« 前へ次へ »
LESSONS IN GEOLOGY.-XI.
or fir-tree, if examined under the microscope, is readily distinTYS VEGETABLE KINGDOM-CLASSIFICATION OF ROCKS. minute dotted vessels.
guished from the true wood of the exogens by the presence of Fossil botany is in a very unsatisfactory state, therefore we The Phanerogamic dicotyledons are exogens—that is, the sap shall not describe the vegetable kingdom so fully as we have rises up the interior of the tree, and, reaching the extremity of that of the animals.
the branches, it descends by the bark, and puts on every year Examining the structure of all vegetable organisms, we shall at another layer of wood. The tree thus "grows from the outside," once divide them into CELLULAR and VASCULAR—that is to say, so that, when a section of a tree is made, the number of rings in one class we shali not be able to discern any regular forma- counted from the outside to the centre indicates the age of the tion; but the substance of the plant appears to be made up of tree. fibres interlaced, without any definite order. This peculiar The above classes are subdivided into orders, which contain growth may be seen in Fungi (mushrooms, etc.) or in Algæ about 300 genera and 100,000 species. (sea-weeds), and is considered the lowest development of vege Remembering that the fossiliferous rocks are of aqueous table life.
origin, it will readily be expected that the great majority of The Vascular plants exhibit a more complex structure. They fossil remains must be of aquatic animals and plants, chiefly, contain vessels, through which sap—the blood of the vegetable however, marine. world-circulates, by means of which the plant grows, flowers, Any land animal or plant which is found in a fossil state must and fructifies.
have been embedded by The manner in which
accident. For instance, plants are propagated
a flooded river carries affords another means
down to the sea the of classification.
bodies of animals surMany of the cellular
prised by the rising plants have no seed
waters, and also plants, organs, but they seem
which are torn up by to be produced from
the impetuosity of the sprouts, which shoot off
swollen current; but, from the mother plant;
in comparison to the from this peculiarity
number of aquatic ani. they are called Thalo
mals and plants which gens.
exist in the water, and The vascular plants
when they die become bear a division both as
embedded in the sedito their seeds and the
ment, the number of manner of their growth.
land organisms must 1. The Cryptogams
be very small. Still do not show any seed
fewer remains of birds organs, nor yet perfect
may we expect to find; flowers. Ferns belong
and those which would to this family ; the
be most likely to be prespore or seed of which
served in the accumuappears attached to the
lating strata would be under-surface of the
birds which inhabited fronds. Mosses, equi
the sea-shores, or the setums, mares-tails,
banks of rivers or etc., are all cryptogams;
marshes. and many fossil plants,
When we bearin mind we shall find, belong to
the almost insignificant
scratchings of geolo2. Phanerogamic mo.
gists in the rocky sur. nocotyledons, or "flower
face of the earth-what ing plants with one
a very small portion of seed-lobe" grasses, IDEAL FOREST OF THE CARBONIFEROUS PERIOD, SHOWING GIGANTIC TREE the crust has been exalilies, palms, canes—are
mined-we cannot but of this family.
wonder at the very 3. Phanerogamic gymnosperms.-Flowering plants, but having numerous list of fossils which have been collected, and be led to naked seeds. The very widely-distributed tribe of the Conifere, think what vast records of animal and vegetable life the rocks or firs, belongs to this family.
could unfold had we power to examine the strata fully. To give 4. Phanerogamic dicotyledons.-Flowering plants having two the reader some idea of the number of fossils, and the relation seed-lobes. This is by far the largest class, and comprehends the past bears to the present orders of life, we transcribe a list all true forest trees and shrubs.
