Solutions of the Cambridge Senate-house Problems and Riders for the Year 1875Sir George Greenhill Macmillan and Company, 1876 - 236 páginas |
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Página 1
... drawn three parallel straight lines meeting B'C ' , C'A ' , A'B ' in a , b , c respectively ; prove that the triangle abc is half the triangle ABC and that be passes through A , ca through B , ab through C. For ( fig . 1 ) Δ △ ABa + ...
... drawn three parallel straight lines meeting B'C ' , C'A ' , A'B ' in a , b , c respectively ; prove that the triangle abc is half the triangle ABC and that be passes through A , ca through B , ab through C. For ( fig . 1 ) Δ △ ABa + ...
Página 2
... drawn from O and P to the sides of the quadrilateral lie on a fixed circle , the centre of which is at the middle point of OP . Let Q ( fig . 2 ) be the middle point of OP ; a , b , c , d the feet of the perpendiculars from P on AB , BC ...
... drawn from O and P to the sides of the quadrilateral lie on a fixed circle , the centre of which is at the middle point of OP . Let Q ( fig . 2 ) be the middle point of OP ; a , b , c , d the feet of the perpendiculars from P on AB , BC ...
Página 3
... drawn through the middle points of the sides of this triangle will intercept portions of the equal sides such that a regular pentagon can be inscribed in the circle having these portions as two of its sides . If D , E , F ( fig . 4 ) be ...
... drawn through the middle points of the sides of this triangle will intercept portions of the equal sides such that a regular pentagon can be inscribed in the circle having these portions as two of its sides . If D , E , F ( fig . 4 ) be ...
Página 4
... drawn meeting two fixed lines OD , OE in B and C respectively , and on it a point P be taken such that AC.AP = AB2 ; prove that the locus of P is a parabola which passes through A and O and has its axis parallel to OD 4 [ Jan. 4 ...
... drawn meeting two fixed lines OD , OE in B and C respectively , and on it a point P be taken such that AC.AP = AB2 ; prove that the locus of P is a parabola which passes through A and O and has its axis parallel to OD 4 [ Jan. 4 ...
Página 5
... draw PM parallel to OE to meet AF in M. By similar triangles PM OF : AP : AB :: AP : AC :: AM : AF ; therefore the ... drawn through N and T , prove that it is cut at right angles by the auxiliary circle of the ellipse . Let the circle ...
... draw PM parallel to OE to meet AF in M. By similar triangles PM OF : AP : AB :: AP : AC :: AM : AF ; therefore the ... drawn through N and T , prove that it is cut at right angles by the auxiliary circle of the ellipse . Let the circle ...
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Solutions of the Cambridge Senate-House Problems and Riders for the Year 1875 George Greenhill Sin vista previa disponible - 2016 |
Términos y frases comunes
apse line Arabic numbers axes axis Cambridge centre of inertia circle coefficient conic section coordinates cos² cose cosec Crown 8vo curvature curve density diameter differential equation distance dx dy dz dx² Edition electricity ELEMENTARY TREATISE ellipse ellipsoid equal equations of motion equilibrium Extra fcap Fellow of St fixed fluid force given GREEK harmonic Hence hyperbola hypocycloid integral intersect J. P. MAHAFFY John's College late Fellow LATIN length lines of curvature liquid lunar precession magnets middle points normal numerous Illustrations orbit Owens College parabola parallel particle perpendicular plane polar pressure prism Professor prove radius ratio refracting right angles Roman numbers School shew sin sin sin sin² sphere straight line surface tangent triangle ABC Trinity College velocity vertical
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