Geometrical Researches On the Theory of Parallels
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In our eReader you can find the full English version of the book. Read Geometrical Researches On the Theory of Parallels 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 Geometrical Researches On the Theory of Parallels
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If, finally, the point H falls outside the triangle c ABC (Fig. 18), the perpendicular CG- goes, in Fig. 17. consequence, through the triangle, and so we go over from the triangle ABC to the quadrilateral AFGC by adding the triangle FAD = DBH, and then taking away the triangle CGE — EBH.
Supposing in the spherical quadrilateral AFGC a great circle passed through the points A and G, as also through F and C, then will their arcs between AG and FC equal one another (Theorem 15), consequently also ...the triangles FAC and ACG be congruent (Theorem 15), and the angle FAC equal the angle ACG.
Hence follows, that in all the preceding cases, the sum of all three angles of the spherical triangle equals the sum of the two equal angles in the quadrilateral which are not the right angles.
Therefore we can, for every spherical triangle, in which the sum of the three angles is S, find a quadrilateral with equivalent surface, in which are two right angles and two equal perpendicular sides, and where the two other angles are each £S.
What to read after Geometrical Researches On the Theory of Parallels?
You can find similar books in the "Read Also" column, or choose other free books by George Bruce Halsted to read onlineMoreLess
To quickly assess the difficulty of the text, read a short excerpt:
If, finally, the point H falls outside the triangle c ABC (Fig. 18), the perpendicular CG- goes, in Fig. 17. consequence, through the triangle, and so we go over from the triangle ABC to the quadrilateral AFGC by adding the triangle FAD = DBH, and then taking away the triangle CGE — EBH.
Supposing in the spherical quadrilateral AFGC a great circle passed through the points A and G, as also through F and C, then will their arcs between AG and FC equal one another (Theorem 15), consequently also ...the triangles FAC and ACG be congruent (Theorem 15), and the angle FAC equal the angle ACG.
Hence follows, that in all the preceding cases, the sum of all three angles of the spherical triangle equals the sum of the two equal angles in the quadrilateral which are not the right angles.
Therefore we can, for every spherical triangle, in which the sum of the three angles is S, find a quadrilateral with equivalent surface, in which are two right angles and two equal perpendicular sides, and where the two other angles are each £S.
What to read after Geometrical Researches On the Theory of Parallels?
You can find similar books in the "Read Also" column, or choose other free books by George Bruce Halsted to read onlineMoreLess
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