ama aut cujus vocem libentissime audiret, ejus a quo sua virtus optime praedicaretur. Itaque ille Marius item eximie L. Plotium dilexit, cujus ingenio putabat ea quae gesserat, posse celebrari. Praedicaretur, audiret, patiatur. 3. Sed tamen cum in animis hominum tantae latebrae sint et tanti recessus, augeamus sane suspicionem tuam : simul enim augebimus diligentiam. Nam quis est omnium tam ignarus rerum, tam rudis in re publica, tam nihil umquam nec de sua nec de communi salute cogitans, qui non intelligat tua salute contineri suam et ex unius tua vita pendere omnium ? Sint, augeamus, intelligat. 4. Etenim quaero, si quis pater familias, liberis suis a servo interfectis, uxore occisa, incensa domo, supplicium de servo non quam acerbissimum sumpserit, utrum is clemens ac misericors an inhumanissimus et crudelissimus esse videatur? Mihi vero importunus ac ferreus, qui non dolore et cruciatu nocentis suum dolorem cruciatumque lenierit. Videatur, lenierit. Frigida, Daphni, boves ad flumina; nulla nec amnem Et foliis lentas intexere mollibus hastas. Quid delubra iuvant ? Est mollis flamma medullas Quam procul incautam nemora inter Cresia fixit Dictaeos; haeret lateri letalis arundo. Write out metrically in 6, lines 6 and 7. ARITHMETIC. X 2.25 3 [Give the whole work.] 1. THE sum of of of and is how many times 0.5 their difference ? 2. A owns is of a field, and B owns the remainder; } of the difference between their shares is 5 A.3 R. 161 P. What is B's share in acres ? 3. A man earns $325 in 2 months, and spends in 6 months what he earns in 43 months. What does he save in a year? 11.846 x .004 4. Find, by logarithms, 1 of ♡.0777 How many 5. One decagramme is 0.3527 oz. Avdp. pounds Avdp. are there in a quintal? 6. What per cent is gained in buying oil at 80 cents a gallon, and selling it at 12 cents a pint ? 7. If 12 pipes, each delivering 12 gallons a minute, fill a cistern in 3 h. 24 min., how many pipes, each delivering 16 gallons a minute, will fill a cistern 6 times as large in 6 h. 48 min. ? 8. Find the cube root of 0.001295029. ALGEBRA. COURSE I. [Write legibly and without crowding; give the whole work ; and reduce the answers to their simplest forms.] 1. SUBSTITUTE Y +3 for in * -208 + 2x2 -3, and simplify and arrange the result. a— bc + b 2. Divide by the product of and 4y ca 22' a2 + ax 3x 6. Find the least common multiple and greatest common divisor of x2 + 4x 21 and 22 2 - 56. 7. It takes A 10 days longer to do a piece of work than it takes B: and both together can do it in 12 days. In how many days can each do it alone ? ADVANCED ALGEBRA. [Give the whole work.] 1. SOLVE one of the following equations: 2018 4x 22 -1 (a) + = 39; 2 2+1 (6) 22 - 2x +6 V 22 - 3x +2=x+14; (c) x1 + x-2= 6. 2. One root of the equation 8 -37x = 84 is 3. What are the other two roots ? 3. The sum of a certain number of terms of the series 21, 19, 17... is 120. Find the number of terms, and the last term. 4. The sum of three numbers in Arithmetical Progression is 15; if 1, 4, and 19 be added to them respectively, the results are in Geometrical Progression. Find the numbers. 5. With the digits 1, 2, 4, 5, 7, 0 how many even numbers between 100 and 1000 can be formed ? 17. A sets off from London to York, and B at the same time sets off from York to London, and each travels uniformly: A reaches York 16 hours, and Breaches London 36 hours, after they have met on the road. Find in what time each has performed the journey. PLANE GEOMETRY. a 1. DEFINE a plane, a parallelogram, a trapezoid, a tangent to a circle. 2. Prove that when two triangles have two sides of the one respectively equal to two sides of the other and the included angle of the first greater than the included angle of the second, the third side of the first is greater than the third side of the second. 3. Show how to draw a tangent to a circle from a point without the circle, and prove your method correct. 4. Draw from one of the vertices of a triangle a line cutting the opposite side into parts proportional to the other two sides. Give proof. 5. Prove that the square described on the hypothenuse of a right triangle is equivalent to the sum of the squares described upon the other two sides. 6. Given two similar polygons, to construct one similar to them both and equivalent to their sum. 7. Given + (the ratio of circumference to diameter) andr (radius). Find expressions in terms of r and r for the circumference and area of a circle. π SOLID GEOMETRY. 1. PROVE that, if two planes are perpendicular to each other, the straight line, drawn through any point of the common intersection perpendicular to one of the planes, must be in the other plane. 2. Prove that the solidity of any parallelopiped is the product of its base by its altitude. |