Augustus De Morgan - Subject Quotes

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I am far from saying that this Treatise will be easy; the subject is a difficult one, as all know who have tried it.

Augustus De Morgan
All the men who are now called discoverers, in every matter ruled by thought, have been men versed in the minds of their predecessors, and learned in what had been before them. There is not one exception. I do not say that every man has made direct acquaintance with the whole of his mental ancestry... But... it is remarkable how many of the greatest names in all departments of knowledge have been real antiquaries in their several subjects.
I may cite among those... in science, Aristotle, Plato, Ptolemy, Euclid, Archimedes, Roger Bacon, Copernicus, Francis Bacon, Ramus, Tycho Brahe, Galileo, Napier, Descartes, Leibnitz, Newton, Locke.

Augustus De Morgan
Experience has convinced me that the proper way of teaching is to bring together that which is simple from all quarters, and, if I may use such a phrase, to draw upon the surface of the subject a proper mean between the line of closest connerion and the line of easiest deduction. This was the method followed by Euclid, who, fortunately for us, never dreamed of a geometry of triangles, as distinguished from a geometry of circles, or a separate application of the arithmetics of addition and subtraction; but made one help out the other as he best could.

Augustus De Morgan
I have throughout introduced the Integral Calculus in connexion with the Differential Calculus.... Is it always proper to learn every branch of a direct subject before anything connected with the inverse relation is considered? If so why are not multiplication and involution in arithmetic made to follow addition and precede subtraction? The portion of the Integral Calculus, which properly belongs to any given portion of the Differential Calculus increases its power a hundred-fold...

Augustus De Morgan
The work now before the reader is the most extensive which our language contains on the subject.

Augustus De Morgan
No part of mathematics or mathematical physics involves considerations so strange or so difficult to handle correctly, and there is no subject upon which opinions have been more freely hazarded by the ignorant, or rational dissent more unambiguously expressed by the learned.

Augustus De Morgan
If you wish to oppose a mathematician, confront him on some question in the parts of his subject which are supposed to be perfectly demonstrated.

Augustus De Morgan
Montucla remarked, that if any subject might be expected to baffle the mathematician, it would be chance.

Augustus De Morgan
The greatest writers on mathematical subjects have a genius which saves them from their own slips, and guides them to true results through inaccurate expression, and sometimes through absolute error.

Augustus De Morgan
In all matters we have learnt to say that we do not know what things are, we only know something about them: that is, we have subjects with attributes, and therefore propositions which can be affirmed.

Augustus De Morgan