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The philosophy of the nineteenth century was dominated in the main by biological conceptions, while it seems as if that of the twentieth was to be chiefly mathematical in its outlook on the world. We must not, of course, make too much of such formulas, but it is instructive to study such alternations in the philosophy of the Greeks, where everything is simpler and more easily apprehended.

Neither is it enough, to consult concerning persons secundum genera, as in an idea, or mathematical description, what the kind and character of the person should be; for the greatest errors are committed, and the most judgment is shown, in the choice of individuals. It was truly said, optimi consiliarii mortui: books will speak plain, when counsellors blanch.

He had just that thin smattering of modern science which enables shallow youth to make a merit of disbelief in all things beyond the limit of mathematical demonstration. He had skimmed Darwin, and spoke lightly of mankind as the latest development of time and matter, and no higher a being, from a spiritual point of view, than the first worm that wriggled in its primeval slime.

By the help of this new library, the city still kept its trade in books and its high rank as a school of letters; and, when the once proud kingdom of Egypt was a province of Rome, and when almost every trace of the monarchy was lost, and half a century afterwards Philo, the Jewish philosopher of Alexandria, asked, "Where are now the Ptolemies?" the historian could have found an answer by pointing to the mathematical schools and the library of the Serapeum.

He is lieutenant of engineers, with high character for mathematical science is acute, very well-mannered, and, I think, good-hearted. He has seen enough of the world too, to regulate his own course through life, better than most lads at his age. February 3. This is the first morning since my troubles that I felt at awaking "I had drunken deep Of all the blessedness of sleep."

Yet it seems to me clear, that some such hypothetical origin for our satellite would have had to be assumed if Sir George Darwin had not deduced it by means of purely mathematical argument based upon astronomical facts. Returning now to the problem of the moon's temperature, I think the phenomena this presents may be in part due to the mode of formation here described.

Would stupid Oliver Goldsmith have written his immortal 'Vicar of Wakefield' and 'She Stoops to Conquer, or would idle Sheridan have penned the exquisite comedies that have not to this day been approached by any subsequent writer, if their idleness and stupidity had been submitted to the test of an enforced academic training for classical or mathematical honours?

The difficulties of work, like the difficulties of a mathematical problem called out the athletic qualities of an otherwise shy and almost effeminate nature. He loved to pit his brains against other men, rejoiced to discover obstacles in his path, never despaired when things went against him, and infinitely preferred the battle for success to the success itself.

The value of mathematical instruction as a preparation for those more difficult investigations, consists in the applicability not of its doctrines, but of its method.

Yet they deal with them as if they were as definite as mathematical quantities or geometrical figures. What would become of arithmetic if the figure 2 meant three for one man and five for another and twenty for a third, and all the other numerals were in the same way variable quantities? Mighty intelligent correspondence business men would have with each other!