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LESSONS IN ARCHITECTURE.- No. I.

ARCHITECTURE is the art of planning, constructing, and adorn-structed them. It is easy to understand how their different ing public or private buildings according to their intended arrangements and structures are but the reflection of the reuse. The word architecture is derived from the Greek apxw, ligion or the manners of the people. The general style of the archo, I command, and 7:*TW, tecton, a workman. This etymo-monuments of a country is a durable image of the different logy (derivation) indicates the operatives engaged in the building phases of its civilisation. In these, we see it in its primitive, on the one hand, and the leader or chief, the man of science and refined, or degraded state, as civilisation arose, approached to practical skill, putting in action all his resources in order to perfection, or decayed. execute his plan on the other. Such a division as this was, no Nations naturally established great divisions in their architecdoubt, established from the beginning of the art. According, ture. They first built their private dwellings; then their public therefore, to the literal meaning of the etymology, mankind buildings; and these, in their numerous subdivisions, constituted must have, at the origin of architecture, possessed a degree of civil architecture. Religion caused them to build temples and civilisation sufficient for the organisation of different kinds other edifices, attaching to them ideas of duty and moral of industrial operations, and acquired a degree of skill in obligation: thus arose sacred architecture. The fortification of the art, which enabled some men by their experience to be their frontiers, their towns, and their conquered countries,

gave birth to military architecture. In this hasty sketch, we the leaders or directors of others. In this way, we may sup- see how extensive is the series of buildings which cover the pose that the art itself, or rather the symmetry, the harmony face of the globe, some of which belong to the first ages of its hisof proportions, and good taste in structures, at first began to tory, and others of which are being rediscovered in our own day. be developed. Before arriving at this point mankind must

The study of these will be duly appreciated by the historian, have overleapt ages. One of the first wants of society was a

the philosopher, the archæologist, and the artist, who, each

with his own particular view, knows how to find a great covering or shelter from the inclemency of the weather, lesson in these silent witnesses of past civilisation, as well as whether of heat or of cold. Simple was the art employed in in those existing in full vigour around us. constructions of this kind. Grottoes or caves hollowed square Architecture is founded upon three great principles which to make them more habitable, and cottages constructed of ought to be immutable : 1, the useful, without which states and branches of trees and blocks of stone—such were the primitive private individuals would be led into superfluous and ruinous

expenses ; 2, the true, because it ought to express in all its constructions in wood and stone which formed the rudiments varied forms the great principles of construction upon which of architecture. From the simplicity of early structures men it rests; 3, the beautiful, which is the end of all the arts depassed to the study of proportions; they then dared to attempt pending upon design, and no less of architecture the most useful. the grand ; and, at last, reached the sublime. The origin of On these principles, every style of architecture has the same

value; architecture cannot be assigned to any particular country. himself to the study of one particular style. It is only the

and an artist should not curb his genius by confining Every nation produced its own art, or style, by employing the

man of talent, to whom the construction of an edifice is envarious materials within its reach, and by giving to them such trusted, who can combine the different arrangements and forms, forms as their wants required. Proceeding at first from the harmonise the various parts, and particularly express by high table-lands of Asia, in order to people the earth, the early plans, skilfully worked out, the disposition of the whole or of fathers of our race could have but little idea of architecture, plans rests the reputation of an architect, and science demands

every part of the building. Upon these arrangements and or of a well-established system of construction. As wandering of him a well-grounded assurance of the good construction and pastoral tribes, they lived in tents or wretched cottages, and durability of his work. which had no pretensions to architecture. It was not until Architecture is not an imitative art, like her sister arts, they became more settled that they sought the means of ren- , sculpture and painting. We see nothing in nature like our dering their buildings,more durable

, by employing in their buildings as a whole ; or rather nothing which could serve to

guide us in its applications, or in the harmony of its lines. In construction, wood or stone, and bricks baked in the sun.

