Oben das Schloss hellweiss in Kastanien! Vorn auf der Wies' hin Röthliche Küh'; und der Storch, wie vertraut er dazwischen einhertritt! Voss, Luise. FRIDAY, Dec. 17, 1858. 6 to 74 P.M. II. c. 4. German. (SECOND PAPER.) 1. TRANSLATE into ENGLISH PROSE: Lebe glücklich, sagt'er. Ich gehe; denn alles bewegt sich Und es lös't der Besitz sich los vom alten Besitzer, Mehr ein Fremdling als jemals ist nun ein jeder geworden. 2. Translate into GERMAN (Roman characters may be used): He that would seriously set upon the search of truth, ought in the first place to prepare his mind with a love of it: for he that loves it not, will not take much pains to get it, nor be much concerned when he misses it. There is nobody in the commonwealth of learning who does not profess himself a lover of truth: and there is not a rational creature that would not take it amiss to be thought otherwise of. And yet for all this, one may truly say, there are very few lovers of truth for truth's sake, even amongst those who persuade themselves that they are so. How a man may know whether he be so in earnest, is worth inquiry: and I think there is this one unerring mark of it, viz. the not entertaining any proposition with greater assurance, than the proofs it is built upon will warrant. 3. Grammatical Questions. LOCKE. (1) What cases are respectively governed by the following verbs: reuen, ärgern, träumen, pflegen, zahlen, bezahlen, lehren? and what by the following prepositions: um, mit, nach, ohne, nebst, zu, in, auf, halben, wegen? (2) What is the full force of the line (in § 1), "Gold und Silber schmilzt," &c.? Of the verbs, gehen, ruhen, fallen, schlafen, rufen, schicken, kommen; which are construed with sein, and which with haben? With which is schmelzen construed? (3) Give (a) the Present and (b) Imperf. Indicative, and (c) the Imperfect Subjunctive, of the first person sing., as also (d) the Imperative sing., of the verbs, befehlen, heissen, empfangen, friern, bergen. (4) Give the different meanings, with the gender in each case, of each of the following nouns: Mensch, Thor, Erbe, Band, Geissel, Hut. Give Baum with the Adj. grün and the definite article, in the Nom., Gen. and Dat. both sing. and pl. (5) When is a compound verb said to be separable, and when inseparable; and how is the conjugation of the verb affected by the difference? What is the force of the particles er, ver, zer, ent, anheim? 4. Point out (without translating into English) the unidiomatic constructions in the following lines: Der Neudeutsche. Mit dem prosaischen Geschwätz Und sonst von Andern keinen. Was ob Ihr durch Autorität Ist bei der Jetztwelt gleich mein Stil Erreichen ganz gewiss mein Ziel Denn endlich doch in dieser Welt, Die alte, wie die junge, Auch die der Adelunge. STIEGLER. THURSDAY, Dec. 16, 1858. 9 to 11 A.M. II. D. Euclid and Conic Sections. 1. DEFINE a superficies, an angle, adjacent angles, parallel straight lines. If two triangles have two sides of the one equal to two sides of the other, each to each; and have likewise the angles contained by those sides equal to each other, they shall be equal in every respect. Construct a triangle of which the base, the sum of the other sides, and the vertical angle are given. 2. If a side of any triangle be produced, the exterior angle is equal to the two interior and opposite angles, and the three interior angles of every triangle are together equal to two right angles. At what angles are the sides of a regular duodecagon inclined to each other? 3. If a straight line be divided into two equal, and also into two unequal parts; the squares of the two unequal parts are together double of the square of half the line, and of the square of the line between the points of section. If the sum of the squares of the distances of a point P from two fixed points is constant, the locus of P is a circle. 4. When is one circle said to touch another? If one circle touch another internally, they shall not have the same centre. Find the ratio of the diameters of the two circles when every line drawn from the point of contact to cut the circles is bisected by the inner one. 5. Two tangents are drawn to a circle from an external point, construct circles to touch the tangents and circle. 6. Give Euclid's construction (without proof) for making an isosceles triangle with the angles at the base double of the third angle, and explain for what purpose such a triangle was needed. If at the centre of the great circle a tangent be drawn to the little circle cutting the base of the triangle produced, the produced part of the base is equal to a side of the inscribed isosceles triangle. 7. Give Def. 5, Book v. of Euclid, and shew whether the areas 3, 4, 7, 8 are proportionals. Similar triangles are to one another in the duplicate ratio of their homologous sides. Shew how to inscribe a rectangle DEFG in a triangle ABC, so that the angles D, E may be in the straight lines AB, AC respectively, the side FG coincident with the base, and the area of the rectangle be equal to half that of the triangle. 8. To draw a straight line perpendicular to a plane from a given point (1) without, (2) within, the plane. A triangular pyramid stands on an equilateral base, and the angles at the vertex are equal angles; shew that the sum of the perpendiculars on the faces from any point of the base is con stant. 9. Give some mechanical mode of describing a parabola. If a perpendicular is drawn from the focus of a parabola upon any tangent, the point of intersection lies in the tangent at the vertex. If P be a point in a parabola, S the focus, PG the normal cutting the axis in G, PK the perpendicular on the directrix, prove that (1) PS, KG bisect each other, and (2) are at right angles if SP be equal in length to the latus rectum. 10. If a chord be drawn from any point of an ellipse perpendicular to the axis major, the ratio of the product of the segments of the axis major to the square of half the chord is equal to the ratio of the squares of the axes major and minor. If PGG' be a normal at P cutting the major and minor axis in G, G' respectively, then the angle PGH is equal to the angle PSG'. 11. Define a conjugate hyperbola, a conjugate diameter, an asymptote; and illustrate by a figure. If tangents be drawn at the vertices of the hyperbola and of its conjugate, the diagonals of the rectangle so formed will be asymptotes to the hyperbola. If TPT" be a tangent at Pcutting the asymptotes T, T", then TT" is equal to the diameter conjugate to the diameter through P. 12. State the different kinds of sections of a right cone which can be made by a cutting plane. Prove that if the cutting plane be parallel to a plane touching the cone along a slant side the section is a parabola. If A be the vertex of the parabola, and AM be drawn perpendicular to the axis of the cone, and MS perpendicular to axis of parabola, S is the focus. FRIDAY, Dec. 17, 1858. 9 to 12. II. D. Arithmetic, Algebra, Trigonometry, and 1. Two parcels of sugar of the same size and quality are sent to three persons A, B, C. A is to have three-fourths of a parcel, B two-thirds, C the remainder of the two. Before the division, A purchases four-sevenths of C's share, and B twothirds of the remainder; shew how to divide the parcels that only one may be broken open, and yet each have his own. |
