Scholarship examinations of 1846/47 (-1853/54). |
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Página 10
... may be solved as a plane triangle whose sides are equal to the sides of the spherical triangle , and whose angles are these reduced angles . 21. Find the position of the centre , the magnitude 10 SCHOLARSHIP QUESTIONS .
... may be solved as a plane triangle whose sides are equal to the sides of the spherical triangle , and whose angles are these reduced angles . 21. Find the position of the centre , the magnitude 10 SCHOLARSHIP QUESTIONS .
Página 11
... planes referred to rectangular co - ordinates , find the angle of inclination of the planes to one another . 25. Shew , from geometrical considerations , that the first differential co - efficient of cos x with regard to x is equal to ...
... planes referred to rectangular co - ordinates , find the angle of inclination of the planes to one another . 25. Shew , from geometrical considerations , that the first differential co - efficient of cos x with regard to x is equal to ...
Página 12
... plane . 4. Explain the mechanical action of wheels in assisting the motion of a carriage ; and of springs in relieving the shock . 5. Prove that if two forces acting upon a point are represented in magnitude and direction by two sides ...
... plane . 4. Explain the mechanical action of wheels in assisting the motion of a carriage ; and of springs in relieving the shock . 5. Prove that if two forces acting upon a point are represented in magnitude and direction by two sides ...
Página 14
... plane . Show what the relation between the weights of the voussoirs and the angles of inclina- tion of the joint should be that equilibrium may subsist even supposing there were no friction between the voussoirs . Is this theoretical ...
... plane . Show what the relation between the weights of the voussoirs and the angles of inclina- tion of the joint should be that equilibrium may subsist even supposing there were no friction between the voussoirs . Is this theoretical ...
Página ii
... plane from a given point above it ....... ............... Trigonometry , Plane and Spherical . 11. Prove the following : Sin a Cos ( 3 T = ..................... 3 ( 3 TM + a a ) 2 Cos a = Sin ( 37 + a π a ) 2 15 20 25 25 25 20 and show ...
... plane from a given point above it ....... ............... Trigonometry , Plane and Spherical . 11. Prove the following : Sin a Cos ( 3 T = ..................... 3 ( 3 TM + a a ) 2 Cos a = Sin ( 37 + a π a ) 2 15 20 25 25 25 20 and show ...
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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.