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In this summary view, many facts regarding gender, number, and case, are of necessity omitted. They may be found in the works to which reference has already been made. It seems, however, desirable to add, that grammarians recognise in Latin what is called a common gender. Those nouns are said to be of the common gender (c.), which may be applied indifferently, either to a male or a female. Such nouns are hospes, a guest; hostis, an enemy; incola, an inhabitant; parens, a parent; sacerdos, a priest or priestess; testis, a witness; bos, a bull or a cow; canis, a dog or a bitch; lepus, a hare; mus, a mouse, &c.

GENERAL EXERCISES ON THE FIVE DECLENSIONS.

VOCABULARY.

Húmidus, a, um, humid, wet; hiems, hiemis, f. winter; divitiae, arum, f. riches; ultimus, a, um, the last; lepus, õris, m. a hare; cadâcus, a, um, falling, frail; pavidus, a, um, fearful, timid; barbarus, a, um, barbarous; sermo, ónis, m. speech; Látinus, a, um, Latin; Graecus, a, um, Greek; exoptatus, a, um, wished for, desired; quies, quietis, f. rest, quiet: tumidus, a, um, tumid, swelling; profundus, a, um, deep; inspiratus, a, um, unhoped for; nox, noctis, night; frigidus, a, um, cold; magnificus, a, um, magnificent; ligneus, a, um, wooden; commodus, a, um, convenient; glacies, ei, f. ice; lubricus, a, um, slippery; nemo, neminis, c. no one; felix, felícis, happy; credulus, a, um, credulous, too believing; palus, palúdis, f a marsh; clarus, a, um, clear, distinguished; gelidus, a, um, cold; gradus, ûs, m. a step; potens, potentis, powerful; nunquam, adv. never; avárus, a, um, avaricious; fames, is, f. hunger; sitis, is, f. thirst; rotondus, a, um, round: infidus, a, um, unfaithful; sempiternus, a, um, everlasting; tardus, a, um, slow; contentus, a um, satisfied; limpidus, a, um, limpid, bright; exiguus, a, um, short, narrow; acutus, a um, sharp; humus, i, f. the ground or soil; eximius, a, um, eminent, remarkable; morosus, a, um, morose, illtempered; semper, adv. always.

LATIN-ENGLISH.

Est mihi amicus fidus et carus; infídus est servus tuus; terra est rotunda; vera amicitia est sempiterna; fames et sitis sunt molestae; avárus nunquam est contentus; rex est potens; gradus tuus tardus est; virtus patris tui est eximia; fons est clarus et gelidus; nomen clarum est ducibus; amnis limpidus delectat omnes; cervo sunt alta cornua; res est magna et insolita; hic sunt vastae paludes; opes credula fallit pueros; hominibus exigua est dies; nemo semper felix est; glacies est lubrica; pons ligneus custoditur; non omnes milites sunt fortes; magnificae porticus defenduntur; portus est commodus; dentibus acutis edimus; nox est longa et frigida; bonus laudatur, improbus vituperatur; senectus saepe est morosa; insperata salus venit; mare est vastum, profundum, tumidum; quies valde exoptata facile amittitur; sermonem Latinum discimus; nonne doces Graecam linguam? gentes barbarae remotae sunt; lepores pavidi evolant; fos est caducus; hora ultima venit; incertae sunt divitiae; mores antiquos amat mater mea; verba tua sunt dura; quam humida est humus! non facile in hieme agri arantur.

ENGLISH-LATIN.

Faithful friends are loved; I have great riches; they lose wished-for friendship; the ground is wet; wet ground injures; hares have sharp teeth; with sharp teeth we all eat; thy soldiers are brave; are thy father's soldiers brave? they delight in (abl.) credulous hope; the horns of the bull are strong; the virtues of the king are remarkable; how beautiful is the portico; you ought to learn Latin; men fear the last hour; the house is guarded by a strong band; avaricious men are avoided; ill-tempered women are never loved; the ill-tempered are troublesome; is friendship eternal? hope is eternal; how slow are thy steps! ice is slippery in winter; no one loves hunger and thirst; quiet quickly flies aay; the harbour is convenient for ships; the fearful are never safe; art thou satisfied with the speech of thy father? they strike a powerful prince; falling flowers are gathered (lego 3); he gathers flowers in the march; the Greek language is beautiful; swelling seas are often found; the rest and solace of true friend-hip are wished for; no one is always happy.

To how large an extent Latin words enter into the composition of our present English is strikingly seen in the last vocaThese words found therein have their English bulary. representatives.