of British fossils, compiled by Professor Jukes. Since the table The division as to their manner of growth is interesting. The was constructed, some of the numbers have altered; but it is cryptogams increase at the point only, which is pushed further sufficiently accurate for our purpose. and further, elongating the leaf. This is readily observed in
LIVING AND FOSSIL SPECIES IN THE BRITISH ISLANDS. the mosses and the ferns, which latter unroll the leaf or frond
Number of already formed from the root. From this “point-growth" they
Number of Proportion of
Living Species. Fossil Species. Living to l'ossil are termed Acrogens. The next class, the Phanerogamic monocotyledons, grow in a
435 very peculiar way, which is well illustrated in the cane and
3.7 bamboo. They shoot out from the knots or joints ; not a thin *Testacea
8.9 twig, which gradually increases in size, but a thick, succulent Echinodermata
1 piece, which hardens, but does not increase. Thus they are said Crustacea
1 to " grow from within," and are termed Endogens. The struc- Fishes
162 ture exhibited by a section of sugar-cane illustrates the appear- Reptiles
: 10-0 ance of the "wood ;” it is full of minute holes, with no marks Birds.
7) 110 1 : 1:5 The Phanerogamic gymnosperms are a connecting link be • "Testacea" is a word usually applied to all molluscs which are tween the endogens and the exogens. The wood of the pine “shielded” by sliells.
1 1 1
258 4590 492 298 741 180
We are more likely to have registered all the species of exist- | by a tremendous upheaval of the surface, a series of strata has ing molluscs which inhabit our seas, than to have discovered been actually turned over ; but this is very local, and not at all individuals of every species which lie entombed in the rocks of difficult to discover. Yet the order of superposition is not always our island; and yet, as far as our research has gone, we already satisfactory, for it very frequently happens that between the know ten times the number of fossil Testacea than we have deposition of the two strata vast periods of time intervened; living species.
and, to complete the series, it would be necessary to insert This means to say that our rocks chronicle the history of the perhaps several strata between the two adjacent rocks-strata rise and fall of ten complete populations of the seas which girt which are found to have been deposited in this very period in our island. We have no reason to think that the land animals other areas. For instance, suppose England were submerged, change less slowly than the species which inhabit the sea, and and a layer of rock deposited over the whole surface of our yet we only discover that fossil species of Mammalia are more island, in Wales this newly-deposited rock would rest on the old numerous by one-half than those which now exist; because, as Silurians-rocks hoary with the vastness of their age-while we have said, when we do discover such a fossil, we have this same rock is found on the opposite coast to be resting on the happened to hit upon the place where a land animal was tertiary formations-that is, those last upheaved from the ocean accidentally deposited amid the accumulating sediment. bed. Obviously it would be a great error to conclude that,
The Distribution of Fossils.-From the foregoing remarks the because this new rock was found superimposed upon the Silurian, reader will readily perceive that the distribution of fossils is not therefore it was deposited immediately after that foundation. indiscriminate, but is regulated by certain considerations. The Hence, although the order of superposition may and does fossils contained in one stratum of rock represent that order of determine the relative times of deposition of the whole series of life which was existing at the time the rock was being deposited; rocks, yet we cannot infer that any one rock was immediately and if, at some distant place, the same kind of rock was deposited after another because it happens to lie upon it. discovered in which we found one fossil similar to any of those The mineral character of a rock, although it may be put in which the former rock contained, we should continue our search, as evidence as to its age, yet is by no means conclusive. For confidently expecting to find other members of the same group. we find the same kind of rock appearing again and again in the
For instance, the Mediterranean Sea may be looked upon as different formations. This a glance at the following tabulations one area of life. Occasionally we find a species peculiar to one will at once decide ; and, moreover, it is not unusual to find a locality, but the great majority of shells is common to all the limestone growing gradually more arenaceous until it became a coasts. The rivers which discharge themselves into that sea sandstone, which merely means to say that the area of the are depositing strata. Suppose that the bed were elevated, and deposition of the limestone was on the same level and conthe rocks found by the Rhone, the Po, and the Nile were tiguous to the area of the deposition of the sandstone; but we examined, the mineral matter of the rocks would vary, but the cannot assert that the two rocks could not be deposited at the fossils would be well nigh all the same.
