A Short Account of the History of Mathematics Quotes

“Whatever was the extent of their [the Chaldaeans] attainments in arithmetic, it is almost certain that the Phoenicians were equally proficient.”

“Generally I have not referred to the results obtained by practical astronomers and physicists unless there was some mathematical interest in them.”

“A Short Account of the History of Mathematics (1908)*oogle Books”

“A Short Account of the History of Mathematics (1888)*oogle Books”

“The fact... that various nations in the vicinity of Greece had reached a high state of civilisation does not justify us in assuming that they had studied mathematics.”

“Greek tradition uniformly assigned the special development of geometry to the Egyptians, and that of the science of numbers either to the Egyptians or to the Phoenicians.”

“A Short Account of the History of Mathematics (1960 Dover reprint of 1908 edition)*roject Gutenberg”

“He [Ahmes] concludes the work with some arithmetico-algebraical questions, two of which deal with arithmetical progressions and seem to indicate that he knew how to sum such series.”

“Their [the ancient Chinese] arithmetic was decimal in notation, but their knowledge seems to have been confined to the art of calculation by means of the swan-pan.”

“The subject-matter of this book... primarily it is intended to give a short and popular account of those leading facts in the history of mathematics which many who are unwilling, or have not the time, to study it systematically may yet desire to know.”

“In quoting results I have commonly made use of modern notation; the reader must therefore recollect that, while the matter is the same as that of any writer to whom allusion is made, his proof is sometimes translated into a more convenient and familiar language.”

“A Babylonian table of the numerical value of the squares of a series of consecutive integers has been found, and this would seem to indicate that properties of numbers were studied.”

“The first edition was substantially a transcript of some lectures which I delivered in the year 1888 with the object of giving a sketch of the history, previous to the nineteenth century, that should be intelligible to any one acquainted with the elements of mathematics.”

“According to Strabo the Tyrians paid particular attention to the sciences of numbers, navigation, and astronomy; they had, we know, considerable commerce with their neighbours and kinsmen the Chaldaeans.”

“There appeared in December 1921, just before this reprint was struck off, Sir T. L. Heath's work in 2 volumes on the History of Greek Mathematics. This may now be taken as the standard authority for this [first] period.”

“Ahmes then goes on to find the area of a circular field … and gives the result as (d - 1/9d)², where d is the diameter of the circle: this is '''equivalent to taking 3.1604 as the value of ''π''''', the actual value being very approximately 3.1416.”

“Our acquaintance with the early attainments of the Chinese... serves to illustrate the fact that a nation may possess considerable skill in the applied arts while they are ignorant of the sciences on which those arts are founded.”

“We know nothing of the applied mathematics (if there were any) of the Egyptians or Phoenicians. The astronomical attainments of the Egyptians and Chaldaeans were no doubt considerable, though they were chiefly the results of observation: the Phoenicians are said to have confined themselves to studying what was required for navigation.”

“Ahmes goes on to the solution of some simple numerical equations. For example, he says "heap, its seventh, its whole, it makes nineteen," by which he means that the object is to find a number such that the sum of it and one-seventh of it shall be together equal to 19; and he gives as the answer 16 + 1/2 + 1/8, which is correct.”

“Our knowledge of the mathematical attainments of those who preceded the Greeks is very limited; but... the early Greeks learned the use of the abacus for practical calculations, symbols for recording the results, and as much mathematics as is contained or implied in the Rhind papyrus. It is probable that this sums up their indebtedness...”