Reduced Quotes (3 quotes)
At the sea shore you pick up a pebble, fashioned after a law of nature, in the exact form that best resists pressure, and worn as smooth as glass. It is so perfect that you take it as a keepsake. But could you know its history from the time when a rough fragment of rock fell from the overhanging cliff into the sea, to be taken possession of by the under currents, and dragged from one ocean to another, perhaps around the world, for a hundred years, until in reduced and perfect form it was cast upon the beach as you find it, you would have a fit illustration of what many principles, now in familiar use, have endured, thus tried, tortured and fashioned during the ages.
No part of Mathematics suffers more from the triviality of its initial presentation to beginners than the great subject of series. Two minor examples of series, namely arithmetic and geometric series, are considered; these examples are important because they are the simplest examples of an important general theory. But the general ideas are never disclosed; and thus the examples, which exemplify nothing, are reduced to silly trivialities.
Who shall declare the time allotted to the human race, when the generations of the most insignificant insect also existed for unnumbered ages? Yet man is also to vanish in the ever-changing course of events. The earth is to be burnt up, and the elements are to melt with fervent heat—to be again reduced to chaos—possibly to be renovated and adorned for other races of beings. These stupendous changes may be but cycles in those great laws of the universe, where all is variable but the laws themselves and He who has ordained them.