Introduction to Quaternions, with Numerous ExamplesMacmillan, 1873 - 227 σελίδες |
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Αποτελέσματα 1 - 5 από τα 83.
Σελίδα 5
... give a history of the science , and shall accordingly content ourselves with saying , that the notion of sepa- rating addition from multiplication - attributing to the one , motion from a point , to the other motion about a point - had ...
... give a history of the science , and shall accordingly content ourselves with saying , that the notion of sepa- rating addition from multiplication - attributing to the one , motion from a point , to the other motion about a point - had ...
Σελίδα 14
... gives 1 = 1 — a + EG = y + 3 ( B− y ) , 2 D G C F H X 1 and AX AE + = EG 2 = 1 4 ( a + B + y ) , A E B which being symmetrical is a , ß , y in the same as the vector to the middle point of HF . X is called ( Art . 14 ) the mean point ...
... gives 1 = 1 — a + EG = y + 3 ( B− y ) , 2 D G C F H X 1 and AX AE + = EG 2 = 1 4 ( a + B + y ) , A E B which being symmetrical is a , ß , y in the same as the vector to the middle point of HF . X is called ( Art . 14 ) the mean point ...
Σελίδα 15
... gives xa - ẞ = p { ≈ ( a + ß ) − ß } , - .. ( Art . 6 ) x = pz , -1 = pz - p ; .. p = x + 1 . Similarly BQ = qBE gives yẞ - a = q { ≈ ( a + ß ) − a } , y = qz , -1 = qz - I .. q = y + 1 , and since z х Ρ = y q we have EX . 9. ] ...
... gives xa - ẞ = p { ≈ ( a + ß ) − ß } , - .. ( Art . 6 ) x = pz , -1 = pz - p ; .. p = x + 1 . Similarly BQ = qBE gives yẞ - a = q { ≈ ( a + ß ) − a } , y = qz , -1 = qz - I .. q = y + 1 , and since z х Ρ = y q we have EX . 9. ] ...
Σελίδα 18
... gives whence P B E x ( nẞ− a ) + y ( ẞ — ma ) = ß — a , - xn + y = 1 , x + my = 1 , .. X = - ' m - 1 mn 1 ' and AP : = AC = { { a + - m 1 mn 1 ( nẞ- B - a ) } 1 m ( n − 1 ) a + n ( m − 1 ) ß = 2 - AQ mn 1 1 - 1Q = ( a + B ) ...
... gives whence P B E x ( nẞ− a ) + y ( ẞ — ma ) = ß — a , - xn + y = 1 , x + my = 1 , .. X = - ' m - 1 mn 1 ' and AP : = AC = { { a + - m 1 mn 1 ( nẞ- B - a ) } 1 m ( n − 1 ) a + n ( m − 1 ) ß = 2 - AQ mn 1 1 - 1Q = ( a + B ) ...
Σελίδα 22
... and and Let OA a , OB = B , OC = Y , OA ' = ma , OB ' = nẞ , OC ' = py , BA = a - ẞ , BR = x ( α - B ) ; B'A ' = ma- nẞ , B'R = y ( ma — nẞ ) . - R ཊ B B cr P Now BB ' = BR – B'R gives ( n 22 [ CHAP . II . QUATERNIONS .
... and and Let OA a , OB = B , OC = Y , OA ' = ma , OB ' = nẞ , OC ' = py , BA = a - ẞ , BR = x ( α - B ) ; B'A ' = ma- nẞ , B'R = y ( ma — nẞ ) . - R ཊ B B cr P Now BB ' = BR – B'R gives ( n 22 [ CHAP . II . QUATERNIONS .
Άλλες εκδόσεις - Προβολή όλων
Introduction to Quaternions, with Numerous Examples Philip Kelland,Peter Guthrie Tait Πλήρης προβολή - 1873 |
Introduction to Quaternions, with Numerous Examples. Philip Kelland Δεν υπάρχει διαθέσιμη προεπισκόπηση - 2010 |
Introduction to Quaternions, with Numerous Examples P. Kelland,P. G. Tait Δεν υπάρχει διαθέσιμη προεπισκόπηση - 2017 |
Συχνά εμφανιζόμενοι όροι και φράσεις
ABCD aßy axis centre chord circle cone conjugate diameters constant diagonals drawn ellipse ellipsoid equal example find the equation find the locus given lines given point given straight lines gives Hence hyperbola latus rectum line of intersection line which joins m₁ mean point meet middle points multiplication notation nẞ operating parabola parallelepiped parallelogram prove quadrilateral Quaternions right angles rotation Sapa Saß scalar second order semi-diameters shews sides Similarly simple shear squares ß² ß³ strain subtraction Tait tangent plane tensor tetrahedron three vectors triangle unit vectors values Vaß vector parallel vector perpendicular Vẞy whence William Rowan Hamilton yẞ αβγ γαβ δαβ φρ
Δημοφιλή αποσπάσματα
Σελίδα 9 - Any two sides of a triangle are together greater than the third side.
Σελίδα 90 - A point moves so that the sum of the squares of its distances from the points (0, 0), (1, 0) is constant.
Σελίδα 10 - FG [Hypothesit. and joined towards the same parts by the straight lines BE, CH. But straight lines which join the extremities of equal and parallel straight lines towards the same parts are themselves equal and parallel.
Σελίδα 91 - Thus a parabola is the locus of a point which moves so that its distance from a fixed point is equal to its distance from a fixed straight line (see fig.
Σελίδα 71 - Find the locus of a point whose distances from two given straight lines are in a given ratio.
Σελίδα 67 - Find the locus of a point such that the ratio of its distances from two fixed points is constant.
Σελίδα 6 - Hamilton extended algebra to space : ' ' He had done a considerable amount of good work, obstructed as he was, when about the year 1843, he perceived clearly the obstruction to his progress in the shape of an old law, which prior to that time, had appeared like a law of common sense. The law in question is known as the commutative law of multiplication. Presented in its simplest form it is nothing more than this : ' five times three is the same as three times five' ; more generally, it appears under...
Σελίδα 91 - IF we define a conic section as "the locus of a point which moves so that its distance from a fixed point bears a constant ratio to its distance from a fixed straight line
Σελίδα 153 - a where p is the perpendicular from the centre on the tangent plane, r the distance from the focus, and A, B the constants of integration.
Σελίδα 7 - A vector is the representative of transference through a given distance, in a given direction.