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(3.) If a, b, c, A, B, C, be the sides and angles of a triangle then the radius of a circle described about a triangle whose sides are, a cos A, 6 cos B, and c cos C = } that described about the original triangle.
(4.) Two equal circles intersect at right angles, and with the points of intersection, as centres two arcs are drawn touching the circles, so as to form an oval; shew that the space common to the two circles is equal to each of the spaces exterior to both.
(5.) If two observers A and B, at the distance of one mile from each other, see at the same moment a large bird, directly West and NorthWest of them respectively, A finds the angle of elevation made by the bird and a horizontal line to be 45°, and B finds it to be 30°; required the distance of the bird from each of the observers, and its perpendicular height above the plane.
(6.) If (r) be the radius of the circle inscribed between the base of a right angled triangle, and the other two sides produced and r' be the radius of the circle inscribed between the altitude of the same triangle and the other two sides produced; the area of the triangle shall be equal to the rectangle rr!
(7.) Expand cos o in a series ascending by powers of 0, and thence
2 Deduce cos (0 + 0)
= cos 0 cos $ — sin o sin • (8.) Having given the chord of an arc of a circle; deduce an approximate rule for finding the length of the arc.
A semicircular arch is made with stones 3 feet long, the span of the arc being 40 feet, and its height 16 feet, what is the area of the front of the arch?
FOR ALL THE CLASSES.
On language as an instrument of civilization, with special reference to the effects which may be expected from the diffusion of knowledge through the medium of the English language in India.
Diligence, Industry and Honesty are the principal means of increasing national wealth. যত্ন পরিশুম এব°, সরলতা দেশীয় সল্পত্তি বৃদ্ধির প্রধান উপায়।
Quis inter Romanos summum Imperatoris laudem, quis boni sanctique viri præ cæteris meruerit?
JUNIOR SCHOLARSHIPS, 1851.
CROMBIE'S ETYMOLOGY AND SYNTAX, Part II.
(1.) Give rules for prefixing or rejecting the article in the phrases subjoined
“ A man considered as a moral being may be defined to be the responsible animal.”
“Whoever has power abuses it: every page of history proves the fact : -individual, body, the people,—it is all the same,-power is abused.”
* More I try, less I succeed.”
(3.) Certain nouns of the singular form, require sometimes a plural, sometimes a singular, verb.
Why is this? Give an example.
(4.) Priestley contends for the expression, “ He is greater than me,” in preference to “ greater than I.” Explain his reasons, and Crombie's answer to them.
(5.) Adverbs have sometimes an article (definite or indefinite) prefixed to them. State the reasons and give examples of the above usage.
(6.) With what cases are interjections joined ?
Though for no other cause, yet for this; that posterity may know we have not loosely through silence permitted things to pass away as in a dream, there shall be for men's information extant thus much concerning the present state of the church established amongst us, and their careful endeavour which would have upheld the same.”
(9.) The relative agrees with its antecedent in what particulars ? Point out the antecedents to this and it in the subjoined.
“The more methods there are in a state for acquiring riches without industry or merit, the less will there be of either in that state ; this is as evident, as the ruin which attends it.
He came lately.
(2.) When the relative who refers to a personal pronoun as its antecedent, explain the difference of meaning according as the verb is in the first or third person.
Example. “ I am he who commands you, or command you.”
(3.) Under what circumstances do intransitive verbs govern the objective case ?
(4.) When would you employ the subjunctive or conditional mood after a conjunction ?
(5.) Certain prepositions only follow particular verbs and nouns. What prepositions may follow the verb “to start," and the adjective " disappointed,” and what is the meaning of the resulting phrases ?
(6.) Briefly correct if necessary the subjoined sentences.
The messenger came and told Brutus that his son has just died; and that he therefore cannot perform the sacrifice.
In consequence of the inundation the price of corn rose too much, and the people suffered great distress.
By this a Newton, a Lagrange, a Laplace were famous in their age.
Troubridge having run aground, signalised to the other ships to warn them of the danger.
In this eminent danger these first principals of defence were neglected : but the governor, when the matter was investigated, ingeniously confessed his error, and saved the rest from disgrace.
“ When he inquired, Will I wait on you? I answered. By no means, I shall not allow it.”
Andrien pleaded earnestly that he had no right to be hanged as a spy when he had merely obeyed the instructions of his general.
That we are capable of forming to ourselves an imperfect idea even of the infinite mind is, I think, a strong presumption of our own immortality. Happily to me I had retreated back from the edge of the cliff. “ The victories of Hannibal at land contrasted with those of the consul's on sea left little absolute advantage on either side.”
(7.) Modernise the following.
“ That which hath been ordained ill at the first, may wear out that evil in tract of time, and then what doth let but that the use thereof may stand without offence ?
“ Alcidamas the sophister hath many notable arguments to prove that voluntary and extemporal far excelleth premeditated speech.”
HISTORY: STEWART'S BENGAL.
Morning Paper. (1.) The date, and most remarkable circumstances of the first conquest of Bengal by the Mohammedans.
A brief account of the last expedition of the conqueror.
(2.) The slave viceroys of Bengal originally purchased by Altumsh and Bulbun (Balin), with the date and particulars of the revolt of the last of them.
The policy of promoting foreign slaves to the highest offices.
(3.) The date of the accession of the first of the independent Mohammedan Kings of Bengal; with that of the expulsion of the last of them.
What King introduced African slaves into Bengal ?
The names of those who mounted the throne. By whom were they finally driven from the country; and where, and under what name, did they afterwards settle ?
(5.) The circumstances and date of the death of the last of the Affghan Kings.
In what respects did the government of the Affghans resemble the Feudal system of Western Europe ?
(6.) An outline of the services performed by the Rajahs Todermul and Mān Sing.
(7.) The name and situation of the ancient capital of Bengal.
The dates, and circumstances of the removal of the seat of Government to the following cities, viz. Gour.
Moorshedabad. (8.) A brief account of the expiring effort made by the Affghans to recover superiority in Bengal, with its date.
Who ruled at Dacca at the time ?