How, being so contained and implied, it could be new truth, and how the theorems of geometry, so different in appearance from the definitions and axioms, could be all contained in these, was a difficulty which no, one, I thought, had sufficiently felt, and which, at all events, no one had succeeded in clearing up.

On my sheets I find integrals and differential equations of every kind, astronomical corrections (of which I prepared a book), chances, Englefield's comets, investigation of the brightness within a rainbow, proof of Clairaut's theorem in one case, metacentres, change of independent variable applied to a complicated case, generating functions, principal axes.

Do you also show not your theorems to the uninstructed, but show the acts which come from their digestion.

He begins with definitions, adds to these axioms (or postulates), follows with propositions or theorems as the chief thing, finally with demonstrations or proofs, which derive the later propositions from the earlier, and these in turn from the self-evident axioms.

Surely, the far larger part of these assumed difficulties rests on a misapplication either of the senses to the sense, or of the sense to the understanding, or of the understanding to the reason;in short, on an asking for images where only theorems can be, or requiring theorems for thoughts, that is, conceptions or notions, or lastly, conceptions for ideas.