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 páginas |
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Página 1
... circle CEF . Let the circles intersect in C. Join AC , BC . Then AC , BC being radii of the two circles are each equal to 2AB ; and therefore ABC is the triangle required . 1850 . ( A ) . The opposite sides and angles of parallelograms ...
... circle CEF . Let the circles intersect in C. Join AC , BC . Then AC , BC being radii of the two circles are each equal to 2AB ; and therefore ABC is the triangle required . 1850 . ( A ) . The opposite sides and angles of parallelograms ...
Página 5
... circle AHD . Pro- duce CB to H. It is then proved that square on BH rectangle AC . We thus have suggested the following solution of ( B ) : Let AB be the given side of the rectangle : draw BH at right angles to AB , equal to a side of ...
... circle AHD . Pro- duce CB to H. It is then proved that square on BH rectangle AC . We thus have suggested the following solution of ( B ) : Let AB be the given side of the rectangle : draw BH at right angles to AB , equal to a side of ...
Página 6
... circle on all equal straight lines in the circle are equal to one another . Therefore a circle may be described through the extremities of all these perpendiculars , having its centre at the centre of the given circle : and since each ...
... circle on all equal straight lines in the circle are equal to one another . Therefore a circle may be described through the extremities of all these perpendiculars , having its centre at the centre of the given circle : and since each ...
Página 7
... circle , the angle in a semicircle is a right angle . ( III . 31. ) ( B ) . The greatest rectangle that can be inscribed in a circle is a square . Here ( B ) is a direct application of the fact asserted in ( A ) . Let ABCD ( fig . 9 ) ...
... circle , the angle in a semicircle is a right angle . ( III . 31. ) ( B ) . The greatest rectangle that can be inscribed in a circle is a square . Here ( B ) is a direct application of the fact asserted in ( A ) . Let ABCD ( fig . 9 ) ...
Página 8
... circle is AGCH , which is evidently a square . 1850. ( 4 ) . Cut off a segment from a given circle which shall contain an angle equal to a given rectilineal angle . ( B ) . Divide a circle into two segments , such that the angle in one ...
... circle is AGCH , which is evidently a square . 1850. ( 4 ) . Cut off a segment from a given circle which shall contain an angle equal to a given rectilineal angle . ( B ) . Divide a circle into two segments , such that the angle in one ...
Otras ediciones - Ver todas
The Principles of the Solution of the Senate-House 'Riders: Exemplified by ... Francis J. Jameson Sin vista previa disponible - 2018 |
The Principles of the Solution of the Senate-House 'Riders: Exemplified by ... Francis J. Jameson Sin vista previa disponible - 2015 |
Términos y frases comunes
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
Pasajes populares
Página 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.
Página 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.
Página 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.
Página 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...
Página 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.