...principles of the theory of combinations with the following elementary theorems and their reciprocals : " If two triangles be such that the lines joining corresponding vertices meet in a point (which we shall call the pole of the two triangles), the intersections of corresponding sides will...

...5. Find the locus of the point at which two given portions of the same line subtend equal angles. 7. If two triangles be such that the lines joining corresponding vertices meet in a point (which we shall call the pole of the two triangles), the intersections of corresponding sides will...

...principles of the theory of combinations with the following elementary theorems and their reciprocals: "If two triangles be such that the lines joining corresponding vertices meet in a point (the centre of homology of the two triangles), the intersections of corresponding sides will lie in one...

...the converse of Brianchon's theorem, that this other hexagon can be circumscribed about a conic. no. 2. Note. — Each of the eight sets of lines is connected...same straight line. In Fig. 2 the two triangles are GKH, LNH. It will be found that the line *l=2 is the Pascal ABEDCF, and that A=Z. mnm » is the Pascal...

...the converse of Brianchon's theorem, that this other hexagon can be circumscribed about a conic. PIO. 2. Note.— Each of the eight sets of lines is connected...found that the line ^=? is the Pascal ABEDCF, and that *Lt mnmn is the Pascal DBEACF. 2101. (Proposed by M. DAKBOTTX.) — Trouver Irs conditions necessnires...