this art, man has done everything himself. He has employed From the differences in the materials, and from the variety of matter; he has invented forms and proportions to produce in tastes and feelings, arise the varied appearances which the the minds of his fellow-creatures ideas correlative of order, monuments of different nations present, and which constitute harmony, grandeur, richness, and durability. He has been their peculiar style of architecture. Thus the Egyptian, born enabled, by the force of art, to give, as it were, thought to in the hot climate of Africa, in a country destitute of wood fit ternal forms of nature. Like the poet and the musician, the

matter, without being indebted for his ideas to any of the exfor building, and near the mountains of the valley of the Nile, architect can transport the spectator into an ideal world, by containing large blocks of freestone and granite, created for creating forins and effects formerly unknown; but, very different himself a vigorous style of buildings, which completely shel. from them in results, he renders his creations palpable, and tered him from the burning rays of the sun. These buildings the beautiful, must be ever present to his view; and, however

gives them durability. Moreover, the useful, the true, and were formed of colossal masses, which were easily transported fruitful his imagination may be, he cannot emancipate it along the waters of that famous river. The Greek, inhabiting from science, the eternal basis of all the productions of his a milder climate, surrounded by forests and quarries, gave a lighter form to his edifices ; and employed wood in their con

The architect is not, therefore, as the vulgar think, and, more struction, which harmonised well with the marble-a material unhappily, still, as ignorant men who usurp the title thinkof which the fineness admitted of a greater delicacy of struc

simply a head workman or common decorator of miserable

constructions, a species of animal always to be found. He ture and arrangement. The Chinese, surrounded by rivers spends his youth in the study of his art, and of the splendid bordered with bamboo, had only a meagre and tortuous species examples left on the face of the old world by ancient civili, of architecture, as ephemeral in its duration as it was fragile sation. In conjunction with these studies he makes himself in its origin and construction. The very different character with precision, and study the nature of their construction. He

master of the exact sciences, in order that he may execute his plans exhibited in local architecture enable us to judge of a country also makes himself acquainted with the physical sciences, in by its monuments, inasmuch as the buildings themselves are order that he may become acquainted with the nature of the the expression of the various wants of the people who con materials which he must some day employ, and be able to calVOL. I.

18

art.

[graphic]

culate their effects. In short, he devotes himself to practical presented the square form, if they did not give them this form experience, and to the working part of architecture, in order by manual labour. Stonehenge in Bagland exhibits a number to render himself capable of executing public or private build- of square pillars supporting enormous architraves, the whole ings, and to make himself responsible for the stability of appearing to have constituted a large and well-constructed edifices entrusted to him either by private individuals or by edifice. These evidences of the first attempts of past civilisathe state.

tion are gradually and daily disappearing under the progress BUILDINGS OF UXHZWA STONES,

of those which are being developed around them. Thus Asia

has lost the most of her ancient monuments, owing to the early After these preliminary remarks, we may shortly trace the state of her progress in the arts. Africa, for the same reason, progress of architecture amongst the different nations of anti- presents as few examples, although they are mentioned by quity, for the purpose of reaching our own times in chronologi- ancient authors. Greece and Italy, and their neighbouring cal order. Before entering into details, we may point out the islands, only exhibit examples of the same kind in places particular features which characterise the grand periods of the nearly deserted. The northern countries of Europe alone preart, and the different systems in which its resources were de- serve some, because that civilisation was later there ; and the veloped, in order to satisfy the numerous demands of the civili- history of their sudden and unexpected conquests extends only sation in which it originated.

to a period of about two thousand years. In America the later Architecture, like all the productions of the human mind, civilisation of the Aztecs (1196) and the Mexicans caused the presents at first only simple rudiments, quite in accordance with primitive monuments

around them to disappear, by the deprimitive manners. From the earliest ages we find three velopment of their own. This process is perfectly analogous great divisions established amongst all nations : 1st, private to that which took place first in Asia, then in Greece, in buildings; 2nd, religious edifices ; 3rd, military constructions. Africa, and in Italy, and which we see taking place in the

The first care of a people, as we remarked before, would be western countries, where every day they are destroyed in to construct individual dwellings; but being at first hunters order that the materials may be used for roads and private and shepherds, they would be necessarily wanderers, and their buildings. dwellings would be tents constructed of the skins of animals, This simple and primitive style of architecture appears to or cottages made of branches of trees. When they dwelt on the borders of rivers they would employ reeds; Asia and

Fig. 1.

