PHYSICAL SCIENCE. 



Vii 



The Arabians likewise represent numbers by 

 the letters of the alphabet, precisely as the He- 

 brews: the first nine letters representing the 

 nine digits; the second nine, the nine tens; and 

 the third nine, the nine hundreds. The twenty- 

 eighth letter of the Arabian alphabet represents 

 1000. 



The Greeks obviously borrowed their mode 

 of expressing numbers from the Hebrews or 

 Phenicians. The first five letters of the Greek 

 alphabet represent the first five digits. As the 

 Greeks have no letter corresponding to the He- 

 brew 1, which denotes six, they introduced for 

 -that purpose the mark / or 5, which they called 

 episemum. The next three letters, , , d, re- 

 present 7, 8, 9, corresponding with the Hebrew 

 characters f, T"T, Z0> which stand for the same 

 numbers. The next eight letters of the alphabet 

 correspond with those of the Hebrew, and repre- 

 sent the numbers, 10, 20, 30, 40, 50, 60, 70, 80. 

 There being no letter in the Greek alphabet 

 corresponding with the Hebrew JJ, which stands 

 for 90, the Greeks introduced for that purpose 

 the character^, or l|, or ^, to which they gave 

 the name of koppa, probably from the Hebrew 

 letter koph. The last eight letters of the Greek 

 alphabet, beginning with />, denote 100, 200, 300, 

 400, 500, 600, 700, 800. To stand for 900, they 

 invented the mark "?) , which they called sanpi. 

 Thousands were denoted by the letters of the 

 alphabet with an accent under them. Thus, a, 

 was 1 ; <*, 1000 ; /, 3, and y 3000, and so on. 



The most defective mode of notation is that of 

 the Romans, who employed the following letters : 

 I for 1 ; V for 5; X for 10; L for 50; D for 

 500 ; and M for 1000. By means of these sym- 

 bols, they contrived to represent moderate num- 

 bers. But such an imperfect method was in- 

 compatible with almost any progress in the most 

 common rules of arithmetic. Accordingly, the 

 Romans produced no mathematicians, nor any 

 person skilled in the science of numbers. 



The mode of expressing all numbers by the 

 ten symbols, 1, 2, 3, 4, 5, 6, 7, 8, 9, 0, with which 

 every body is familiar, seems to have originated 

 in India. In that country it has been used from 

 time immemorial. Not the smallest proof remains 

 that they ever made use of the letters of the al- 

 phabet for that purpose. The Arabians call the 

 decimal scale of arithmetic, Hindosi, or Indian 

 arithmetic, clearly pointing out the source from 

 which their mode of notation was derived. 

 Whether the Indians were the original contri- 

 vers of this astonishing improvement, or whether 

 they borrowed it from some other nation, we have 

 no means of determining. The Chinese, it is said, 

 possess treatises on arithmetic and geometry; but 

 as no translation, or even abstract, of the contents 

 of any such work has been published in Europe, 



we are ignorant how far their knowledge of these 

 subjects extend. Had they been acquainted with 

 the Indian mode of notation, it is hardly possi- 

 ble, considering the numerous mercantile trans- 

 actions which have taken place between them 

 and Europeans, that it should have entirely 

 escaped our knowledge- 



The Arabians became acquainted with the In- 

 dian notation when they began to prosecute 

 science under the caliphs, and they had libera- 

 lity enough to be sensible of its superiority, and 

 to adopt it. Along with the Mahomedan religion, 

 it made its way into Spain; which, during the 

 dark ages, was the most enlightened country in 

 Europe, and to which all those resorted from 

 every country, who wished to be initiated in the 

 rudiments of science. 



About the beginning of the tenth century, the 

 monastery of Fleuri, of the order of St Benedict, 

 had for its abbot, Abbon, who was a zealous cul- 

 tivator of the sciences, particularly of those con- 

 nected with mathematics. He rendered his 

 monastery a celebrated school of knowledge and 

 of piety ; and all the monks of St Benedict, who 

 gave proofs of abilities, were sent thitherto receive 

 instruction. Among these was Gerbert (afterwards 

 pope Sylvester II.), a native of Auvergne. After 

 having acquired all the knowledge that Fleuri 

 could furnish, he obtained leave to repair to 

 Spain, where two celebrated schools at that 

 time existed at Cordova and Grenada, which 

 belonged to the Mahomedan conquerers of 

 that country. These schools were much fre- 

 quented both by Mahomedans and Christians. 

 Gerbert made such progress in mathematical 

 knowledge, that he soon surpassed his masters. 

 Arithmetic, music, geometry, and astronomy, 

 had occupied his attention ; and, on his return 

 to France, he communicated to his countrymen 

 the knowledge which he had thus acquired. 

 But the greatest boon which he conferred on 

 Europe was the introduction of the Indian num- 

 bers, which he found in common use among the 

 scientific Mahomedans in Spain. The date of 

 this introduction must be fixed between the years 

 970 and 980. 



With the knowledge of the Indian figures, 

 the rules of arithmetic became also plain, and 

 came to be familiarly understood. It is obvious 

 from the translation of the Lilawati, by Dr 

 Taylor, a treatise on Arithmetic and Geometry, 

 by Bhascora Acharya, who was born in the year 

 1114, that in his time, the four common rules of 

 arithmetic, the rule of three, the management 

 of vulgar fractions, the method of extracting the 

 square and cube roots, and most of the various 

 rules at present met with in our books of arith- 

 metic, were known in India. No doubt they 

 were also taught at Cordova and Grenada, and 



