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sous mes ordres ne fut un fléau que sur le champ de bataille; plus d'une fois les nations ennemies m'ont rendu ce témoignage, et cette conduite je la croyais aussi propre que nos victoires à faire des conquêtes à la France.
Le roi et la famille royale arrivèrent à Châlons vers les quatre ou cinq heures de l'après-midi du 21. Là un homme de la ville, qui se trouva par hasard à la poste, lorsque la voiture changeait de chevaux, crut reconnaître le roi; tourmenté de cette idée, il va trouver le maire, lui communique sa découverte, et lui propose de faire arrêter la voiture. Le maire mit tant d'adresse à l'effrayer sur les conséquences, pour l'un et l'autre, d'une pareille démarche, que le pauvre homme finit par convenir que le plus sage était de garder le silence. Échappé à ce danger, le roi avait passé Châlons, lorsque la voiture étant arrêtée un moment sur la grande route, un inconnu, vêtu comme un bourgeois, s'en approche, met la tête à une des portières auprès de laquelle était Madame de I... et dit assez haut: "Vos mesures sont mal prises, vous serez arrêtés." Il s'éloigna tout de suite sans qu'on eût le temps de savoir ni son nom ni ce qu'il était.
"I had devoted myself," says Moreau, "to the study of the law at the commencement of this revolution, which was to found the freedom of the French people; it changed the destiny of my life; I devoted it to the pursuit of war. I did not go and rank myself among the troops of freedom through ambition, I embraced the military profession through respect for the nation's rights. I became a warrior because I was a citizen. I bore this character under the banners; I always preserved it there. The more I loved freedom, the more I submitted to discipline. When I reached the position of commander-in-chief, when victory made us promoted in the midst of the nations opposed to us, I did not a whit less bend my energies towards making them respect the character of the French people than to making them fear their arms. War under my régime was not a scourge save on the battle-field; more than once the enemy bore witness to me in this, and I thought this manner of proceeding as likely as our victories to obtain for us conquests in France.
The king and the royal family arrived at Châlons towards 4 or 5 p.m. on the 21st. There a man of the town, who chanced to be at the posting inn, when the carriage was changing horses, thought he recognised the king; tortured by this thought he went to find the mayor, told him of his discovery and proposed to him to have the carriage stopped. The mayor showed such skill in frightening him about the consequences to both of them, of such a step, that the poor man ended by agreeing that the wisest plan was to keep silence. Having escaped from this danger the king had passed Châlons, when, on the carriage stopping for a moment on the high road, a stranger, dressed like a citizen, drew near, put his head in at one of the doors, by the side of which was Madame de I . ., and said in a pretty loud voice: "Your plans are ill conceived; you will be arrested." He got away immediately without there being time to know either his name or who he was.
[For figures to solutions, see end of the pamphlet.]
Thursday, September 1st, 1881. 10 A.M.-12.30 P.M.
1. On a given map, 32 miles are represented by 9 inches.
(1) Construct a plain scale of miles for the map, so as to show
(2) Construct a comparative scale of yards for the same map, and divide it to show distances of 1000 yards. Figure your scales properly, show your calculations, and give the representative fraction.
Thirty-two miles represented by 9 inches :
56320) 90000 (1.598 x the length of line to represent
2. The sides of a quadrilateral figure ABCD are as follows:AB 3 inches, BC the diagonal AC = 4 inches.
2 inches, CD 23 inches, AD 2 inches, and
Draw the figure, and within it draw a second, within the second a third, and within the third a fourth similar figure, having their sides parallel to those of the first, and at a distance of inch, inch, and inch respectively from the first. Reduce the outer largest figure to a triangle of equal area. The first measurement to be taken is that of the line AB 3 inches, then from A with A C 4 inches an arc is described, then from B with a radius of 2.5 inches we cut the arc having its centre at A, and determine the exact position of C, and so on. To obtain the concentric figures, bisect
each side of the given figure and also its angles; on each bisecting line passing through the side mark off the required distances. The bisecting lines of the angles of the figure enable the student to determine the intersection of the sides of the concentric figures with exactness.
