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Easingwold

Encourage all honest and virtuous actions.

Encouragement most commonly animates the mind.

Formentera

Fame most commonly accompanies merit.

Fear is commonly the companion of quilly actions.

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Goodness and mercy the atticbutes of the Divinity.

Huntingdon

Humility most commonly leads to honour.

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THE POPULAR EDUCATOR,

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LESSONS IN LATIN.-No. XXIX.

not uncommon for a verb of one conjugation thus to pass into

another conjugation. By John R. BEARD, D. D.

ii. Sto, stěti, stāre, slātum, to stand (with abl. to cost). The
DEVIATIONS FROM THE MODEL-CONJUGATIONS. compounds with monosyllables have in the perfect stiti, as

consto (I consist of), constiti, constare ; participle future active.
The four conjugations are only so many classes into which
Latin verbs are puta These classes are determined by the with dissyllables retain slēti, and have neither supine nor par-

praestaturus, constaturus, obstaturus, &c. The compounds
tokens already stated, and the verbs in them are formed ac- ticiple future active; also circumsto (I stand around), circumsiēti

.
cording to the models already given, But the verbs which
make up these classes, do not exhaust the whole stock of

VOCABULARY.
Latin verbs. There are others that more or less depart from Circumdo, circumdedi, circumdăre, circumdă um (dat. and acc. or
the models. The verbs that depart from the models may, in acc. and abl.), to surround (some one with soinethiny) or lo put something
general, be ranked under three descriptions. i. They differ round some one ; consto, constě i, constare, constătum (abl.), lo consist
from the model-verbs in the perfect and the supine. ii. They of, to cost; persto, perste i, perstare, pers tātum, to continue; praesto,
differ from the model-verbs in other parts. iii. They lack several praestiti, praestare, praestitum and pracstátum, to stand before, is
parts which are possessed by the model-verbs. As these three be distinguished (with dat. to surpass) ; praestare se fortem, to shony
classes do not conform to the rule or standard afforded in the oneself vrave; obsto, I stand in the way of

, hinder; forum, i, n, a narkid; four conjugations, they might all be termed irregular. The stipendium, I, n, pay; interfector, o is, m, a slayer, murderer; proepithet irregular, however, is commonly applied only to the pugnator, oris, m, a defender; classis, is, f. a fleet; vestis, is, 1.e second class, and as no good reason compels us to depart from insperans, antis, hoping nothing, against hope , uber, uběris, rich; certo,

garment; conservatio, onis, 1. preservation ; invitus, a, um, unwilling; the ordinary usage in this case, we shall specially apply the certainly ; exirinsécus, adv., outwardly. denomination of "the irregular verbs to those verbs which differ from the models in other parts than the perfect and the

Observe that a noun or pronoun may be governed in the supine. The verbs which differ in the perfect and the supine ablative case by an adjective in the comparative degree ; exmay be callad deviational, as in a marked way deviating (de, ample: from, and via, a way) from the ordinary forms, and those that Noun. Aurum est gravius argento. are without certain parts may be termed defective (de, from,

Gold is heavier than silver. and facio, I make). Thus we obtain four classes of verbs. i.

Pronoun. Lux quâ nihil est carius. The regular, or those which mainly follow the paradigms of the

Light than which nothing is dearer. four conjugations. ii. The deviational, those that depart from This is a kind of abbreviated comparison. If the fuller those paradigins in the perfect tense and the supine. iii. The form with quam were used, then the noun after the quam irregular, those that depart from the paradigms in other parts. would be in the same case as that before quam ; e.: iv. The defective, those that are wanting in mood, tense, and

Full form. Nihil est divinius quam clementia. person. The verbs that follow the forms of the four conjuga

Nothing is more divine than mercy, tions are dignitied with the term regular, because such verbs exist in greater number than any other class. The same facts

EXERCISES.-LATIN-ENGLISK. may be set forth in this

Deus nobis dedit animum, quo nihil est praestantius; multo
VIEW OF THE LATIN VERBS.

sanguine nobis victoria stetit (cost, so we say stood in) mater om

nium bonarum artium sapientia est, quâ nihil a Deo immortali Regular.

