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1
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dh 24. From subtract

Ans.

denominators, may be omitted. The answer is then
2263
a3b3

ry

adh

be retained, the product will be ; and this reduced to 1 1

1
25. From subtract
Ans.

ary
2
*+1°
2? +2

dh
lower terms, will become the same answer as before,

a-6-3 26. From 7 subtract 37 Ans, 43 6

70

ad m η
ah

ah
11. Multiply
and together.

Ans. m2 3a 2d

6 4x4 27. From subtract Ans.

atd my

amtam 12. Multiply by

Ans.

al

ar 22 g

2ya 28. From 1 subtract

Ans.
22ty

amtd h

Зg" 13. Multiply

and

together. h

ба MULTIPLICATION OF FRACTIONS.

zamrt3dr

Ans, 140. By the definition of multiplication, to multiply by a

5am fraction is to take a part of the multiplicand as many times as there are like parts of an unit in the multiplier,

143. To multiply a fraction and an integer together.

RULE.--Multiply the numerator of the fraction by the integer, Thus : suppose a is to be multiplied by Here, a fourth and the product with the same denominator is the answer; or divide

the denominator by the integer, and the quotient with the same

numerator is the answer.
;
and this taken three times is ++

4

4

14. Multiply by ac За and so of other cases,

Y 4

Here Хат

For a

은, * 141. To nultiply one fraction by another,

y
g

Y

Y Multiply their numerators together, and also thoir denominators;

Ans. the products are respectively the funerator and conominator of the

15. Multiply by.d.
30
d

3bd 1. Multiply by

Ans. 27

2cm Here, dividing the denominator by a, we have which is

3

a

part of a is

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4. Multiply 24q+3°c

by 8.

by 5x.

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203.

3%

it was, without being pointed, it might be translated either “ Thou 5%

2 Ans.

shalt go, and shalt never return, thou shalt perish in battle," or 2 36

26

| " Thou shalt go and shalt return, thou shalt never perish in battle."

The correct translation depends on the placing of a comma after the 3aty

3xty Ans.

word nunquam, or after redibis. 24a

3a +40

The invention of the modern system of punctuation has been

attributed to the Alexandrian grammarian Aristophanes, after +6

ato 5. Multiply

Ans.

whom it was improved by succeeding grammarians; but it was so 20625xy

4+5y entirely lost in the tirae of Charlemagne, that he found it necessary

to have it restored by Warnefried and Alcuin. It consisted at first 3 42

40 of only one point, used in three ways, and sometimes of a stroke, and

Ans, 3

together. 7

b

formed in several ways. But as no particular rules were followed in the use of these signs, punctuation was exceedingly uncertain,

until the end of the fifteenth century, when the learned Venetian abcd 3x-ty 7. Multiply by

Ans. 1.

printers, the Manutii, increased the number of the signs, and esta3xty abed

blished some fixed rules for their application. These were so gene

rally adopted, that we may consider them as the inventors of the ab

Y 8. Multiply

present method of punctuation; and although modern grammarians by

Ans. 6

bave introduced some improvements, nothing but a few particular

rules have been added since their time. 3

38 Ans.

The design of the system referred to was purely grammatical, and x 7

4d" had no further reference to enunciation, than to remove ambiguity

in the meaning and to give precision to the sentence. This, thereatb

fore, is the object of punctuation, and although the marks employed 10. Multiply by

Ans.

in written language may sometimes denote the different pauses and 4 3

12

tones of voice which the sense and accurate pronunciation require,

yet they are more generally designed to mark the grammatical be 11. Find the product ex

Ans. 2abc.

divisions of a sentence, and to show the dependence and relation of 3:1

words and members which are separated by the intervening clauses.

