224 W. M. Gillespie on Practical Surveying. 
Art. XX VIIL—A Problem in Practical Surveying: demonstrated 
_ by means of Transversals ; by W. M. GiLuEsPIE, Prof. of Civil 
- Engineering in Union College. 
_ Ler A and B represent two points, inaccessible, and invisible 
:from one another. Let it be required to find a third point, C, in 
“the line of A and B, but invisible from them. It is supp 
‘that no. means of measuring either distances or angles are at 
hand. 
_ The problem may be solved thus. Set three stakes, D, E, F, 
in a straight line. Set a stake, G, in the line of DB and EA; 
FB, and at the same time in the line of GH. Then range out 
the lines DA and EJ, which will meet in a point, C, which will 
be the one required. Any number of such may be similarly 
obtained to verify the work. 
is problem is given in a recent number of the Vienna En- 
gineer’s Journal (Zeitschrift des Ocsterreichischen Ingenieur Verein, 
1856, p. 245) by an Austrian mathematician, who represents it 
as employed by practical surveyors, but as not having any known 
geometrical proof. He proceeds to give an analytical investiga 
tion of it, saying, “I have in vain tried to prove the problem 
in the synthetic way, by pure geometry.” The “Th 
Transversals,” however, the foundation of the “ Recent Geome- 
try,” or “Geometry of Segments,” (too little cultivated beyond 
: = 4 
a small circle of French geometers) will furnish a simple aad 
3. 
The theorem to be proved is equivalent to the assertion that if 
A, B, C, and D, E, F, lie respectively in two straight lines, and 
lines be drawn as in the figure, then will the intersections G, H,J 
lie in one and the same straight line. : 