For the reduction of the quadrilateral figure to a triangle of equal area, it is necessary to join DB and a line from C drawn parallel to D B to meet the base produced in E. Then DCB and DE B being triangles upon a common base DB and between the parallel lines CE and D B are equal to each other, and the portion of the figure (2) cut off by D E is compensated for by the part (1) added to it, and the triangle ADE is equal to the quadrilateral figure A B C D.
3. On a base A B, 4 inches long, describe a triangle having the side AC = 31 and BC inches. Bisect A C in D, and from C and D draw two straight lines meeting at a point in the base A B, and making equal angles with it.
Having drawn the figure, drop a perpendicular from C to cut the base in F, make F E equal to CF, then draw a line from E to D, then draw a line from C to G the point of intersection of the line ED with A B. Then the angles AGD and B G C will be equal.
4. Describe a circle of 1 inches radius, and show how to draw a straight line by construction from a given point 3 inches from its centre, cutting the circumference in two points, A and B, so that A B, the part of the line within the circle, may be equal to 2 inches.
Draw any chord line D E 2 inches long, and then draw the dotted circle as shown tangental to it, then a tangent drawn from P, cutting the circle in the points A and B will be the required line, and A B will be the required chord line 2 inches long.
5. Describe an equilateral triangle of 2 inches sides, and on one of its sides describe an isosceles triangle of 3 inches side, in the quadrilateral figure thus obtained describe a square.
A B C is the given equilateral triangle, and CD B the isosceles triangle; BE is equal to BC and the sides of the square are drawn parallel to the diagonals of the figure; the point of intersection F of the line A E with BD determines the initial corner of the square.
6. Describe a circle of inch radius, and take any point P in the circumference. Take a point Q 1 inch from P and 1 inches from the centre of the circle, and determine the centre of a circle that shall touch the first in P, and pass through the point Q.
C is the given circle and PQ the given points; the line RS bisecting PQ and meeting CP produced in the point R determines the centre of the required circle R.
7. With a radius of 13 inches, describe a circle, and in it inscribe three equal circles, touching each other and the original circle.
The given circle is divided into six equal parts; from the extremity of any one of the radii (P in this case) a tangent is drawn to meet the radius Q produced at the point S; the bisection of the angle P SQ and the production of the bisecting line to meet the radius C P in the point R determines the radius of the circle C R; the intersections of the circumference of CR with the radii of the larger circle give the centres for the inscribed circles as shown.
(Euclid, Book I.)
Thursday, Sept. 1st. 1.30 P.M.-3.15 P.M.
[You need not answer more than FOUR of the questions.]
I. If two triangles have two sides of the one equal to two sides of the other, each to each, and likewise their bases equal; the angle contained by the two sides of the one shall be equal to the angle contained by the two sides, equal to them, of the other.
This is the eighth proposition of the First Book of Euclid.
II. Construct a triangle, of which the three sides shall be equal to three given straight lines.
This is the twenty-second proposition of the First Book.
III. If a straight line falling on two other straight lines, makes the alternate angles equal, these two straight lines shall be parallel.
This is the twenty-seventh proposition.
IV. Describe a parallelogram which shall be equal to a given triangle and have one of its angles equal to a given rectilineal angle. This is the forty-second proposition.
V. A B C is an isosceles triangle, having the sides A C and B C equal. If C B be produced to any point D and D A be joined, prove that the angle A D B is equal to the difference of the angles BA C, B A D.
Let A B C be an isosceles triangle having the sides A C and B C equal. Produce C B to any point D, and join A D; then the angle A D B shall be equal to the difference of the angles B A C, B A D. Because the exterior angle ABC is equal to the two interior angles BAD and B DA, but the angle A B C is equal to the angle B AC; therefore the angle B A C is equal to the angles B A D and B D A, and therefore the angle A D B = BACBAD. Q. E. D.
[At the last moment we have been unable to obtain the rest of the Questions set. We must apologise to our readers for the incompleteness of this first issue, which we hope to make up for in the February number. We have given Test Papers on Geography and Arithmetic, to compensate in part for the omission of these papers.-ED.]
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