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Updated: May 23, 2025
"Exactly so," chimed in M'Nicholl; "it must describe and keep on describing either a parabola or a hyperbola." "Precisely," said Barbican; "at a certain velocity it would take a parabolic curve; with a velocity considerably greater it should describe a hyperbolic curve."
"You promise, M'Nicholl, that you're not going to brain the President!" "I brain the President! Ho! ho! ho!" "I want merely to convince him that it is a parabola!" "I only want to make it clear as day that it is hyperbola!" "Does it make any real difference whether it is one or the other?" yelled Ardan. "The greatest possible difference in the Eye of Science."
The great advantage of the mathematical sciences above the moral consists in this, that the ideas of the former, being sensible, are always clear and determinate, the smallest distinction between them is immediately perceptible, and the same terms are still expressive of the same ideas, without ambiguity or variation. An oval is never mistaken for a circle, nor an hyperbola for an ellipsis.
Generally the zone of fusion imitates the area comprised between the two branches of an equilateral hyperbola, but the fall can be so graduated as to restrict this zone, which then takes other forms, somewhat different, but always symmetrical. and on multiplying this quantity of heat by 425 we find, for the value of its equivalent in work,
He is acute and He is obtuse, because He is at one and the same time all possible triangles; his radii are at once equal and unequal, because He is both the circle and the ellipse and He is the hyperbola besides, which is an indescribable figure." While the holy Giovanni was still pondering these sublime verities, he heard the Subtle Doctor suddenly burst out a-laughing.
Mercator published a demonstration of this quadrature; much about which time Sir Isaac Newton, being then twenty-three years of age, had invented a general method, to perform on all geometrical curves what had just before been tried on the hyperbola.
"The eccentricity is less than unity!" screamed M'Nicholl. "Talking of eccentricity " put in Ardan. "Therefore it's a parabola, and must be!" cried Barbican, triumphantly. "Therefore it's hyperbola and nothing shorter!" was the Captain's quite as confident reply. "For gracious sake! " resumed Ardan. "Then produce your asymptote!" exclaimed Barbican, with an angry sneer.
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.
Literally, not figuratively, Robert would kiss the place where her foot had trod; but I know that once he rose from such a kiss 'to trace the hyperbola by means of a string. It had been arranged between Ericson and Robert, in Miss Napier's parlour, the old lady knitting beside, that Ericson should start, if possible, a week earlier than usual, and spend the difference with Robert at Rothieden.
"Is it possible!" exclaimed Michel Ardan in a serious tone, as if they had told him of some serious event. Nicholl and Barbicane cared little for Michel Ardan's fun. They were deep in a scientific discussion. What curve would the projectile follow? was their hobby. One maintained the hyperbola, the other the parabola. They gave each other reasons bristling with x.
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