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Updated: May 23, 2025
His chief work was a treatise on Conic Sections. It is said that he was the first to introduce the words ellipse and hyperbola. So late as the eleventh century his complete works were extant in Arabic. Modern geometers describe him as handling his subjects with less power than his great predecessor Archimedes, but nevertheless displaying extreme precision and beauty in his methods.
The close-set trees, seen from above, appear like scrub, like close-set ti-tree. They are massed at the top, and among them lie white houses. Beyond them the lower slopes of the Devil's Peak are yellow and red sand, but the grey-green waters of the bay, which is shaped like a great hyperbola, are edged with white sand.
He also wrote various sorts of hands, fearful and marvellous to the uninitiated, with which he was wont to decorate my monthly reports to my grandfather. I can shut my eyes and see now that wonderful hyperbola in the C in Carvel, which, after travelling around the paper, ended in intricate curves and a flourish which surely must have broken the quill.
Again, if one supposes the point B to be infinitely distant, in lieu of our first oval we shall find that CDE is a true Hyperbola; which will make those rays become parallel which come from the point A. And in consequence also those which are parallel within the transparent body will be collected outside at the point A. Now it must be remarked that CX and KS become straight lines perpendicular to BA, because they represent arcs of circles the centre of which is infinitely distant.
It is thus, for instance, that the circle seen sideways is changed into that kind of oval which among geometricians is known as an ellipse, and sometimes even into a parabola or a hyperbola, or actually into a straight line, witness the ring of Saturn. The external senses, properly speaking, do not deceive us. It is our inner sense which often makes us go too fast.
Nevertheless, abundant instances are at hand of the mode in which we may pass to the most diverse forms by insensible gradations. Arguing the matter some time since with a learned professor, I illustrated my position thus: You admit that there is no apparent relationship between a circle and an hyperbola. The one is a finite curve; the other is an infinite one.
Barbicane inclined to the opinion that this curve would be a parabola and not an hyperbola. However, if the parabola was admitted, the bullet ought soon to come out of the cone of shadow thrown into the space on the opposite side to the sun. This cone, in fact, is very narrow, the angular diameter of the moon is so small compared to the diameter of the orb of day.
The projections in perspective of the conic sections of the circle show that one and the same circle may be represented by an ellipse, a parabola and a hyperbola, and even by another circle, a straight line and a point. Nothing appears so different nor so dissimilar as these figures; and yet there is an exact relation between each point and every other point.
In other words, the application of the proper correction for the terrestrial movement, and the effects of attraction by which each individual shooting-star is compelled to describe a hyperbola round the earth's centre, reduces the extended line of radiants to a compact group, with the cometary radiant for its central point; the cometary radiant being the spot in the sky met by a tangent to the orbit of the Perseid comet of 1862 at its intersection with the orbit of the earth.
What does it matter about hyperbola or parabola if they both carry us indefinitely into space?" Barbicane and Nicholl could not help laughing. They cared for art for its own sake. Never had more useless question been discussed at a more inopportune moment.
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