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It is no fable that a student of the higher mathematics, when his master, a practical engineer upon the Boston water-works, required his services, exclaimed, "I had no idea that you had sines and tangents out of doors." With such, "Nothing goes for sense or light That will not with old rules jump right; As if rules were not in the schools Derived from truth, but truth from rules."
In the Preface to the first edition of the "Principia," Newton says, "It is ten years since, being in correspondence with M. Leibnitz, and having instructed him that I was in possession of a method of determining tangents and solving questions involving maxima and minima, a method which included irrational expressions, and having concealed it by transposing the letters, he replied to me that he had discovered a similar method, which he communicated, differing from mine only in the terms and signs, as well as in the generation of the quantities."
"I suppose," he remarked reflectively, going off on one of his strange tangents, and lapsing once more into his customary picturesque speech, "that these old boys that burned those Salem witches was pretty well thought of in Salem deacons in the church, and all such; p'ticular elect, and held up to the kids for high moral examples? had the plumb universal approval in those torchlight efforts of theirn?"
For many a long, sunshiny mile it had come floating placidly eastward, issuing from the great water-shed of the continent, drifting leisurely between low-lying, grassy banks all criss-crossed with ancient buffalo-trails, or the recent footprints of long-horned cattle, past the broad plateau, crowded by the wooden walls of Fort Ransom, past the roofs and spires of bustling Butte, a prairie metropolis, a railway and cattle town that rivalled Braska, past long miles of gleaming tangents of the transcontinental railway until it met the bold bluffs east of Alkali Station and was shouldered from its course and sent on long, tortuous détour to the northeast, until, beyond the great reservation of the red men in the loveliest hill country of the wild frontier, it once more turned sharply eastward at the point described in the sonorous language of the plains as "the Big Bend of the Mina Ska."
"I am elected by the Tangents," he said; "and, by what I can learn, it is the intention of our friends to steer a middle course; and one of our leaders is already selected, who, at a proper stage of the affair, is to move an amendment." "Can you refer me, my dear friend, to anything connected with the Great National Allegory that bears on this point?"
If a woman holds an assistant professorship of mathematics in a university, it is a foregone conclusion that she should fall in love with someone who is proficient in trigonometry and holds his tangents and cosines in high esteem. Happy evenings could then be spent with a book of logarithms and sheets of paper specially cut to accommodate a problem.
Down the short tangents and around the constantly recurring curves the special seemed to be towing the passenger at the end of an invisible but dangerously short drag-rope. Lidgerwood began to grow uneasy.
Josephine made no reply. She had flown off on one of her tangents. She had suddenly thought of Cyril. Wasn't it more usual for the only grandson to have the watch? And then dear Cyril was so appreciative, and a gold watch meant so much to a young man. Benny, in all probability, had quite got out of the habit of watches; men so seldom wore waistcoats in those hot climates.
To this hour, knowing all her life as I do, I can only regard her as a splendid achievement of nature, convincing even when at the most awkward tangents with the general sense and the straitest interpretation of life; convincing even in those other and later incidents, which showed her to be acting not so much by impulse as by the law of her nature.
I look upon its formulae, its strophes as superb, without feeling at all astonished when others do not agree. My colleague's satirical look came back when I was imprudent enough to confide my extrageometrical raptures to his ears: 'Nonsense, said he, 'pure stuff and nonsense! Let's get on with our tangents.
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