have been originally universal, if it was

not simultaneous with the progress of Egypt present us with examples of this kind. In some ex

civilisation, which marched from east to ceptional cases they dwelt in caverns, or in shallow excava

west; and has left monuments and editions. The cottages were usually circular; piles of stones and

fices so varied, as to occasion them to be earth, arranged in a circle, constituted their foundation. This

classified, and have names given to each form is found amongst all nations; that of the square, requir

class. These names are borrowed from ing more complicated combinations was not adopted at first.

the old Celtie tongue, or language of the The simplicity of the first erections for religious purposes may

Druids. Thus, class Ist was called Peulbe seen in the construction of the altars of early times. The

tans, or Men-hirs, which consisted of long first sacrifices, which the Bible and ancient tradition trace up

stones, erect and isolated (standing singly) to the creation, were made upon consecrated heaps of stones,

like obelisks. (Fig. 1.) 2nd, Cromlechs, which they collected upon high places. These first altars,

which were great circles, elliptical or called Beth-EL (the House of God), were erected in Chaldea,

spiral, formed

of huge stones slightly elein Judea, and in Egypt. They were built, according to the vated. 3rd, Dolmens, consisting of large tables or platforms of Scriptures, of stones without cement, if the places where they stone, supported by several huge vertical stones. (Fig. 2.) 4th, were raised afforded proper materials. In other places they Rows, or Uncovered Alleys, of up

Fig. 2. were constructed of turf and earth, where the plain country pre right stones, placed in rows like sented no solid materials. Such erections or mounds are found trees, and occupying a very conin Asia Minor and in India ; at Heliopolis, celebrated for the siderable area, like those of the worship of the sun, and the great Sidereal divinity of the plain of Carnac in the department Syrians. Lucian describes a throne or altar to the sun com- of Morbihan, or the province of posed of four great stones arranged in the form of a table. At Brittany in France. 5th, Covered Ortosia, in Syria, there is an edifice of this kind raised in an Alleys, or long rows of parallel open enclosure,

and built of stones in a square form. Strabo stones set upright, and supporting masses of stone placed relates, that travelling in Egypt, he saw his road covered with horizontally so as to form a ceiling. (Fig. 3.) 6th, the mili. temples devoted to the god Mercury, which were composed of

Fig. 3. two unhewn stones, which supported a third. Artemidorus, quoted by Strabo, mentions that in Africa, near Carthage, the god Melkart (Moloch), or the Phænician Hercules, the worship of which was brought from Tyre, was worshipped in a similar manner, three or four stones being placed one upon another.

This simple manner of building applied to primitive altars, and to the sacred enclosures which surrounded then, after having been developed, as we have seen, in Asia and

Africa, extended into Europe from the borders of the Black Sea and tary constructions of early times appear to have been mounds the Caucasus, where M. Dubois, of Neufchatel, saw a great or artificial hills, at the summit of which there was a shallow exnumber, even to the Atlantic Ocean and to the northern seas. cavation, of which the edges formed a rampart. It is certain that Pausanias describes some of those in Argolis, and recent tra- in countries, where hills naturally occurred, they fortified them vellers have seen others in Greece. It is well known that in the same way as those which were raised by art. And these they exist in France, in England, in Norway, and in Sweden, where all these works of early civilisation are known under

Fig. 4.

natural fortifications are still to

be seen in the neighbourhood of the name of Celtic and Druidical monuments. America pre

Athens and the Piræus ; they sents numerous examples of similar constructions, which show

were of immense service in the how rising nations exhibit the same analogies, as their arts are

last war of independence. Manin the process of formation.

kind in a savage or wandering Simple as this system of building is, for it cannot yet be

state having no instruments for called architecture, we recognise the periods of its commence

raising the earth or digging ment, its progress, and its development. Thus the most

ditches, made fortified enclosures ancient of these edifices, such as were erected by the most

with heaped stones, having a ignorant people, were built of enormous stones in the shape double slope. The entrances to these fortresses were defended which nature gave them. Moreover they selected

those which by artificial hills, placed inside near the gates. (Fig. 4.)

1. am em

am er

am or
am abar

am

8. Am abo 4. am ans

ama ra

1. ama rem 2. ama

ama

amay

3. amav ero

ama

} amo bam

amay

$

ama
re

ama amare

tum

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QUESTIONS ON THB PRECEDING LESSON.

