Examinations Papers1900 |
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Page 49
... equations y2 — ( m + n ) xy + mnx2 = 0 . ax2 + bxy + cy2 + dx + ey + ƒ = 0 . 2. Define a harmonical progression , and prove that the reciprocals of any number of quantities in harmonical progression are in arithmetical pro- gression ...
... equations y2 — ( m + n ) xy + mnx2 = 0 . ax2 + bxy + cy2 + dx + ey + ƒ = 0 . 2. Define a harmonical progression , and prove that the reciprocals of any number of quantities in harmonical progression are in arithmetical pro- gression ...
Page 51
... equation of the first degree represents a straight line . Find the equation of the straight line passing through the intersection of ax + by + c = 0 a'x + by + c = 0 and through the point h , k . 2. Find the general equation of a circle ...
... equation of the first degree represents a straight line . Find the equation of the straight line passing through the intersection of ax + by + c = 0 a'x + by + c = 0 and through the point h , k . 2. Find the general equation of a circle ...
Page 54
... equation . Determine the parallelopiped of maximum volume inscribed in a given ellipsoid with its edges parallel to the axes . 3. Shew how to find the asymptotes of a curve whose equation is given in the form Un + Un - 1 + Un - 2 + ...
... equation . Determine the parallelopiped of maximum volume inscribed in a given ellipsoid with its edges parallel to the axes . 3. Shew how to find the asymptotes of a curve whose equation is given in the form Un + Un - 1 + Un - 2 + ...
Page 56
... equation is homogeneous . 11. Shew how to find the complementary functions and the particular integrals of two simultaneous linear differential equations with constant co- efficients . Integrate dx + ay + bxect dt dy + ax + by ect , dt ...
... equation is homogeneous . 11. Shew how to find the complementary functions and the particular integrals of two simultaneous linear differential equations with constant co- efficients . Integrate dx + ay + bxect dt dy + ax + by ect , dt ...
Page 57
... equation of energy in as general a form as you can . A mass of 10 lbs . is hung up by an elastic string of natural length 1 foot , and modulus . 50 lbs . weight . A mass of 2 lbs . is let fall from the point of suspension of the string ...
... equation of energy in as general a form as you can . A mass of 10 lbs . is hung up by an elastic string of natural length 1 foot , and modulus . 50 lbs . weight . A mass of 2 lbs . is let fall from the point of suspension of the string ...
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Popular passages
Page 432 - She dwelt among the untrodden ways Beside the springs of Dove, A Maid whom there were none to praise And very few to love : A violet by a mossy stone Half hidden from the eye! Fair as a star, when only one Is shining in the sky.
Page 431 - La scène sur la terre n'était pas moins ravissante : le jour bleuâtre et velouté de la lune descendait dans les intervalles des arbres et poussait des gerbes de lumière jusque dans l'épaisseur des plus profondes ténèbres. La rivière qui coulait à mes pieds, tour à tour se perdait dans les bois, tour à tour reparaissait brillante des constellations de la nuit qu'elle répétait dans son sein.
Page 210 - To move, to breathe, to be; I wandering went Among the haunts and dwellings of mankind, And first was disappointed not to see Such mighty change as I had felt within Expressed in outward things; but soon I looked...
Page 433 - Nor do we see any sign which indicates that the term of her long dominion is approaching. She saw the commencement of all the governments and of all the ecclesiastical establishments that now exist in the world ; and we feel no assurance that she is not destined to see the end of them all.
Page 11 - The birds their choir apply ; airs, vernal airs, Breathing the smell of field and grove, attune The trembling leaves, while universal Pan, Knit with the Graces and the Hours in dance, Led on the eternal Spring.
Page 49 - The glories of our blood and state Are shadows, not substantial things ; There is no armour against fate ; Death lays his icy hand on kings : Sceptre and crown Must tumble down, And in the dust be equal made With the poor crooked scythe and spade.
Page 433 - ... really more valuable in that point of view than any other means or appliance whatsoever? We can fancy him as radiant aloft over all the Nations of Englishmen, a thousand years hence.
Page 49 - Two Voices are there ; one is of the Sea, One of the Mountains ; each a mighty Voice : In both from age to age Thou didst rejoice, They were thy chosen Music, Liberty...
Page 46 - Lebe glücklich, sagt' er. Ich gehe; denn alles bewegt sich Jetzt auf Erden einmal, es scheint sich alles zu trennen. Grundgesetze lösen sich auf der festesten Staaten, Und es löst der Besitz sich los vom alten Besitzer, Freund sich los von Freund: so löst sich Liebe von Liebe.
Page 431 - Je vois ces effroyables espaces de l'univers qui m'enferment, et je me trouve attaché à un coin de cette vaste étendue, sans que je sache pourquoi je suis plutôt placé en ce lieu qu'en un autre, ni pourquoi ce peu de temps qui m'est donné à vivre m'est assigné à ce point plutôt qu'à un autre de toute l'éternité qui m'a précédé et de toute celle qui me suit.