same time because of their different mineral characters. From this instance, which is in progress under our observa The organic remains in a rock are the surest of all tests of age. tion, we deduce another fact, that although the mineral matter The same fossils may be found in several succeeding strata, bat which composes rocks may be essentially different, yet, provided every strata has some fossils peculiar to itself by which it is at that the deposition of those rocks be during the same period and once known, and referred to its proper position. A knowledge within the same area of life, their fossil contents will bear a of Palæontology is therefore absolutely necessary to the miner. close resemblance; and it is possible that every species in the Many a coal shaft has been sunk in a class of rocks which never one will be found in the other.
yield coal, and that, too, when every bucket brought up silent Yet it must not be concluded that rocks deposited at the same witnesses, which, had they found an interpreter, would have pretime of necessity contain the same fossils. A deposition of vented much useless expenditure. strata may be going on off the shores of Siberia, and
another in As we describe the various formations, we shall note and the Bay of Bengal; but no one will expect that these two areas delineate those fossils which are characteristic of them. of deposition are included in the same area of life. In the one The earliest classification seems to have been made by Steno an Arctic fauna, or a generation of Arctic life, is being enfossilled, in 1669, who divided all rocks into primary and secondary. and in the other the fauna is truly tropical; and yet, for all that, Some ten years later, Leibnitz improved upon this nomenclature the conditions of climate are so widely different, that certain by substituting the words stratified and unstratified. cosmopolite species will be detected in each, and, to use Von Then came Werner and Hutton. The former conceived that Buch's phrase, a peculiar “facies," or general resemblance-a the deposition of all existing rocks was due to the action of family likeness--will pervade the character of the two groups; water; whereas the Vulcanists, the followers of Hutton, differed so that, although two classes of rocks may have been deposited from the Neptunists in ascribing the production of the Primary at very distant places and under very different conditions, but and Transition rocks to igneous action. Each of these leaders at the same period, the geologist is seldom at fault to show that classified the rocks according to their theories. such is the case from common characteristics possessed by their At the beginning of this century, William Smith, “the father fossils, although the majority of those fossils belong to different of English geology," commenced his labours, and from him a species.
race of investigating geologists has sprung, by whom the rocks The distribution of life, and the laws which regulate it, is a have been classified in the following order. The formations are most interesting subject; but, from our imperfect knowledge in a descending order :of Palæontology, it can only be studied with regard to living 1. Post-Tertiary. The latest ac 6. Permian,or New Red Sandstone. species. From such study, however, we have learned sufficient to cumulations.
7. Carboniferous or Coal System, teach us that it is very dangerous to assert what may have been 2. Tertiary.
8. Deronian, or Old Red Sandthe climate and the nature of the country when a certain species, 3. Cretaceous or Chalk.
stone. now in a fossil condition, were in existence. Experience, how: 4. Oolitic.
9. Silurian, ever, seems to point out that all changes in species which
10. Metamorphic. occupied a certain area were very gradual ; and if the fossil con Below these lie the Primary Rocks, but it must not be suptents of two adjacent
strata are widely different from each other, posed that the rocks of igneous origin are not found in the it argues that long ages interposed between their respective stratified rocks, for it will be shown that granite was in a deposition, and that a series of intermediate deposits are wanting, state of fluidity when the Oolite was being deposited; but we which, had they been present, would have established a gradation shall explain this in our next lesson. in the forms of life.
A division of the rocks has been made according to their CLASSIFICATION OF ROCKS.
fossils, or the types of life they exhibit, as compared with one
present orders of life : Three prominent characteristics aid as in classifying rocks according to their chronological order :-(1) Their order of
1. Cainozoic period (Post-tertiary.
Permian. (Recent life) Tertiary.
3. Palæozoic pesuperposition ; (2) their mineral characters; and (3) their fossil
Deronian. contents. If two strata are discovered, one lying on the other, 2. Mesozoic period
Silurian. we may at once infer that the one which is beneath was (Middle life).
