Elementary Projective Geometry
Elementary Projective Geometry
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In our eReader you can find the full English version of the book. Read Elementary Projective Geometry Online - link to read the book on full screen. Our eReader also allows you to upload and read Pdf, Txt, ePub and fb2 books. In the Mini eReder on the page below you can quickly view all pages of the book - Read Book Elementary Projective Geometry
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To quickly assess the difficulty of the text, read a short excerpt:
= (f>, we must have tan (6 + a) tan (^ — a) = k, tan^ — tan^ a = ^ (1 — tan^ . Tan^ a), or tan^^ (1 +^tan"^a) = A; + tan^a; 1 — tan^ a ■•*-^^=tan^. (l-T + k tan^ a/ ' this gives two real and different, coincident, or imaginary double rays, according as 1 — tan^ a I 1 + A; tan^ a, I. E. As k^ — tan^ a.
Projective Rows and Pencils 57 EXAMPLES. III.
1. A line KL parallel to AB cuts TA, TB at K, L, and P is taken on TA. By means of a common perspective row find Q on TB, such that {TBLQ} = {ATKP}.
2.... If K, L are the mid-points of TA, TB respectively, find a point Q on TB corresponding to any point P on AT, so that {TBLQ} may be equal to {ATKP}. Also prove that AP : PT as TQ : QB.
3. If K, K' and L, L' be corresponding pairs of points on two projective rows KL, K'L', prove that the locus of the intersection of KL' and K'L is a straight line ; and find where this line cuts the two rows.
4. If /e, Hn a pencil correspond to k\ V respectively in another pencil projective with the former one, prove that the join of the intersections of k, V and k', I passes through a fixed point.
What to read after Elementary Projective Geometry?
You can find similar books in the "Read Also" column, or choose other free books by Alfred Garside Pickford to read onlineMoreLess
To quickly assess the difficulty of the text, read a short excerpt:
= (f>, we must have tan (6 + a) tan (^ — a) = k, tan^ — tan^ a = ^ (1 — tan^ . Tan^ a), or tan^^ (1 +^tan"^a) = A; + tan^a; 1 — tan^ a ■•*-^^=tan^. (l-T + k tan^ a/ ' this gives two real and different, coincident, or imaginary double rays, according as 1 — tan^ a I 1 + A; tan^ a, I. E. As k^ — tan^ a.
Projective Rows and Pencils 57 EXAMPLES. III.
1. A line KL parallel to AB cuts TA, TB at K, L, and P is taken on TA. By means of a common perspective row find Q on TB, such that {TBLQ} = {ATKP}.
2.... If K, L are the mid-points of TA, TB respectively, find a point Q on TB corresponding to any point P on AT, so that {TBLQ} may be equal to {ATKP}. Also prove that AP : PT as TQ : QB.
3. If K, K' and L, L' be corresponding pairs of points on two projective rows KL, K'L', prove that the locus of the intersection of KL' and K'L is a straight line ; and find where this line cuts the two rows.
4. If /e, Hn a pencil correspond to k\ V respectively in another pencil projective with the former one, prove that the join of the intersections of k, V and k', I passes through a fixed point.
What to read after Elementary Projective Geometry?
You can find similar books in the "Read Also" column, or choose other free books by Alfred Garside Pickford to read onlineMoreLess
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