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The student of Latin will be greatly assisted, if before he attempts to commit a Latin word to memory, he tries to find an English word which is derived from it, and with which he may associate it in his mind.

LESSONS ON PHYSIOLOGY.-No. V.

MAN.

We wish to make our lessons so simple and plain, that you may thoroughly understand them. In treating of digestion, we showed you that the process begins with taking our food into the mouth. It is there masticated or chewed; in being chewed, it becomes mixed with the saliva of the mouth, until it takes on the character of a soft pulp. It is then swallowed; passes down the oesophagus into the stomach, where it comes in contact with the gastric juice. By the action of this fluid, it is converted into chyme. This chyme passes gradually into the duodenum, where it meets the bile and the pancreatic juice, undergoes a complete chemical change, and reappears in the form of a white milky liquid, known by the name of chyle. This is taken up by the lacteals, and by them poured into the thoracic duct or canal, which is in communication with the greater portion of the absorbent vessels of the body. In this canal the chyle becomes mixed with the lymph, and is thence conveyed into the vein which passes under the left clavicle, and mingling with the venous blood, is carried to the heart and lungs to receive its vital and life-giving properties.

If the food which we eat is thus at last converted into blood, and if it be the blood which builds up every individual part of the body, it is of great importance that our food should be good

and wholesome. The blood can contribute to growth and common egg-shell, which is nothing more than so many layen health only as it exists in a pure and healthy condition. If of fibrous tissue enveloping the albumen, and forming that thus precious vital fluid be itself diseased, it cannot fail to com- thin membrane which comes between the outer shell and the municate the disease to the various parts or organs which it inner substance. These fibres constitute the first and simplest has to supply with their appropriate nutriment. For example: forms of anima tissue. If this solid earth, which we wal -If a fit of passion may suddenly and immediately occasion with so firm a step, be but an aggregation of particles or atoms, such a change in the milk of a nurse as to render it a rank held together by the one great law of attraction, our bodies are poison to the little dependant infant, there is nothing to con-nothing more than a mere combination and union of elements tradict the theory, that the blood itself may undergo such under the law of organisation. Nor is it difficult to become changes as to convert it from a wholesome nutriment and in some degree acquainted with these elementary or compo stimulus to vital action, into a most violent poison, fatal nent parts, with their physical, chemical, and vital properties. even to life itself. Another example:-In vaccination, a Since the growth of the cell is dependant on its absorbing surgeon introduces into the arm of a child a very minute por- certain particles of matter from the fluid which surrounds tion of virus, which in some way or other, not well known,-in this nutrient fluid, in the process of organisation, or before affects and alters the whole of the blood; and this morbid the process begins, we must look for the components of the state of the blood continues for a length of time. Or, again, animal structure, with their essential or peculiar properties. suppose a student in the course of dissection should prick his finger, the putril matter thus introduced may so effectually get into his system as to poison the blood and occasion death itself. It follows that a man may wilfully and knowingly induce disease, and injure his system. A drunkard is never a healthy man. Some men may more easily and for a longer period resist the effects of intemperance than others; but that the free use of ardent spirits is prejudicial to health is a truth which all the facts of physiology but too clearly demonstrate. An intemperate man does everything to contravene nature. He is working against God, and against the most beneficent laws of his universe. The great Creator has introduced into the blood all those elements which are adapted to preserve it pure and uncorrupt. What other end can we conceive to be involved in the fact, that in the blood is to be found a certain portion of saline matter? The presence of such an agent in the circulating fluid must be regarded as a beautiful and beneficent provision to prevent its decomposition. Were the blood to decompose in the body, it would cease to possess any vital property; and, deprived of its vitality, it could no longer minister to the nutriment and growth of a single structure.

