such as are 

 unprofitable. 



Mixed mathematics has for its subject axioms and the 



4 In nature no two beings exist perfectly equal, and the same being cannot 

 retain its qualities unchanged for an instant of time together. In the universe 

 everything moves in a constant progression and series, and it probably was the 

 presentiment of this truth that led the greatest mathematicians after Bacon s 

 time to turn nearly all their attention to this department of mathematics. Be 

 yond the analogy, however, there is nothing in these phenomena which has any 

 relation with the reality of things ; nor have auy philosophers since Flud s day 

 ever dealt with them except as pure conditional verities. With data sufficiently 

 determinate, we may approach the solution of any question to which they refer; 

 but if these facts are not given, the problem must remain unresolved. The 

 mathematician may draw consequences ; but it is not allowed him to form prin 

 ciples, and if he attempt to apply figures to any hypothesis not warranted by 

 facts, he must be content with the fate of the Samian who constructed the 

 world out of arithmetic, and has been rewarded by the derision of ages for 

 his pains. 



No part of learning has perhaps been more cultivated since this author 

 wrote than mathematics, as every other science, or the body of philosophy 

 itself, seems rendered mathematical. The doctrine of solids has been improved 

 by several; the shorter ways of calculation here noted as deficient are in a 

 great measure supplied by the invention of logarithms. Algebra has been so 

 far improved and applied as to rival, or almost prejudice, the ancient geometry ; 

 add to this the new discoveries of the Method of Fluxions, the Method of Tan 

 gents, the Doctrine of Infinites, the Squaring of Curves, etc. For the general 

 system of mathematical learning, see &quot;Wolfii Elementa Matheseos Universae,&quot; 

 in two volumes 4to, printed at Halle in the year 1715; or for a more cursory 

 view, Father Castel s &quot;Mathe&quot;matique Universelle, &quot; published in the year 1731; 

 but for the history of mathematics, see Yossius &quot;De Universee Matheseos Na- 

 tura et Constitutione&quot; ; the &quot;Almagest&quot; of Ricciolus; Morhof s &quot;Poly hist. 

 Mathemat&quot;; and &quot;Wolfius s &quot;Commentatio de Scriptis Mathematicis, &quot; at the 

 end of the second volume of his &quot;Elementa Matheseos Universe;&quot; &quot;Montucla e 

 &quot;Hist. Math. ;&quot; and De la Croix s &quot;Analysis of Infinites.&quot; Ed. 



6 He ought to have said from lamblicus. Proclus was, like himself, totally 

 ignorant even of the little mathematical learning extant in his day. Ed. 



