Elements of the philosophy of the human mind. By Dugald Stewart. Rev. and abridged, with critical and explanatory notes, for the use of colleges and schools. By Francis Bowen ...

REASONING AND DEDUCTIVE EVIDENCE. 453
2. The geometer's sutperposition of triangles is ideal, and not
actual. -- It yet remains for me to say a few words upon that
superposition of triangles, which is the groundwork of all our
geometrical reasonings concerning the relations which different
species bear to one another in respect of magnitude. And here
I must take the liberty to remark, in the first place, that the
fact in question has been stated in terms much too loose and
incorrect for a logical argument. When it is said, that " all the
James Ferguson, author of the justly popular works on Astronomy and
Mechanics. In the year 1768, he paid a visit to Edinburgh, when I had
not only an opportunity of attending his public course of lectures, but of
fiequently enjoying, in private, the pleasure of his very interesting conversation. I remember distinctly to have heard him say, that he had more
than once attempted to study the Elements of Euclid; but found himself
quite unable to enter into that species of reasoning. The second proposition of the first book he mentioned particularly, as one of his stumbling.
blocks at the very outset; - the circuitous process by which Euclid sets
about an operation which never could puzzle, for a single moment, any
man who had seen a pair of compasses, appearing to him altogether capricious and ludicrous. He added, at the same time, that as there were various geometrical theorems of which he had daily occasion tfo make use, he
had satisfied himself of their truth, either by means of his compasses and
scale, or by some mechanical contrivances of his own invention. Of one
of these I have still a perfect recollection; -his mechanical or experimental demonstration of the 47th proposition of Euclid's first book, by
cutting a card so as to afford an ocular proof, that the squares of the two
sides actually filled the same space with the square of the hypothenuse.
To those who reflect on the disadvantages under which Mr. Ferguson
had labored in point of education, and on the early and exclusive hold
which experimental science had taken of his mind, it will not perhaps
seem altogether unaccountable, that the refined and scrupulous logic of
Euclid should have struck him as tedious, and even unsatisfactory, in
comparison of that more summary and palpable evidence on which his
judgment was accustomed to rest.
"Mr. Ferguson's general mathematical knowledge," says Dr. Hutton,
"was little or nothing. Of algebra, he understood little more than the
notation; and he has often told me he could never demonstrate one proposition in Euclid's Elements; his constant method being to satisfy himself, as to the truth of any problem, with a measurement by scale and
compasses." - Hutton's Mllathematical and Philosophical Dictionary, article
[.tsore.