The teacher, therefore, who directs his pupils to " mind their pauses 24ab 3xy

9 by in reading," gives but an unintelligible direction to those who are 12. Find the product X Х

Ans,
37 sa
7

4

unversed in the rules of analysis. A better direction would be to disregard the pauses, and endeavour to read the sentence with just

such 22-422

pauses and tones as they would employ if the sentence were 13. Multiply by

their own, and they were uttering it in common conversation. In*+28

deed it is often the case that correct and tasteful reading requires Ans. a*? -20. pauses, and these too of a considerable length, to be made, where

such pauses are indicated in written * language by no mark what72

a48

It is not unfrequently the case that the sepse will allow no 14. Multiply by

Ans.
Oxual ma

pause whatever to be made in cases where, if the marks alone were

observed, it would seem that a pause of considerable length is re1 tata 1-a

1-3

quired. The pupil, therefore, who has been taught to mind his 15. Multiply

by

Ans,

pauses, must first be tanght to unlearn this direction and endeavour 1-5+62 1 +

to mderstand the sentence which he is to read, before he attempts

to enunciate it. 2y

4xy 16. Multiply l- by 2+

Ans.

The characters employed in written language are the following: xty

The Comma,

The Hyphen, 633_4.1--9-26 3x3+242 +9376

The Semicolon,

The Breve, 17. Multiply

by
62.h+3x+2

The Colon,
623-4422--9-76

The Apostrophe,
The Period,

The Brace,
The Dash,
1826 +1931-93x9 +36
Ans.

The Exclamation,

The Acute Accent,
362.-52x4-9622_437* +12° The Interrogation,

The Grave Accent,
The Quotation Marks

The Circumflex Accent,
The Diæresis,

The Caret,
The Crotchets,

The Cedilla,
LESSONS IN READING AND ELOCUTION.-No. I.

The Brackets,

The Asterisk,
The Obelisk or Dagger,

The Section,
PUNCTUATION.

The Double-Obelisk or

The Paragraph,
Double Dagger

The Parallels,
PUNCTUATION is peculiar to the modern languages of Europe. It
was wholly unknown to the Greeks and Romans; and the languages The Ellipsis, sometimes expressed by Periods, thus,
of the East, although they have certain marks or signs to indicate

sometimes by Hyphens, thus, tones, have no regular system of punctuation. The Romans and the

sometimes by Asterisks or Stars, thus, Greeks also, it is true, had certain points, which, like those of the

sometimes by a Dash prolonged, thus, languages of the East, were confined to the delivery and prounciation of words ; but the panses were indicated by breaking up the written

These characters, when judiciously employed, fix the meaning matter into lines or paragraphs, not by marks resembling those in the and give precision to the signification of sentences, which, in a modern system of punetuation. Hence, in the responses of the written form, would be ambiguous or indefinite without them. ancient oracles, which were generally written down by the priests Thus," I said that he is dishonest it is true and I am sorry for it.” and delivered to the inquirers, the ambiguity-doubtless intentional Now the meaning of this sentence can be ascertained only by a

- which the want of punctuation caused, saved the credit of the correct punctuation. If it be punctuated as follows: “I said that oracle, whether the expected event was favourable or unfavourable. he is dishonest, it is true, and I am sorry for it;" the meaning As an instance of this kind, may be cited that remarkable response will be, that it is true that I said he was dishonest, and I am sorry which was given on a well-known occasion when the oracle was that I said .so. But if it be punctuated thus, “I said that he was consulted with regard to the success of-a certain military espedition. • Ibis et redihis nunquam peribis in bello." Written, as Wigritten here, of course, includes printed language.

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dishonest; it is true ; and I am sorry for it;" the meaning will sound of the vowel, is called the Macron, from the Greek, signifybe, I said that he was dishonest; it is true that he was dishonest, ing long. and I am sorry that he was so.

