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Updated: May 29, 2025
But I have fallen suddenly into the frame of mind of knowing exactly what all my friends here are going to say and think, and that rather takes the edge off conversation; and I have learned the undergraduate mind too. It's an inconsequent thing, but there's a law in inconsequence, and I seem to have acquired a knowledge of their tangents."
It was no longer a loose assemblage of thirteen independent bodies, revolving, indeed, around a central power, but with a centrifugal motion that might at any time send them flying off into space, or destroy them by collisions at various tangents.
One of the strangest phases of human life here is the almost universal resistance to improvement. But this conservative attitude is also a balance, prevents running off on tangents. It has been popularly reported that science has driven God out of the world.
"I looked just as you do now- -I felt just as you do now all in a fright and a puzzle, when I first heard of angles and sines, and cosines, and arcs and centres, and complements and tangents." "Oh mercy! mercy!" interrupted Francisco, whilst Carlo laughed, with a benevolent sense of superiority. "Why," said Carlo, "you'll find all these things are nothing when you are used to them.
A few of his auditors were too far gone with fatigue or intoxication to follow him, and elbowing their way through the crowd shot off into the night upon their various tangents of stupidity or crime; but most of the spectators listened with a sort of rapt and involuntary attention.
To do him justice, he studied for two or three hours everyday, and it was not his fault if he did not advance but his head was confused with technical terms; he mixed all up together, and disparts, sines and cosines, parabolas, tangents, windage, seconds, lines of sight, logarithms, projectiles and traverse sailing, quadrature and Gunter's scales, were all crowded together, in a brain which had not capacity to receive the rule of three.
From this tangential point of view we try to grasp the genesis of the curve as envelope, or rather, and better still, the birth of successive tangents as instantaneous directions. Speaking non-metaphorically, we cling to genetic methods of conceptualisation and proceed from the generating principle to its conceptual derivatives.
Sines, cosines, and tangents, of fractional angles figured profusely in the processes; and in the result courses to be steered would be laid down to an eighth of a point, when to keep a single vessel, let alone a column, steady within half a point was considered good helmsmanship.
When people begin to make so very few words serve their purpose it shows that their circumferences have intersected no mere tangents now. A portion of the area of each is common to both. Forgive geometry this intrusion on the story, and accept the metaphor. "Yes, that's what it is," said Aunt Constance.
Normals are treated, not in connexion with tangents, but as minimum or maximum straight lines drawn to the curves from different points or classes of points. Certain propositions of great difficulty enable us to deduce quite easily the Cartesian equations to the evolutes of the three conics. He was also a master of the theory of epicycles and eccentrics.
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