Elements of Quaternions |
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Page vii
... Triangle OAB , and representing by its length the Double Area of that triangle ; while the Rotation round this Index , from the Multiplier to the Multiplicand , is positive . This right part , or vector part , Vaß , of the product ...
... Triangle OAB , and representing by its length the Double Area of that triangle ; while the Rotation round this Index , from the Multiplier to the Multiplicand , is positive . This right part , or vector part , Vaß , of the product ...
Page xxv
... triangle ABC in a system of four right lines , whereof three are the sides of that triangle , and the fourth is the intersection of the two planes , ABC and DEF . If then we investigate the intersection of this surface ( S1 ) with the ...
... triangle ABC in a system of four right lines , whereof three are the sides of that triangle , and the fourth is the intersection of the two planes , ABC and DEF . If then we investigate the intersection of this surface ( S1 ) with the ...
Page xli
... Triangle ABC = A + B + C − π , ( V1⁄2 ′′ ) what may be called the Spheroidal Excess of that triangle , the total area ( 47 ) of the unit - sphere being represented by eight right angles : with extensions to Geodetic Polygons , and ...
... Triangle ABC = A + B + C − π , ( V1⁄2 ′′ ) what may be called the Spheroidal Excess of that triangle , the total area ( 47 ) of the unit - sphere being represented by eight right angles : with extensions to Geodetic Polygons , and ...
Page 6
... triangle ABC , or of A a quadrilateral ABCD , or of any other D Fig . 10 . B closed polygon , their sum is a null line , aa ; and conversely , CHAP . I. ] FUNDAMENTAL PRINCIPLES - VECTORS . 7 6 [ BOOK I. ELEMENTS OF QUATERNIONS . 296.
... triangle ABC , or of A a quadrilateral ABCD , or of any other D Fig . 10 . B closed polygon , their sum is a null line , aa ; and conversely , CHAP . I. ] FUNDAMENTAL PRINCIPLES - VECTORS . 7 6 [ BOOK I. ELEMENTS OF QUATERNIONS . 296.
Page 7
... , namely , as a triangle with evanescent area ; and we have the equation , as well as A " B " + B " C " + C " A " = 0 , A'B ' + B'C ' + C'A ' = 0 , and AB + BC + CA = 0. ) SECTION 4. - On Coefficients of Vectors . 12. The.
... , namely , as a triangle with evanescent area ; and we have the equation , as well as A " B " + B " C " + C " A " = 0 , A'B ' + B'C ' + C'A ' = 0 , and AB + BC + CA = 0. ) SECTION 4. - On Coefficients of Vectors . 12. 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