Charles Taylor

Name: 1911 Encyclopædia Britannica
Author: Charles Taylor

1911 Encyclopædia Britannica (1911)

Summary

“1911 Encyclopædia Britannica”, published in 1911, is a work by Charles Taylor. It explores elements such as infinity, focus and geometry.

Quotes from 1911 Encyclopædia Britannica (Charles Taylor)

Charles Taylor, 1911 Encyclopædia Britannica (1911)

“ Kepler dearly loves analogies, his most trusty teachers, acquainted with all the secrets of nature, “omnium naturae arcanorum conscios.” And they are to be especially regarded in geometry as, by the use of “however absurd expressions,” classing extreme limiting forms with an infinity of intermediate cases, and placing the whole essence of a thing clearly before the eyes.
Here, then, we find formulated by Kepler the doctrine of the concurrence of parallels at a single point at infinity and the principle of continuity (under the name analogy) in relation to the infinitely great. ”

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Charles Taylor, 1911 Encyclopædia Britannica (1911)

“ Any point P of the parabola, in which the second focus is missing or infinitely distant, is equidistant from the focus B and the line through D which we call the directrix, this taking the place of either circle when its centre C is at infinity, and every line CP being then parallel to the axis. Thus Briggs, and we know not how many “savans géomètres” who have left no record, had already taken up the new doctrine in geometry in its author’s lifetime. ”

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Charles Taylor, 1911 Encyclopædia Britannica (1911)

“ Boscovich’s first principle was that of Kepler, by whose quantumvis absurdis locutionibus the boldest applications of it are covered, as when we say with Poncelet that all concentric circles in a plane touch one another in two imaginary fixed points at infinity. In G. K. Ch. von Staudt’s Geometrie der Lage and Beiträge zur G. der L. (Nürnberg, 1847, 1856–1860) the geometry of position, including the extension of the field of pure geometry to the infinite and the imaginary, is presented as an independent science, “welche des Messens nicht bedarf.” (See Geometry: Projective.) ”

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Source: Wikisource

Charles Taylor, 1911 Encyclopædia Britannica (1911)

“ From the line-pair we pass through an infinity of hyperbolas to the parabola, and thence through an infinity of ellipses to the circle. Related to the sections are certain remarkable points which have no name. Kepler calls them foci. The circle has one focus at the centre, an ellipse or hyperbola two foci equidistant from the centre. The parabola has one focus within it, and another, the “caecus focus,” which may be imagined to be at infinity on the axis within or without the curve. ”

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Charles Taylor, 1911 Encyclopædia Britannica (1911)

“ To carry out the analogy we must speak paradoxically, and say that the line-pair likewise has foci, which in this case coalesce as in the circle and fall upon the lines themselves; for our geometrical terms should be subject to analogy. ”

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Charles Taylor, 1911 Encyclopædia Britannica (1911)

“ As a doctrine of development and as an ethical principle it is reflected in Clement of Alexandria's view of philosophy as a φραγμός of the vineyard (Strom. i. 20) , and Polycarp's saying “ He that has love is far from all sin.” ”

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Charles Taylor, 1911 Encyclopædia Britannica (1911)

“ In form it is a series of numbered groups of things, from the ten creative Sayings to the triads of qualities which differentiate the disciples of Balaam and Abraham. R. Jacob ben Sh1mshon's commentary makes Aboth end with the saying of jehudah ben Tema (v. 23) , “ Be bold as a leopard, and swift as an eagle, and fleet as a hart, and strong as a lion, to do the will of thy Father who is in heaven.” Chapter vi., on acquisztio legzs, is thought to have been added for use on the last ot the six sabbaths above-mentioned (Strack, J. F. Ap. p. 61) . In some manuscripts there are seven chapters. ”

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Source: Wikisource

Charles Taylor, 1911 Encyclopædia Britannica (1911)

“ These sections (i. 1-15, i1 9-21) contain the “ Kern der Sammlung ” (Strack) . After the sayings of Shammal (i. 15) come interpolated sayings (i. 16-li. 8) of Rabban Gamaliel I., Rabban Simeon, “ Rabbi, " i.e. R. jehudah ha-Nasi (cent. A.D. I-2) , the traditional redactor of the Mishnah, Rabban Gamaliel II. and Hillel, which break the sequence. Chapters in., iv -Maxims of numerous authorities, mostly Mishnah teachers and called Rabbis (Matt. xxii. 7 seq.; J. F. p. 27) , not in exact chronological order.
Chapters v., vi.-Chap. ”

Charles Taylor

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Quotes from 1911 Encyclopædia Britannica (Charles Taylor)

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