Scholarship examinations of 1846/47 (-1853/54). |
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Página 9
... equal to one angle of the other , and the sides about two other angles proportionals ; then , if each of the remaining angles be either less , or not less than a right angle , or if one of them be a right angle , the triangles shall be ...
... equal to one angle of the other , and the sides about two other angles proportionals ; then , if each of the remaining angles be either less , or not less than a right angle , or if one of them be a right angle , the triangles shall be ...
Página 10
... equal roots . 13. Prove the truth of the following formula : sin A + sin ( 36o — A ) + sin ( 72o + A ) = sin ( 36o + A ) + sin ( 72o —A ) , and explain its use in verifying tables of trigonometric functions . 14. Shew how to adapt the ...
... equal roots . 13. Prove the truth of the following formula : sin A + sin ( 36o — A ) + sin ( 72o + A ) = sin ( 36o + A ) + sin ( 72o —A ) , and explain its use in verifying tables of trigonometric functions . 14. Shew how to adapt the ...
Página 11
... equal to sin x . 26. Find the second differential co - efficients with regard to x of the following expressions : - 1 -1 √b - a cos x COS ( 1 ) ✓b- - ) ; 1 a tan T ( 2 ) log ε a tan + b + √ b2 a2 b√ b2 a2 :) : : 5 27. Shew that for ...
... equal to sin x . 26. Find the second differential co - efficients with regard to x of the following expressions : - 1 -1 √b - a cos x COS ( 1 ) ✓b- - ) ; 1 a tan T ( 2 ) log ε a tan + b + √ b2 a2 b√ b2 a2 :) : : 5 27. Shew that for ...
Página 13
... equal to the space through which a body , carried up from the earth to the elevation of the Moon and left to fall back , would descend in the same time : the attraction of the Earth being supposed to vary inversely as the square of the ...
... equal to the space through which a body , carried up from the earth to the elevation of the Moon and left to fall back , would descend in the same time : the attraction of the Earth being supposed to vary inversely as the square of the ...
Página 14
... equal to the weight of a cubic foot of sea water taken from the surface of the Ocean , the density is increased by a 4th part of the density at the surface . Would a piece of metal seven times as heavy as the same bulk of sea water at ...
... equal to the weight of a cubic foot of sea water taken from the surface of the Ocean , the density is increased by a 4th part of the density at the surface . Would a piece of metal seven times as heavy as the same bulk of sea water at ...
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Página 3 - Peace to all such! but were there one whose fires True genius kindles, and fair fame inspires, Blest with each talent and each art to please, And born to write, converse, and live with ease: Should such a man, too fond to rule alone, Bear, like the Turk, no brother near the throne, View him with scornful, yet with jealous eyes, And hate for arts that caused himself to rise, Damn with faint praise, assent with civil leer, And without sneering, teach the rest to sneer...
Página 54 - O Cromwell, Cromwell, Had I but served my God with half the zeal I served my king, he would not in mine age Have left me naked to mine enemies.
Página 5 - ... as if there were sought in knowledge a couch whereupon to rest a searching and restless spirit, or a terrace for a wandering and variable mind to walk up and down with a fair prospect, or a tower of state for a proud mind to raise itself upon, or a fort or commanding ground for strife and contention, or a shop for profit and sale ; and not a rich store-house for the glory of the Creator and the relief of man's estate.
Página 6 - Deign on the passing world to turn thine eyes, And pause awhile from letters, to be wise; There mark what ills the scholar's life assail, Toil, envy, want, the patron, and the jail.
Página 1 - O poor hapless nightingale, thought I, How sweet thou sing'st, how near the deadly snare ! Then down the lawns I ran with headlong...
Página 13 - 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.
Página 37 - There is only one cure for the evils which newly acquired freedom produces; and that cure is freedom. When a prisoner first leaves his cell he cannot bear the light of day ; he is unable to discriminate colors or recognize faces.
Página 29 - Tis greatly wise to talk with our past hours ; And ask them, what report they bore to heaven : And how they might have borne more welcome news.