A sequel to the first six books of the Elements of Euclid, containing an easy introduction to modern geometry, with numerous examples. By John Casey.

BOOK SIXTH.
SECTION I.
ADDITTIONAL PROPOSITIONS.
Prop. 1.-ITf two triangles have a common base, but
diafferent vertices, they are to one another as the segments
into which the line joining the A
vertices is divided by the common
base or base produced.
Let the two L~sbe AGB AGO, r
having the base AG common;
let AG cut the line BC, joining
the vertices in A'; then c
AGB:AGO: BA': A'C.
Dern. -TheL LABA': ACA': BA' A'C;
and GBA':GOCA'::BA':A'C;
therefore
ABA'-GOBA': ACA'-GOCA': BA': A'C;
or AGB:.AGC::BA':A'C.
Prop. 2.-If three concurrent lines AG, BG, CG, drawn
from the angular _points of a triangle, meet the opposite,
sides in the points A', B', C', the product of the three
ratios
BA' CB' AC' iy
~F Wi' ~ s niy
r 2