Triassic. 4. Azoic period Metamorphic. deposited before the other. Cases, however, are known where,
This classification was objected to on the ground that we had
FEMININE, no right to say that there were no fossils in the Metamorphic -EURRE beurre, butter.
violoncelle, violoncello; ocks because as yet we had found none; and, therefore, for Azoic -IDKE
chèvre-feuille, honeythe term Hypozoic (below life) was substituted : and, seeing it -ISME prisme, prism.
suckle ; portefeuille,
risque, risk. was impossible to draw the line of demarcation between the -ISQUE
pocket-bool; vaudeville, Exception.-Bisque, soup.
ballad. Mesozoie period and the Palæozoic on the one hand, or the
-ISTE ébéniste, cabinet-maker. -OSSE bosse, bunch. Cainozoic on the other, the Mesozoic and the Cainozoic were
Exceptions. Carrosse, included in the term Neozoic, or new life. Hence the division
cambric; liste, list;
coach; colosse, colossus. now stands
not preceded by u. Neozoie
Exceptions. -- Lierre, ivy; Triassic. Hypozoic (Below
parterre, hower-garden ; Metamorphic. life)
tonnerre, thunder ; para
tonnerre, lightning-rod; Our illustration shows an ideal forest of the Carboniferous
verre, glass. period, when the coal deposits were formed.
-TIE amitié, friendship.
leton; amulette, amulet.
-URE nature, nature. $ 6.-GENDER BY THE TERMINATION (continued).
-USE excuse, eccuse. (3.) VOWEL TERMINATIONS.
Nouns ending in i.
midi, noon. acacia, acacia. Exceptions.-Vinula, a sort
faith; of caterpillar; sépia, sepia.
fourmi, ant; après-midi,
afternoon ; Nouns ending in E.
merci, mercy. A complete classification of nouns ending in e mute (a majority
Nouns ending in u. ef which are feminine) would be, from its length, of little prac
revenu, revenue. tical use to the student, who would find it easier to apply to his
Exceptions.—Bru, daughterdictionary than to such a list. We will give here the principal
in-law; vertu, virtue; terminations, classing them according to their gender, and
glu,bird-lime; eau, water; placing the exceptions under the examples given for the termi
peau, skin; tribu, tribe. nations, instead of putting them, as hitherto, in the opposite column.
$ 7.-NOUNS MASCULINE IN ONE ACCEPTATION, AND MASCULINE. FEMININE.
FEMININE IN ANOTHER.
Cartouche,ornaments(sculpture) Cartouche, cartridge. macle, a mineral, -ANCE importance, importance. Couple, male and female.
Couple, a pais, a brace, troo. - ACRE sacre, consecration.
Délices (pl.), delights.
Espace, leading (in printing). cournge, courage.
cameo, colisée, coliseum. Greffe, office of clork of a court, Greffe, graft.
Héliotrope, a mineral.
Hymne, Christian hymn.
marriage; périgée, peri Mode, mode (grammar), system. Mode, fashion.
Euvres, literary works.
dee; scarabée, beetle.
Ombre, shadow, spectre. snake-root; pariétaire, -EINE baleine, a whale.
Orgue (sing.), organ.
Orgues (pl.), organ. pellitory, and a few -ENCE cadence, cadence.
Palme, hand, a measure.
Palme, the advantage.
Parallèle, parallel line.
Période, period, epoch. chaume, thatch.
Pivoine, a flower.
Plane, joiner's tool, not immediately preceded -IE charpie, lint.
Platines, small metallic plates,
Prétexte, « Roman robe.
Régale, right of receiving the Norway. pavie, clingstone peach.
revenues of a vacant bishopric. Carême, Lent. -IÈRE chaudière, boiler.
Un remise, fly, hired carriage. Remise, carriage-hottse. Exceptions. Crêre, -INE doctrine, doctrine.
Serpentaire, dragon-tort. cream; brême, bream ; -IQUE pratique, practice.
Solde, balance of account.
Solde, pay. birème, trirème, galley -IVE rive, shore.
Somme, nap, sleep.
Somme, sun. with two or three rows of -ISSE coulisse, sliding.shutter.
Tour, tour, turn, trick.
Vase, inire, slime.
$ 8.-FORMATION OF THE PLURAL OF NOUNS.