The mark called a Breve, indicating the short sound of the Again, the following sentence, as here punctuated, is an innocent vowel, is from the Latin, signifying short. remark: "

“ Beliering Richard Brothers to be a prophet sent by The word Ellipsis, also from the Greek, means an omission, and God, I have painted his portrait.' But the sentence, as it was properly refers to the words, the members, or the sentences originally written by its author, with the comma after sent, instead which are omitted, and not to the marks which indicate the omisof after God, is a piece of horrid profanity.

sion. A further instance of the importance of correct punctuation was

The word Apostrophe, also from the Greek, signifies the turning afforded by a late advertisement, in which the commissioner for away, or the omission of one letter or more. The word apostrophe, lighting one of the most commercial cities of Europe, by the mis- as here used, must not be confounded with the same word as the placing of a comma in his advertisement, would have contracted for name of a rhetorical figure. the supply of but half the required light. The advertisement repre

The word Diæresis is also from the Greek, and signifies the sented the lamps as “ 4,050 in number, having two spouts each, taking apart, or the separation of the vowels, which would othercomposed of not less than twenty threads of cotton. This ex-wise be pronounced as one syllable. pression implied that the lamps bad each two spouts, and that the The term Accent is derived from the Latin language, and imtwo spouts had twenty threads, that is, each spout had ten threads. plies the tone of the voice with which a word or syllable is to be But the meaning that the commissioner intended to convey was, pronounced. that each spout had twenty threads; and his advertisement should The word Section, derived also from the Latin, signifies a cuthave had the comma after “ spouts," instead of after “ each," thus: ting, or a division. The character which denotes a section seems The lamps have two spouts, each composed of twenty threads, &c. to be composed of ss, and to be an abbreviation of the words

These instances night suffice to illustrate the nature and the signum sectionis, or the sign of a section. This character, which propriety of correct punctuation ; but the following instance, was formerly used as the sign of the division of a discourse, is known to many, will show the importance of the subject. The now rarely used except as a reference to a note at the bottom clerk of a congregation, in Scotland, had a paper handed to him, of the page. as the custom is, to read just before the minister stood up to

The word Paragraph is derived from the Greek language, and

pray with and for the congregation, containing the following words, un signifies a writing in the margin. This mark, like that of the secpointed: “A man going to sea his wife desires the prayers of the tion, was formerly used to designate those divisions of a section congregation.” The clerk read it as if a comma had been put at the which are now indicated by unfinished lines or blank spaces. end of the word wife, and unfortunately excited, in no small de- This mark, as well as the section, is now rarely used except as gree, the risible faculties of the people assembled :---thus, “A a reference. man going to sea (see) his wife, desires the prayers of the congre

It may further be remarked, that notes at the bottom of the gation,

page, on the margin, or at the end of the book, are often indiBut although the meaning of a sentence is thus materially af- cated by figures, or by letters, instead of the marks which have fected by the punctuation, it will be seen in the following lessons already been enumerated. that the punctuation alone is an unsafe guide to follow in the enun

The word Caret is from the Latin, and signifies it is wanting. ciation of any collection of words. For, in many cases, these This mark is used only in manuscripts. marks indicate no pause, emphasis, or other remarkable circum

The Cedilla is a mark placed under the letters c and g to indicate stance requiring notice in the enunciation of the sentence.

the soft sound of those letters. The nature of the marks used in written language may also be

The Asterisk, Obelisk, Double Obelisk, and Parallels, with the understood by a reference to the origin of their names.

section and paragraph, are merely arbitrary marks to call attention The word Comma is derived from the Greek language, and pro- to the notes at the bottom of the page. perly designates a section, or part struck off from a complete sen

As these marks which have now been enumerated all have a tence. In its usual acceptation, it signifies the point which marks meaning, and are employed for some special purpose, it is recomthe smaller portions of a period. It therefore represents the short-mended to the student never to pass by them without being assured est pause, and consequently marks the least constructive, or most that he understands what that purpose is. Correct and tasteful dependent parts of a sentence.

reading can never be attained without a full appreciation of the The word Colon is from the Greek, and signifies a member of a meaning which the author intended to convey; and that meaning sentence, and the Latin prefis semi means half. Hence, a Semi- is often to be ascertained by the arbitrary marks employed by him colon is used for the purpose of pointing out those parts of a com

for the purpose of giving definiteness to an expression. At the pound sentence, which although they each constitute a distinct same time the student should consider these marks as his guide to proposition, have yet a dependence upon each other, or on some the meaning only, not to the enunciation of a sentence. Correct common clause. The Colon is used to divide a sentence into cpre delivery must be left to the guidance of taste and judgment otheror more parts, which, although the sense be complete in eacti.

wise acquired. not independent.

