An Elementary Treatise on QuaternionsClarendon Press, 1873 - 296 pagina's |
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Pagina 12
... constant . ( e . ) , To find the centre of inertia of any system . If OA = a , OB = a1 , be the vector sides of any triangle , the vector from the vertex dividing the base AB in C so that BC : CA :: m : m1 is ma + 12 [ 31 . QUATERNIONS .
... constant . ( e . ) , To find the centre of inertia of any system . If OA = a , OB = a1 , be the vector sides of any triangle , the vector from the vertex dividing the base AB in C so that BC : CA :: m : m1 is ma + 12 [ 31 . QUATERNIONS .
Pagina 13
... centre of inertia B = Σ ( ma ) Σ ( m ) This may be written Ση ( α - β ) = 0 . Now a - ẞ is the vector of m , with respect to the centre of inertia . Hence the theorem , If the vector of each element of a mass , drawn from the centre of ...
... centre of inertia B = Σ ( ma ) Σ ( m ) This may be written Ση ( α - β ) = 0 . Now a - ẞ is the vector of m , with respect to the centre of inertia . Hence the theorem , If the vector of each element of a mass , drawn from the centre of ...
Pagina 20
... centre ) of a point in a hyperbola be one diagonal of a parallelogram , two of whose sides coincide with the asymptotes , the other diagonal is parallel to the tangent at the point . 41. ] Let us reverse this question , and seek the ...
... centre ) of a point in a hyperbola be one diagonal of a parallelogram , two of whose sides coincide with the asymptotes , the other diagonal is parallel to the tangent at the point . 41. ] Let us reverse this question , and seek the ...
Pagina 23
... centre with their point of intersection bisects the lines joining the points where the tangents meet the asymptotes : and the tangent at the point where it meets the curves bisects the intercepts of the asymptotes . 9. Any two tangents ...
... centre with their point of intersection bisects the lines joining the points where the tangents meet the asymptotes : and the tangent at the point where it meets the curves bisects the intercepts of the asymptotes . 9. Any two tangents ...
Pagina 29
... centre of the unit - sphere . Now Hence ос or qr = OD a great circle . rOD = OB , and qOB = OC , qr OD = = OC , , and may therefore be represented by the arc DC of But rq is easily seen to be represented by the arc E. For whence qOA ...
... centre of the unit - sphere . Now Hence ос or qr = OD a great circle . rOD = OB , and qOB = OC , qr OD = = OC , , and may therefore be represented by the arc DC of But rq is easily seen to be represented by the arc E. For whence qOA ...
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Veelvoorkomende woorden en zinsdelen
a₁ axes axis Cartesian centre of inertia Chapter circle condition cone conjugate cöordinates coplanar curvature curve developable surface differential direction drawn easily Eliminating ellipsoid envelop equal evidently expression extremity Find the equation Find the locus formula given equation given lines given point gives Hamilton Hence hodograph integral intersection LAOB last section length linear and vector magnetism normal obviously once operator origin osculating plane P₁ parabola parallel pass perpendicular properties prove quaternion radius represents result right angles rotation S.aßy Saß scalar scalar equations second order shew solution sphere spherical conic straight line suppose surface surface of revolution tangent plane tensor tetrahedron theorem three vectors triangle unit-vectors Vaß vector function vector perpendicular versor write written Τρ φρ
Populaire passages
Pagina 299 - SCRIPTURES, &c. The Cambridge Paragraph Bible of the Authorized English Version, with the Text revised by a Collation of its Early and other Principal Editions...
Pagina 298 - VILLEMAIN, with a Biographical Sketch of the Author, a Selection of Poems on Greece, and Notes Historical and Philological. By the same Editor, is.
Pagina 299 - Students of the Bible should be particularly grateful to (the Cambridge University Press) for having produced, with the able assistance of Dr Scrivener, a complete critical edition of the Authorized Version of the English Bible, an edition such as, to use the words of the Editor, 'would have been executed long ago had this version been nothing more than the greatest and best known of English classics.
Pagina 138 - The locus of the middle points of a system of parallel chords in a parabola is called a diameter.
Pagina 11 - The perpendicular bisectors of the sides of a triangle meet in a point which is equidistant from the vertices of the triangle. Let the -l. bisectors EE' and DD
Pagina 299 - Mr. Scrivener has carefully collated the text of our modern Bibles with that of the first edition of 1611, restoring the original reading in most places, and marking every place where an obvious correction has been made ; he has made the spelling as uniform as possible ; revised the punctuation (punctuation, as those who cry out for the Bible without note or comment should remember, is a continuous commentary on the text); carried out consistently the plan of marking' with italics all words not found...