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Jackson, however, is now hurrying up to the relief of the flying and disordered remnants of Bee's, Bartow's, and Evans's Brigades; and these subsequently rally, with Hampton's Legion, upon Jackson's strong brigade of fresh troops, so that, on a third new line, to which they have been driven back, they soon have 6,500 Infantry, 13 pieces of Artillery, and Stuart's cavalry-posted in a belt of pines which fringes the Southern skirt of the Henry House plateau in a line-of-battle which, with its left resting upon the Sudley road, three-quarters of a mile South of its intersection with the Warrenton Pike, is the irregular hypothenuse of a right-angled triangle, formed by itself and those two intersecting roads, to the South-East of such intersection.
As the mechanic frequently wants to make an oval having a given width and length, but does not know what the distance between the foci must be to produce this effect, a few directions on this point may be useful: It is a fact well known to mathematicians that if the distance between the foci and the shorter diameter of an ellipse be made the sides of a right angled triangle, its hypothenuse will equal the greater diameter.
I did not find it; but one day in a shad-blow tree, within a few feet from the corner of my own house, I found what I was searching for, perfect in every particular the right angle and the supporting brace, or hypothenuse. It gave me a hint I have not forgotten.
The following sentence, for instance, is devoid of style: "The square on the hypothenuse of a right-angled triangle is equal to the sum of the squares on the other two sides": for, although by its content it conveys to the intellect a meaning which is entirely clear and absolutely definite, it does not by its sound convey to the senses a suggestion which is cognate.
We might just as well turn the argument the other way, and infer from the variety of religious opinions that there must necessarily be hostile mathematical sects, some affirming, and some denying, that the square of the hypothenuse is equal to the squares of the sides. But we do not think either the one analogy or the other of the smallest value.
But, if we could once satisfy ourselves that in ANY single right-angled triangle the square of the hypothenuse might be less than the squares of the sides, we must reject the forty-seventh proposition of Euclid altogether.
Beyond this space stood the big brown hospital on the north; the back-yards of the surgeon's and sutler's quarters on the east; while the hypothenuse of the right-angled triangle thus limited was the unsightly fence that bounded the back-yards of officers' row. Mr. Dick Swiveller's delightful view "of over the way" was a gem of landscape in comparison.
She was particularly perplexed by geometry; she aroused our hilarity by always calling a parallelogram a parallel-O-gram, with a strong emphasis on the penultimate syllable; and she spent several days repeating over to herself, with a mystified countenance, the famous words, "The square of the hypothenuse is equal to the sum of the squares of the two legs."
It was Daniel O'Connell, I believe, who defeated the female champion of Billingsgate by calmly referring to her as the hypothenuse of a right-angled triangle, which was something utterly beyond her powers of repartee: it was he, at all events, who silenced another virago with the cutting response, "Sure every one knows, ma'am, ye're no better than a parallelogram, and you keep a whole parallelopipedon concealed in your closet at home;" and it was one of the trimmest, nattiest, most punctilious of our captains who stood in front of the silent ranks, listening in apparently absorbed attention to the furious tirade lavished on him by the spokeswoman of the mob, a street drab of uncommon stature and powers of expression and command of expletive.
Miss Josie Beemis, narrowly constricted between shoulders that barely sloped off from her neck, with arms folded flat to her flat bosom and her back a hypothenuse against the counter, looked up. "Watch out, Loo! I read in the paper where a man up in Alton got caught in the middle of one of those gaps and couldn't ungap." Miss Hassiebrock batted at her lips and shuddered. "It's my nerves, dearie.
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