Irregular.

uberius, nihil praestabilius hominum vitae datum est; Deus corpus, The Four Conjugations. I. Deviational. II. Irregular. III. Defective. quorum patres aut majores aliquâ gloriâ praestiterunt, (ii) student

ut quandem restem, animo circumdedit, et restivi: extrin sécus; The departure from the models would be very much lessened, plerumque eodem in genere laucis excellere; parentes córis : mos were we at liberty to enter at length into the processes. by ficium, qui invitus profuit; quinam magis sunt tui quam (i)

habere debemus, quod ab iis nobis vita tradita est; non dedit benewhich the present tenses now in use were formed, and exhibit quibus tu salútem insperantibus reddidisti? civcs acerrinos piethe real roots or stems of the several verbs. In the restricted

pugnatores libertatis se praestiterunt; ingens hominuin multitudo space, however, here at our disposal, we can only give one or

oratorem in foro circumstetit; eloquentia ad salutem homitum two instances. Take sino, I suffer or allow. You think the data ost a naturâ; eloquentia 'ad conservationem hominum daia stem to be sin. It is not so; the n is introduced into the est a naturâ; malus orator eloquentiam ad bonorum pestem, present merely for the sake of strength in pronunciation. The perniciemque convertit; quid est iam inhumanum quam ti quen stem is si. Sio would be a weak sound, two vowels coming fiam, a naturâ ad salutem hominum et ad conserrationem datam, id together; and the Latins preferred saying sino. From si, bonorum pestem, perniciemnque convertěre; stipendium ex longo teiphowever, is regularly formed both the perfect and the supine, pore militibus non erat datum; seditio inter milites orta est; quum thus : si, si-vi, si-tum. Take rumpo. Here, to obtain the stiperdium ex longo tempore non esset datum, seditio inter mullites stem, you must elide the m (that is, n which before becomes

orta est; tu mi amice, mihi fidem praestaturus es ; certo scio te m), and you have rup, from which are regularly formed rup-i nobis obstaturum est; victoriam adipiscamur ; credo, nihil nubis

mi amice, mihi fidem praestaturum esse; nihil nobis obstat; nihil and rup-tum. In cresco, you must in the same way leave outcbataturum esse, quominus victoriam adipiscimur; victoria con sc, and thus getting as the stem cre, you form the perfect by stitit multorum fortium virorum morte; non dubitabamus quin adding vi; e. g., cre-vi. I subjoin similar instances; sue-sc-0, multorum virorum fortium morte victoria constatura esset; perstasue-vi; pa-sc-o, pa-vi, no-sc-o, no-vi; so the supines, cre-ium, turus ne es in sententiâ tuâ ? Nescio perstaturus ne sis in sententiâ sue-tum, pa-stum (the s of the present is retained before the tus. t), no-tum. Disco represents a peculiar class of verbs; namely,

ENGLISH-LATIX. those that form i he perfect by what is called reduplication; that He gave the general a fieet; he will give thee a fleet ; dost thou is, the repetition«t the initial consonant with a connecting vowei, I think ihat he is about to give a fleet to my brother? nothing has thus : disco, dise arr, didici; the root' is properly dic; di(ci: cost men more (pluris) than avarice; God has given me a sis:er 8C-o, di-dic-i. H. ving given these intimations, and inviting than whoin nothing is dearer to me; my sister will show herself our pupils in due tiine to follow the thread, we now resume loving to me all her life (acc. with per); the soldiers showed thein. the order of the four conjugations, and shall set forth the selves very brave, but the victory cost the death of many brave men; principal deviations from the model forms.

nothing hinders our gaining the victory (hinders, lest we shouli

gain, stands in the way to prevent our gaining the victory); I I. DEVIATIONS IN TIIE FIRST CONJUGATION.

beliere we shall gain ihe victory; Socrates surpassed all philoso

phers; who does not know that Socrates surpassed all philo.o. 1. The Perfect with Reduplication.

phers ? dost thou believe that thy son will surpass all his equals ? i. Do, dedi, dăre, dăcum, to give; the a is short in the stems a great inultitude surrounds the orator; pay has

been As dăbam, dabo, dărein, except outs and dā. According to do given to the soldiers; will give pay to the soldiers; take care lest form the compounds of do, of which the tirst part is a dissyl- sedition arise among the soldiers; will thou persist in thy opinion? lable, as circumdo, circuindědi, circumdatum, circumdáre. I do not know whether I shall persist in my opinion. The compounds of do having monosyllables as prefixes follow It may be desirable to illustrate mor: tully the constructior the third conjugation, its addo, addére, aduidi, additum. It is of circumdare and quominus.

not

LESSONS IN GEOMETRY.

CONSTRUCTION OF CIRCUMDO.

1. Aliquid alicui rei, that is, a nominative or accusative of the thing with a dative of the thing. 2. Aliquem or aliquid triangle is that which has three equal sides. aliquâ re, that an accusative of the person or thing, with an ablative of the thing.

