Solutions of the Cambridge Problems: From 1800 to 1820, Volum 2 |
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Resultat 1-5 av 68
Side xvii
... whence by substituting in the given equation we get , y = 0 for a minimum value at the origin A , ( See Fig . 1 ) . and y = ± indicates two pairs of maximum values PM , α 2 PM ' ; pm , pm ' corresponding to the two values of x . To find ...
... whence by substituting in the given equation we get , y = 0 for a minimum value at the origin A , ( See Fig . 1 ) . and y = ± indicates two pairs of maximum values PM , α 2 PM ' ; pm , pm ' corresponding to the two values of x . To find ...
Side 3
... ( a - x ) . tan . 0 , whence tan . = α 3x α - x And y = ( a - x ) tan . = √ ( a − x ) . ( a — 3x ) = √ a2 - 4ax + 3x2 ) which indicates a conic section . Let y = 0 α Then x a or Take :: CA , and CONSTRUCTION OF CURVES .
... ( a - x ) . tan . 0 , whence tan . = α 3x α - x And y = ( a - x ) tan . = √ ( a − x ) . ( a — 3x ) = √ a2 - 4ax + 3x2 ) which indicates a conic section . Let y = 0 α Then x a or Take :: CA , and CONSTRUCTION OF CURVES .
Side 7
... whence by reduction we get y2 - 2 cos . a . cos . B. ( x 2 - b ) y = f . ( a + x - b . sin . B ) - ß ) — b ) cos . B , which is the general equation of the section of a solid of revolution . ( x - Now , since in the conic sections y2f ...
... whence by reduction we get y2 - 2 cos . a . cos . B. ( x 2 - b ) y = f . ( a + x - b . sin . B ) - ß ) — b ) cos . B , which is the general equation of the section of a solid of revolution . ( x - Now , since in the conic sections y2f ...
Side 71
... lc- — . l . ( 1 − p3 ) = l . ( 1 − p3 ) } whence substituting dy for p , & c . , we easily dx get .. 1 C3 y3 ydy ( y3 - c3 ) } which being integrated ( if possible ) will give the dx = CONSTRUCTION OF CURVES . 71 dy ...
... lc- — . l . ( 1 − p3 ) = l . ( 1 − p3 ) } whence substituting dy for p , & c . , we easily dx get .. 1 C3 y3 ydy ( y3 - c3 ) } which being integrated ( if possible ) will give the dx = CONSTRUCTION OF CURVES . 71 dy ...
Side 73
... Whence as before , x = y2 + x2 ay2 x2 2x .... ( 2 ) x2 + y2 2x Hence y2 = x3 2a -- X .... ( c ) the equation to a cissoid , the diameter of whose generating circle is 2a or the latus rectum of the parabola . The above process will apply ...
... Whence as before , x = y2 + x2 ay2 x2 2x .... ( 2 ) x2 + y2 2x Hence y2 = x3 2a -- X .... ( c ) the equation to a cissoid , the diameter of whose generating circle is 2a or the latus rectum of the parabola . The above process will apply ...
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Solutions of the Cambridge Problems, from 1800 to 1820, Volum 2 John Martin Frederick WRIGHT Uten tilgangsbegrensning - 1836 |
Solutions of the Cambridge Problems: From 1800 to 1820, Volum 2 John Martin Frederick Wright Uten tilgangsbegrensning - 1825 |
Solutions of the Cambridge Problems, from 1800 to 1820, Volum 2 John Martin Frederick Wright Uten tilgangsbegrensning - 1836 |
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abscissa accelerating force altitude angular axes axis base bisected body centre of gravity chord circle co-declination co-ordinates cone curve cycloid cylinder denote density descending diameter distance earth ecliptic ellipse equal equation fluid focus given point gives Hence horizon hyperbola inclination intersection latitude latus rectum length locus logarithmic spiral moving force orbit ordinate orifice oscillation parabola paraboloid parallel perpendicular plane position problem projection Prop question radius ratio right angles right ascension shew sides specific gravity sphere spherical straight line substituting subtangent supposing surface tangent triangle values velocity vers vertex vertical Vince weight whence whole