Elements of Quaternions |
From inside the book
Results 1-5 of 100
Page xiii
... Osculating Planes , and Absolute Normals , to Curves of Double Curvature , . . . 511-515 SECTION 5. - On Geodetic Lines , and Families of Surfaces , 515–531 In these Sections , dp usually denotes a tangent to a curve , and v a normal to ...
... Osculating Planes , and Absolute Normals , to Curves of Double Curvature , . . . 511-515 SECTION 5. - On Geodetic Lines , and Families of Surfaces , 515–531 In these Sections , dp usually denotes a tangent to a curve , and v a normal to ...
Page xiv
... Osculating Circle defined , as the limit of a circle , which touches a given curve ( plane or of double curvature ) at a given point P , and cuts the curve at a near point a ( see Fig . 77 , p . 511 ) . Deduction and interpretation of ...
... Osculating Circle defined , as the limit of a circle , which touches a given curve ( plane or of double curvature ) at a given point P , and cuts the curve at a near point a ( see Fig . 77 , p . 511 ) . Deduction and interpretation of ...
Page xv
... osculating plane ; general theory of manant lines and planes , vector of rotation , axis of displacement , oscu ... osculating sphere : and if p and P denote the linear and angular elevations , of the centre ( s ) of this sphere above ...
... osculating plane ; general theory of manant lines and planes , vector of rotation , axis of displacement , oscu ... osculating sphere : and if p and P denote the linear and angular elevations , of the centre ( s ) of this sphere above ...
Page xvi
... osculating plane . De- viation of curve , at any near point q , from the osculating circle at P , decomposed ( p . 566 ) into two rectangular deviations , from osculating helix and parabola . Additional formulæ ( p . 576 ) , for the ...
... osculating plane . De- viation of curve , at any near point q , from the osculating circle at P , decomposed ( p . 566 ) into two rectangular deviations , from osculating helix and parabola . Additional formulæ ( p . 576 ) , for the ...
Page xvii
... Osculating Sphere ; and then it satisfies , among others , the equations ( pp . 579 , 581 , comp . ( V ) ) , Ø = V ... osculating circles ; but the latter requires the consideration of two consecu- tive osculating spheres , and therefore ...
... Osculating Sphere ; and then it satisfies , among others , the equations ( pp . 579 , 581 , comp . ( V ) ) , Ø = V ... osculating circles ; but the latter requires the consideration of two consecu- tive osculating spheres , and therefore ...
Contents
xxxix | |
xlv | |
lii | |
1 | |
3 | |
7 | |
8 | |
9 | |
12 | |
14 | |
17 | |
21 | |
37 | |
55 | |
60 | |
61 | |
67 | |
83 | |
86 | |
89 | |
92 | |
95 | |
143 | |
206 | |
226 | |
227 | |
263 | |
269 | |
271 | |
289 | |
307 | |
315 | |
321 | |
345 | |
347 | |
354 | |
371 | |
379 | |
387 | |
389 | |
391 | |
411 | |
418 | |
427 | |
435 | |
453 | |
483 | |
495 | |
501 | |
504 | |
569 | |
574 | |
575 | |
581 | |
585 | |
591 | |
593 | |
595 | |
598 | |
601 | |
604 | |
621 | |
629 | |
634 | |
641 | |
642 | |
649 | |
666 | |
669 | |
671 | |
674 | |
676 | |
681 | |
686 | |
689 | |
690 | |
694 | |
700 | |
705 | |
706 | |
709 | |
713 | |
719 | |
726 | |
729 | |
735 | |
736 | |
738 | |
742 | |
757 | |
761 | |
Other editions - View all
Common terms and phrases
ABCD algebra angle anharmonic axis centre CHAP circle coefficients collinear comp Compare the Note complanar cone conic conjugate considered construction curvature curve cyclic deduced denote derived differential diplanar direction ellipsoid equal equation expression formula four fourth proportional function geometrical given plane given points harmonic conjugate imaginary interpreted intersection length line oa linear locus multiplication negative notation osculating osculating circle osculating plane P₁ parallelogram perpendicular positive quadratic quadrilateral quinary radius reciprocal relative direction represented right line right quaternions right quotient right versors roots rotation round scalar SECTION sides sphere spherical spherical angle sub-articles supposed surface symbol tangent tensor ternion theorem tion triangle ABC twisted cubic variable vector VIII whence whereof write