XXV.

1. "Aer omnibus est rebus circumdatus."-Lucretius. Lit. Trans. :-The air to all is to things surrounded.

Id. Trans.:-All things are surrounded with air.

1. "Tectis ignes circumdatos restinximus "-Cicero.

Lit. Trans. :-To the roof fires put round we extinguished.

Id. Trans. :-We extinguished the fires which had been set to the houses.

2. "Oppidum vallo et fossâ circumdedi."-Cicero.

Lit. Trans. :-The town with a rampart and ditch I have surrounded.
Id. Trans. :-I have surrounded the town with a rampart and ditch.

2. "Circumdato me brachiis."-Plautus.

Lit. Trans. :-Surround me with arms.

Id. Trans. :-Put thy arms round me.

·

VOCABULARY.

Impedio 4, I hinder; repugno 1, I fight against (E. R. repugnant); interpello 1, to question; latus, a, um, broad; lectus, i, m, a bed collum, i, n, the neck; brachium, i, n, the arm; cancelli (can orum, m, limits (E. R. chanel, chancellor, chancery); fautor, oris, a patron, favourer.

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An isosceles [that is, equal-legged] triangle is that which has only two sides equal.

XXVI.

Ascalone [that is, unequal] triangle is that which has three unequal sides

CONSTRUCTION OF QUOMINUS.

Quominus is made up of quo, in order that or so that; and minus, less (least, lest) or not; consequently quominus is equivalent to so that not; a more simple way is to render it by, to prevent. Quominus takes a subjunctive mood. If you use "to prevent" you must in English use also the idiomatic construction of "to prevent," but in putting that construction back into Latin and so employing quominus, you must employ, of course, the proper Latin construction; e. g.:

"Nihil de me tulistis quominus in civium essem numero."-Cicero. Lit. Trans. Nothing from me you bore so that not in of the citizens number I should be.

Id. Trans. :-You got nothing from me to prevent my being in the number is redundant. of the citizens.

XXIV.

Of three-sided figures, an equilateral, [that is, equal-sided]

XXVIII.

An obtuse-angled triangle is that which has an obtuse angle.
XXIX.

An acute-angled triangle is that which has three acute-
angles. The acute angled triangle must have three acute
angles, because the two preceding species of triangles
have each two acute angles, as will be shown in the
sequel.

XXXVII.

A right-angled triangle is that which has a right angle.

XXX.

Of four-sided figures, a square is that which has all its sides equal, and all its angles right angles. This definition If the general definition annexed to the 34th Prop. of this book be considered, the square is only a species of parallelogram, viz, that which has one angle a right angle and the sides which contain it equal to

one another.

XXXI.

An oblong is that which has all its angles right angles, but has not all its sides equal. This definition is also redundant; for an oblong [or rectangle, that is a right-angled parallelogram] is that which has one angle a right angle, and the sides which contam it unequal.

A 1

[4 segment of a 'circle is the figure part of the circumference it cuts off.]

III. Definition VI.

EXERCISES.-LATIN-ENGLISH.

Nihil impedit quominus id quod maxime placeat facere possimus; non repugnabo quominus omnia legat; mors non deterret sapientem quominus reipublicae consulat; interpellent me quominus honoratus sim; dum ne interpellent quominus respublica a me commode administrari possit; nemini civi ulia, quominus adesset, satis justa excusatio est visa (no pretext appeared sufficient to excuse any citizen from being present); fossam latam lecto circumdedit; exercitum circumdat hostium castris; circumdat sibi milites; circumdabit brachia collo tuo; circumdedit urbem tumulo; extra hos cancellos egredi conabor quos mihi ipse circumdedi; egregiam famam paci circumdedit (gave to, invested with); fautores illi hanc famam circumdederunt.

ENGLISH-LATIN.

Nothing hinders you from being a good boy; I will surround thee with fame; he will put a garment round me; he has surrounded his sister with honour; surround the city with fire to prevent the citizens from going out; that is no excuse for your absence.

LESSONS IN GEOMETRY.-No. XII.
LECTURES ON EUCLID.
DEFINITIONS. BOOK I. FROM XIX. TO XXXV. INCLUSIVE.
XIX.

contained by a straight line, and the
This definition is repeated in Book

XX.
Rectilineal (or, rectilinear, that is, formed of straight lines] figures are
those which are contained [or, bounded] by straight lines.

XXXII.

