James Gow (scholar) Quotes

15 Sourced Quotes

The bones... are given in a heap to a student who has no idea of a skeleton. Here is the defect which I am trying partly to supply...

James Gow
With Diophantus the history of Greek arithmetic comes to an end. No original work, that we know of, was done afterwards.

James Gow
Sometimes... Diophantus solves a problem wholly or in part by synthesis....Although...Diophantus does not treat his problems generally and is usually content with finding any particular numbers which happen to satisfy the conditions of his problems,...he does occasionally attempt such general solutions as were possible to him. But these solutions are not often exhaustive because he had no symbol for a general coefficient.

James Gow
The solution of the higher indeterminates depends almost entirely on very favourable numerical conditions and his methods are defective. But the extraordinary ability of Diophantus appears rather in the other department of his art, namely the ingenuity with which he reduces every problem to an equation which he is competent to solve.

James Gow
Though the defects in Diophantus' proofs are in general due to the limitation of his symbolism, it is not so always. Very frequently indeed Diophantus introduces into a solution arbitrary conditions and determinations which are not in the problem. Of such "fudged" solutions, as a schoolboy would call them, two particular kinds are very frequent. Sometimes an unknown is assumed at a determinate value... Sometimes a new condition is introduced.

James Gow
The oldest definition of Analysis as opposed to Synthesis is that appended to Euclid XIII. 5. It was possibly framed by Eudoxus. It states that "Analysis is the obtaining of the thing sought by assuming it and so reasoning up to an admitted truth: synthesis is the obtaining of the thing sought by reasoning up to the inference and proof of it." In other words, the synthetic proof proceeds by shewing that certain admitted truths involve the proposed new truth: the analytic proof proceeds by shewing that the proposed new truth involves certain admitted truths.

James Gow
It happened fortunately that during this period of turmoil the guidance of the Christian Church, the one powerful and permanent institution, was chiefly in the hands of the splendid order of St. Benedict. This saint... seeing that idleness was the besetting danger of monastic establishments, founded at Monte Cassino... a model abbey, in which industry was the daily rule. Among other employments, reading and writing were approved as powerful agents in distracting the mind from unholy thoughts, and in Benedictine monasteries the mechanical exercise of copying mss. became one of the regular occupations.

James Gow
The history of Greek mathematics is, for the most part, only the history of such mathematics as are learnt daily in all our public schools....If it was not wanted, as it ought to have been, by our classical professors and our mathematicians, it would have served at any rate to quicken, with some human interest, the melancholy labours of our schoolboys.

James Gow
Officials could be removed during their year of office by vote of the ecclesia, and periodical opportunities were given for raising complaints...

James Gow
Probably Greek logistic, or calculation, extended to more difficult operations... and... probably Greek arithmetic, or theory of numbers, owed much more to induction than is permitted to appear by its first and chief professors.

James Gow
Each of these smaller corporations... to which an Athenian citizen belonged, had... business of its own—money to spend, officers to appoint, rules to make—very similar to that which the state transacted on a larger scale. And it is not to be supposed that Athenians were at all ashamed to take part in such minor business, as English gentlemen are to sit on a vestry or a town council. On the contrary, a large part of the population left their private affairs for slaves to manage, and devoted themselves entirely to their public duties.

James Gow
Every official was required to undergo, before assuming office... approval before a law court. This was an inquiry into his conduct, his exactness in paying taxes, etc., and it sometimes happened that he was rejected... Every official was also required to take an oath of allegiance.

James Gow
The history of Alexandrian mathematics begins with the Elements of Euclid and closes with the Algebra of Diophantus, both of which are founded on the discoveries of several preceding centuries.

James Gow
A student of history, who cares little for Greek or mathematics in particular, but who likes to watch how things grow, will be able to extract from these pages a notion of the whole history of mathematical science down to Newton's time...

James Gow
My aim is... to place before a young student a nucleus of well-ordered knowledge, to which he is to add intelligent notes and illustrations from his daily reading.

James Gow