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Updated: May 28, 2025
To proceed we must have realities, conditions and forms taken from real material things; representations of lines, planes, angles, polygons, spheres, etc., are all borrowed from reality, and it is just naive ideology to believe the mathematicians, who assert that the first line was made by causing a point to progress through space, the first plane by means of the movement of a line, and the first solid by revolving a plane, etc.
Has not each cell in a honey comb six sides, or as many as a bee has feet, the art of which arrangement appears in the teaching of the geometricians that of all polygons the hexagon covers the largest area within a circle.
Many a promising child is sacrificed in this way. Scarcely one out of ten survives. Yet so strong is the parental ambition among those Polygons who are, as it were, on the fringe of the Circular class, that it is very rare to find the Nobleman of that position in society, who has neglected to place his first-born in the Circular Neo-Therapeutic Gymnasium before he has attained the age of a month.
There are many bodies, vegetable, mineral, and congealed salts, which are formed with certain regular angles and figures. Thus among flowers there are many which have their leaves disposed in ordered polygons, to the number of 3, 4, 5, or 6 sides, but not more. This well deserves to be investigated, both as to the polygonal figure, and as to why it does not exceed the number 6.
He concentrated it, he focused it, and one of the polygons rose slowly from the ground and drifted into the air above the Martians' heads. Dark could feel the strength that went out and raised the polygon, like an invisible extension of himself. Then he felt another force seize the polygon, and it was drawn back firmly and without hesitation to its former place.
Q. What shape is the top or crown of my bat? A. Circular. Q. What shape is that part which comes on my forehead and the back part of my head? A. Oval. The other polygons are taught the children in rotation, in the same simple manner, all tending to please and edify them. Some amusing circumstances have occured from the knowledge of form thus acquired. "D'ye ken, Mr.
Nicholas now, albeit he had buried both teacher and hope, began once more to draw his circles and triangles and polygons on the soft mould, as it grew damply and darkly through the wearing snow coverlid.
Before the door there is frequently a little wooden bridge for in many houses the ground floor is made lower than the street and in front of the bridge are two small stone pillars surmounted by two balls; below these stand other pillars united by iron chains made of large links in the shape of crosses, stars, and polygons. In the space between the street and the house are pots of flowers.
Even the most refined statistics are nothing but an abstraction. But if that truth is held clearly before the mind, the polygons and curves of the statisticians can be used as a skeleton to which the imagination and our general sense of life give some flesh and blood reality. Human statistics are illuminating to those who know humanity.
The two first books are principally geometrical, and relate to regular polygons inscribed in a circle; the third book is a treatise on music, in which musical proportions are derived from figures; the fourth book is astrological, and treats of the harmony of rays emanating on the earth from the heavenly bodies, and on their influence over the sublunary or human soul; the fifth book is astronomical and metaphysical, and treats of the exquisite harmonies of the celestial motions, and of the celebrated third law of the universe, which we have already referred to.
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