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Amalia, Euler's daughter, had set herself at once to acquaint Louisa with local details: with the topography of the district, the habits and advantages of the house, the time when the milkman called, the time when she got up, the various tradespeople and the prices that she paid. She did not stop until she had explained everything.
Thus, in Cicero's De Finibus, 'Cupiditas, which usually implies vice, is used to express certain desires the moral character of which is the point in question. Such, again, was Euler's argument, that minus multiplied by minus gives plus, because it could not give the same as minus multiplied by plus, which gives minus.
The computation of their perturbations and ephemerides by Euler's and Lagrange's method of variable elements became so laborious that Encke devised a special process for these, which can be applied to many other disturbed orbits.
That of 1781 contains De la Caillie's catalogue of fixed stars reduced to the commencement of that year, and a table of the aberrations and nutations of the principal stars. 1784 contains the same catalogue with the nébuleuses of Messier. 1785 contains the famous catalogue of Flamsteed, with the positions of the stars reduced to the beginning of the year 1784, and which supersedes the use of that immense book. 1786 gives you Euler's lunar tables corrected; and 1787, the tables for the planet Herschel.
Euler's stories used invariably to begin with: "As I used to say to your poor grandfather..." He could remember nothing else. He had heard only what he had said himself. Perhaps Jean Michel used only to listen in the same way. Most friendships are little more than arrangements for mutual satisfaction, so that each party may talk about himself to the other.
To Ångström, indeed, belongs the great merit of having revived Euler's principle of the equivalence of emission and absorption; but he revived it in its original crude form, and without the qualifying proviso which alone gave it value as a clue to new truths.
In his optical researches, Optiska Undersökningar, presented to the Stockholm Academy in 1853, he not only pointed out that the electric spark yields two superposed spectra, one from the metal of the electrode and the other from the gas in which it passes, but deduced from Euler's theory of resonance that an incandescent gas emits luminous rays of the same refrangibility as those which it can absorb.
Nevertheless, his remarkable memory, still further heightened by his blindness, enabled him to carry out the elaborate computations frequently involved. Euler's first memoir, transmitted to the Academy of Sciences of Paris in 1747, was on the planetary perturbations. This memoir carried off the prize that had been offered for the analytical theory of the motions of Jupiter and Saturn.
The honest man told her that he was no mathematician: he could lend her Euclid, but he could do no more. The first great step was now taken; Euclid was quickly read; other books were borrowed from other friends; Bonnycastle's and Euler's Algebra were obtained, and she exulted in the use of those mystic symbols, x, y, and z.
There I listened for a moment to the solicitations of my family, who pressed me to renounce the prospects which the Polytechnic School opened. But my taste for mathematical studies soon carried the day; I increased my library with Euler's "Introduction
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