Cambridge University Examination Papers.Michaelmas Term,1884 to Easter Term,1885.Volume XIV |
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Page 9
... find an expression for the nth term in terms of the first term and common difference . Find the 15th term of an arithmetical progression whose 8th and 12th terms are respectively 17 and 25 . 2. Find an expression for the sum of an ...
... find an expression for the nth term in terms of the first term and common difference . Find the 15th term of an arithmetical progression whose 8th and 12th terms are respectively 17 and 25 . 2. Find an expression for the sum of an ...
Page 10
... find the number of terms , and explain the double answer . 3. Define a geometrical progression , and find the sum of a series of n terms in geometrical progression . Prove that in a geometrical series of an odd number of terms , the ...
... find the number of terms , and explain the double answer . 3. Define a geometrical progression , and find the sum of a series of n terms in geometrical progression . Prove that in a geometrical series of an odd number of terms , the ...
Page 11
... find expressions for each in terms of the other . 3. Find the sine and tangent of 30 ° and of 45o . 4. Prove the formulæ cos ( AB ) = cos A cos B + sin A sin B , ( i ) ( ii ) cos B - cos A = 2 sin A + B 2 A - B sin 2 ( iii ) cot ( 1 + 0 ) ...
... find expressions for each in terms of the other . 3. Find the sine and tangent of 30 ° and of 45o . 4. Prove the formulæ cos ( AB ) = cos A cos B + sin A sin B , ( i ) ( ii ) cos B - cos A = 2 sin A + B 2 A - B sin 2 ( iii ) cot ( 1 + 0 ) ...
Page 12
... find an expression for each in terms of the other . 3. Find the cosine and cotangent of 45 ° and of 60 ° . 4 . Prove the formulæ : ( i ) sin ( AB ) = sin A cos B - cos A sin B , ( ii ) sin Asin B = 2 cos π ( iii ) tan ( + ) + tan .0 ...
... find an expression for each in terms of the other . 3. Find the cosine and cotangent of 45 ° and of 60 ° . 4 . Prove the formulæ : ( i ) sin ( AB ) = sin A cos B - cos A sin B , ( ii ) sin Asin B = 2 cos π ( iii ) tan ( + ) + tan .0 ...
Page 13
... Find the magnitude and line of action of the resultant of two parallel forces acting in the same direction . 5. Find a formula for the position of the centre of gravity of any number of heavy particles situated in one plane . A hole of ...
... Find the magnitude and line of action of the resultant of two parallel forces acting in the same direction . 5. Find a formula for the position of the centre of gravity of any number of heavy particles situated in one plane . A hole of ...
Popular passages
Page 434 - And it shall come to pass in the last days, that the mountain of the Lord's house shall be established in the top of the mountains, and shall be exalted above the hills ; and all nations shall flow unto it. And many people shall go and say, " Come ye, and let us go up to the mountain of the Lord, to the house of the God of Jacob ; and he will teach us of his ways, and we will walk in his paths : " for out of Zion shall go forth the law, and the word of the Lord from Jerusalem.
Page 67 - Moreover as for me, God forbid that I should sin against the Lord in ceasing to pray for you...
Page 427 - Having therefore obtained help of God, I continue unto this day, witnessing both to small and great, saying none other things than those which the prophets and Moses did say should come : that Christ should suffer, and that he should be the first that should rise from the dead, and should shew light unto, the people, and to the Gentiles.
Page 115 - Jesus saith to Simon Peter, Simon, son of Jonas, lovest thou me more than these ? He saith unto him, Yea, Lord ; thou knowest that I love thee.
Page 428 - His glorious power, unto all patience and long-suffering with joyfulness ; giving thanks unto the FATHER, which hath made us meet to be partakers of the inheritance of the saints in light : Who hath delivered us from the power of darkness, and hath translated us into the kingdom of His dear SON : in whom we have redemption through His blood, even the forgiveness of sins...
Page 247 - There is a pleasure in the pathless woods, There is a rapture on the lonely shore, There is society, where none intrudes, By the deep Sea, and music in its roar: I love not Man the less, but Nature more, From these our interviews, in which I steal From all I may be, or have been before, •To mingle with the Universe, and feel What I can ne'er express, yet cannot all conceal Roll on, thou deep and dark blue Ocean— roll!
Page 247 - Roll on, thou deep and dark blue Ocean— roll! Ten thousand fleets sweep over thee in vain; Man marks the earth with ruin — his control Stops with the shore; upon the watery plain The wrecks are all thy deed...
Page 132 - Reign thou over us. But the olive tree said unto them, Should I leave my fatness, wherewith by me they honour God and man, and go to be promoted over the trees ? And the trees said to the fig tree, Come thou, and reign over us.
Page 423 - Then cometh he to Simon Peter : and Peter saith unto him, Lord, dost thou wash my feet ? Jesus answered and said unto him, What I do thou knowest not now; but thou shalt know hereafter. Peter saith unto him, Thou shalt never wash my feet. Jesus answered him, If I wash thee not, thou hast no part with me.
Page 593 - This land of such dear souls, this dear, dear land, Dear for her reputation through the world, Is now leas'd out (I die pronouncing it), Like to a tenement, or pelting farm: England, bound in with the triumphant sea, Whose rocky shore beats back the envious siege Of watery Neptune, is now bound in with shame, With inky blots, and rotten parchment bonds: That England, that was wont to conquer others, Hath made a shameful conquest of itself.