Cambridge Senate-house Problems and Riders for the Year 1860: With SolutionsMacmillan, 1860 - 198 páginas |
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Página 1
... triangle ABC , so as to cut off equal parts AD , AE from the sides AB , AC , produced if necessary , respectively , then shall BD be equal to CE . = Through C draw CF parallel to AB , and cutting DE in F. Then the two triangles DMB ...
... triangle ABC , so as to cut off equal parts AD , AE from the sides AB , AC , produced if necessary , respectively , then shall BD be equal to CE . = Through C draw CF parallel to AB , and cutting DE in F. Then the two triangles DMB ...
Página 2
... triangle of the same kind . = For ADE is an isosceles triangle , and the angle AED at the base is the supplement of the angle ACD in the opposite segment of the circle . Hence AED BCD and therefore by Euclid = ABD , and also the angles ...
... triangle of the same kind . = For ADE is an isosceles triangle , and the angle AED at the base is the supplement of the angle ACD in the opposite segment of the circle . Hence AED BCD and therefore by Euclid = ABD , and also the angles ...
Página 4
... triangles PQ SY PQ HZ = and QT YT QTZT PQ SY.HZ .. = QT TY.TZ But TY . TZ = TQ2 by Euclid , III . 36 , and SY . HZ = BƠ2 ... triangle CPO . But the radii CP , PO are perpendicular to the sections AB , DE , therefore VP bisects the angle ...
... triangles PQ SY PQ HZ = and QT YT QTZT PQ SY.HZ .. = QT TY.TZ But TY . TZ = TQ2 by Euclid , III . 36 , and SY . HZ = BƠ2 ... triangle CPO . But the radii CP , PO are perpendicular to the sections AB , DE , therefore VP bisects the angle ...
Página 7
... curve concave to the star . The rest of the question is too obvious for explanation . xiii . If a , b , and B be given , shew under what circum- stances there will be two triangles satisfying the conditions of 11-4 . ] 7 AND RIDERS .
... curve concave to the star . The rest of the question is too obvious for explanation . xiii . If a , b , and B be given , shew under what circum- stances there will be two triangles satisfying the conditions of 11-4 . ] 7 AND RIDERS .
Página 8
... triangles are equal in magnitude , and that the distance between their centres is ( 6 cosec2 B - a3 ) . The radius of the circumscribing circle is the same for both triangles . See fig . 3 . 1 = - b 2 sin B ' and this The centres of the ...
... triangles are equal in magnitude , and that the distance between their centres is ( 6 cosec2 B - a3 ) . The radius of the circumscribing circle is the same for both triangles . See fig . 3 . 1 = - b 2 sin B ' and this The centres of the ...
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acceleration angular velocity Arabic numbers asymptotes attraction axes axis bisects Cambridge centre of force centre of gravity chord circle circular cloth co-ordinates cone conic conic section constant cos² Crown 8vo curvature cylinder described diameter differential equation direction directrix distance drawn dt dt ellipse ellipsoid equal angles equiangular spiral equilibrium extremity Fcap fixed point fluid foci focus given point Hence horizontal hyperbola inclined intersection latus rectum length locus MACMILLAN & CO.'S meridian motion normal parabola parallel particle perpendicular point of contact position pressure prove ratio respectively right angles Roman numbers SENIOR MODERATOR shew sides sin² singular solution smooth sphere spherical straight line string subtend surface tangent tension triangle Trinity College uniform vertex vertical Vis Viva weight аф
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