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 1848-1851Macmillan & Company, 1851 - 116 σελίδες |
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Σελίδα 13
... focus , meets it in the tangent at the vertex . ( B ) . If PM be the ordinate at P , and T the intersection of the tangent at P with the axis , TP.TY TM.TS. Since , by ( 4 ) , SYT ( fig . 15 ) is a right angle , the triangles STY , PTM ...
... focus , meets it in the tangent at the vertex . ( B ) . If PM be the ordinate at P , and T the intersection of the tangent at P with the axis , TP.TY TM.TS. Since , by ( 4 ) , SYT ( fig . 15 ) is a right angle , the triangles STY , PTM ...
Σελίδα 15
... focus H remain fixed . For , if C and therefore S move off to an infinite distance , PS will become parallel to A'A . Hence the tangent ZPY , which always makes equal angles with HP and PS , will in this case make equal angles with HP ...
... focus H remain fixed . For , if C and therefore S move off to an infinite distance , PS will become parallel to A'A . Hence the tangent ZPY , which always makes equal angles with HP and PS , will in this case make equal angles with HP ...
Σελίδα 16
... focus is the tangent at the vertex . 1848. ( A ) . In an ellipse the sum of the squares of any two conjugate diameters is invariable . ( B ) . When is the square of their sum least ? 2 ( CP + CD ) = CP * + CD + 2CP.CD , ( fig . 20 ) ...
... focus is the tangent at the vertex . 1848. ( A ) . In an ellipse the sum of the squares of any two conjugate diameters is invariable . ( B ) . When is the square of their sum least ? 2 ( CP + CD ) = CP * + CD + 2CP.CD , ( fig . 20 ) ...
Σελίδα 19
... focus are severally equal to 4SP . ( B ) . If the circle of curvature at the point P intersect the parabola in another point R , and RQ , drawn parallel to the axis , meet the circle in Q , shew that PQ is the chord of curvature through ...
... focus are severally equal to 4SP . ( B ) . If the circle of curvature at the point P intersect the parabola in another point R , and RQ , drawn parallel to the axis , meet the circle in Q , shew that PQ is the chord of curvature through ...
Σελίδα 20
... focus . * 1850 . ( A ) . Find the diameter of curvature at any point of an ellipse . ( B ) . If an ellipse , a parabola , and a hyperbola have a common tangent and the same curvature at the vertex , the ellipse will lie entirely within ...
... focus . * 1850 . ( A ) . Find the diameter of curvature at any point of an ellipse . ( B ) . If an ellipse , a parabola , and a hyperbola have a common tangent and the same curvature at the vertex , the ellipse will lie entirely within ...
Άλλες εκδόσεις - Προβολή όλων
The Principles of the Solution of the Senate-House 'Riders: Exemplified by ... Francis J. Jameson Δεν υπάρχει διαθέσιμη προεπισκόπηση - 2018 |
The Principles of the Solution of the Senate-House 'Riders: Exemplified by ... Francis J. Jameson Δεν υπάρχει διαθέσιμη προεπισκόπηση - 2015 |
Συχνά εμφανιζόμενοι όροι και φράσεις
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
Δημοφιλή αποσπάσματα
Σελίδα 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.
Σελίδα 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.
Σελίδα 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.
Σελίδα 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...
Σελίδα 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.