1. Present subj. active with the pres. ind. and subj. passivo. What is the etymology of the word Architecture ?

2. Imperf. ind. act. and pass.

3. Future ind. act. and pass. What are the two classes of persons which the etymology indicates ?

4. Participle pres. act. i fut. pass. and the gerund. What was the simplest kind of Architecture first resorted to ? Accordingly we have Whence did men proceed to establish them in different countries?

2. am abam What was the nature of the constructions they then employed ?

am abor What is the origin of different styles of Architecture?

am andus am andum Describe the peculiarities of the primitive Egyptian, Grecian, and The future of the third and fourth conjugations have the Chinese Architectures. Describe the origin of civil, sacred, and military Architecture.

terminations am, ar, instead of bo. The subjunctive passive of State the three great principles upon which Architecture is the third and fourth conjugations ends in ar instead of er. founded, and the necessity for attending to those principles.

II. From the stem of the infinitive in a, a, I, and in the third What is it that constitutes a good Architect; and what sort of conjugation from the consonantal stem with the connecting education should he have ?

vowel ě; that is, from ama, doce, lege, and audi, are formed State the nature of the buildings of unhewn stones, and for what 1. The imperfect subjunctive, active and passive. purposes they were first employed. Mention some of the countries %. The imperative, active and passive. where the Celtic and Druidical remains are found.

8. The infinitive passive. State the different classes of these buildings; and mention some of the Celtic names of these classes.

Accordingly,

åma re

3. ama ri LESSONS IN LATIN.-No. XVII.

III. Again, from the stem of the perfect active; that is, from •By JOHN R. BEARD, D.D,

amav, docu, leg, and audiv are formed THE LATIN VERB (continued).

1. The perfect subjunctive active.

2. The pluperfect indicative and subjunctive active. Now, by comparing these tables together, you may learn that

3. The second future. o is the sign of the present tense; re, of the infinitive mood; , 4. The infinitive perfect active. of the perfect tense ; and um of the supine. In other words,

1. amav erim by adding o to am, you form the present tense indicative mood

2. amav eram amay issem first person singular; by adding ham to ama, you form the corresponding imperfect tense ; by adding i to amay, you obtain

4. amav isse the perfect tense; by adding re to ama, you get the infinitive IV. Finally, from the stem of the supine in um; that is, mood; and finally, by adding tum to ama, you make the from amat, doct, lect, audit, are formed supine ; thus:

1. The supine in the

2. The passive past participle. "

bam
} amabar

} amavi } } amarum. 8. The participle future active. You thus see that there is a present stem, an imperfect stem, Accordingly,

1. amatu a perfect stem, an infinitive stem, and a supine stem.

Of these, the imperfect and the infinitive are nearly the same. Properly

8. amatúrus speaking, the present stem in amo is the same as the imperfect and the infinitive, for the second a is a part of the root of simplicity. It will be a good exercise for you to draw

out

I have here confined myself to amo and its parts for the sake Hence amo is a contraction for ama o.

We have previously seen that a long (ā) characterises the the forms of the three other conjugations according to these first conjugation to which amo belongs; also, that e long (7)

examples. characterises the second conjugation; and i long (1) the fourth.

The forms of the verb not mentioned above are made by Hence only one class of verbs is characterised by a short combination with the participles and parts of the verb esse, vowel, and that is the class which bears the name of the third to be. Thus the perfect, pluperfect, and second future passive conjugation. This e short () however does not strictly belong

are formed by joining to the perfect passive participle sum, sim, to the verb, but is only a connecting vowel between two con

eram, essem, ero, or fuero; e. g., amatus suno, amatus essem, sonants in this conjugation, the essence of which is that its amatus ero, &c. The infinitive future active is formed by stem is consonantal or ends in a consonant. Thus, in the in- adding esse to the participle future active as amaturum esse. finitive mood č is introduced for the sake of sound between The infinitive perfect passive is formed by joining esse with the the stem and the ending of the infinitive ; e.g., leg(e)re, for legre; participle perfect passive as amandum esse. in the same way leg(e)bam instead of legbam. But the other con

GENERAL VIEW OF THE TENSE-ENDINGS, INDICATIVE, AND jugations have vowel stems, as ama, doce, audi. The verbs of

CONJUNCTIVE OF THE FOUR CONJUGATIONS.

