Introduction to Quaternions |
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Page 39
... squares of the diagonals of a paral- lelogram is equal to the sum of the squares of the sides . Retaining the notation and figure of Ex . 1 , Art . 7 , CB = a + ß , AD = a - ẞ ; :: CB2 + DA2 = 2a3 + 2ß3 , and , changing all the signs ...
... squares of the diagonals of a paral- lelogram is equal to the sum of the squares of the sides . Retaining the notation and figure of Ex . 1 , Art . 7 , CB = a + ß , AD = a - ẞ ; :: CB2 + DA2 = 2a3 + 2ß3 , and , changing all the signs ...
Page 40
... squares of the sides of the triangle fall short of three times the squares of the distances of the angular points from O , by the square of three times the distance of the mean point from 0 . Let then ( Art . 14 ) , or Now OA = a , OB ...
... squares of the sides of the triangle fall short of three times the squares of the distances of the angular points from O , by the square of three times the distance of the mean point from 0 . Let then ( Art . 14 ) , or Now OA = a , OB ...
Page 41
... squares of half the sides . Retaining the notation of the last example , and the figure of Ex . 4 , Art . 7 , 1 1 1 ... squares of the sides of any quadrilateral exceed the squares of the diagonals by four times the square of the line ...
... squares of half the sides . Retaining the notation of the last example , and the figure of Ex . 4 , Art . 7 , 1 1 1 ... squares of the sides of any quadrilateral exceed the squares of the diagonals by four times the square of the line ...
Page 42
... squares of the sides , the squares of the diagonals and the square of four times the distance of the point from the mean point of the figure . With the notation of Art . 14 , and the figure of Ex . 7 , Art . 7 , we have squares of the ...
... squares of the sides , the squares of the diagonals and the square of four times the distance of the point from the mean point of the figure . With the notation of Art . 14 , and the figure of Ex . 7 , Art . 7 , we have squares of the ...
Page 43
... squares of the edges exceeds the sum of the squares of the diagonals by eight times the square of the straight line which joins the points of inter- section of the two pairs of diagonals . Let OA = a , OB = ß , OC = y , OD = 8 ; sum of ...
... squares of the edges exceeds the sum of the squares of the diagonals by eight times the square of the straight line which joins the points of inter- section of the two pairs of diagonals . Let OA = a , OB = ß , OC = y , OD = 8 ; sum of ...
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Common terms and phrases
A. S. WALPOLE A. W. VERRALL ALGEBRA ARITHMETIC Assistant Master aßy axis BEGINNERS bisects Cambridge centre chord circle cone CONIC SECTIONS conjugate diameters constant drawn Edited ELEMENTARY TREATISE ellipse ellipsoid ENGLISH equal EXAMPLES Exercises Fcap find the locus G. E. FASNACHT GEOMETRY given lines given point gives GRAMMAR GREEK Hence HISTORY hyperbola Illustrated intersection Introduction and Notes ISAAC TODHUNTER J. P. MAHAFFY LATIN Litt Litt.D LL.D M.A. BOOK M.A. Cr MACMILLAN'S Mathematics middle points parabola parallelepiped parallelogram PRIMER Prof Professor quaternion revised right angles rotation Sapa Saß scalar School shews Spop squares strain tangent plane tetrahedron Translated triangle Trinity College unit vectors values Vaß vector parallel vector perpendicular Vẞy whence yẞ αβγ φρ
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