John Sturgeon Mackay

Name: 1911 Encyclopædia Britannica
Author: John Sturgeon Mackay

1911 Encyclopædia Britannica (1911)

Summary

“1911 Encyclopædia Britannica”, published in 1911, is a work by John Sturgeon Mackay. It explores elements such as Euclid, Pappus and theorems.

Quotes from 1911 Encyclopædia Britannica (John Sturgeon Mackay)

John Sturgeon Mackay, 1911 Encyclopædia Britannica (1911)

“ For the past twenty centuries parts of the Elements, notably the first six books, have been used as an introduction to geometry. Though they are now to some extent superseded in most countries, their long retention is a proof that they were, at any rate, not unsuitable for such a purpose. They are, speaking generally, not too difficult for novices in the science; the demonstrations are rigorous, ingenious and often elegant; the mixture of problems and theorems gives perhaps some variety, and makes their study less monotonous ”

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Source: Wikisource

John Sturgeon Mackay, 1911 Encyclopædia Britannica (1911)

“ Proclus preserves a reply made by Euclid to King Ptolemy, who asked whether he could not learn geometry more easily than by studying the Elements—“There is no royal road to geometry.” Pappus of Alexandria, in his Mathematical Collection, says that Euclid was a man of mild and inoffensive temperament, unpretending, and kind to all genuine students of mathematics. This being all that is known of the life and character of Euclid, it only remains therefore to speak of his works.
Among those which have come down to us the most remarkable is the Elements (Στοιχεῖα) (see Geometry) . ”

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Source: Wikisource

John Sturgeon Mackay, 1911 Encyclopædia Britannica (1911)

“ The question has often been mooted, to what extent Euclid, in his Elements, is a discoverer or a compiler. To this question no entirely satisfactory answer can be given, for scarcely any of the writings of earlier geometers have come down to our times. We are mainly dependent on Pappus and Proclus for the scanty notices we have of Euclid’s predecessors, and of the problems which engaged their attention; for the solution of problems, and not the discovery of theorems, would seem to have been their principal object. ”

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Source: Wikisource

John Sturgeon Mackay, 1911 Encyclopædia Britannica (1911)

“ Thus the arrangement of the propositions seems arbitrary; associated theorems and problems are not grouped together; the classification, in short, is imperfect. Other objections, not to mention minor blemishes, are the prolixity of the style, arising partly from a defective nomenclature, the treatment of parallels depending on an axiom which is not axiomatic, and the sparing use of superposition as a method of proof.
Of the thirty-three ancient books subservient to geometrical analysis, Pappus enumerates first the Data (Δεδομένα) of Euclid. ”

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Source: Wikisource

John Sturgeon Mackay, 1911 Encyclopædia Britannica (1911)

“ The object of the Data is to show that when certain things—lines, angles, spaces, ratios, &c.—are given by hypothesis, certain other things are given, that is, are determinable. The book, as we are expressly told, and as we may gather from its contents, was intended for the investigation of problems; and it has been conjectured that Euclid must have extended the method of the Data to the investigation of theorems. ”

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Source: Wikisource

John Sturgeon Mackay, 1911 Encyclopædia Britannica (1911)

“ From these authors we learn that the property of the right-angled triangle had been found out, the principles of geometrical analysis laid down, the restriction of constructions in plane geometry to the straight line and the circle agreed upon, the doctrine of proportion, for both commensurables and incommensurables, as well as loci, plane and solid, and some of the properties of the conic sections investigated, the five regular solids (often called the Platonic bodies) and the relation between the volume of a cone or pyramid and that of its circumscribed cylinder or prism discovered. ”

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Source: Wikisource

John Sturgeon Mackay, 1911 Encyclopædia Britannica (1911)

“ The Latin translation, which accompanies the Greek on the same page, is for the most part that of Commandino. The French edition has the title, Les Œuvres d’Euclide, traduites en Latin et en Français, d’après un manuscrit très-ancien qui était resté inconnu jusqu’à nos jours. Par F. Peyrard, Traducteur des œuvres d’Archimède. It was published at Paris in three volumes, the first of which appeared in 1814, the second in 1816 and the third in 1818. It contains the Elements and the Data, which are, says the editor, certainly the only works which remain to us of this ever-celebrated geometer. ”

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Source: Wikisource

John Sturgeon Mackay, 1911 Encyclopædia Britannica (1911)

“ Of translations of the Elements into modern languages the number is very large. The first English translation, published at London in 1570, has the title, The Elements of Geometrie of the most auncient Philosopher Euclide of Megara. ”

John Sturgeon Mackay

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Quotes from 1911 Encyclopædia Britannica (John Sturgeon Mackay)

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