ACTIVE the third conjugation are called strong, and appear to be the most ancient. The verbs with vowel stems bear the name of

Indicative, Subjunctive. Indicative. Subjunctive. weak, and are of later origin.

18t, em

S 1st, er Frequently, in order to understand a formation, you will re

2d, 3d, 4th, am

2d, 3d, 4th, ar quire to know how letters are related one to another. For Imperfect. bam

bar instance, the supine of lego is lectum. Here the g seems to

bo

Future. have disappeared. It is however represented by the c. Thus

3d & 4th, am

{ bord & 4th, ar instead of the hard leglum we have lectum. In rexi the perfect Perfect.

erim

tus sim of rego, the g seems to have disappeared. But it has its re.

Pluperfect. eram

issem

Second presentation in the cor k in zi, thus rexi, if written according

tus ero }

Future. to the sound (phonetically) would be regsi or recsi (reksi).

or fuero The sibilant (8) is also introduced for the sake of euphony.

I next lay before you a tabular view of the To pursue this subject in detail would require more space than PersoN•ENDINGS, INDICATIVE AND SUBJUNCTIVE OF ALL THE we have to give. It must suffice to have put you in the right

TENSES. direction. When your ear by constant practice is accustomed

Persons.
ACTIVE. .

PASSIVE. to the combinations of letters which the Latins were fond of,

ri. 0, or m (em, am) Perf. Ind. i r (or, er, ar)

Sing. you will have received a great assistance towards correctly forming the several parts for yourself. Let us now take up the chief parts separately, and the pre

mini sent stems, am(a), doce, leg, and audi. From these are

Plur.

erunt formed

3.

atus

or 0

amat 2. amatus

PASSIVE.

Tenses.

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amo-am 20
amor-amaor

m

If

you take from the first person of any tense the termina- | jugations the tense-stem, as in the subjunctive present, ends in tions 0, 1, r, and where or appears the syllable or, then you get am, ar ; as,— the tense-stem which appears in all the other persons of the

legam, Active. audiam, Active. tense. This you may see exemplified in the ensuing

legar, Passive. audiar, Passive. TENSE-STEMS.

But the a of the first person is changed into e in the rest; as,ama, Present.

Active. Passive. Active.

Passive.

legam legar audiam audiar amabam

leges amaba, Imperfect.

legeris audies
amabar

audieris
leges
legetur audiet

audietur amabo

legemus amab, Future.

legemur audiemus amabor

audiemur

legetis legemini audietis audiemini amavi, amav, Perfect Indicative.

legent legentur

audient

audientur amaveram, amavera, Pluperfect Indicative. amaverim, amaveri, Perfect Subjunctive.

But if the tense-stem ends in a consonant or in u, you must amavissem, amavisse, Pluperfect Subjunctive.

employ a connecting vowel; as shown thus :amavero, amaver, Second Future.

amab(i)mus leg(i)mus

docu(i)mus So it is with the three other conjugations. To these stems are s require i, e. g. amab(i)s leg(i)s

docu(i)sti added the consonantal person-endings just given. If the tense.

amab(i)t leg(i)t

docu(i)t stem ends in a vowel (except u) the person-endings are made

r require e, amab(e)ris leg(?)ris, Present. without any connecting vowel ; e. 8.,—

u, amab(u)nt leg(u)nt

acu(u)nt ACTIVE. PASSIVE.

The course of instruction through which you have now Stems. Person-endings. Stems. Person-endings.

gone will require constant repetition. When you have made ris, 2nd singular.

yourself master of the forms which ensue, by imprinting them amaba 8, 2nd singular.

on your memory, you will do well to go over and over again amaba tur, 3rd singular. these instructions. With diligence combined with observation t, 3rd singular.

you will then make yourself familiar with the Latin verb, not mus, 1st plural.

mur, Ist plural. as a mere matter of rote, but understandingly; knowing well tis, 2nd

how the parts are formed one from the other, and how they are amaveri

mini, 2nd

all connected with the common stem. I advise you, however, amavisse

(ntur, 8rd » to question yourself very narrowly, and again and again, before In the third person plural indicative active and passive the you attempt to pass to the conjugation-forms which I am about connecting vowel u is found after i and u, as audi(u)nt, to supply you with, though you will do well to refer to these audi(u)ntur, so acu(u)nt.

forms for aid in understanding my remarks, and seeing their In the future active and passive of the third and fourth con- | application,

n

ama

ama

amavera ame amare

ame

nt, 3rd

amare

GENERAL VIEW OF THE TENSE AND PERSON ENDINGS OF ALL FOUR CONJUGATIONS.