In many excellent selections for lessons in reading, the pieces The word Period is derived from the Greek, and means a ciru., have been arranged in regular order, according to the nature of or well-rounded sentence. Hence, when the circuit of the s heir respective subjects, under the heads of Narrative, Descriptive, completed, with all its relations, the mark bearing this name is Didactic, Argumentative, and Pathetic pieces, Public Speeches, used to denote this completion.

Promiscuous pieces, the Eloquence of the Bar, of the Pulpit and The word Interrogation is derived from the Latin, and means ooi the Forum. question. Hence, the mark so called is put at the end of a By Narrative pieces is meant those pieces only which contain a question.

simple narration or story. Descriptive pieces are those in which The word Exclamation is from the same language, and means something is described, chiefly from nature. Didactic pieces are a passionate utterance. Hence, the mark so called is put at the those designed to convey some particular kind of instruction, end of such utterances.

whether moral, religious or scientific. Argumentative pieces are The word Parenthesis is derived from the Greek language, and those in which some truth is designed to be proved in an agreemeans an insertion. A sentence, clause, or phrase, inserted between able manner. Pathetic pieces are those by which the feelings of the parts of another sentence for the purpose of explanation, or of pity, love, admiration and other passions, are excited. Promiscalling particular attention, is properly called a parenthesis. cuous pieces are those which do not fall exclusively under any of It is to be remarked, however, that the name parenthesis belongs the classe

name parenthesis belongs the classes which have been enumerated, or which consist of a only to the sentence inserted between brackets or crotchets, and not to mixture of those classes. The Eloquence of the Bar consists of those marks themselves.

speeches (or pleas as they are technically called) made by distinThe word Hyphen is derived from the Greek language, and sig- guished lawyers in the courts of justice in favour of or against a nifies under one, that is, together ; and is used to imply that the supposed criminal. The eloquence of the Pulpit consists of serletters or syllables between which it is placed are to be taken mons or discourses delivered on religious occasions. The Elotogether as one word.

quence of the Forum consists in the speeches, addresses, orations, The hyphen, when placed over a vowel, to indicate the long 1 &c., addressed to political or promiscuous assemblies.

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To many, this information may seem superfluous or puerile. But Whom he carries along with | Send me, man-da-te-mi ast hese lessons are designed for the young and the unlearned, it must him, ch'é-gli -na -co Dozen, doz-zi-na (cs), f. not be forgotten that their sources of information are few and that Beggar, men-di-co, m.

Lemon, li-inó-ne, m. they will not always take the pains to inform themselves of the Who follows him, che gli va Two, -e meaning of words, even when they are familiar to their eyes in die-tro

Pound, lib-bra, f. capital letters, and in the running titles of thie books before them Here are, éc-co

Fig, fi-co, m. (pl. ji-chi) every day. It is often the case that the teacher also, taking for Ten, die-ci

Which you have received, che granted that his pupils are familiar witb the meaning of words se Yard, bruc-cio, m. (pl. le brúc- a-se-te ri-ee-oz-often presented to their eyes, negłects to question them on the cia, f.)

From, ja subject; and in riper years it becomes a matter of surprise to the Taffeta, taf-fe-, in.

Smyrna, Smir-na pupil himself that, in early life, words which he had heard sounded Some of which you wanted, Spare me, ce-ide-te-mi almost every day at school presented no idea to his mind beyond del quá-le vo-le-oc-te - -re Bottle, fia-schet-ta, f. that of an unmeaning, or ratber an unintelligible sound.

