Hodge conjecture
And that if a straight-line falling across two (other) straight-lines [he uses 'falling' as 'passing through' or 'passing over'] makes internal angles on the same side (of itself whose sum is) less than two right angles, then the two (other) straight-lines, being produced to infinity, meet on that side (of the original straight-line) that [It is more proper to say 'meet on the side that,'] the (sum of the internal angles) [This is actually a parenthetical error; 'sum' should be outside.] is less than two right angles (and [Hodge is referring to the lines] do not meet on the other side)."