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Lung-shan is in the province of Shantung, near Chinan-fu. This culture, discovered only about twenty-five years ago, is distinguished by a black pottery of exceptionally fine quality and by a similar absence of metal. The pottery has a polished appearance on the exterior; it is never painted, and mostly without decoration; at most it may have incised geometrical patterns.
Sometimes we find a rich and elaborate ornamentation in place of the wedges; it is made up of geometrical forms and conventional foliage and flowers; the figures of men and animals are never introduced. Such an arrangement was in better taste than the mosaic thresholds of the Romans where men were shown in pictures destined to be trodden under foot.
The two kinds of speculation have been pursued, for the most part, by two different classes of persons, the geometers and the metaphysicians; for it has been far more the occupation of metaphysicians than of geometers to discuss such questions as I have stated, the nature of geometrical proofs, geometrical axioms, the geometrical faculty, and the like.
From the initiative of scientific astronomy, when the early Greek geometers referred the apparent diurnal movements to geometrical laws, to the creation of the nebular hypothesis, the logical filiation of the leading astronomical conceptions obeys corresponding tidal movements in humanity. Thus it is that
On the neck, within a zigzag "geometrical" pattern, is a doe, feeding, and a tall water-fowl. H. von Rohden, Denkmaler, iii. pp. 1945, 1946: "Probably dating from the seventh century." Taking the vase, with Mr. Walters, as of the eighth century, I do not suppose that the amateur who gave it to a dancer and scratched the hexameter was of a later generation than the jug itself.
Not even the geometrical perfection of the island detracted from its primitive and rugged beauty. True, it had no bays or wooded coves where pirates might have lurked, and it was fickle to any one spot.
The other magnitude, which drew near with a step at once elusive and fascinating, revealed as she walked a figure so exquisite in its every curve as to call from her geometrical acquaintances the ecstatic exclamation, "Let it be granted that M is a parabola." Guided thus along their respective paths, the two magnitudes presently met with such suddenness that they almost intersected.
As we go up we find, above another layer of DEBRIS, the Solutreen type of tools and weapons represented by bone implements and numerous arrow-heads, this time stalked and notched. The four following levels correspond with those belonging to what is known as the Madeleine type, and the arrow-heads are decorated with geometrical designs.
Add to this that the glass was generally renewed and restored by one Peckett about 1780, who inserted patches and curious geometrical patterns of his own manufacture wherever possible, and an idea may be obtained of the difficulties which will beset anyone who tries to write an adequate book on the subject.
Under the dome of the vast mausoleum a high and beautiful screen of open tracery in white marble rises around the two tombs, or rather cenotaphs of the emperor and his princess; and in this marvel of marble the carving has advanced from the old geometrical patterns to a trellis-work of flowers and foliage, handled with great freedom and spirit.
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