Twelve, do-di-ci

Eau, á-cqua, f. (water) The object of all education is not so much to fill the mind with Cambric, -la ba-ti-sta, f. Cologne, Co--nia knowledge as to strengthen its powers, and enlarge its capacity. Which ycu have demanded, which has been sent to you, Those exercises, therefore, are always most beneficial in education,

che c--te do-man-du-ta

che vi è stú til man-du-ta which tend most effectually to produce this result. There is, perhaps, no branch of study connected with popular education, which, when

A properly pursued, is more highly subservient to this end than the

The use of this particle frequently coincides with the use of study of correct and tasteful reading, as an art. It necessarily the preposition to in English grammar. Generally speaking, inrolves a complete knowledge of the subject to be read, the rela- any kind of directior., expressed by a verb, to or towards a pertion and dependencies of the phrases, clauses and members of the son or thing, is denoted by this word. The ideas of siinilurity sentences, the proper meaning of the words employed, and the or resemblance, of approaching or approximation, of a direction or connexion between the sentences themselves. This cannot be mere reference to any thing, end, aim, or point of time, forn, acquired without a vigorous employment of the perceptive powers, as it were, only parts or branches of this fundamental significiiaided by those of comparison, of analysis, of reasoning, of judg- tion of the particle a, and whenever the action of the subject of ment, of taste, and of discrimination. Subordinate and auxiliary a sentence (i. e. of the nominative) expresses such direction or to the acquisition of this important art, the student is recommended approach to or towards persons or things, a must be placer? to exercise also the power of classification, while studying a read- bəfore then; e. g. ac--sta-ti il-la -vo-la, approach thyself ing lesson (which should always be studied previous to practising to the table; al--ne äá-te gli ós-si, give the bones to the dog; it), to ascertain under which of the above mentioned classes, lit ti-gli ras-50-mi-ylia al -dre, the son is like the father; no whether narrative, descriptive, didactic, &c., the piece ne is about par.ie-al cu-gi-120, I shail speak of it to the cousin; al cár. to read belongs. The student who thus employs his faculties cannot ito si ri-co-no-sce luc-cêl-lo, by the song one knows the bird ; fail to feel a vigorous growth of intellect springing up in his own ( a-v1-0 non pên-sa che al da-md-ro, the avaricious man only mind, and will be amply compensated for his labour, by a com- thinks of money; 2-o lo dis-si al a-mi-co -stro, I told it your mand over the stores of literature not to be gained by any other friend ; é-gli lo' diê-de a -ve-ri, he gave it to the poor; 1-0 method.

-do a -ma, I go to Rome; non cre--te a -ro, do not believe them; dis-si a lui, an-da-te a -sa, I told him, go honie

(i. e, to the house); pic-chiá-re ál-la pôr-ta, to knock at the LESSONS IN ITALIAN GRAMMAR.No. XVI.

door; scri-ve-re a qual-che--no, to write to somebody; age

giú-ge-re it-ma cổ-sa ad an al-tra, to add one thing to another; BY CHARLES TAUSENAU, V.D.,

-de-re -o di-rit-to a qual-che--no, to transmit or cede one's of the University of Pavia, and Professor of the Italian and German right to any one ; co-strin-ge-re ú-no ad ú-na Q-wió-ne, to compel Languages at the Kensington Proprietary Grammar School, or force any one to some action; ver-a méz-o giór-no, a méz

za arôt-te, el-le -e, al têm-po fis-sd-to, al pri-ino del -se, I shall VOCABULARY.

come at noon, at midnight, at two o'clock, at the appointed Time, têm-po, m. Use, ú-so, m.

time, on the first of the month. Present, a-des-s0 (adv, now) Vessel, vci-so, m.

