Certainly. Can you not see how, in every rectangular triangle, a perpendicular may be drawn from the right angle to the hypothenuse?
Yes, in your figure; but since what is in my head is not a triangle, for I imagine some with sides a thousand miles long, and there is not in my head room enough—
There is no question of what is in your head, but of triangles themselves—
But these triangles do not exist; therefore, we can say nothing of them.
Yes; but may they not exist?
Who doubts it?
Well then, if they do exist, be they large or small, in one position or another, here or there, is it not true that a perpendicular may be drawn from the vertex of the right angle to the hypothenuse?
Evidently.
I have then only to say that, in every rectangular triangle, this perpendicular may be drawn.
Then you do not speak of those which do not exist? Is it not so?