2. Explain the rule for " borrowing"

in subtraction.

3. Explain the principle on which the rule for division is founded. The quotient being 15,238, the remainder 86, and the divisor 144, find the dividend.

From 1234
Take 345

889

5 from 4 we cannot; but if we borrow 1 out of the 3 tens (leaving 2 tens) and treat it as 10 units, we shall now have 14 units in the upper line; we can now say 5 from 14, 9, i.e. 9 units, and we set down 9 as the units-figure of the result. We have now to take 4 tens from 2 tens (3 tens1 ten), and so on.

Division is the method of finding how often one number is contained in another, i.e. how often one number must be taken to make up another. Hence Division bears the same reference to Subtraction as Multiplication bears to Addition; for we might go on subtracting the divisor from the dividend, and then from the 1st remainder, then from the 2nd remainder, and so on, until the final remainder is either zero, or is less than the divisor itself; and if we counted the number of times we had subtracted it, this would be the result required, or, as is called, the quotient. But the multiplication-table will enable us much more easily to divide one number by another; thus, since 7 times 9 is 63, if we divide 63 by 7 we shall have the quotient 9, or if by 9, the quotient 7. (Vide Colenso.)

7. In a given year the Income-tax was 6d. in the pound and yielded £6,184,166: what was the amount of income taxed?

8. Reason out a test for determining by a method short of actual division, whether a number be divisible by 11 without a remainder.

9. There are three quantities: (a) £5, (b) 8s., (c) 75 gallons. Multiply one of them by the quotient of the other two. State accurately the result of the operations, and perform it in as many ways as possible.

Example :-392381=

300000+90000+2000+300+80+1=

3×100000+9×10000+2× 1000+3×100+8×10+1= [+1=

3(100001-1)+9(9999+1)+2(1001—1)+3(99+1)+8(11−1) 300003-3+89991+9+2002—2+297+3+88—8+1

-349-243-8+1. Therefore 392381 is divisible by 11 and does not leave a remainder.

As like concrete numbers can only be divided by one another: therefore

£588. =
12, hence 8s. is contained 12} times in £5;
88.£5, hence £5 is contained th times in 88.
Then 75 gallons x 124 937 gallons,
and 75 gallons X

=

6 gallons.

Verbs of asking, teaching, entreating and warning may have two accusatives, one of the person, and another of the thing: as

"Racilius me primum sententiam rogavit,"

"Quis musicam docuit Epaminondam ?"

66 Nunquam divitias deos rogavit."

"Quid nunc te litteras doceam."

"Cæsar flagitat frumentum Æduos."

"Puer partrem nihil celavit."

"Pacem te poscimus omnes."

Factitive verbs, that is, of making, calling, thinking and the like, have two accusatives, one of the object, the other of the complement: as

The ablative case is used to express―
Cause:

"Oderunt peccare boni virtuti amore."
"Cœptis immanibus effera Dido."

"Metu supplicii aut mortis multi vim tormentorum pertu-
lerunt."

sen

7. Translate the
following
tences:-(1) Nul-
lus dolor est, quem
non longinquitas
temporis minuat
ac molliat; (2)
Suo cuique ju-
dicio est utendum;
(3) Nemo morta-
lium omnibus ho-
ris sapit; (4) De-
mosthenes coronâ
aureâ donatus est
virtutis ergo; (5)
Alienum est mag-
no viro quod al-
teri præceperit id
ipsum facere non
posse.

Qua facie fuit, cui dedisti symbolum?"

"Cæsar traditur fuisse excelsa statura, colore candido, nigris oculis, valetudine prospera."

Respect:

'Angor animo."

(1) There is no sorrow which length of time may not lessen or soothe.

(2) Every one must use his own judgment.

(3) No mortal is wise at all times [hours].

(4) Demosthenes was presented with a golden crown on account of his valour.

(5) It is foreign to a great man not to be able to do what he has bid another.

VII. Latin Translations.

Candidates were required to translate three of the four following pieces selected from Virgil's Æneid, Book I.:

(1) From "Urbs antiqua fuit; Tyrii tenuere coloni; line 12; to Tantæ molis erat Romanam condere gentem;" 33.

(2) From " Æneas scopulum intereà conscendit, et omnem; 180; to Durate, et vosmet rebus servate secundis;" 207.

(3) From "At pius Æneas, per noctem plurima volvens; 305; to Aut spumantis apri cursum clamore prementem;" 324. (4) From "At Cytherea novas artes, nova pectore versat; 657; to Ne quà scire dolos, mediusve occurrere possit;" 682.

Passages were also selected from Livy, Book I.