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Updated: May 26, 2025
I followed d'Alembert's precept in his advice to young mathematical students: 'Have faith and go ahead, said the great geometrician. Faith I had; and I went on pluckily. And it was well for me that I did, for I often found behind the wall the enlightenment which I was seeking in front of it.
The geometrician, without quiting nature, will calculate the active force of matter; it will then become obvious to him, that to explain its phenomena, it is by no means necessary to have recourse to that which is incommensurable with all known powers.
This, he says, is an axiom of justice as well as of mathematics; and he asks whether there is not a true coincidence between commutative and distributive justice, and arithmetical and geometrical proportion. But I would ask in my turn whether the certainty that any arithmetician or geometrician has of the arithmetical or geometrical truth will lead him to discover this coincidence.
His father Fazio was a geometrician of repute and a student of applied mathematics, and, though his first desire was to make his son a jurisconsult, he gave Jerome in early youth a fairly good grounding in arithmetic and geometry, deeming probably that such training would not prove a bad discipline for an intellect destined to attack those formidable tomes within which lurked the mysteries of the Canon and Civil Law.
If the intuitive imagination is combined with the deductive spirit we have the analytical talent of the systematic naturalist, of the geometrician. In Linnaeus and Cuvier the intuitive element predominates; in Gauss, the analytical element.
The spangled heavens should be used as a pattern and with a view to that higher knowledge; their beauty is like the beauty of figures or pictures excellently wrought by the hand of Daedalus, or some other great artist, which we may chance to behold; any geometrician who saw them would appreciate the exquisiteness of their workmanship, but he would never dream of thinking that in them he could find the true equal or the true double, or the truth of any other proportion.
Here is no reference to type, but a definition rigorous enough for a geometrician. And such is the character which every scientific naturalist recognises as that to which his classes must aspire knowing, as he does, that classification by type is simply an acknowledgment of ignorance and a temporary device.
John Marr, an excellent mathematican and geometrician, whom I conceive you remember: he was servant to King James and Charles the First. At first, when the Lord Napier, or Marchiston, made publick his Logarithms, Mr.
At Megara Plato passed some time with the Megarian Eucleides, his fellow-disciple in the society of Socrates and the founder of what is termed the Megaric school of philosophers. He next visited Cyrênê, where he is said to have become acquainted with the geometrician Theodôrus and to have studied geometry under him.
The truth is that the geometrician does not introduce us to a new world at all. He merely gives us a fuller and a more exact account than was before within our reach of the space relations which obtain in the world of external objects, a world we already know pretty well.
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