Elements of Quaternions |
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Page ii
... Anharmonic Co - ordinates and Equations of Points and Lines in one Plane , SECTION 5. - On Plane Geometrical Nets , resumed , SECTION 6. - On Anharmonic Equations and Vector Ex- pressions , for Curves in a given Plane , . . 20-24 24-32 ...
... Anharmonic Co - ordinates and Equations of Points and Lines in one Plane , SECTION 5. - On Plane Geometrical Nets , resumed , SECTION 6. - On Anharmonic Equations and Vector Ex- pressions , for Curves in a given Plane , . . 20-24 24-32 ...
Page iii
... anharmonic generation of a ruled hy- perboloid ( or paraboloid ) is employed to illustrate anharmonic equa- tions ; and ( among other examples ) certain cones , of the second and third orders , have their vector equations assigned . In ...
... anharmonic generation of a ruled hy- perboloid ( or paraboloid ) is employed to illustrate anharmonic equa- tions ; and ( among other examples ) certain cones , of the second and third orders , have their vector equations assigned . In ...
Page 15
... anharmonic function , or anharmonic quotient , or simply the anharmonic of the group , A , B , C , D : we shall have , in the present case , the equation , ( ACBC ' ) = AC AC ' yx ' : CB C B xy 26. When the anharmonic quotient becomes ...
... anharmonic function , or anharmonic quotient , or simply the anharmonic of the group , A , B , C , D : we shall have , in the present case , the equation , ( ACBC ' ) = AC AC ' yx ' : CB C B xy 26. When the anharmonic quotient becomes ...
Page 16
... anharmonic quotient m = yx ' xy is any constant scalar , then in another known and modern phraseology , the points c and c ' will form , on the indefinite line AB , two homographic divisions , of which A and B are still the double ...
... anharmonic quotient m = yx ' xy is any constant scalar , then in another known and modern phraseology , the points c and c ' will form , on the indefinite line AB , two homographic divisions , of which A and B are still the double ...
Page 24
... anharmonic quotients , and the introduction of a certain system of anhar- monic co - ordinates , for points and lines in one plane , to which we shall next proceed : reserving , for a subsequent Chapter , any applications of the same ...
... anharmonic quotients , and the introduction of a certain system of anhar- monic co - ordinates , for points and lines in one plane , to which we shall next proceed : reserving , for a subsequent Chapter , any applications of the same ...
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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