Quotes · Quote card
Quotation from Elements, Books I-VI by Euclid
“If two right lines (AB, CD) meet a third line (AC), so as to make the sum of the two interior angles (BAC, ACD) on the same side less than two right angles, these lines being produced shall meet at some finite distance”
Elements, Books I-VI, Book I, Axiom xii, trans. John Casey (3rd ed., 1885)
Casey's statement of Euclid's parallel postulate, the assumption whose independence was established only in the nineteenth century.
Citation: "If two right lines (AB, CD) meet a third line (AC), so as to make the sum of the two interior angles (BAC, ACD) on the same side less than two right angles, these lines being produced shall meet at some finite distance" — Euclid, Elements, Books I-VI, Book I, Axiom xii, trans. John Casey (3rd ed., 1885). (id euclid-elements-books-i-vi-q4)