PLURAL. (1.) The plural in French, as in English, is formed by the
Gentilshommes, noblemen. addition of s to the singular :
(4.) For the sake of euphony, the mark of the plural and of Ville, town.
the feminine also is omitted in the adjective of the following (2.) First Exception. Nouns ending in the singular with s, x,
compound words :
SINGULAR. or , have the same form in the plural :
Grand mère, grandmother.
Grand'mères, grandmothers. SINGULAR.
Grand'messe, high mass.
Grand'messes, high masses. Fils, son,
(5.) The words Monsieur, Sir, Mr., gentleman; Madame, Nez, nose.
Madam, or Mrs.; Mademoiselle, Miss, form their plural thus :(3.) Second Exception.— Nouns ending in the singular with au
SINGULAR. and eu, take x in the plural:
Monsieur, Sir, etc.
Messieurs, Sirs, gentlemen. Madame, Madam, etc.
Mesdames, ladies, etc. (etc. SINGULAR. Chapeau, hat. Chapeaux, hats. Mademoiselle, Miss, etc.
Mesdemoiselles, young ladies, Feu, fire.
(6.) In words composed of a noun and a verb, a preposition or .(4.) Third Exception.— The following nouns ending in ou take an adverb, the noun takes the form of the plural; provided, in the plural :
however, there is plurality in the idea :
Avant-gardes, vanguards. Chou, cabbage.
(7.) Compound nouns of which the second word indicates Genou, knee.
plurality, take s in the singular and plural:Hibou, owl. Hiboux, owls.
Casse-noisettes, nut-crackers. Casse-noisettes, nut-crackers. (5.) Fourth Exception.—The following nouns ending in ail,
(8.) Words composed of two verbs, or of a verb joined to an change that termination into aux in the plural :
adverb, or a preposition, are invariable:
Passe-partout, master-keys. Coraux, corals. Email, enamel. Emaux, enamels.
Pour-boire, coachman's fee. Pour-boire, coachman's fees. Soupirail, air-hole. Soupiraux, air-holes.
§ 10.- NOUNS WHICH HAVE NO PLURAL. Sous-bail, under-lease.
(1.) The nouns of metals considered in themselves : as, or, Vantail, windou-shutler.
Vantaux, window-shutters. gold; argent, silver; plomb, lead; étain, pewter; fer, iron; (6.), Fifth Exception. The following nouns form their plural cuivre, copper; vif-argent, quicksilver ; etc. irregularly :
(2.) Aromas : such as baume, balsam ; encens, incense ; etc. SINGULAR.
(3.) The names of virtues and vices, and some names relating Ail, garlic.
to physical and moral man: as, le jeunesse, youth ; la beauté, Bétail, cattle.
beauty ; la bonté, goodness ; le courage, courage. Bercail, sheepfold, has no plural.
(4.) Adjectives used substantively: as, le beau, the beautiful; (7.) Sixth Exception. Nouns ending in the singular wita al, l'utile, the useful ; etc. change that termination into aux in the plural:SINGULAR.
EXERCISES IN EUCLID.-II.
PROPOSITION VI.-In the figure of Euc. I. 5, if Go (Fig. 6) Mal, evil.
drawn at right angles to AG, meet a h in o, I being the inter Aval, endorsement; cal, callosity; cantal, kind of cheese ; nopal, nopal ;
section of BG and CF, then 0 pal, pale; serval, tiger-cat; bal, ball; carnaval, carnival ; chacal, jackal;
shall be perpendicular to AF. régal, treat, follow the general rule-i.e., form their plural by the addition of an s, as, avals, cals, cantals, nopals, etc.
In Proposition IV. we proved
that Al will bisect the rerti (8.) Ciel, cil, aïeul, travail, have two plurals :
cal angle BAC; therefore the SINGULAR.
angle Gao is = to angle O AT Ciel, heaven. Cieux, heavens.
Hence in the two triangles GA tester of
O AF, because GA=AF an
Ao is common, also include Eil-de-bæuf, oval window. Eils-de-boeuf, oval windows.
angle GAO = included ang Aieul, ancestor.
