Three towns are known to d ave been destroyedHerculaneum at the western base of the y olcano, Pompeii on the south-east side, and Stabiae, still farther sl outh, on the site of the modern Castellamare.

If a line S2 cut an arc aa at b, so that the two segments ab, ba lie on opposite sides of the line, then projecting the figure so that the line Sl goes off to infinity, the tangent at b is projected into the asymptote, and the arc ab is projected into a hyperbolic leg touching the asymptote at one extremity; the arc ba will at the same time be projected into a hyperbolic leg touching the same asymptote at the other extremity (and on the opposite side), but so that the two hyperbolic legs may or may not belong to one and the same branch.

To technical logic. It may be attributed in some sl i ght degree, perhaps, to incidental flashes of logical insight where his thought is least of what he himself calls logic, e.g.