According to the fundamental
canon, a conic section should be a beautiful curve; and the proof that
it is so is to be found in the attention which these curves have always
drawn upon themselves from artists and from mathematicians. Plato,
equally great in mathematics and in metaphysics, is said to have been
the first to investigate the properties of the ellipse. For about a
century and a half, to the time of Apollonius, the beauty of this
curve, and of its variations, the parabola and hyperbola, so fascinated
the minds of Plato's followers, that Apollonius found theorems and
problems relating to these figures sufficient to fill eight books with
condensed truths concerning them. The study of the conic sections has
been a part of polite learning from his day downward. All men confess
their beauty, which so entrances those of mathematical genius as
entirely to absorb them. For eighteen centuries the finest spirits of
our race drew some of their best means of intellectual discipline from
the study of the ellipse. Then came a new era in the history of this
curve. Hitherto it had been an abstract form, a geometrical
speculation. But Kepler, by some fortunate guess, was led to examine
whether the orbits of the planets might not be elliptical, and, lo! it
was found that this curve, whose beauty had so fascinated so many men
for so many ages, had been deemed by the great Architect of the Heavens
beautiful enough to introduce into Nature on the grandest scale; the
morning stars had been for countless ages tracing diagrams beforehand
in illustration of Apollonius's conic sections.
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