Phrases, not literally or strictly expressing an abode, resiBest, mi-gliore Copper, ad-me, m.

dence, stay, continuance, or being in a place, but merely He had hidden himself, é gli Has been prohibited, è stri-to nearness or presence, require the particle a and not in, which si ê-a na-scó-sto

pro-i-bi-to

always denotes a real and not merely imaginary continuance Room, stán-za (or ca-me-ra) Sweden, Svê-zia

or being in (i.e. in the interior of) a place or thing, cr some Back, die-tro (ady, behind) Shambles, bec-che-ria, action taking place in it; e. g. é-gli è al bál-lo, he is at the ball; Our, mô-stro, m., -stra, f. (slaughter-house)

aja-ti-ro, at the (dancing and gaming) evening party; a tiHas, ha

Are for sale, si trôat'l terzo-la, at table; al con-cêr-to, in the concert; a gino--re, ai Bridge, pón-te, m.

vén-de-re

pisy or game; a stu-dia-re, (engaged) in study. Stone, pie-tra, s. f.

Meat, cár-ne, f.
Yours, -stro, m., mô-stra, f. Young ox, mán-zo, m.

t..? what has been explained, it is obvious that in those Has only, ha so-la-nnén-te Calf, vi-têl-lo, m.

phrases which merely denote the moving, approaching, or One, ú-no, m., ú-na, f. Wether, ca-stro-ne, m. (meat tendency to or towards a place or thing, and not strictly

' the Wood, -gno, m.

of ox, of calf, of wether)

entering or penetrating into it, a and not in must be used; for Edward, E-du-ár-do What means, che si-gni-fi-ca

in menns the actual motion or penetration into the interior of Has received, ha ri-ce-vu-to Ringing, sun-no, m.

any locality; e... i-o -do al bál-lo, I go to the ball; a triFrom, da Bell, cam--na, f.

vola, to table; « -na, to supper; a im-pa-ru-le, to learn, i.e. Watch, 0-90--gio (o-re--lo) What do you say, che di-te

to the pursuit of) learning; a giuo--re, to play, i. e, to (the Gold, ô-90, s. m.

(with the case-sign di)

diversion of) playing. Sword, spá-da, f.

Which I have bought, che The proper nouns of towns, cities, boroughs, or similar locaSilver, ar-gên-to, s. m

com-prd-to

lities, are an exception to the last-mentioned rule, for it is Pair, -jo, m. It is, és-80 è

quite allowable indiscriminately to place a or in before thein Shoe-buckle, fib-bia, f.

Good, buô-no, m., buônna, f. wherever the abode, residence, stay, arrival, continuance, or Steel, ac-cid-jo, s. m.

Fine, fi-no, m., fi-, f. being in or within them (i. e. in their interior) is to be Once, ú-na vól-ta Colour, co--re, m.

designated ; e. g. é-gli è a or in -po-li, he is at or in Naples; They wore, si por--va-no

tro-van-do-si e-gli i-na vól-ta a Pa-ri-gi, being once in Paris; Dress, á-bi-80, m.

Wor Cloth, pán-no, m.

-te (with the case-sign di) The verbs par-ti-re, to depart, set out or off, and con-ti-nuWaistcoat, gi-lè, m. (pl. un. Man, đuô-70, m.

d-re, to continue, proceed on (one's journey), are another exaltered)

Whom you see, che ve-de-te ception, for they require the preposition per before the name Velvet, vel--to, m. Boy, re-gáz-20, m.

of that locality or even country, towards which a journey or

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LECTURES ON EUCLID.

BOOK I.--PROPOSITION XXI.-THEOREM:

any motion is directed; e. g. é-gli è par-ti-to per Co-stan-ti-no- | for life to the galleys ; ès-86-re sen-st-bi-le a quál-che cô-sa; to feel po-li, per Fie-tro-búr-go, per la Sviz-ze-ra, he has started for compassion for (or to be susceptible of) something by the Constantinople, for Sč. Petersburgh, for 'Switzerland; con-ti- preposition by; è. g. lo fa-rái a fôr-za, thou wilt do it by contot-4-re ii -o viag-gio per la Pa--nia, per -sca, to proceed on straint: by the preposition of; e. g. chiê-de-re ad al-cu-no, to one's journey to Poland, to Moscow.

