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Take the word isosceles; a schoolboy can be shown what an isosceles triangle is, but, if he knows nothing of the derivation, he will wonder why such an apparently outlandish term should be necessary to express so simple an idea. If mathematicians had had more Greek, perhaps the misspelt form 'hypothenuse' would not have survived so long.
The inquiry is, Are the angles at the base of an isosceles triangle equal or unequal? The first thing to be considered is, what inductions we have, from which we can infer equality or inequality. For inferring equality we have the following formulæ:—Things which being applied to each other coincide, are equals. Things which are equal to the same thing are equals.
From the black markings on the tips of its fins, I recognized the dreadful Squalus melanopterus from the seas of the East Indies, a variety in the species of sharks proper. It was more than twenty-five feet long; its enormous mouth occupied a third of its body. It was an adult, as could be seen from the six rows of teeth forming an isosceles triangle in its upper jaw.
He said he would rather go to the missionaries' hell, full of Englishes, than go on learning Egbert, Ethelbald, Ethelbert, Ethelwulf, Ethelred, Alfred, Edward the Elder, Edred, Edwy, Edgar, Ethelred the Unready, and If two triangles have two sides of the one equal to two angles of the other each to each and the sides so subtended equal then shall the bases or fourth sides be equal each to each or be isosceles.
Nothing would induce an aspiring Isosceles, who has hopes of generating an Equilateral Son, to take a wife who reckoned a single Irregularity among her Ancestors; a Square or Pentagon, who is confident that his family is steadily on the rise, does not inquire above the five-hundredth generation; a Hexagon or Dodecagon is even more careless of the wife's pedigree; but a Circle has been known deliberately to take a wife who has had an Irregular Great-Grandfather, and all because of some slight superiority of lustre, or because of the charms of a low voice which, with us, even more than with you, is thought "an excellent thing in a Woman."
He proposed to take some leading proposition of Euclid's, and show by construction that its truth was known to us, to demonstrate, for example, that the angles at the base of an isosceles triangle are equal, and that if the equal sides be produced the angles on the other side of the base are equal also, or that the square on the hypotenuse of a right-angled triangle is equal to the sum of the squares on the two other sides.
The rhythmical and, if I may so say, well-modulated undulation of the back in our ladies of Circular rank is envied and imitated by the wife of a common Equilateral, who can achieve nothing beyond a mere monotonous swing, like the ticking of a pendulum; and the regular tick of the Equilateral is no less admired and copied by the wife of the progressive and aspiring Isosceles, in the females of whose family no "back-motion" of any kind has become as yet a necessity of life.
Whether composed of two or three stages this battlement was always inscribed within an isosceles triangle; in fact, when a third story was added, the height and the width at the base increased in the same proportions. M. Place lays great stress upon this triangle.
Right things do come in so terribly askew, like good old Mr. Isosceles, sidling up the broad aisle of a Sunday! Couldn't you wait awhile, Ruth?" "And then somebody else would get the chance." "There's nobody else to be had." "Nobody knows till somebody starts up. They don't know there's me to be had yet." "O Ruth! Don't offer to teach grammar, anyhow!" "I don't know. I might.
You might as well call me an isosceles triangle. You're just crazy sore at me when I want to be friends with you. Instead of pulling my gun, Duke, I'll lay it out on the case, here, to show you that all I ask of you is to talk reason."
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