in the above passage is used in a sense which it has also in דבר .(6) .סרבנא .(e) Hebrew? Primary signification of the root? The usual signification of this word in Chaldee is not its original meaning ? How used in Hebrew ? VIII.-Ezek. xvii. 21. in loc.) : Translate the following from Rashi (Comm. ואת כל מברהו' בתרגמו וית כל גיברוהי ומנהם חברו עם ברח דודי וכה פתרונו ואת כל הבורחים : בכל אגפיו בכל כנפיהם כלומר בכל כחם בהרב יפולו : יפרשו (a). How is the word given in the '? שרונאפנדין בלעז : (b). How is fugitivi ejus xplained? (c). The Targum here quoted, as well as the Syriac, may have originated in a different reading of the Hebrew text, as Rosenmüller suggests? (d). Explain the exposition of Menachem referred to by Rashi. ברה דודי e). What is the passage of Scripture quoted by the words) and where does it occur? (f). DD. Primary meaning of the word in Hebrew? Rashi here, and other Jewish interpreters, connect it with an Aramaic word, and ? כנפים render it .שרוני אפנדוך Explain the French word .(9) (h). What words are represented by the abbreviation ha? SCHOLARSHIP EXAMINATION. Science Scholarships. Examiners. JOHN L. MOORE, D. D., Vice-Provost. ANDREW SEARLE HART, LL. D. JOHN H. JELLETT, M. A., Professor of Natural Philosophy. JOSEPH A. GALBRAITH, M. A., Professor of Experimental Philosophy. GEOMETRY. DR. HART. 1. If the quadrilateral ABCD is circumscribed to a circle, prove that AB sin A sin B + CD sin C sin D = BC sin B sin C + DA sin D sin A. 2. Find the locus of foci of conics inscribed in a given parallelogram. 3. If a system of parallel lines is terminated by two parabolas, find the locus of the intersection of diameters through the extremities of each line. 4. a, b, c, a, ß, y, are the sides of two triangles inscribed in the same conic; prove that lines joining the points aß, ab, by, ßc, ca, ya, will meet in one point. 5. If two given lines have the same poles with regard to a system of conics, find the locus of the centres of the conics, and account geometrically for its equation being of the second degree. 6. State and prove the relation between the equations of two conics that a triangle inscribed in one may circumscribe the other. 7. Three conics have double contact with the same conic; prove that if three of their common tangents meet in a point, three other common tangents will also meet in a point. 8. If two conics have double contact, prove that the distances of their centres from the chord of contact are proportional to the rectangles under the diameters parallel to the common tangents. MR. M. ROBERTS. 1. If a, ẞ, y, d are the roots of ao x + 4α1 x3 + 6α2x2 + 4α3 x + as find the value of symmetric function ao2 Σa2ß2 (y −8)2. 2. If the second term is removed from the above equation, and 4 is the absolute term of the transformed equation, prove that ão3А1 = αo2 (α。 αş − 4α1 аз +3α22) − 3 (α12 — ao a2)2 and express this function of the coefficients of the original equation as the product of four linear functions of the roots. 3. Determine the real quadratic factors of 2. If tan (-4) = m tan p, find the value of f sin dø. 7. If U = √( 1 − k2 sin 2ø) ( 1 − k2 sin 24 ) – k2 sin 4 cos sin cos Ꮴ 1 - k2 sin 24 sin 2 ✓ (1 − k2 sin 24 ) ( 1 − k2 sin 24) + k2 sin o cos o sin cos↓ 1 - k2 sin 24 sin 2 prove that UV can be expressed as a fraction whose denominator is 1- k2 sin 24 sin 24. 1. State and prove Legendre's theorem for the calculation of the areas of small spherical triangles. 2. Express the angle between the chords of two sides of a spherical triangle in terms of the sides of the triangle. 4. A, B, C are the angles of a plane triangle; let S be the area of the triangle whose vertices are the points of contact of the inscribed circle, and S the area of the triangle whose vertices are the intersections of the bisectors of the angles with the opposite sides; prove that S S' · { 1 + cos (A−B) + cos (A − C') + cos (B - C) } ASTRONOMY. DR. HART. 1. Supposing the Moon to move uniformly in the ecliptic, compute her daily retardation in rising in terms of her longitude and the latitude of the place. 2. Compute the hourly change of azimuth of the plane of oscillation of a pendulum at a given latitude. 3. Supposing perihelion to coincide with the winter solstice, find a formula for computing the Sun's longitude when the equation of time is greatest. 4. If the Sun and Moon are together at the ascending node at the moment of the summer solstice, find the locus of places on the Earth's surface where the eclipse will be central, the angular motion of the Sun and Moon being supposed uniform. 5. In the same case, compute the approximate latitudes of the first and last place in which the eclipse is central, and the interval of time between the two events, considering the motion of the Sun and Moon during this interval to be rectilinear. 6. Compute the effects of aberration on the right ascension and declination of a given star, and find at what time of the year each is greatest. 7. Describe the construction of a vertical sun-dial which faces the East, and determine the position of the hour line for 9 o'clock. 8. If the orbits of the Earth and of a planet were circular, and in the same plane, find the elongation of the planet when stationary. MECHANICS. PROFESSOR JELLETT. 1. Three equal rods, AB, BC, CD, are connected by smooth hinges at B and C; the extremities A, D being fastened together by a string of given length. If the whole system be placed in a vertical position on a smooth horizontal plane, find an equation for determining the tension of the string. a. If there be no string, and the plane be rough, find an equation for the extreme position of equilibrium. 2. It is required to raise a beam, moveable about one extremity, from a horizontal to a vertical position, by means of a rope attached to one extremity of the beam, passing through a ring situated vertically over the other extremity, and sustaining a weight which is allowed to descend. nd the smallest weight which will suffice. 3. Find the position of equilibrium of a uniform beam, one end of which rests against a vertical plane, and the other on the interior surface of a given hemisphere. |
