Elements of Quaternions |
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Page xiii
... 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 a surface . Some of the theorems or constructions may perhaps ...
... 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 a surface . Some of the theorems or constructions may perhaps ...
Page xiv
... curvature , we have generally , Vector of Curvature = ( p − x ) ́1 = · V dUdp 1 d2p Τάρ do dp = & c .; ( S ) and if the arc ( s ) of the curve be made the independent variable , then Vector of Curvature = p " D , 2p = d2p d82 ( S ...
... curvature , we have generally , Vector of Curvature = ( p − x ) ́1 = · V dUdp 1 d2p Τάρ do dp = & c .; ( S ) and if the arc ( s ) of the curve be made the independent variable , then Vector of Curvature = p " D , 2p = d2p d82 ( S ...
Page xv
... Curvature ; this radius r may be either positive or ne- gatire ( whereas the radius r of first curvature is always treated as positive ) , and its reciprocal r1 may be thus expressed ( pp . 563 , 559 ) , Second Curvature * = r1 = S d3p ...
... Curvature ; this radius r may be either positive or ne- gatire ( whereas the radius r of first curvature is always treated as positive ) , and its reciprocal r1 may be thus expressed ( pp . 563 , 559 ) , Second Curvature * = r1 = S d3p ...
Page xvi
... curvatures be constant , the proposed curve is a geodetic on a cylinder : new proof that if each curvature ( r , r1 ) be constant , the cylinder is right , and therefore the curve a helix , Pages . . . 559-578 ARTICLE 398. - Properties ...
... curvatures be constant , the proposed curve is a geodetic on a cylinder : new proof that if each curvature ( r , r1 ) be constant , the cylinder is right , and therefore the curve a helix , Pages . . . 559-578 ARTICLE 398. - Properties ...
Page xvii
... curvature , there is drawn a tangent plane to the sphere , which occulates ( 395 ) to the curve at that point ; and that then the elope of all these planes is determined , which envelope ( for reasons afterwards more fully explained ) ...
... curvature , there is drawn a tangent plane to the sphere , which occulates ( 395 ) to the curve at that point ; and that then the elope of all these planes is determined , which envelope ( for reasons afterwards more fully explained ) ...
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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