The Principles of the Solution of the Senate-house 'riders,' Exemplified by the Solution of Those Proposed in the Earlier Parts of the Examinations of the Years 1848-1851 |
From inside the book
Results 1-5 of 13
Page 6
... extremities of all these perpendiculars , having its centre at the centre of the given circle : and since each of the equal straight lines is thus drawn through the extremity of a diameter at right angles to it , each will be a tangent ...
... extremities of all these perpendiculars , having its centre at the centre of the given circle : and since each of the equal straight lines is thus drawn through the extremity of a diameter at right angles to it , each will be a tangent ...
Page 14
... extremities of their latera- recta will all meet the minor axis in the same point . Let SL ( fig . 18 ) be the semi - latus - rectum of one of the ellipses , U the point where the tangent at L meets the minor axis . By ( 4 ) , But ...
... extremities of their latera- recta will all meet the minor axis in the same point . Let SL ( fig . 18 ) be the semi - latus - rectum of one of the ellipses , U the point where the tangent at L meets the minor axis . By ( 4 ) , But ...
Page 16
... extremities of conjugate diameters CP , CD ; t ̧tëtât another parallelogram circumscribing the ellipse . Draw PF perpendicular to DCD ' . Then area of TTTT = 2PF.DD ' , area of tttt 2PF.dd ' . 1234 1 2 3 4 Now DD ' is the least possible ...
... extremities of conjugate diameters CP , CD ; t ̧tëtât another parallelogram circumscribing the ellipse . Draw PF perpendicular to DCD ' . Then area of TTTT = 2PF.DD ' , area of tttt 2PF.dd ' . 1234 1 2 3 4 Now DD ' is the least possible ...
Page 46
... extremity A , which is fixed ; CD is another rod equal to 2AB , and attached at its middle point to the extremity B of the former , so as to turn freely about this point ; a given force acts at C in the direction CA : find the force ...
... extremity A , which is fixed ; CD is another rod equal to 2AB , and attached at its middle point to the extremity B of the former , so as to turn freely about this point ; a given force acts at C in the direction CA : find the force ...
Page 65
... extremity , we may consider the other extremity as moving very nearly in a cycloid the radius of whose generating circle is 2 ; and therefore time of oscillation = T Hence we can apply this formula to ( B ) . √ Since I is the length of ...
... extremity , we may consider the other extremity as moving very nearly in a cycloid the radius of whose generating circle is 2 ; and therefore time of oscillation = T Hence we can apply this formula to ( B ) . √ Since I is the length of ...
Other editions - View all
The Principles of the Solution of the Senate-House 'Riders: Exemplified by ... Francis J. Jameson No preview available - 2018 |
The Principles of the Solution of the Senate-House 'Riders: Exemplified by ... Francis J. Jameson No preview available - 2015 |
Common terms and phrases
AC² AN.NM Arithmetic arithmetical progression axis bisects body C₁ Cambridge centre of gravity chord CHURCHILL BABINGTON circle cloth cone Conic Sections conjugate hyperbola constant curvature curve cycloid describe diameter direction directrix distance drawn Edition ellipse equations equilibrium Fellow of St fluid focus geometrical given point Hence horizontal hyperbola inches inclined inscribed John's College joining latus-rectum least common multiple Lemma length locus meet mirror move number of seconds oscillation parabola parallel parallelogram particle perpendicular plane polygon pressure prop proportional proposition prove pullies quadrilateral quantity radius ratio rays rectangle refraction right angles sewed shew sides specific gravity spherical square straight line string surface tan² tangent triangle ABC Trinity College tube V₁ vary vertex vertical W₁ weight
Popular passages
Page 4 - To divide a given straight line into two parts, so that the rectangle contained by the whole and one of the parts, shall be equal to the square of the other part.
Page 6 - The angle at the centre of a circle is double of the angle at the circumference upon the same base, that is, upon the same part of the circumference.
Page 11 - AB is a diameter, and P any point in the circumference of a circle; AP and BP are joined and produced if necessary ; if from any point C of AB, a perpendicular be drawn to AB meeting AP and .BP in points D and E respectively, and the circumference of the circle in a point F, shew that CD is a third proportional of CE and CF.
Page 9 - IF the angle of a triangle be divided into two equal angles, by a straight line which also cuts the base; the segments of the base shall have the same ratio which the other sides of the triangle have to one another...
Page 4 - In any right-angled triangle, the square which is described upon the side subtending the right angle, is equal to the squares described upon the sides which contain the right angle.