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Updated: May 27, 2025
§ XVI. I have also supposed Yb, when expanded from beneath Xb, as always expanded into a square, and four spurs only to be added at the angles. But Yb may be expanded into a pentagon, hexagon, or polygon; and Xb then may have five, six, or many spurs.
Warned by the unanswerable arguments of Zeno against infinitesimals, mathematicians substituted for this the statement that, by continuing the construction, we can inscribe a polygon approaching equality with the circle as nearly as we please. The method of exhaustion used, for the purpose of proof by reductio ad absurdum, the lemma proved in Eucl.
Our physicians have discovered that the small and tender sides of an infant Polygon of the higher class can be fractured, and his whole frame re-set, with such exactness that a Polygon of two or three hundred sides sometimes by no means always, for the process is attended with serious risk but sometimes overleaps two or three hundred generations, and as it were double at a stroke, the number of his progenitors and the nobility of his descent.
It was Pantocyclus the illustrious Circle mentioned above, as the queller of the Colour Revolt who first convinced mankind that Configuration makes the man; that if, for example, you are born an Isosceles with two uneven sides, you will assuredly go wrong unless you have them made even for which purpose you must go to the Isosceles Hospital; similarly, if you are a Triangle, or Square, or even a Polygon, born with any Irregularity, you must be taken to one of the Regular Hospitals to have your disease cured; otherwise you will end your days in the State Prison or by the angle of the State Executioner.
The new line extended from the French position west of the Ypres-Langemarck Road and proceeded through "shell-trap" farm to the Haanebeek and the eastern part of the Frezenberg ridge where it turned south, covering Bellewaarde Lake and Hooge and bent around Hill 60. This resulted in leaving to the Germans the Veldhoek, Bosche, and Polygon Woods, and Fortuin and Zonnebeke.
As soon as my uncle Toby had laid a foundation, and taught him to inscribe a regular polygon in a circle, he sent him to a public school, where, excepting Whitsontide and Christmas, at which times the corporal was punctually dispatched for him, he remained to the spring of the year, seventeen; when the stories of the emperor's sending his army into Hungary against the Turks, kindling a spark of fire in his bosom, he left his Greek and Latin without leave, and throwing himself upon his knees before my uncle Toby, begged his father's sword, and my uncle Toby's leave along with it, to go and try his fortune under Eugene.
Beside us, the innumerable, water-logged shell-holes, in which, at one time or another in the swaying forward and backward of the fight, the lives of brave men have been so piteously lost, strangled in mud and ooze; here a mere sign-post which tells you where Hooge stood; there the stumps that mark Sanctuary Wood and Polygon Wood, and another sign-post which bears the ever-famous name of Gheluvelt.
He dived in and out of those crooked lanes, which were more like cracks than thoroughfares; and by the time that he had completed about twenty alternate angles and described an unthinkable polygon, he paused to listen for any sound of pursuit. There was none; there could not in any case have been much, for the little streets were thick with the soundless snow.
But how long would it take to turn that circle into a polygon, unless some mighty counteracting force should prevent it? See the iron tire brought hot from the furnace and laid around the smoking circumference.
I acquired a taste for it myself and joined the nest-hunters, putting off the polygon till later. It was thus that I first saw Reaumur's Mason-bee, knowing nothing of her history and nothing of her historian.
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