Introduction to quaternions, by P. Kelland and P.G. Tait1873 |
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Σελίδα 2
... satisfied ; and accord- ingly the master goes on to say : " If I multiply by more than one , the thing is increased ; if I take it but once , it is not changed ; and if I take it less than once , it cannot be so much as it was before ...
... satisfied ; and accord- ingly the master goes on to say : " If I multiply by more than one , the thing is increased ; if I take it but once , it is not changed ; and if I take it less than once , it cannot be so much as it was before ...
Σελίδα 22
... satisfy the con- dition required , the proposition is proved generally ( Art . 11 ) . 13. Conversely , if a , B , y are coinitial coplanar vectors , and if both aa + bB + cy = 0 and a + b + c = 0 , then do a , ẞ , y terminate in a ...
... satisfy the con- dition required , the proposition is proved generally ( Art . 11 ) . 13. Conversely , if a , B , y are coinitial coplanar vectors , and if both aa + bB + cy = 0 and a + b + c = 0 , then do a , ẞ , y terminate in a ...
Σελίδα 75
... satisfied by the values of p to both points of sec- tion ; and being the equation of a straight line ( 32. 3 ) is the equation of the line joining the points of section of circle D with circle A - call it line 1 , and so of the others ...
... satisfied by the values of p to both points of sec- tion ; and being the equation of a straight line ( 32. 3 ) is the equation of the line joining the points of section of circle D with circle A - call it line 1 , and so of the others ...
Σελίδα 79
... satisfied for both points of contact , and since it is the equation of a straight line ( 32. 3 ) it must be satis- fied for every point in the straight line which passes through those points : it is therefore the equation of the chord ...
... satisfied for both points of contact , and since it is the equation of a straight line ( 32. 3 ) it must be satis- fied for every point in the straight line which passes through those points : it is therefore the equation of the chord ...
Σελίδα 86
... satisfied by σ = a2 8 , c2 i . e . the planes all pass through a point G in CE , such that CG = a2CE , or CE . CG a3 ... satisfy both equations , and therefore their difference 2S ( B− y ) p = c −b , which , being the third equation ...
... satisfied by σ = a2 8 , c2 i . e . the planes all pass through a point G in CE , such that CG = a2CE , or CE . CG a3 ... satisfy both equations , and therefore their difference 2S ( B− y ) p = c −b , which , being the third equation ...
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
addition apply assume aẞy axes axis becomes bisects centre chord circle condition cone conjugate constant corresponding diagonals diameter direction distance drawn ellipse ellipsoid equal equation evident example expression extremities fixed given plane given point gives Hence intersection joins meet middle points multiplication notation obvious operating opposite origin parabola parallel parallelogram pass perpendicular prove Quaternions represented respectively Retaining right angles rotation Saß satisfied scalar shews sides Similarly simple sphere squares straight line strain surface tangent plane tion triangle unit vectors values Vaß vector perpendicular whence write written yẞ αβγ
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