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The conic section is submitted to algebra, an obstetrical appliance which brings forth the equation; and behold, entreated now in one direction, now in another, the womb of the formula gives birth to the ellipse, the hyperbola, the parabola, their foci, their radius vectors, their tangents, their normals, their conjugate axes, their asymptotes and the rest.
Noah was too much occupied to discover this well-managed movement; and by the time he had sworn to throw the mate overboard if he did not instantly relinquish all ambitious projects of this nature, he found that the Tangents were off. Supposing they had gone to some other vessel, the captain allowed himself to be soothed, and all went on smoothly again.
His own brain shot off at queer tangents and led him constantly into unexpected places. The narrow side lane that opened up came into view so suddenly that Peter, with the innocence of a four-year-old, turned with military precision at the suggestion and looked over the premises for the exact location of Linda.
Once off the mountain, however, the greater peril began to assert itself. For a time the Irishman kept himself fully awake and alert by pushing the 956 to the ragged edge of hazard, scurrying over the short tangents and lifting her around the curves in breath-taking spurts. Later this expedient began to lose its fillip.
They have only to apply sines and co-sines, tangents and logarithms to a stock exchange quotation for me to grovel before their superior wisdom and consult them at every turn in life. Honoria had resolved to turn her great acquirements in Algebra and the Higher Mathematics to practical purposes. Moreover Honoria's purpose was two-fold.
A clear conception of this fact led almost immediately to the Method of Tangents of Fermat and Barrow; and this again is the stepping-stone to the Differential Calculus, itself a particular application of that instrument. Dr. Barrow regarded the tangent as merely the prolongation of any one of these infinitely small sides, and demonstrated the relations of these sides to the curve and its ordinates. His work, entitled "Lectiones Geometricae," appeared in 1669. To his high abilities was united a simplicity of character almost sublime. "Tu, autem, Domine, quantus es geometra!" was written on the title-page of his Apollonius; and in the last hour he expressed his joy, that now, in the bosom of God, he should arrive at the solution of many problems of the highest interest, without pain or weariness. The comment of the French historian conveys a sly sarcasm on the Encyclopedists: "On voit au reste, par-l
To briefly illustrate their respective powers arithmetic can express in one formula the value of a particular tangent to a particular curve; algebra can express in one formula the values of all tangents to a particular curve; transcendental analysis can express in one formula the values of all tangents to all curves.
But Tasso was dull to-night. The printed page was before my eyes, but my thoughts sped off in tangents to dwell upon the birds, the trees, the flowers. The thought of flowers suggested my botanical collection and to it I turned. But it, too, had lost its zest. It must be that this mental preoccupation has a physical side. Beyond peradventure the lassitude of spring is upon me.
That cannot be done without discipline and drills for the mind; and they will abhor doing that; their minds will work better when they are left free to run off at tangents. Compare them in this with other species. Each has its own kind of strength. To be compelled to be so quick-minded as the simians would be torture, to cows.
In 1676 Newton had communicated to Leibnitz the fact that he had discovered a general method of drawing tangents, concealing the method in two sentences of transposed characters. Before Newton had published a single word upon fluxions the differential calculus had made rapid advances on the Continent.
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