Elements of Quaternions |
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Page iv
... -162 The student ought to make himself familiar with these laws , which are all included in the Fundamental Formula , i2 = ja = k2 = ijk = − 1 . ( A ) CONTENTS . In fact , a QUATERNION may be symbolically iv CONTENTS .
... -162 The student ought to make himself familiar with these laws , which are all included in the Fundamental Formula , i2 = ja = k2 = ijk = − 1 . ( A ) CONTENTS . In fact , a QUATERNION may be symbolically iv CONTENTS .
Page v
Sir William Rowan Hamilton William Edwin Hamilton. CONTENTS . In fact , a QUATERNION may be symbolically defined to be a Quadrino- misi Expression of the form , q = w + ix + jy + kz , ( B ) in which w , z , y , z are four scalars , or ...
Sir William Rowan Hamilton William Edwin Hamilton. CONTENTS . In fact , a QUATERNION may be symbolically defined to be a Quadrino- misi Expression of the form , q = w + ix + jy + kz , ( B ) in which w , z , y , z are four scalars , or ...
Page xvi
... fact , while tan H is represented by the expressions ( V ' ) , whereof one is - tan P , tan J admits ( with many transformations ) of the following analogous expression ( p . 581 ) , tan JR - tan P ; ( X ) CONTENTS . where E ' depends ...
... fact , while tan H is represented by the expressions ( V ' ) , whereof one is - tan P , tan J admits ( with many transformations ) of the following analogous expression ( p . 581 ) , tan JR - tan P ; ( X ) CONTENTS . where E ' depends ...
Page xxxix
... fact it is easy to see otherwise ( comp . p . 645 ) , that v2 || 7 || v , and Spr2 = 1 Spv , whence v2 v as before . = ( z ) . More fully , the two sheets of the reciprocal ( j ) of the surface of centres may have their separate vector ...
... fact it is easy to see otherwise ( comp . p . 645 ) , that v2 || 7 || v , and Spr2 = 1 Spv , whence v2 v as before . = ( z ) . More fully , the two sheets of the reciprocal ( j ) of the surface of centres may have their separate vector ...
Page xlviii
... fact , it is shown ( p . 720 ) , that for any law of central force , the radius of curvature of the hodograph is equal to the force , multi- plied into the square of the distance , and divided by the doubled areal velocity ; or by the ...
... fact , it is shown ( p . 720 ) , that for any law of central force , the radius of curvature of the hodograph is equal to the force , multi- plied into the square of the distance , and divided by the doubled areal velocity ; or by the ...
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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