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6. What is the relation of the Vulgate to the Ante-Hieronymian Version ?
7. State the Recension theory of Griesbach.
9. Mr. Scrivener lays down three fundamental rules for the employment of ancient authorities in the textual criticism of the New Testament?
10. What is the “ Textus receptus" ? Give a sketch of the history of its formation.
11. Earliest printed, and earliest published, Greek Testament?
12. Give a brief account of Cod. &, and of the controversy which has arisen respecting it.
13. Mention some of the most important of the other Uncial MSS.
14. One of the Cursive MSS. has occupied the foremost place in a famous doctrinal controversy? Give a sketch of this controversy.
15. When, where, and why, was the Douay Version made ?
16. How long has our present Authorized Version been in use ? and on what previous English Versions is it mainly based ?
17. The obsolete words in our Authorized Version fall into two distinct classes Give examples of each.
18. The Latin title of the sixth Article furnishes an important indication of the views of our Reformers respecting the inspiration of the Scriptures ?
Write a brief Essay on each of the following subjects :1. A popular reply to the modern aspect of Pantheism.
2. Miracles are not inconsistent with the fact that the government of the universe is carried on by general laws.
3. What place does Christ's “satisfaction" for sin hold in the doctrine of the Atonement ?
3. In a plane triangle prove that
2 (ab + bc + ac) > a2 + b2 +02, and
А B с cos A + cos B+ cos C=1+4 sin sin sin
2 4. Find the sum of n terms of the series
sin’a + sin? (a +B) + sino (a +2B) + &c. 5. If the alternate angles of a regular polygon of n sides be joined so as to form another regular polygon of n sides; express the ratio of their areas, and apply to the cases where n=4 and n=6.
6. If D be the middle point of the base AB of a spherical triangle (ABC), prove
cot A - cot B= 2 cos - cot BDC. 7. If O be the point of intersection of the bisectors of the sides of a spherical triangle, prove for the bisector CD, that
C sin CO= 2.sin OD.cos
8. In a spherical triangle, prove that
6 tan tan
COS (8and hence deduce the formula
b cot.cot- + cos C cot
sin C 9. Being given
sin y sin a'
cos (+) = sin ß sin y,
tana B+tan? y. 10. If a, b, y denote the distances of a point from the angles of a spherical triangle, find its locus when
cos a + cos ß + cos y = 0.
1. Find expressions for the secant and cosecant of 18°, and calculate their values to four decimal places without the aid of logarithms.
2. Prove that the modulus of the common system of logarithms is equal to ; and calculate the value of loge 10 to five places of de
logo 10 cimals.
3. The sides of a spherical triangle are 36°.27', 41°39', 45°.44'; calculate its spherical excess.
4. The mast-head of a ship is 210 feet above the water; calculate its distance from the visible horizon.
5. In a spherical right-angled triangle one side is 169o.20, and the adjacent angle 23°.27; calculate the remaining sides.
6. Assuming the ordinary expansions for sin x and cos x, calculate to five decimal places the value of either sin 3° or cos 3o.
7. Two sides of a plane triangle are 645.4 and 372.3, and the included angle 73o.25'; calculate the third side.
8. Given log 15 = 1.17609, and log 108 = 2.03342; find the logarithms of 2, 3 and 0.23.148'.
ALGEBRA AND ARITHMETIC.
