and came to be known again only through the possession of that school-book by some soldier or campfollower of a ruthless army;-we have found that man at this day, two millennia after his death, taking part, by means of that small book, in the development of the mind and formation of the character of all the ingenuous youth of all civilised lands; we have found that on that small book of his as a foundation has been reared the magnifical fabric of our science and art and enterprise and commerce. How has this been? It is because this man did with his might what his hand found to do, and because the Supreme Ruler has decreed that not by might or by power, but by His own Spirit, His mighty ends are to be accomplished; and because for the accomplishment of these ends He ofttimes uses as His instruments not the mighty or the powerful among men, nor the might nor the power of those whom He does employ, but only their quiet faithfulness, and their forgetfulness of themselves in accomplishing the task, however humble, which He assigns to them. So faithful and so self-forgetful was Euclid, and thus he ranks high this day as one of THE WORLD'S EPOCH-MAKERS.

CALCULUS, differential and integral Dodgson, Euclid and His Rivals,

EDUCATION, must not be too much | Glass, its invention, 115.

constrained, 133; general, pre-
liminary to all professional, 134;
primary, importance of arithmetic
in, 151; secondary, should be
kept apart from professional or
technical, 153; mathematical,
sketch of, 182.

Elements, plan of, 50; defects in,
53; saved from the destruction
of the Alexandrian Library, 68;
translated into Arabic, ibid.;
Greek MSS. afterwards found in
Rome, 74; vernacular versions
of, 82, 85.
Eratosthenes, 11.

Euclid, who was he? 4; a Greek,
probably an Athenian, 7; his
contemporaries, ibid. ; studied in
the Academy, 8; his knowledge
of the discoveries of his pre-
decessors, 40; went to Alexandria
300 B.C., 47; his writings, 48;
order of their production, 49; in
what sense an epoch-maker, 56;
two anecdotes of, 58; his methods,
184; attempts to improve on,
185; his definitions and axioms,
187; His Prop. I. 16 a blot, 205;
his doctrine of ratio and propor-
tion, 215.
Eudemus, 13, 21.
Eudoxus, 29.

Evolution, inept in the region of
material science, suicidal in the
science of mind, 166; not incom-
patible with theism, 168.

FLUXIONS, 97.

GEOGRAPHY and hydrography,

124.

Geometrical study the best cul-
ture of the reasoning faculty,

135.
Geometricians, not infallible, 155;
instances of their errors, 156.
Geometry, pre-Euclidean, 9.

Greenwich Observatory, its time
department, 122.

HAMILTON, Sir William, 136; his
treatise on Education, ibid.; the
headlines, 137; quoted, 138; his
lack of definitions, 139, 144; on
Descartes, 141.

Hipparchus the founder of astro-
nomical science, 108.
Hippocrates of Chios, 32; his
quadrature of a circular segment,
ibid.

Historical Criticism, 35.

Honain Ben Ishak, translator of
the Elements, 71.

Hypatia, 60; not a martyr of Platon-
ism, nor of science, but of
politics, 61.

IMAGINATION the chief faculty in
mathematical invention, 145.
Incommensurables, 217.
Introduction, 1.

JULIAN the Apostate, 63.

LAGRANGE, his estimate of Newton,

110.

Laplace, 110; and Newton, 111;
Napoleon's estimate of, 177.
Legendre, 86, 99.
Leslie, Sir John, 101; his defini-
tion of a straight line, 192.
Light, Greek notion of, 116.
Logarithms, 90.

Logic, its rules not arbitrary, 154;
their use, ibid.

Lytton, Lord, his "Hygienic Chem-
istry of Books," 169.

MAGAZINES, their general char-
acter, 162.

Mascheroni, Geometrie de Compas,
87.

Mathematical science, its progress,
89.

Geometry, the "auspicious key," 6; Mathematical study not too easy,

origin in Egypt, 11.

148.

Results and processes, their several WALLACE, Professor, of Edinburgh,
values, 127.