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The only satisfaction we can feel in our treatment of the great geometrical problems of antiquity is that we have shown their solution to be impossible. The mathematician of to-day admits that he can neither square the circle, duplicate the cube or trisect the angle.
Now, the three great problems of antiquity which engaged the attention and wonderment of geometricians throughout the Middle Ages, were "the Squaring of the Circle," "the Duplication of the Cube," and lastly, "the Trisection of an Angle," even Euclid being unable to show how to do it; and yet it will be seen that the diagonal of one of the subsidiary figures in the tri-subdivision, together with the diagonal of the whole figure, actually trisect the angle at the corner of the rectangle.
The almost breathless silence was broken only by the click of the chalk on the board and the scratching of pencils and pens on paper. When he had finished he ran through the calculations aloud, and said in the most commonplace voice: "Now, gentlemen, if, as I hope, you have found my working correct, I may draw the two lines which will trisect the triangle."
It is true that it only showed them how to trisect one kind of angle, but it was that particular angle which was so dear to them as symbolising their craft, and which was created by the Equilateral Triangle.
But the parents had chosen for the work one who was favourably known by his manuals, and capable of interesting even a budding poet in the mathematics; for our author tells that at Oxford, and ever after, he knew his Euclid without the figures, and that he spent all his spare time in trying to trisect an angle. An old letter from Rowbotham informs Mr.
Even when they stand about gossiping they fall naturally into geometric figures: if two disconnected men are smoking silently in the roadway, they trisect it; and if another man arrives he converts the company into an equilateral triangle.
In vain Pinchas reminded the President they would need Collectors to make house to house calls; three other members were chosen to trisect the Ghetto. All felt the incongruity of hanging money bags at the saddle-bow of Pegasus. Whereupon Pinchas re-lit his cigar and muttering that they were all fool-men betook himself unceremoniously without.
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