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Updated: May 26, 2025
The generation of the line from the point, the plane from the line, and from the plane, the solid, is a matter, again, which chiefly interests the geometrician, but the inevitable sequence stands revealed in seed, stem, leaf, and fruit: a point, a line, a surface, and a sphere.
If an author had written like a great genius on geometry, though its practical and speculative morals were vicious in the extreme, it might appear, that in voting the statue, they honoured only the geometrician. But Rousseau is a moralist, or he is nothing.
First, therefore, Hermeas the geometrician demanded of Protogenes the grammarian a reason why Alpha was the first letter of the alphabet. And he returned the common answer of the schools, that it was fit the vowels should be set before the mutes and semi-vowels. And of the vowels, some being long, some short, some both long and short, it is just that the latter should be most esteemed.
If a knowledge and love of literature is part of the birthright of our children, and a part which, as things are, very many of them will never obtain away from school, then we teachers must strive to give it them, even if the process seems shockingly frivolous to the grammarian or the geometrician.
I shall be satisfied with showing that none of these forms can be employed or imitated in philosophy in the sense in which they are understood by mathematicians; and that the geometrician, if he employs his method in philosophy, will succeed only in building card-castles, while the employment of the philosophical method in mathematics can result in nothing but mere verbiage.
Thus we have, on the one hand, isolation, inequality, enmity, war, robbery, murder; on the other, society, equality, fraternity, peace, and love. Choose between them! M. Joseph Dutens a physician, engineer, and geometrician, but a very poor legist, and no philosopher at all is the author of a "Philosophy of Political Economy," in which he felt it his duty to break lances in behalf of property.
Now this old geometrician, who had passed through seventy-five seasons, had built many powerful engines, and by the triple pulley, with the aid of the left hand alone, could launch a merchant ship of fifty thousand medimni burden.
It is for the mariner, that the astronomer explores his arduous science; it is for him the geometrician calculates; for his use the mechanic plies his craft: it is for the mason, for the carpenter, for the labourer, that the skilful architect studies his orders, lays down well-proportioned elaborate plans.
If then we may assume that there is an objective truth, and that the constitution of the human mind is in correspondence with it, and acts truly when it acts according to its own laws; if we may assume that God made us, and that what He made is good, and that no action from and according to nature can in itself be evil; it will follow that, so long as it is man who is the geometrician, or natural philosopher, or mechanic, or critic, no matter what man he be, Hindoo, Mahometan, or infidel, his conclusions within his own science, according to the laws of that science, are unquestionable, and not to be suspected by Catholics, unless Catholics may legitimately be jealous of fact and truth, of divine principles and divine creations.
Thus he sweeteneth the water with a wood, preserveth the creatures in the ark, which the blast of his mouth might have as easily created; for God is like a skillful geometrician, who when more easily, and with one stroke of his compass, he might describe or divide a right line, had yet rather to do this in a circle or longer way, according to the constituted and forelaid principles of his art: yet this rule of his he doth sometimes pervert to acquaint the world with his prerogative, lest the arrogancy of our reason should question his power and conclude he could not.
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