By Luther Pfahler Eisenhart

This textbook explores the configurations of issues, traces, and planes in area outlined geometrically, interprets them into algebraic shape utilizing the coordinates of a consultant aspect of the locus, and derives the equations of the conic sections. The Dover variation is an unabridged republication of the paintings initially released by means of Ginn and corporate in 1939.

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1) are degenerate, but the situation in this case is given in the table so that the algebraic treatment may be complete the statements made. ; the reader should verify In illustration of some of the above results ing equations we consider the follow- : 22. 5), which The determinant in in this case are that If is, xi = 22 1/2, y\ now we *i = take the and the equation + 11 - = 0, 22 yi + 22 = 0, 1. 3]. 6]. is the first mul- Points and Lines in trie Plane [Chap. y + 4 = + y + 2 = 0, using determinants, and check the result by solving Find the 1.

6] if c 2 = kci. 15) = 01 C2 if = 9 01 with the understanding that if either term in any ratio equal to zero so also is the other term; for example, 62 = 0, so 0/so is bi This theorem is is if = 0. 1) is a constant multiple of the other, in which case any solution of either equation other. 14) are equal to zero. 14) are equal to zero. 7] discussion is set forth in the following table, the column giving the number of 44 common solutions of the two Two Sec. 1), or, what is the geometric equivalent, the number of common points of two lines with these equations : One a2 b2 None not both zero C2 b 2 1 \ 02 C2 = 0i,bi,a2 b2 not , 02 b2 C &i|_|0i b2 c2 Ici \ 1 I| 02 c2 zero all .

1) are degenerate, but the situation in this case is given in the table so that the algebraic treatment may be complete the statements made. ; the reader should verify In illustration of some of the above results ing equations we consider the follow- : 22. 5), which The determinant in in this case are that If is, xi = 22 1/2, y\ now we *i = take the and the equation + 11 - = 0, 22 yi + 22 = 0, 1. 3]. 6]. is the first mul- Points and Lines in trie Plane [Chap. y + 4 = + y + 2 = 0, using determinants, and check the result by solving Find the 1.