The fourth dimension

THE SECOND CHAPTER IN THE HISTORY OF FOUR SPACE 43

the town? He must be far off.’ And as to three different places to which he had been he asked me to tell him about them in one word. I did not know what he meant, and then he asked me if one was in a line with the other and all in a row, or if they were in a triangle.

“ He enjoys cutting paper figures with a pair of scissors, and without my ever having told him about triangles remarked that a right-angled triangle which he had cut out was half of an oblong. I exercise his body with care, he can dig well in the earth with his little hands. The blossom can fall and no fruit left. When he is fifteen I want to send him to you to be your pupil.”

In Johann’s autobiography he says :—

“My father called my attention to the imperfections and gaps in the theory of parallels. He told me he had gained more satisfactory results than his predecessors, but had obtained no perfect and satisfying conclusion. None of his assumptions had the necessary degree of geometrical certainty, although they sufficed to prove the eleventh axiom and appeared acceptable on first sight.

“He begged of me, anxious not without a reason, to hold myself aloof and to shun all investigation on this subject, if I did not wish to live all my life in vain.”

Johann, in the failure of his father to obtain any response from Gauss, in answer to a letter in which he asked the great mathematician to make of his son “an apostle of truth in a far land,” entered the Engineering School at Vienna. He writes from Temesvar, where he was appointed sub-lieutenant September, 1823 :—

“Temesvar, November 3rd, 1823.

“Dear Goop FATHER,

“JT have so overwhelmingly much to write about my discovery that I know no other way of checking myself than taking a quarter of a sheet only to write on. I want an answer to my four-sheet letter.