: \ 
Biography of Johann Nepomuk von Fuchs. 225 
Conceive the two given lines produced to meet in Z, beyond 
the limits of this figure. The triangle BFZ is so cut by the trans- 
versal CE as to give the equality, he ee 
BJ X FEXZC==JF X EZX BC.* 
The triangle AFZ, cut by CD, gives FHX ACK DZ=HAXCZXFD* ° 
The triangle ABG, cut by OD, gives BCX ALKGD=BDXCAXGL.* _~ 
The triangle DEG, cut by OZ, gives GAXEZXBD=EA X DZX BG.* 
The triangle DEG, cut by AF, gives GK X DFX AE=KD X EF AG.* 
The triangle AGK, cut by HD, gives KDXGLxX AH=GDXALXKH.* 
H, J, lie in a straight line, which is a trans- 
versal to the triangle BFK. 
What Poinsot said, forty years ago, that “The simple and 
fruitful principles of this ingenious theory of transversals de- 
seryed well to be admitted into the number of the elements of 
geometry,” is even more true and desirable at the present time. 
a 
Arr. XXIX—Biography of Johann Nepomuk von Fuchs; by 
FRANZ VON KOBELL. 
[Concluded from p. 101.] 
te n already, as it might appear, thoroughly studied, 
Fuchs occupied himself anew with the processes of burning and 
Properties of soluble and insoluble silica, ascribing their differ- 
ences di 
a the theorem “If a straight line be drawn so as to cut any two sides. of a 
and the third side, one or all being pitt ie Pate them into at 
the prol sides and the prolongations being taken as segmen 
rodeo if © begments Whose extremities are not 
ous, be equal to the product of the other three segments.” 
t By the converse of the preceding theorem. 
_ SECOND SERIES, VOL. XXIII, NO. 68.—MARCH, 1857. 
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