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Updated: June 18, 2025
To do him justice, he studied for two or three hours everyday, and it was not his fault if he did not advance but his head was confused with technical terms; he mixed all up together, and disparts, sines and cosines, parabolas, tangents, windage, seconds, lines of sight, logarithms, projectiles and traverse sailing, quadrature and Gunter's scales, were all crowded together, in a brain which had not capacity to receive the rule of three.
"There is no measure of value, no standard of value," it said in its conclusions; "economic science tells us this, just as mathematical science tells us that there is no perpetual motion or quadrature of the circle, and that these never will be found.
Among the special problems he treated of may be mentioned the quadrature of the circle, his determination of the ratio of the circumference to the diameter being between: 3·1428 and 3·1408, the true value, as is now known, being 3·1416 nearly. He also wrote on Conoids and Spheroids, and upon that spiral still passing under his name, the genesis of which had been suggested to him by Conon.
"This place does not at all please me, for I do not think these walls are adapted to lucubration; they have not the proper repercussion; the room itself has not the right quadrature; the thoughts rebound too violently and make a clatter; and if ever you want to continue them in a fugue, they will be sure all to clash in a hubbub together.
This is an evil tendency, a delusion which the Academy cannot oppose too strongly, because it is not only a chimera, but a dangerous sophism. Let us respect good and honest intentions; but let us not fear to say that to publish a book upon the ORGANIZATION OF LABOR is to rewrite for the fiftieth time a treatise upon the quadrature of the circle or the philosopher's stone."
"The properties of the spiral, and the quadrature of the parabola were added to ancient geometry by Archimedes, the last being a great step in the progress of the science, since it was the first curvilineal space legitimately squared."
A solution of the secular problem of the quadrature of the circle, government premium 1,000,000 pounds sterling. Was vast wealth acquirable through industrial channels? The reclamation of dunams of waste arenary soil, proposed in the prospectus of Agendath Netaim, Bleibtreustrasse, Berlin, W. 15, by the cultivation of orange plantations and melonfields and reafforestation.
But the Earth having been carried along during this time to C, increasing thus its distance from Jupiter, it follows that if Light requires time for its passage the illumination of the little planet will be perceived later at C than it would have been at B, and that there must be added to this time of 30 times 42-1/2 hours that which the Light has required to traverse the space MC, the difference of the spaces CH, BH. Similarly at the other quadrature when the earth has come to E from D while approaching toward Jupiter, the immersions of the Satellite ought to be observed at E earlier than they would have been seen if the Earth had remained at D.
So highly did he esteem this, that he directed the diagram to be engraved on his tombstone. He also treated of the quadrature of the circle and of the parabola; he wrote on Conoids and Spheroids, and on the spiral that bears his name, the genesis of which was suggested to him by his friend Conon the Alexandrian. As a mathematician, Europe produced no equal to him for nearly two thousand years.
In 1644 he published a tract on the properties of the cycloid in which he suggested a solution of the problem of its quadrature. This led to a long debate, during which Torricelli was seized with a fever, from the effects of which he died, in Florence, October 25, 1647.
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