1. Apply Sturm's theorem to the equation
243 +64 + 4 = 0. 2. Approximate, by Horner's method, to the real roots of
323 +52 — 40 =0. 3. Find the reducing cubic in Euler's solution of the biquadratic
24 - 2522 +60% – 36 =0;
** + y + x2 – 29 = 0. 5. Resolve into its partial fractions,
203 + 230
6. If a, b, c be the roots of 28 - Px2+2x– =0, then will
(6-6)(-a)(a - b) = *(39-p) (3pr-2)-3(PI-98) 7. The reciprocal of the root of the equation
2n + pan-1 +222 + &c. = 0 may be expanded in a series
- (272 -- pr) &c. P
po 8. Find the coefficient of w in the expansion of
a + bx
+ mx in a series of ascending powers of x, and show that if this be An and Bn the coefficient of the expansion of the same fraction in a series according to descending integer powers of x; then
(ma – 6)2 An x By
m2 62 pi
and &c., be successive convergents to v2, then will 91, :
9n-1 2 tan-1
+(-1)" tan-1 an
pan 4 10. If 28 = a +b+c, then will 3abe = 53 – (8—a)– (8 – 6)3– (8 – c)3.
11. If a be an approximate value of x in any equation, and b, c be the results when a is substituted for x in the original and limiting equations,
6 then <= a-- nearly.
12. If d, a + BV-1 be the roots of the cubic x3 + ax2 + bx+c=o, of which ð is real, and if x3 + Ax+ Bx=o be the equation which results from the diminution of the roots of the above by d, then
a=-=> +8; B=-1 (B+ 36 - a2). 13. A person engaged in business employs a capital of $1500 with a view to retire in 25 years; the business makes a return of 10 per cent. four times a year; half the profits are regularly invested in extending the business. What sum will he have to retire upons and what will be his income if he invests his capital on retiring in the 3 per cent. Consols at 941?
14. Find an equation whose roots are the squares of the differences between the roots of : 1523 +63.32 - 411 - 120=0.
15. Find to three places of decimals the roots of 28 – 11x + 12 =0.
1. Given of a quadrilateral the sides and the area, construct it; and determine, from your construction, the limits of possibility as to the magnitude of the latter when the former only are given.
2. Given of a quadrilateral the diagonals and the angles, construct it; and determine, from your construction, the limits of possibility as to the ratio of the former when the latter only are given.
3. Given the species of a quadrilateral, construct it—(a) so that its vertices shall lie on given lines ; (6) so that its sides shall pass through given points.
4. Given the species of a triangle, construct it-(a) so that its vertices shall lie on given circles, and its area be a minimum; (b) so that its sides shall touch given circles, and its area be a maximum.
5. For two triangles in perspective prove that
a. The three pairs of corresponding vertices divide equianharmonically the three segments determined on their lines of connexion by the centre and axis of perspective.
a'. The three pairs of corresponding sides divide equianharmonically the three angles determined at their three points of intersection by the axis and centre of perspective. b. The centre is the
pole of the axis of perspective with respect to the vertices of both triangles for the same system of multiples.
6. The axis is the polar of the centre of perspective with respect to the sides of both triangles for the same system of multiples.
6. For any two figures in perspective prove that,
a. Every two corresponding points divide in a constant anharmonic ratio the segment determined
on their line of connexion by the centre and axis of perspective.
a'. Every two corresponding lines divide in a constant anharmonic ratio the angle determined at their point of intersection by the axis and centre of perspective.
7. When two circles intersect at right angles, prove the following polar properties of their centres and axes of perspective
a. The pole of either axis of perspective with respect to either circle is the pole of the other axis of perspective with respect to the other circle.
a'. The polar of either centre of perspective with respect to either circle is the polar of the other centre of perspective with respect to the other circle.
b. Every two points of either circle which connect through a pole of either axis of perspective are conjugate points with respect to the other circle.
6. Every two tangents to either circle which intersect on a polar of either centre of perspective are conjugate lines with respect to the other circle.
8. If X, Y, Z be any three collinear points on the three sides BC, CA, AB of any triangle ABC, show that
a. The three circles on the three lines AX, BY, CZ as diameters are coaxal.
b. The three intersections of perpendiculars of the three triangles YAZ, ZBX, XCY are on their radical axis.
c. The three polar circles of the three triangles YAZ, ZBX, XCY are coaxal.
d. The three middle points of the three lines AX, BY, CZ are on their radical axis.