desire or require of somebody: by the word as; e. g. mêt-terNext to di, the particle a is of the most extensive use, and servant ; a-vé-re a si-gnó-re, to have as a master: by at a time;

si a sêr-vo con al--no, to engage one's self to somebody as a though the relations in which this word stands to others are not quite so loose and vague as those of di, they are various expressions or phrases; e. g. a beson ser-cd-to, at a small price,

e. g. a -e a -e, two at a time, two and two: by adverbial enough to admit of modes of application which, even in cheap ; ál-la sca-pe-stra-ta, licentiously, dissolutely; dl-la pegItalian, might sometimes be more suitably dispensed with by gio, as bad as possible ; -la rin-ft-sa, confusedly, promiscuthe use of prepositions of a more logical distinctness

, and conse- ously; a mén-te, a me-mo-ria, by heart (to learn or know); quently a greater clearness in special instances ; e. g. non--bóc-ca, by word of mouth ; ve-ni-re al-le ma-ni, to come to blows re a ca-val-lo (for só-pra un 64-vál-lo), to get or mount on horse or to engage in close fight; an-da-re a spás-80

, & di-pôr-to, to, back; - a pô- di gior-a ri-ton-mò (for do-po -chi gió-mi), he take

awak; 4 quát-tro đe-e, a te-sta a -sta, in private, alone returned a few days after ; -re a vo-lon-ta di cia-sci-no (for together (t.e. between four eyes, tête-à-tête); * a ba-stdm-reno se-con-do la vo-lon-ta), to act according to, or to conform to the enough; a má-no, at hand, near at hand, in readiness; with will of everybody ; bat--an-si a pál-me (for col-le pál-one), they or by the hand; artificially; by election; underhand, by fraud fought with the palms of their hands; le rot-tu-re fic-ro-no mu

or deceit. -te a pie-tra e a cal-ci-na (for con piê-tra e con cal-ci-na), the breaches were walled up with stone and lime; non ci con-ver- I have already stated that to avoid hiatus by a succession of com-bát-te-re a si -ca gên-te (for con-tra si -ca gén-te), it Fowels, generally ad, in the place of a, is used before a vowel, will not become us to fight against so few; mól-ti fán-no -ne and I shall conclude this explanation of the uses of a by the a spe-rán-za di gua-di-gno (for per i-spe-rán-za), many are honest remark that, in Italian classics, not a few passages, where at through the hope of profit, &c.

first sight the particle a appears to be a somewhat arbitrary It is obvious that this variety of the significations of a will, of construction, will admit of a perfect elucidation by ellipsis.

substitute for other prepositions or words, without any change for the purpose of translating it into English, require the use of many prepositions or other words, and sometimes even of Other uses, and some omissions of the particle a, will be adverbial expressions or phrases, which only practice and a commented on hereafter. patient method of reading good writers, by accurately comparing the idioms and genius of the two languages, fully can teach. In a course of merely elementary lessons, I must naturally restrict myself to some, I think, useful hints in the

LESSONS IN GEOMETRY.NO. XXV. following illustrations :—The particle a may be translated by the objective case (without any preposition); e. g. fá-re ve-dére ad al--no d-na -sa, to let any one see something; do-man-du-re ad al-ci-no, to ask one; toc--re ad

(Continued from p. 196.) al-ci-no, to concern one; 80-prav-vi-ve-re ad al--no, to survive one; sup-plí-re a qudl-che -sa, to complete or make up something: by the preposition to e. g. ap-pli-car-si ad If from the ends of one side of a triangle, there be drown two ú-na -sa, to apply one's self to something ; vôl-ger-si ad al-cú- straight lines to a point within the triangle, these together shalı no, to turn to somebody; a si-ni-stra, a mán-ca, to the left; be less than the other two sides of the triangle, but shall contain a -stra, to the right; an--re, ve-ni-re a un luogo, to go, a greater angle. come to a place; do-lén-te a môr-te, grieved to death ; pas-re a fil di spa-da, to be put to the sword (i. e. to the edge of c, the ends of the side B C, let the two straight lines BD and

