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The third schooner now brought us to. This vessel sent another committee, who announced themselves to be the representatives of a party that was termed the Tangents.

Why, he has been working till his brain must all be in a muddle; and it is the best thing in the world for him, or he would be mixing up the Spaniards and the Romans, and the x's and y's and the tangents, and all the other things into a regular jumble and it is a nice business that would have been.

The breadth and facility of these solutions added a new charm to the investigation of curves; and passing lightly by the Conic Sections, the mathematicians of that day busied themselves in finding the areas, solids of revolution, tangents, etc., of all imaginable curves, some of them remarkable enough.

Meanders, lozenges, and zigzags. Circles joined by tangents replace Mycenaean spirals. Ornament crowded. Rows or single specimens of long-legged water birds. Human figures rare, rude angular silhouettes. Shapes fewer and curves less flowing. Amphorae, plates, bowls, and jugs. Trefoil lip to jug first appears. Terra-cotta loom weights from now onwards often pyramidal in form and glazed. Bronzes.

At the end of the ten miles was a Hudson's Bay Company's post and safety; and through ten hours had the two struggled towards it, going off at tangents, circling on their own tracks; but the Indian, by an instinct as sure as the needle to the pole, getting the direction to the post again, in the moments of direst peril and uncertainty.

A cake of barley bread was on the table, and a little black teapot stood there also. There was no furniture but a low wooden bed, one chair, a settle, and a broad shelf. On the shelf was a slate scrabbled all over with geometrical figures, and one of these figures was a parabola with two tangents drawn touching. This puzzled me much.

It seemed to spread out before him like a great map: the desert and its towns, the hills and mesas, trails and highways over which men scurried like black and red ants, commingling, separating, hastening off at queer tangents, meeting in combat, disappearing in crevices, reappearing and setting off again in haste, searching for food, bearing strange burdens, scrambling blindly over obstacles collectively without seeming purpose yet individually bent upon some quest, impetuous and headstrong in their strange activities.

It is such a funny little train that runs to my new-found Paradise, rocking and puffing and grumbling along on its narrow-gauge track with its cars labelled like grown-up ones, first, second, and third class; and no two painted the same colour; and its noisy, squat engine like the real ones in the toy-stores, that wind up with a key and go rushing off frantically in tangents.

It was only one of many, that arbitrary arrangement of figures, each combination having its own special significance; but, besides these, there was the key to a complete cipher into which any message might be coded, and But why was her brain swerving off at inconsequential tangents? What did a coder or code book, matter at the present moment?

And Butler, in his satirical description of Sir Hudibras, ascribes to his hero more practical philosophy than he appears to have intended, and more, certainly, than is found in some modern systems of education: "In mathematics he was greater Than Tycho Brahe or Erra Pater; For he, by geometric scale, Could take the size of pots of ale; Resolve by sines and tangents straight, If bread or butter wanted weight; And wisely tell what hour o' th' day The clock does strike, by algebra."