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 VI.

81

and is given; and DCE is a right Z;.~. L DCE is
given in species, and CGD is equiangular to DCE;.'. CGD is given in species;.'. the ratios of GD: DC
and of DC: DE are given. Hence the ratio of FD: DE
is given; therefore the ratio of DF: FE is given, and
their rectangle is given. Hence DF and FE are each
given. Hence the Proposition is solved.
Cor.-In a like manner we may solve the Problem:
Given the base, the difference of the base angles, and
the sum of the sides to construct the triangle.
(5). To construct a quadrilateral of given species whose
four sides shall pass through four given points.
D
Analysis.-Let ABCD be the required quadrilateral,
P, Q, R, S the four given points. Let E, F be the extremities of the third diagonal. Now, let us consider
the A ADF; it is evidently given in species, and PQR

G