In fig. 21, let A B C be a triangle, and from the points B and the sword) : by the preposition at; e. g. al le-vár del -le, at C'd be drawn to the point D within the triangle. Then B D and sun-rise ; al pri-mo cén-no, at the first hint or sign; a mi-o sén- pc together shall be less than the other two sides B A and AC 520, to my mind, liking, taste, fancy, will ; se--re a -yo-la, to of the triangle A B C, but shall contain an angle BDC greater ·sit at table; és-se-re (stá-re, tro-vár-si) a un lrtó-go, to be at a than the angle BA C. place: by the preposition on or upon; 'e. g. a -na di mor-te, upon (or under) pain of death; af-fi-dár-siad al--no, to reckon

Produce BD to E. Then, the two sides B A and a E, of the of build upon one ; ap-po-giar-si a qual-che co-sa, to lean, rest; side PE (I. 20). To each of these un

triangle A BE are greater than the third or to rely on something; in-si-ste-re a quil-che co-sa, to insist side 2 (1. 20); on something; a piê-di, a ca-vál-lo, on foot, on horseback;

equals add Ec, and the two sides BA and con-di-zió-ne, on condition ; ad im-prê-sti-to, 'on trust or credit: AC are greater (As, 4) than Be and go. by the preposition in; e. g. a -e mé-si, in two months ; il-la Again, the two sides ce and ed of the sfug-gi-ta, in passing by or in flight; di-pin-ge-re a 6-glio; to third side CD.

To each of these unequals,

triangle CE D are greater (I. 20) than the paint in oil; ve-sti-to a bicen-co, dressed in white; ál-la fran-se, all in glé-se, in the French, English manner or fashion; dia add B, and the two sides c E and EB are all' o-réc-chio , to say or whisper in any one's ear; a têm-po, has been shown that B'A and A C are greater than BE and E C.

greater (Ax. 4) than cd and DB. in time, in the nick of time; de-ri-re a grán-di schiê-re, to come Much more then are BA and A c, greater than B D and Dc: in great crowds or masses : by the preposition according to (or after); e. g. a ma-nie-ra, after the manner or fashion; a 8.-chio,

Again, the exterior angle BDC of the triangle o D E is greater according to a measure taken merely by the eye; a vo-lon-tà di than its interior and opposite angle CBD (I. 16). And the cia-sche-du-no, according to the will or liking of everybody: by exterior angle CEB of the triangle A BB is greater than its the prepositions against or towards ; e.g. ri-bel-lár-si ad al-cú- | interior and opposite angle BAC (Î. 16). But the angle BDC is R0, to rebel or mutiny against somebody; all' o-riên-te, all' oc- greater than the angle CE B. Much more, therefore, is the ci-dên-te, towards the east, west: by the preposition with; e g. angle BDC greater than the angle B AC. Wherefore, if from a tre cól-pi l' ueci-se, he killed him with three blows; an-dáre the ends of, &c. Q. E. D. a grán-di pós-si, to walk with long or great steps ; stä-re a bóc- Schobium. 1.--Respecting this proposition, Dr. Simson ca -per-ta, a 60-chi a-pêr-ti, a brác-cia a-pêr-te, à -po chi-no, a makes the following observation: "Mons. Clairault, in the chio-me sciol-te, to stand with an open or gaping mouth, with preface to his Elements of Geometry, published in French at open arins, with the head inclined, with dishevelled hair; a bri- Paris, anno 1741, says that Euclid has been at the pains to glia sciôl-ta, with slackened reins, at full speed or gallop; cor- prove that the two sides of a triangle which is included within ri-spón-de-re ad al-cis-no, to agree with somebody; 2-ni-to ad al- another, are together less than the two sides of the triangle. -no, united with somebody; pa-ra-go-rd-re ú-na co-sa a qual which includes it :' but he has forgot to add this condition, che as-sa, to compare one thing with another : by the preposi. viz. that the triangles must be upon the same base: because tion for ; e. g. con-dan--to å vi-ta ál-le ga--re, condemned unless this be added, the sides of the included triangle may be

Fig. 21.

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D

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