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Updated: May 21, 2025
Many a long year ago, when I finished my second season, I found myself at Moama, with a hundred and ten notes to the good, and the prospect of going straight ahead, like the cube root or the square of the hypotenuse, is it? I forget the exact term, but no matter.
You seen for yourself, if it was not for Aunt Becky begging him nearly on her knees, how he would have treated us that time with the mortgage. Better, I say, Izzy should stay with his papa in business or get out West like he wants, and where he can't keep such fine white hands to gamble with." Miss Shongut slanted deeper until her slim body was a direct hypotenuse to the chair.
Here and now let me say that I am sorry that I must use so many "big words." I wish that I could write this history in words of one syllable. But it cannot be done. You cannot write a text-book of geometry without reference to a hypotenuse and triangles and a rectangular parallelopiped. You simply have to learn what those words mean or do without mathematics. Why not do it now?
To find from this the obtuse angle BCA, I imagined a sphere having its centre at C, and on its surface a spherical triangle, formed by the intersection of three planes which enclose the solid angle C. In this equilateral triangle, which is ABF in this other figure, I see that each of the angles should be 105 degrees, namely equal to the angle OCN; and that each of the sides should be of as many degrees as the angle ACB, or ACF, or BCF. Having then drawn the arc FQ perpendicular to the side AB, which it divides equally at Q, the triangle FQA has a right angle at Q, the angle A 105 degrees, and F half as much, namely 52 degrees 30 minutes; whence the hypotenuse AF is found to be 101 degrees 52 minutes.
It was just as true at the dawn of creation that the square described on the hypotenuse of a right-angle triangle is equal to the square described on the other two sides, as it was when Pythagoras enunciated the theorem. "Thou shall not kill," is a law written by the Divine hand amid tempest and fire, but it stands.
Peregrine entered upon this branch of learning with all that warmth of application which boys commonly yield on the first change of study; but he had scarce advanced beyond the Pons Asinorum, when his ardour abated; the test of truth by demonstration did not elevate him to those transports of joy with which his preceptor had regaled his expectation; and before he arrived at the forty-seventh proposition, he began to yawn drearily, make abundance of wry faces, and thought himself but indifferently paid for his attention, when he shared the vast discovery of Pythagoras, and understood that the square of the hypotenuse was equal to the squares of the other two sides of a right-angled triangle.
That triangle contains one of the perpendiculars of three, the base of four, and the hypotenuse of five parts, the square of which is equal to the squares of those sides containing the right angle.
"If I keep on I won't even be able to remember that 'the hypotenuse of a right-angled triangle is equal to the sum of the squares of the other two sides. I'm in a muddle over these triangles now. I'll find the girls and get them to go to the woods with me. I really ought to collect a few more botany specimens." Grace's specimens were a source of keen delight to her girlish heart.
And, of course, the Hanoverian much more; through which lies the other Great Road! 'Go by the Harz, advises Landgraf Wilhelm: 'a rugged Hill Country; but it is your hypotenuse towards Berlin; passes at once, or nearly so, from Cassel Territory into Prussian: a rugged road, but a shorter and safer. That is the road Belleisle resolves upon.
"This: If they understand triangles, they must know something about mathematics and geometry. Suppose we draw for them that problem in geometry which states that the sums of the squares constructed on the base and altitude of a right-angled triangle is equal to the square constructed on the hypotenuse? If he knows that, maybe we can get to some understanding with him."
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