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hous(a, um), eram, &c.

PLU-
PERFECT.

amav I.

S. ēram, erat, erat issem, isses, isset
docu II
leg III. (P. eramus, érātis, erant issemus, issētis,
audiv IV.

(issent

i(ae, a), eramus, &c.

amat. &c

SECOND
YUTURE.

amay I.
docu II. S. ero, eris, erit
leg III.
audiv IV.) P. črimus, eritis, erint

amat. &c.

us (a, um), ero, &c. i(ae, a), erimus, &c.

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LESSONS IN GEOMETRY.-NO. VIII.

We have our own opinion, that by a more general spread of

mathematical knowledge over the face of our bappy island, some LECTURES ON EUCLID.

new lines of investigation and discovery may be struck out; and Having in our previous lessons on geometry, given our readers that, by the fortunate invention of some original genius, even some kind of insight into the practicai utility of the science of Euclid himself, great as he is, may one day perhaps be thrown into geometry, and having been urged by a numerous class of readers to the shade. There is the less chance, however, of this taking place give them something more elementary and initiatory, something when we consider the length of time that he has already maintained more adapted to the young or to the old beginner, something that his ground; and when we find, upon examination that he has they really can understand on this most interesting subject, we followed the most natural course in the study of geometry which have been induced, in consequence of the publication of the the human mind could be supposed to follow. In fact, Euclid is " Elements of Euclid' at such a price as to reach almost every simply the expression of the great human mind itself in one of its class of purchasers, to commence a series of lectures on geometry most interesting studies--the parent and the germ of the science in connexion with that masterpiece of antiquity. In these lectures of future ages. If Euclid had not done what he has done, some we propose to smooth the way to the acquisition of this most im. one else must have done it, and that some one else must have had portant branch of human knowledge, by explaining in familiar the glory and the renown of the immortal work ascribed to his terms the technicalities of the science at every step, even at the name. expense of repetition; and to show the practical application of each But it is now time to enter upon the consideration of the work proposition in succession, as far as it can be done without intro- itself. In the lessons which we are about to give, we shall, for the ducing an amount of reference to branches of knowledge which the sake of explicitness, and the clear distinction between what is student cannot be supposed to have yet acquired.

Euclid's and what is not,--at least, as given out by his celebrated edi. In carrying on these lectures we shall suppose ourselves address. tor, Dr. Robert Simson, of the University of Glosgow,-cause to be ing a class of students at a college, a people's college if you please, printed in Italics, all that is really considered to belong to his Eleand we shall frequently use that colloquial style which serves to ments of Geometry. To this we shall add explanations, demonimpress the mind and draw the attention pointedly to the subject strations, annotations, and criticisms of various kinds, all tending in hand. One way of exciting the attention of the student will to elucidate the propositions in band, and to show their practical consist in amusing him with the different explanations, demonstra- bearing in the sciences and in the arts. We shall also add exertions, and solutions which have been given of various theorems cises for solution in a limited time, and if these be well and elegantly and problems, and enabling him to judge of, or criticise if you done by any of our pupils, we shall have much pleasure in giving will, each subject as it comes before him in the course of the lecture. the solutions a place in our work, for the instruction and encourageLike all teachers who have the progress of their pupils at heart, ment of others. The question of prizes for solutions has been sugwe shall be glad to remove difficulties and give explanations when gested to us ; this is a grave question, and one that will depend on applied to by letter, for the benefit of all; but we hope that our the continued success of this great national attempt to instruct the correspondents will continue to be as they generally have been masses in the principles of Geometry. hitherto, courteous and civil in their manner of proposing their Geometry, as laid down by Euclid, consists of several books, in difficulties and requests, and that they will not be too positive as to wbich the properties of different geometrical figures are explained the discovery of what they may fancy to be errors, lest they should and demonstrated, in a series of short chapters called Propositions. turn out to be in error themselves. There is no science in which a To each book is prefixed a list of Definitions, which fixes at once, man is more likely to be mistaken in his conceptions, especially at and for all future investigations, the precise meaning in which the first, than the science of geometry, and we therefore desire to im- technical terms or names of things is to be understood. From these press both ourselves and our readers with the necessity of an humble definitions, no departure is ever allowed in Geometry; and it is to and teachable spirit, in the pursuit of this noble science.

