Principles of Geometry V.1
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(v) The case in which the points A^ B^ C have arbitrary positions can be reduced to that precedinir, in which two of the points, B and C, lie on their respectively associated lines, h and c.
The i^iven lines a, ^, c, and the given points, B, C, define a line, 77?, as follows: taking arbitrary points H, H\ H'\ ..., on the line a, let the joins of these to the point J?, namely the lines HB, H'B, H'B, ..., meet the line b in the respective points A', A"', A", . . . , and the joins of these to the ...point C, namely the lines HC, H C, H'C, ..., meet the line c in the respec- tive points L, L\ L", ... ; the two ranges. A, A', K'\ ..., and L, L', L", . . . , are then related. Therefore, as was proved in Chapter i, the points of intersection of the various pairs of cross joins of these ranges, namely, the points {KL\ K'L\ (KL'\ K"L), {K'L'\ K"L'\ ..., all lie on a line which we denote by m.
Take two corresponding points, A and L, of these two related ranges, lying, respectively, on the lines h and c, and, with these, the point A.
What to read after Principles of Geometry V.1?
You can find similar books in the "Read Also" column, or choose other free books by Baker, H. F. (Henry Frederick), 1866-1956 to read onlineMoreLess
To quickly assess the difficulty of the text, read a short excerpt:
(v) The case in which the points A^ B^ C have arbitrary positions can be reduced to that precedinir, in which two of the points, B and C, lie on their respectively associated lines, h and c.
The i^iven lines a, ^, c, and the given points, B, C, define a line, 77?, as follows: taking arbitrary points H, H\ H'\ ..., on the line a, let the joins of these to the point J?, namely the lines HB, H'B, H'B, ..., meet the line b in the respective points A', A"', A", . . . , and the joins of these to the ...point C, namely the lines HC, H C, H'C, ..., meet the line c in the respec- tive points L, L\ L", ... ; the two ranges. A, A', K'\ ..., and L, L', L", . . . , are then related. Therefore, as was proved in Chapter i, the points of intersection of the various pairs of cross joins of these ranges, namely, the points {KL\ K'L\ (KL'\ K"L), {K'L'\ K"L'\ ..., all lie on a line which we denote by m.
Take two corresponding points, A and L, of these two related ranges, lying, respectively, on the lines h and c, and, with these, the point A.
What to read after Principles of Geometry V.1?
You can find similar books in the "Read Also" column, or choose other free books by Baker, H. F. (Henry Frederick), 1866-1956 to read onlineMoreLess
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