OAF, ... also base o g = base o F (Euc. I. 4). Again, in Aïeul, grandfather,
same triangles, because AG=AF, and oG= OF, also bas Travail, labour.
o A is common, .'. included angle A Go= included angle AF Travail, trave.
But Ago is a right angle by construction; hence, AFO is $ 9.-PLURAL OF COMPOUND NOUNS.
right angle, and or is perpendicular to af. Q. E. D. (1.) When two nouns form a compound substantive, both take PROPOSITION VII.-If A C (Fig. 7), the side of a triangle AB the plural ending :
be bisected in D, and BD SINGULAR.
joined and produced to E, Chef-lieu, chief place.
Chefs-lieux, chief places. so that D E may be equal Lieutenant-colonel, lieutenant. Lieutenants - colonels, licu- to D B, then, if A E be colonel.
joined, the angle A E D (2.) When a compound noun is formed of two substantives shall be equal to the joined by a proposition, the first only takes the plural ending :- angle D BC.
Join CE. Then, since
Chefs-d'oeuvre, masterpieces. BE cut in D, therefore The words tête-à-tête and coq-à-l'âne (an incongruous discourse), re- the angle AD B is equal to the vertical and opposite an main unchanged in the plural.
CDE (Euo. I. 15). Then in the two triangles ADB, CD (3.) When a noun and an adjective form a compound noun, because side Ad=DC by construction, and side BD=I both are varied in the plural:
also by construction, also included angle A DB= inelud
Ciel, kes on a picture.
angle C D E, therefore base AB=C E. Again, in the same Corollary.--It is obvious by symmetry that LE, DM will
triangles ADE, BDC, we see that PROPOSITION XIII.-In a triangle A B C, if Bo, co bisecting
meeting in o, be equal, then
From A draw A C perpendicular shall o A bisect the angle A B C.
to CD (Euc. I. 12), and produce PROPOSITION XV.-In the Fig. 8.
AC to F, so that cr=AC (Post. figure of Euc. I. 1, if the cir.
2, Euc. I. 3). Join B F (Post. 1), cles cat again in F, and c A proand let BF cut c d in E. Join A E (Post. 1), then shall the duced meet the circle again in
Fig. 12. angle A E C be = to angle B E D. For since A c is at right , then c r is greater than CF. angles to EC, and by Euc. I. 15 the vertical or opposite angles PROPOSITION XVI.-In the figure of Euc. I. 5, prove that between two straight lines are equal, therefore the angles BG must be greater than BC. ACE, ECF are equal, and AC=CF
PROPOSITION XVII.--In the figure of Euc. I. 16, if EC and C E is eommon, .'. base A E=
be equal to EF, the angle A B C will be equal to the angle base E F (Euc. I. 4); and because
BOF. AB=I F and Ec is common, also
PROPOSITION XVIII.-In the figure of Euc. I. 22, if the base a c= base CF,... angle A ECO
circles cut again in L, then shall D K be equal to D L. angle CEF (Euc. I. 8). But by Euc.
PROPOSITION XIX.-At a given point in a given straight. I. 15, angle CEF= angle B E D;
line, to make an angle equal to a given rectilineal angle. therefore, by Axiom 1, angle A ECO
*** Another solution of Euc. I. 23. angle BED. Q. E. F.
PROPOSITION XX.-In the figure of Euc. I. 15, if E F, EG: PROPOSITION IX.-In the figure of
be drawn at right angles respectively to A B and CD, the angle, Euclid I. 1, if the circles cut again in F (Fig. 9), and AF, BF be FEG is equal to the angle B E D Or A EC. joined, the figure A FBC is a rhombus.