Blood

The blood is a liquid of a beautiful red colour, and of a peculiar odour. In some animals this odour is very marked. Take blood from a cow, and by the smell of the fluid you can tell from what animal it has been drawn. In its living state, the blood is a transparent liquid, Colding in suspension certain little bodies, of which some are colourless, but the greater portion of which have a red colour, and are known by the name of blood-globules. Now, to under. stand how these little bodies are adapted to nourish and build up the body of the strongest and most powerful, we shall try to set before you the component parts of this precious fluid. Let us open a globule. vein, and take from the body a portion of blood. If we allow it to remain at rest for ten or fifteen minutes, it begins to congeal and take on a more solid form like that of a soft jelly. The fluid has become a solid, and this is the only change which is yet palpable to our senses. After a few hours we and that the clot has a greater degree of consistence, and, as the effect of this contraction, is surrounded with a transparent yellow fluid, which is named serum. Now what is there in this blood to produce this coagulation? Why does it not remain in a fluid state, as when first drawn from the vein? There must be some peculiar law to account for this change. In itself, and as it is seen flowing in the veins of a living creature, it appears a colourless fluid, with minute red particles which give the blood its beautiful scarlet hue; and so long as it is in a fluid state it holds in solution a particular substance called fibrine, which, in its ultimate composition, differs little or nothing from albumen, or the white of an egg. This substance is distributed through the whole body, but is found chiefly in the blood, because the blood, in its course and flow, supplies to every individual part of the complex structure the materials of its growth and development. Take the blood from the living structure, and the fibrine remains no longer in solution. Instead of being diffused, it coagulates and contracts, till it has pressed out the serum by the mutual attraction of its own particles. Now if we look at this clot or congealed blood through a microscope, we shall find that it presents a peculiar arrangement. It is not a mere aggregation or promiscuous accumulation of particles, but a beautiful disposition of fibres crossing one another in every direction. This arrangement may be seen in the

But the blood is not more dependant on the character of the food which we eat, than on the purity of the air which breathe. The heart, from which the blood issues in a condi tion to nourish the body, is situated between the right and the left lung, and with the lungs fills up the whole cavity of the chest, as may be seen by the accompanying cut. Each lung is made up of a countless number of cells or vesicles, which

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are always full of air derived by inspirations from the atmosphere which surrounds us. These cells communicate freely the one with the other; and it is in these air-cells of the lungs that the dark venous blood, by coming into contact with the oxygen, is converted into arterial. Impure air, therefore, can not but be prejudicial to the quality of the blood; and in the degree in which the blood is affected, must the body, with all its peculiar functions, be more or less disordered. No one should sleep in a room into which air has no admission, for it is possible that during the night he may exhaust the whole of the vital air necessary for respiration contained in the apart ment, and the consequence must be suffocation. Nor should we leave our sleeping-room in the morning without throwing open the window and allowing a free current to pass through it. Not only is it important to eat food which is wholesome and easy of digestion, but to breathe the freest and the purat air. No one should choose a house in a crowded, confined, and thickly-peopled neighbourhood. The atmosphere of such a neighbourhood is always more or less impure. Every inspi ration which we take, or every breath which we draw, we take a portion of this air into the lungs, and the blood in its passage through the lungs so filled, must to a certain extent be come tainted, and may set up disease in the system. Hence the importance of daily exercise in the open air. The farther we can get away from the smoke, and dust, and surcharged atme

sphere of large and crowded towns the better. God made the country, and no one can ramble for a single day amid its fields and woods, its hills and vales, without feeling the stream of life bounding through his system with a freer, fresher, mightier, and more living force than before.

All organised bodies are subject to decay, even while actively engaged in performing the functions of life. One of the chief products of that decay is carbonic acid, the removal of which from the system is essential to health and vital action. This removal is affected by the agency of the lungs, which are made

What is the acid which they throw off, and what is the element which they take from the air?

What is the effect of impure air on the health?
Show wherein it is injurious.

Give an example of the bad effect of an excess of carbonic acid on inferior animals.

in it. Then,

LESSONS IN GEOMETRY.-No. IV. PROBLEMS IN PRACTICAL GEOMETRY-Continued. 10. Given two angles of a triangle to find the third angle. Draw a straight line DF (fig. 11), and take any point at the point E, in the straight line ED, make the angle DEC equal to one of the given angles; and at the point E in the straight line E C, make the angle CEI equal to the other given angle; and H E F, will be the third angle required.

Fig. 11.

C

E

F

H

The reason of this construction is plain, D
from Prop. XXXII,, Book I., Euclid, which
asserts that the three angles of every triangle are equal to two right
angles; and from Prop. XIII., Book I., which asserts that the
angles which one straight line makes with another upon one side
of it, are either two right angles, or are together equal to two
right angles.

The proof of the latter proposition is very easy; for by
referring to figs. 12 and 13, it will be seen at once, that the
Fig. 12.
Fig. 13.

