Elements of Quaternions |
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... considered as a directed right line , in space of three dimensions . The Second Book introduces a First Con- ception of a Quaternion , considered as the Quotient of two such Vectors . And the Third Book treats of Products and Powers of ...
... considered as a directed right line , in space of three dimensions . The Second Book introduces a First Con- ception of a Quaternion , considered as the Quotient of two such Vectors . And the Third Book treats of Products and Powers of ...
Page iii
... CONSIDERED AS QUOTIENTS OF VECTORS , AND AS INVOLVING ANGULAR RELA- TIONS , . CHAPTER I. • 103-300 FUNDAMENTAL PRINCIPLES RESPECTING QUOTIENTS OF VECTORS , 103-239 Very little , if any , of this Chapter II . i . , should be omitted ...
... CONSIDERED AS QUOTIENTS OF VECTORS , AND AS INVOLVING ANGULAR RELA- TIONS , . CHAPTER I. • 103-300 FUNDAMENTAL PRINCIPLES RESPECTING QUOTIENTS OF VECTORS , 103-239 Very little , if any , of this Chapter II . i . , should be omitted ...
Page vi
... considered in the foregoing Section , · SECTION 7. - On the Reciprocal of a Vector , and on Har- monic Means of Vectors ; with Remarks on the Anhar- monic Quaternion of a Group of Four Points , and on Conditions of Concircularity , In ...
... considered in the foregoing Section , · SECTION 7. - On the Reciprocal of a Vector , and on Har- monic Means of Vectors ; with Remarks on the Anhar- monic Quaternion of a Group of Four Points , and on Conditions of Concircularity , In ...
Page viii
... considered ( II . i . 10 ) , but are regarded now as denoting Three Rectangular Vector - Units , while the three scalars x , y , z are simply rectangular co - ordinates ; from the known theory of which last , illustrations of results ...
... considered ( II . i . 10 ) , but are regarded now as denoting Three Rectangular Vector - Units , while the three scalars x , y , z are simply rectangular co - ordinates ; from the known theory of which last , illustrations of results ...
Page xlii
... considered in Se- ries 412 , which are at the same time the centres of the two osculating spheres , of which the curvatures are ( algebraically ) the greatest and least and v is the angle at which the curve here considered crosses the ...
... considered in Se- ries 412 , which are at the same time the centres of the two osculating spheres , of which the curvatures are ( algebraically ) the greatest and least and v is the angle at which the curve here considered crosses the ...
Contents
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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