A rhombus is that which has all its sides equal, but its angles are not right angles This is also redundant; for a rhombus is that which has one angle oblique, and the sides which contain it unequal.

XXXIII.

A rhomboid is that which has its opposite sides equal to one another, but all its sides are not equal, nor its angles right angles. This definition may be replaced by that of a parallelogram above mentioned.

XXXIV.

All other four-vided figures besides these, are called trapeziums. Quadrilateral figures whose opposite sides are not parallel, are called trapeziums; but if one opposite pair be parallel and the other pair not, the figure is called a trapezoid.

XXXV.

Parallel straight lines are such as are in the same plane, ever so fur both ways do not and which being produced

meet. The meaning of this definition is, that the space between the lines is always of the same breadth.

Rectilineal figures, as above described, are those that are supposed to be drawn on a plane or flat surface, and are divided into three different kinds: 1st, trilateral or triangular; 2nd, quadri

XXI.

Trilateral [that is, three-sided] figures, or triangles, [that is, three-angled, lateral or quadrangular; and 3rd, multilateral, multangular (many

are those which are contained] by three straight lines.

XXII.

angled) or polygonal. The first kind, the triangular, are divided into six species,-viz., three, according to their sides; and three, Quadrilateral, [that is, four-sided; or, quadrangles, that is, four-angled, according to their angles. Triangles are divided according to their sides, into equilateral, or such as have three equal sides; isosceles, are those which are contained] by four straight lines. or such as have two equal sides; and scalene, or such as have no Multilateral [that is, many-sided] figures, or polygons, [that is, many-angled, equal sides; that is, whose sides are all unequal to one another. Triangles are divided according to their angles, into right-angıca, are those which are contained] by four straight lines.

XXIII.

or such as have one right angle; obtuse-angled, or such as have one obtuse augle; and acute-angled, or such as have neither a right angle nor an obtuse angle; that is, which have three acute angles. Quadrilateral figures are divided into five different species: squares, oblongs, rhombuses, rhomboids, and trapeziums. Taking in the definition of parallel straight lines, before the 30th definition, it is better to divide quadilateral figures first into two kinds. 1st, those whose opposite sides are parallel; and 2nd, those whose sides are not parallel; there is also a third species, viz., those which have two opposite sides parallel, and two opposite sides not parallel. Those quadrilateral figures whose opposite sides are parallel, are, according to definition 36, attached to Prop. 34, Book I., called parallelograms, that is, a parallel diagram or drawing; and of these there are two species, those which have one right angle, and those which have one oblique angle; of the former species, those which have the legs of the right angle equal are called squares, and those which have the legs of the right angle unequal are called blongs or rectangles. Of the other species, those which have the egs of the oblique angle equal are called rhombuses or lozenges; and those which have the legs of the oblique angle unequal are called rhomboids. Those quadrilateral figures whose opposite sides not parallel, are called trapeziums, that is, literally, small tables, or tablets, their tops being of this form; but "unluckily," say the authors of the best Greek dictionary extant, "in spite of Horace, we do not know whether the earliest tables had three or four legs." Certainly the tripod is very ancient, but the tetrapod must have been more so, as human inventions generally become more simple in the progress of improvement. Those quadrilateral figures which have only two sides parallel, are called trapezoids.

In our last Lesson, vol. I., p. 406, we gave some account of the ratio of the diameter of a circle to its circumference, and the endless attempts that have been made,' from the days of Archimedes until now, to find an exact expression for this ratio in ordinary arithmetical terms. We there gave a beautiful expression for this ratio, discovered by Dr. Wallis, which is complete in itself, and which is frequently demonstrated by writers on trigonometry; as it does not, however, approximate very rapidly to the ratios in common use we insert the following ratio, lately discovered, which is one of very great convergency; viz., 1: 16 3 53+

1 1

1 1 1 1

{

5 55 7 57
1 1

1 1 1 1 1

1

+ &c.) — 4 { 70-3 703 + 35 705 &c.} +1

{

1 99

3993+5

1 999

&c.}

; and we refer our readers to another of an older

date, at p. 28, No. 28, col. 2, line 7 from the bottom, which also converges with great rapidity. Persons who are acquainted with vulgar and decimal fractions, as laid down in Cassell's Arithmetic, will be able to put these expressions into ordinary figures with the greatest ease. Well, after having obtained the ratio of the diameter to the circumference, or what is called in the language of mathematicians the rectification of the circle; that is, the making a straight line equal to the circumference; the next question which has puzzled mankind for at least two thousand years, is the quadrature of the circle; that is, the making of a square equal in area to the circle. Now Archimedes demonstrated the following simple and important proposition, that the area of a circle is equal to the rectangle contained by the semidiameter of the circle, and a straight line equal to half the circumference. We have shown at p. 173, vol. I., Problem 2, that the area of a rectangle is equal to its length multiplied by its breadth; and in the case of the rectangle which is equal to a circe,