this fixity of meaning, that the superior excellence of geometrical Two thousand one hundred and fifty years have rolled away reasoning, above all other kinds of reasoning, is to be chiefly attrisince Euclid flourished at Alexandria, and had the king of Egypt buted. The definitions, however, are not mere explanations of terms for one of his pupils ; and during all that period no greater genius or words; they are, in general, something considerably more than this; has risen to publish a work on Geometry, which can take the for they contain the statement or announcement of some simple and place of his. Why is this so? Because he has adopted the obvious property of the thing defined--a property which belongs to strictest system of pure reasoning that the world ever saw in his that thing and to no other. In this view, the definitions may be whole system, and in his demonstrations; and, although his work is considered as a series of self-evident propositions ; cr such, that if not without faults, we do not think it will ever be supplanted in they are not at first self-evident, they must be taken as possessing Great Britain by any better system. You will, perhaps, ask me this property, and made the foundations of our reasoning accordwhy in Great Britain? We answer, because the British mind is ingly. In order to illustrate this by an example, let us take Euclid's like the Greek mind. It is of a noble and solid nature, and the definition of a circle : "A circle is a plain figure contained (or bounded! studies of ancient Greece have ever been cherished by the inhabit by one line, which is called the circumference, and is such that all straight ants of this island, owing to the striking similarity of their minds.

lines drawn from a certain point within the figure The French, our amusing and volatile neighbours, have greatly

to the circumference, are equal to one another." abandoned Euclid. They have adopted systems of their own;

Now what is this definition but a proposition in ingenious and useful systems, and possessing marks of great

which a certain important property of the circle originality; but they want the vigour and solidity of the Greek

is involved ? viz., that all straight lines drawn naster, the favourite of the British in Geometry. Even Professor

from the centre to the circumference are equal. de Morgan, that eminent analyst, and original but singularly ob.

This is the test of circularity, if we may use the scure writer says, in his “ Elements of Algebra," " In England,

term,-lhe method by which we ascertain whether the Geometry studied is that of Euclid, and I hope it will never be

a given figure said to be a circle is really a circle any other ; were it only for this reason, that so much has been or not. But it may be objected to this test, that no circle that ever written on Euclid, and all the difficulties of Geometry have so was made by human hands, was absolutely perfect, or strictly uniformly been considered with reference to the form in which they agreed to the terms of the definition. To this we reply, that it is appear in Euclid, that Euclid is a better key to a great quantity of of no moment to the geometer whether this were ever the case or useful reading than any other.Though the British, as a nation, not; all that he requires for his purpose is that you will admit the appear to surpass the French in the practical application of the existence of such a circle for the sake of argument, and then he is principles of Geometry, and though we believe that this is owing to satisfied ; then be can go on with his propositions and demonstraAeir being well grounded in these principles as laid down in Euclid, tions, and raise you up a beautiful body of science on the strength yet it cannot be denied that the French have long been our of your admissions. Besides it is quite sufficient for the purposes, masters in the higher branches of Mathematics. Of late years, both of theory and practice, that we can make a circle so nearly indeed, there have been some evidences of a healthy attempt at true, as that no sensible difference can be discovered between the original writing on these subjects, and among these, Professor de lengths of any two straight lines drawn from the centre to the cirMorgan deserves credit for the share be has had in this onward cumference. Indeed, for the purposes of theory alone, this atat progiens ; but we cannot refrain from strongly recommending sim. approximation to the truth is not at all necessary; for it is enouga plicity in writing and in notation to all our original writers. that you admit, for the sake of argument, that any two straight

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