Examinations Papers1893 |
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Strana 41
... Shew that similar triangles are to one another in the duplicate ratio of corresponding medians . 4. If a straight line is perpendicular to each of two straight lines at their point of intersection , it shall also be perpendicular to the ...
... Shew that similar triangles are to one another in the duplicate ratio of corresponding medians . 4. If a straight line is perpendicular to each of two straight lines at their point of intersection , it shall also be perpendicular to the ...
Strana 42
... Shew that one of the roots will be n times the other if np2 = ( n + 1 ) 2 q . 6. If α = b ' shew that each of these ratios is also equal to la + mb + no lamb ' + no Prove also that 2 ( a2 + b2 + c2 ) ( a'2 + b22 + c2 ) = ( aa ' + bb ' + ...
... Shew that one of the roots will be n times the other if np2 = ( n + 1 ) 2 q . 6. If α = b ' shew that each of these ratios is also equal to la + mb + no lamb ' + no Prove also that 2 ( a2 + b2 + c2 ) ( a'2 + b22 + c2 ) = ( aa ' + bb ' + ...
Strana 43
... Shew that the value of -- sin2 A + sin2 ( A + B ) 2 sin A cos B sin ( A + B ) is always the same whatever the value of A. 11. Shew that in any triangle sin A = a sin B b sin C с Prove that a b - cos B - cos A = 1 + cos C с 12. Shew how ...
... Shew that the value of -- sin2 A + sin2 ( A + B ) 2 sin A cos B sin ( A + B ) is always the same whatever the value of A. 11. Shew that in any triangle sin A = a sin B b sin C с Prove that a b - cos B - cos A = 1 + cos C с 12. Shew how ...
Strana 44
... point be on the line yy ' = 2α ( x + x ' ) shew that the chord of contact passes through the point x'y ' . 4. Find the relation between the eccentric angles of the 44 ANNUAL EXAMINATION PAPERS , Pure Mathematics -Part II.
... point be on the line yy ' = 2α ( x + x ' ) shew that the chord of contact passes through the point x'y ' . 4. Find the relation between the eccentric angles of the 44 ANNUAL EXAMINATION PAPERS , Pure Mathematics -Part II.
Strana 45
... Shew that the tangents at the extremities of conjugate diameters meet on a fixed ellipse . 5. Enunciate and prove Leibnitz's theorem . Find the nth differential coefficients of ( ax2 + bx + c ) sin x , ( ax2 + bx + c ) e * . 6. Prove ...
... Shew that the tangents at the extremities of conjugate diameters meet on a fixed ellipse . 5. Enunciate and prove Leibnitz's theorem . Find the nth differential coefficients of ( ax2 + bx + c ) sin x , ( ax2 + bx + c ) e * . 6. Prove ...
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Strana 373 - Commentaries remarks, that this law of Nature being coeval with mankind, and dictated by God himself, is of course superior in obligation to any other. It is binding over all the globe, in all countries and at all times; no human laws are of any validity if contrary to this, and such of them as are valid, derive all their force, and all their validity, and all their authority, mediately and immediately, from this original...
Strana 197 - But little do men perceive what solitude is, and how far it extendeth. For a crowd is not company; and faces are but a gallery of pictures; and talk but a tinkling cymbal, where there is no love.
Strana 197 - IT had been hard for him that spake it to have put more truth and untruth together in few words than in that speech, " Whosoever is delighted in solitude, is either a wild beast or a god...
Strana 30 - Qu'il règne donc ce fils , ton soin et ton ouvrage ! Et que, pour signaler son empire nouveau, On lui fasse en mon sein enfoncer le couteau ! Voici ce qu'en mourant lui souhaite sa mère : Que dis-je souhaiter ! je. me flatte , j'espère Qu'indocile à ton joug, fatigué de ta loi , Fidèle au sang d...
Strana 319 - J'aurais vu massacrer et mon père et mon frère, Du haut de son palais précipiter ma mère, Et dans un même jour égorger à la fois (Quel spectacle d'horreur !) quatre-vingts fils de rois ; Et pourquoi ? pour venger je ne sais quels prophètes Dont elle avait puni les fureurs indiscrètes: Et moi, reine sans cœur, fille sans amitié, Esclave d'une lâche et frivole pitié, Je n'aurais pas du moins à cette aveugle rage Rendu meurtre pour meurtre, outrage pour outrage, Et de votre David traité...
Strana 61 - J'aime mieux un ruisseau qui, sur la molle arène, Dans un pré plein de fleurs lentement se promène, Qu'un torrent débordé qui, d'un cours orageux, Roule, plein de gravier, sur un terrain fangeux. Hâtez-vous lentement, et, sans perdre courage, Vingt fois sur le métier remettez votre ouvrage : Polissez-le sans cesse et le repolissez ; Ajoutez quelquefois, et souvent effacez.
Strana 75 - Kennst du es wohl? Dahin! Dahin Möcht ich mit dir, o mein Beschützer, ziehn! Kennst du den Berg und seinen Wolkensteg? Das Maultier sucht im Nebel seinen Weg, In Höhlen wohnt der Drachen alte Brut, Es stürzt der Fels und über ihn die Flut Kennst du ihn wohl?
Strana 26 - His burning idol all of blackest hue; In vain with cymbals ring They call the grisly king, In dismal dance about the furnace blue, The brutish gods of Nile as fast, Isis, and Orus, and the dog Anubis, haste.
Strana 315 - Sate simply chatting in a rustic row ; Full little thought they than That the mighty Pan Was kindly come to live with them below : 90 Perhaps their loves, or else their sheep, Was all that did their silly thoughts so busy keep.
Strana 6 - SONG. Would you know what's soft? I dare Not bring you to the down, or air, Nor to stars to show what's bright, Nor to snow to teach you white ; Nor, if you would music hear, Call the orbs to take your ear ; Nor, to please your sense, bring forth Bruised nard, or what 's more worth ; Or on food were your thoughts placed, Bring you nectar for a taste ; Would you have all these in one, Name my mistress, and 'tis done ! THE PROTESTATION.