3ch

the length is half the circumference, and the breadth is the semidiameter or radius; therefore, the area of a circle is found by multiplying half the circumference by half the diameter. In the case where the diameter of the circle is 1, it is plain from the former

5

proximate answer; that is, the answer nearly; because the ratio of the diameter of a circle to its circumference above assumed is only approximate, as may be seen by consulting the last Lesson in Geometry. But if we take a nearer approximation to the exact ratio, we shall accordingly obtain a nearer approximation to the exact area of the circle. Hence, if we take the numbers obtained from Dr. Wallis's ratio,-viz., 1 to 3.141592653589+, we shall have of 1 multiplied by of the latter number, or of 3.141592653589 785398163397+ as the more correct number to be employed in finding the area of the circle, this being true to the twelfth decimal place of figures; the first six, however,-viz., 785398 are sufficient for ordinary practice, being true to the sixth or millionth decimal place. For those who are content with approximations to the truth in whole numbers, it may be useful to state that the ratio of the square of the diameter of a circle to the area of the circle itself, is nearly as 14 to 11; or than the area of a circle is nearly of the square of its diameter, being more than the truth, by about one twenty-six thousandth part of itself.

LESSONS IN GERMAN.-No. XX.

SECTION XXXV.

German verbs; and, in this use, is translated by our auxiliary,
Werten is used as an auxiliary in forming the future of all

"shall" or "will" (§ 70. 6.).

I. As an independent verb werden signifies, "to become, to grow, to get," &c. Ex.: Er wird alt; he is growing old. Das Wetter wird falter; the weather is growing colder. Es wird bunkei, it is getting dark. Der Rabe wird sehr alt; the raven becomes very old (lives or attains to a great age).

II. Werten with the dative often denotes possession. Ex: Mir wird immer das Meinige; I always obtain my own, (to me comes [becomes] always my own). Meinen armen Unterthanen muß das Ihrige werten; my poor subjects must have their own (property).

CONJUGATION OF THE VERB werden

Infinitive.
PRES. Werden, to become;
PERF. Geworten sein, to have
become;

Singular

3ch werte, I become;
Du wirst, thou becomest;
Er wir, he becomes;

PRESENT.

Ich wurde or wart, I became;
Du wurtest or warest, thou

becamest;

Er wurte or wart, he became ;

Sch war geworten, I had

IMPERFECT

bin geworten, I have be

come;

Du bist geworten, thou hast be-
ift gewarten, he has be-

come;

come;

PRES. Wertend, becoming;
PERF. Geworten, become.

fie wurten, they became PERFECT.

Plural. wir werden, we become; ihr werdet, you become; fie werten, they become.

IN THE INDICATIVE

Participles

PLUPERFECT

be

wir wurten, we became; ihr wurtet, you became;

wir sind geworden, we have be

come;

ihr seid geworden, you have be

come;

fie find geworden, they have be.

come.

lesson that the circumference is nearly 3.1416; therefore the area

of a circle whose diameter is 1, is of 3-1416 multiplied by of 1;
that is, 1.5708 multiplied by, which is 7854, an expression with
which many of our readers are familiar, but of which we believer
they never understood the origin. This we have now given, we
hope to their satisfaction. As Euclid has demonstrated in
Book XII., Prop. II. (see Cassell's Euclid, p. 191), that circles
are to one another as the squares of their diameters; it is plain that
if the area of any circle whose diameter is greater than one be
required, we have only to multiply the square of the diameter by the
decimal 7854 given above, and we have the answer; for the square
of 1, is to the square of the given diameter, as the decimal 7854, is
to the answer required. This, of course, will only give the ap.

come;

Du warst geworten, thou

hadst

become ;

wat gewerten, he had be

come;

3ch iocrbe werten, I shall be

come;

Du wirst werten, thou wilt be

come;

Gr wird werden, he will be

come;

FIRST FUTURE.

wir waren geworten, we had be

come;

ihr waret gewerten, you had be

come;

sie waren geworten, they had be

come.

wir werten werten, we shall be

come;

ihr wertet werten, you will be

come;

sie werten werten, they will be

come.

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