Introduction to quaternions, by P. Kelland and P.G. Tait1873 |
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Σελίδα 58
... origin 0 ; then AP is a vector parallel to ß and gives = xß , say , OP = 0A + AP = a + xß ( 1 ) p = as the equation of the line . 2. Another form in which the equation of a straight line may be expressed is this : let OA = a , OB = ẞ be ...
... origin 0 ; then AP is a vector parallel to ß and gives = xß , say , OP = 0A + AP = a + xß ( 1 ) p = as the equation of the line . 2. Another form in which the equation of a straight line may be expressed is this : let OA = a , OB = ẞ be ...
Σελίδα 60
... origin on a given line . Equation ( 1 ) of Art . 32 is If now we get or p = a + xß . p = OD = 8 ; SS2 = Ssa , - OD2 = Sda ; .. OD = S & a Sa US , OD US being the unit vector perpendicular to the line . COR . The same result is true of a ...
... origin on a given line . Equation ( 1 ) of Art . 32 is If now we get or p = a + xß . p = OD = 8 ; SS2 = Ssa , - OD2 = Sda ; .. OD = S & a Sa US , OD US being the unit vector perpendicular to the line . COR . The same result is true of a ...
Σελίδα 61
... origin = S. aẞy . ( Vaẞ + Vßy + Vya ) ̄1 . 6. To find the equation of a plane which shall pass through a given point and be parallel to each of two given straight lines . γ Let be the vector to the given point , ART . 34. ] THE STRAIGHT ...
... origin = S. aẞy . ( Vaẞ + Vßy + Vya ) ̄1 . 6. To find the equation of a plane which shall pass through a given point and be parallel to each of two given straight lines . γ Let be the vector to the given point , ART . 34. ] THE STRAIGHT ...
Σελίδα 62
... equations ( 2 ) and ( 3 ) is the condition necessary and sufficient for coplanarity . 9. To find the line of intersection of two planes through the origin . Let Sap = 0 , Sẞp = 0 be the 62 [ CHAP . IV : QUATERNIONS .
... equations ( 2 ) and ( 3 ) is the condition necessary and sufficient for coplanarity . 9. To find the line of intersection of two planes through the origin . Let Sap = 0 , Sẞp = 0 be the 62 [ CHAP . IV : QUATERNIONS .
Σελίδα 64
... origin . Here the axes are given , so that i , j , k are known unit vectors . Let ai , bj , ck be the portions cut off from the axes by a plane , the perpendicular on which from the origin is p . Then p - ai is perpendicular to p .. Sp ...
... origin . Here the axes are given , so that i , j , k are known unit vectors . Let ai , bj , ck be the portions cut off from the axes by a plane , the perpendicular on which from the origin is p . Then p - ai is perpendicular to p .. Sp ...
Άλλες εκδόσεις - Προβολή όλων
Introduction to Quaternions, by P. Kelland and P. G. Tait Philip Kelland Δεν υπάρχει διαθέσιμη προεπισκόπηση - 2013 |
Introduction to Quaternions, by P. Kelland and P.G. Tait Philip Kelland Δεν υπάρχει διαθέσιμη προεπισκόπηση - 2018 |
Introduction to Quaternions, by P. Kelland and P. G. Tait Philip Kelland Δεν υπάρχει διαθέσιμη προεπισκόπηση - 2015 |
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 plane given point given straight lines gives Hence hyperbola latus rectum line of intersection line which joins mean point meet middle points multiplication notation nẞ operating P₁ parabola parallelepiped parallelogram prove quadrilateral Quaternions right angles rotation Sapa Saß scalar second order semi-diameters shews sides Similarly simple shear Spop 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 φρ
Δημοφιλή αποσπάσματα
Σελίδα 8 - Any two sides of a triangle are together greater than the third side.
Σελίδα 52 - Thus, for" example, he to whom the geometrical proposition, that the angles of a triangle are together equal to two right angles...
Σελίδα 89 - A point moves so that the sum of the squares of its distances from the points (0, 0), (1, 0) is constant.
Σελίδα 40 - To express the cosine of an angle of a triangle in terms of the sides. Let ABC be a triangle ; and retaining the usual notation of Trigonometry, let CB = a, CA=ß; then (vector AB)' =(a- ß)' = a'-2Saß + ß
Σελίδα 68 - Ex. 5. To find the locus of a point such that the ratio of its distances from a given point and a given straight line is constant — all in one plane. Let S be the given point, DQ the given straight line, SP = ePQ the given relation. Let vector SD = a,SP = p, DQ = yy, y being the unit vector along DQ, then eT(PQ), 5—2 gives p~ = e'PQ', where PQ is a vector, = i'(a»)" = eVa'. = a+yy; . : Sap + xa' = a', for Say = 0; and a;V = (a...
Σελίδα 72 - P is a surfaco of the second order. 3. Prove that the section of this surface by a plane perpendicular to the lin.e to which the generating lines are drawn perpendicular is a circle. 4. Prove that the locus of a point whose distances from two given straight lines have a constant ratio is a surface of the second order. 5. A straight line moves parallel to a fixed plane and is terminated by two given straight lines not in one plane ; find the locus of the point which divides the line into parts which...
Σελίδα 9 - 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 90 - 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 32 - G : shew that FG is parallel to CD. 346. From any point in the base of a triangle straight lines are drawn parallel to the sides : shew that the intersection of the diagonals of every parallelogram so formed lies in a certain straight line. 347. In a triangle ABC a straight...
Σελίδα 90 - IP 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