For since AC, A B, AF are radii of the same circle, Ac and AP are equal to A B (Def. 15), and since B C, BA, B F are LESSONS IN ENGLISH LITERATURE.-II. radü of the same circle, BC and B F are equal to BA (Def. 15). LITERATURE IN ENGLAND BEFORE THE AGE OF CHAUCER. Bat by Axiom 1, things which are equal to the same thing are As we have chosen the age of Chaucer as that at which to equal to one another; therefore A C, A F, BC, B F are all equal. commence the history of English Literature, it would be Hence, by Def. 32, the figure AFBC is a rhombus. Q. E. D. PROPOSITION X.-In an isosceles triangle
inappropriate to attempt any minute or elaborate account of
those remains which have come down to us of earlier forms. ABC (Fig. 10), if Al be drawn from the vertex a perpendicular to the baseB C, and B
of literature. But in order that the student may understand
how great the change was which took place in the latter part if Al be produced to M, so that LM=LA, then shall Bm be=to B A. Join Bm and
of the fourteenth century, and how much English literature XC. Then, because AL=LM by construc
owes to the great writers of that period, it is necessary that he tion, and BL is common, also right angle
should know something of those who preceded them. EL A = right angle B L M, therefore base B A = base B M THE PERIOD BEFORE THE NORMAN CONQUEST. (Euc. I. 4). Q. E. D.
From our knowledge of the character, habits, and pursuits of PROPOSITION XI.-If in any triangle the sides A B, A C (Fig. the Saxon invaders of England, it would not be difficult to guess
11) be bisected in L, M, and what would prove to be the character of the compositione LO, Mo be drawn at right brought by them from their German home, er produced among angles to AB, AC, meeting in them during the earlier days of their contest with the Britons. 0; then on drawn perpen- These “hosts of heathen swarming over northern seas," and dicular to B C will bisect Bc. overrunning helpless Britain, were wild, fierce, and uncivilised ;
Join O A, O B, O C. Then, their life was wholly made up of war and adventure ; their gods because BL= L A, and Lo were gods of battles, and their national heroes were warriors; is common, also right angle their conquest of Britain itself displayed energy and courage in BLO= right angle A Lo, abundance, and the most relentless cruelty in no less degree; and
therefore base B o = base their literature (if we may be allowed to stretch a point, and Fig. 11.
0 A (Euc. I. 4). In a simi- apply the word to compositions which were not generally written,
lar way base co= base oa but handed down from mouth to mouth) consisted of songs of (Esc. I. 4); therefore, by Axiom 1, B0=0C. Therefore, BOC war and adventure, the achievements of heroes related in verse. is an isosceles triangle, and on is drawn perpendicular to the By far the most important specimen of the poetry of this period base. Therefore, by Proposition I., on bisects the base--that is the “ Lay of Beowulf.” The date of the poem is doubtful. is BN=Xc. Q. E. D.
It may have been brought (as some think) by the Saxons from Corollary.--Hence
, obviously o is the centre of a circle passing Germany to their new home in England; or it may have been through A, B, C. This is called the circumscribed circle, or circle composed in England. The scene of the poem, too, is doubtful, described about the triangle ABC.
whether it be Sweden, or Denmark, or England, or mere dreamPROPOSITION XII.- In the figure of Euclid I. 9, if with land. But it is clear that it was composed by and for Saxons centre A (Fig. 12) and radius AF, a circle be described cutting during, if not before, the early years of their settlement in AB, AC in L and , then shall E L be equal to D M.
England; and it is therefore a good representative of the class For since A L, AF, A M are radii of the same circle, they are of which we are speaking. It relates with much energy and all equal (Def. 15); therefore AL=AM. But by construction freshness how Hrothgar, King of Heorut, and his thanes were of Euc. I. 9, AD=AE; therefore, by Axiom 3, the remainders DL, persecuted by a monster
who dwelt in the fens, and 1 x are equal. Also, by Enc. I. 5, the angles on the other side the used to come by night and carry off the thanes as they slept in base of an isosceles triangle are equal; therefore the angle L D E the hall after the feast; how Beowulf, a thane of Hygelac, King angle DEM. Therefore, since ID=EM, and De is common of the Goths, heard
of their distress, and came by sea to their to the two triangles LD E, D E m, therefore base LE = base m. aid; how he slew the monster Grendel, and afterwards its
mother, who sought to avenge her son; how he subsequently
Q. E. D.