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Updated: May 17, 2025
But these early observations, far from affording the expected facilities for the calculation of its orbit, proved a source of grievous perplexity. The utmost ingenuity of geometers failed to combine them satisfactorily with the later Uranian places, and it became evident, either that they were widely erroneous, or that the revolving body was wandering from its ancient track.
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
A fact must follow a certain law, because we see no reason for its deviating from it in one way rather than in another. Geometers often fall into this Fallacy. Thus, the Greeks thought that, by determining the meanings of words, they ascertained facts.
"Your war with the Geometers on the subject of this Comet appears to me like a war of the gods in Olympus, while on Earth there is going on a fight of dogs and cats.... Would to Heaven our friend Moreau-Maupertuis had cultivated his art like you! He was ill, this long while, of a repletion of pride; but I had not reckoned him either a hypocrite or an imbecile.
And upon my word that is most sensible. We are greater poets, greater philosophers, greater orators, greater architects, greater astronomers, greater geometers, than these good people; but they understand better than we the science of good sense and virtue; and if peradventure that science should happen to be the first of all sciences, they would be right in saying that they have two eyes and we have only one, and all the rest of the world is blind."
Such is the cycloid, first conceived by Galileo, and a stumbling-block and cause of contention among geometers long after he had left it, together with his system of the universe, undetermined. Descartes, Roberval, Pascal, became successively challengers or challenged respecting some new property of this curve.
It will probably produce a sensation in the world of science. Its design is the reconstruction of the entire methods of Geometry. All geometers, from the dawn of the science, have built their systems upon these definitions: A line is length without breadth, and A surface is length and breadth, without thickness. Mr.
All geometers heretofore have claimed that there are three kinds of quantity in Geometry, different in their natures, and requiring units of different natures to measure them. Mr. Smith shows that there is but one kind of quantity in Geometry, and but one kind of unit; and that lines, surfaces, and solids are always measured by the same identical unit.
As Voltaire eloquently said, officers of war by land and by sea, magistrates, physicians who knew nature, men of letters whose taste purified knowledge, geometers, physicists, all united in a work that was as useful as it was laborious, without any view of interest, without even seeking fame, as many of them concealed their names; finally without any common understanding and agreement, and therefore without anything of the spirit of party.
He had an extraordinary inventive genius for discovering new provinces of inquiry, and new points of view for old and familiar objects. Like Newton, he had a habit of abstraction from outward things, and would forget to take his meals. Eratosthenes was another of the famous geometers of antiquity, and did much to improve geometrical analysis. He was also a philosopher and geographer.
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