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Newton's preponderance was in some degree due to the fact that, though Huyghens and Euler were right in the main, they did not possess sufficient data to prove themselves right. No human authority, however high, can maintain itself against the voice of Nature speaking through experiment. But the voice of Nature may be an uncertain voice, through the scantiness of data.
Johnson were all distinguished for having great strength of memory. Sir W. Hamilton observed that Grotius, Pascal, Leibnitz, and Euler were not less celebrated for their intelligence than for their memory. Ben Jonson could repeat all that he had written and whole books he had read. Themistocles could call by name the 20,000 citizens of Athens.
Locality or the power of remembering localities, in Kepler, Galileo, Newton, Tycho, Descartes, Sir Walter Scott, and Captain Cook, is large. Number, or a talent for calculation in the portraits of Euler, Kepler, Laplace, Gassendi, &c., and in George Bidder, Humboldt, and Colburn, large. Tune In Gluck, where it has a pyramidal form.
This view of the nature of the "imponderables" was in some measure a retrogression, for many seventeenth-century philosophers, notably Hooke and Huygens and Boyle, had held more correct views; but the materialistic conception accorded so well with the eighteenth-century tendencies of thought that only here and there a philosopher like Euler called it in question, until well on towards the close of the century.
The smaller ones, like Caroline Herschel, Helicon, Leverrier, Délisle, etc., vary from eight to twelve miles in diameter. Lambert is seventeen miles in diameter, and Euler nineteen, while Timocharis is twenty-three miles broad and 7,000 feet deep below its walls, which rise only 3,000 feet above the surface of the Mare.
To the Binomial theorem, previously discovered by Newton, Taylor now added, in his "Method of Increments," the celebrated theorem that bears his name. This was in 1715. The Calculus of Partial Differences was introduced by Euler in 1734. It was extended by D'Alembert, and was followed by that of Variations, by Euler and Lagrange, and by the method of Derivative Functions, by Lagrange, in 1772.
Civilised populations have been known under favourable conditions, as in the United States, to double their numbers in twenty-five years; and, according to a calculation, by Euler, this might occur in a little over twelve years. See the ever memorable 'Essay on the Principle of Population, by the Rev.
Now one is obliged to ask, why minus multiplied by minus must give any product at all? and if it does, why its product can not be the same as that of minus multiplied by plus? for this would seem, at the first glance, not more absurd than that minus by minus should give the same as plus by plus, the proposition which Euler prefers to it.
And the most wretched is not always the one who suffers. Once more Christophe took to avoiding the house. He could not bear it. He could not bear to see the curtainless windows, the empty rooms. A worse sorrow awaited him. Old Euler lost no time in reletting the ground floor. One day Christophe saw strange faces in Sabine's room. New lives blotted out the traces of the life that was gone.
Euler’s Algebra, a book otherwise of great merit, but full, to overflowing, of logical errors in respect to the foundation of the science, contains the following argument to prove that minus multiplied by minus gives plus, a doctrine the opprobrium of all mere mathematicians, and which Euler had not a glimpse of the true method of proving.
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