Falsafa

Comma for either/or — dharma, courage. Spelling forgiving — corage finds courage.

    The Atlas·Ideas

    Reductio ad absurdum

    idea · 1 work · 2 mentions · 8 anchored passages

    if not · if possible, let it have that ratio · which is impossible · which was proved impossible

    spoken of as

    1 expression

    Proof by contradiction“reductio ad absurdum”1 mention

    Elements (Greek)

    For, if possible, let it have that ratio to a greater, LMN;
    book 12

    in the texts

    ElementsHellenistic · Greek

    The recurring proof technique of assuming the negation of what is to be shown (a smaller number with the same property) and deriving a contradiction ('which is impossible'), used throughout every proposition in this window.

    For, if not, there will be some number less than G which will have the parts A, B, C.
    book 7
    therefore they will also measure the remainder CF which is less than E:
    book 7
    Therefore there will be no number less than G that will have the parts A, B, C.
    book 7