B

A

D

B

D

up of a countless number of little aircells. Now between the atmospheric air, which is taken into the lungs at every breath which we draw, and the blood, there is nothing interposed but a very thin and delicate membrane. The carbon discharged from the lungs of a man in good health is from eight to nine ounces in the twenty-four hours. Let a hundred such individuals be shut up together in a room for three hours, and during that space of time not fewer than one hundred ounces of carbonic acid must be evolved; and what is the consequence? The air which is breathed being impregnated with carbonic acid, the quantity of carbon exhaled, becomes, with every successive respiration, less and less. It has been found by experiment, that, when fresh air is taken in at each inspiration, thirty-two cubic inches of carbonic acid may be exhaled in a minute; while, in those cases in which the same air is breathed repeatedly, the quantity of carbonic acid emitted in the same period may not amount to one-third. And if it be true that however often the same air may be respired-should it be respired till it is no longer capable of sustaining life-it never becomes charged with more than ten per cent. of carbonic acid, we see the necessity of a constant supply of fresh air by means of free ventilation. The discomfort inseparable from a crowded audience in a church, lectureroom, or theatre, which is not provided with sufficient ventilation, is due in great part to the continued respiration of the same air, which has become loaded with carbonic acid. - Nor can it be denied that the habitual respiration of such air in the narrow and pent-up dwellings of the poor, or in crowded factories and workshops, has a tendency to impair health, diminish mental activity, and even deteriorate the moral sensibilities. Repeated experiments have brought out the fact, that the blood comes to the lungs charged with carbonic acid, which it gives up, and receives oxygen in its stead. According to the law of mutual diffusion, the quantity of oxygen absorbed, or drawn from the atmospheric air, exactly replaces the quantity of carbonic acid set free. But for this change in the compoThe proof of the 32nd proposition of Book I. is not quite sition of the blood, all the functions of life would soon be arrested. Put a fish in water which is impregnated with car-student for himself as follows:-First, accurately construct a so easy; but a palpable proof of it may be obtained by any bonic acid, and its death is almost instantaneous. Introduce triangle of any kind, on a piece of paper or card, and then cut the human being into some crowded room, in the atmosphere it out entire; next draw a straight line, and cutting off the of which there is wanting a due proportion of oxygen, or in three angles of the triangles at about half the length of each which there is the presence of carbonic acid in excess, and side, apply their three angular points to any point in this fainting ensues. Let the blood be denied its contact with the straight line, so that the legs of the angles shall be contiguous (in atspheric air, and life will speedily ebb and disappear. contact with) to each other, and one of the exterior legs contiThe blood stagnates in the small capillary vessels of the lungs guous to the straight line; when it will be found that the -the heart has not sufficient force to drive the blood through other exterior leg is also contiguous to it; thus showing that those capillaries-the air included in the lungs loses more of the three angles fill up the space of two right angles, and are its oxygen, and becomes overcharged with carbon, and at last the blood becomes so venous, that the pulmonary circulation therefore equal to two right angles. is altogether suspended, and death follows.

QUESTIONS FOR EXAMINATION.

Can you describe the process of digestion?

How is health affected by the condition of the blood?
Give an example of how the blood becomes tainted or corrupted?
What bodies does the blood hold in suspension?

What change takes place in the blood after it is drawn from the vein?

What is the peculiar substance in the blood which goes to build up the various tissues of the body?

Why should we be careful as to the character of the food which we take?

How is the blood affected by the air, and how does it come into contact with the atmosphere?

Of what are the lungs composed, and where are they situated?

angles which one straight line makes with another are either right angles or oblique angles; and that the oblique angles are equal to the right angles is plain, because they occupy it is evident in fig. 13, that whatever the angle DAB wants exactly the same space about the point a; in other words, of a right angle, e angle CAB has just exactly that quantity more than a right angle; and consequently the two toether a just equal to two right angles. From this argu. ment, it is likewise evident, that whatever be the number o straight lines which meet at the same point E, in the straight line DF (fig. 11 above), on the same side of it, all the angles which they make, taken together, are only equal to two right angles.

Another mode of proof may be had from the use of the protractor, fig. 14, described at p. 50, No. 4. Draw any triangle Fig. 14.

N

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G

C

as before; measure each of the three angles by the protraetor five sides,-viz., A B, B C, C D, DE, and Ea; and twice five sides in degrees; add the numbers of the degrees obtained by these are ten sides. Now, taking away four right angles from ten three measurements together; and if they have been carefully right angles, leaves siz right angles; and this is the number of measured, they will always make 180°; for one right angle right angles to which the five angles of the figure, -vIZ., ▲ B €, makes 90°, therefore two right angles make 180°. Thus, if B CD, CDE, DEA, and E A B, are, together, equal. The one angle of a triangle measures 57°, and another measures proof of this is very evident, for, by drawFig. 18. 75°, then the third must measure 48°, because 57+75+48=180. ing straight lines CA, CE, from any angle ▲ From the 13th proposition of Book 1., the 15th is easily in- to the other angles of the figure, there are ferred; viz., that if two straight lines intersect each other, the three triangles, ABC, ACE, and CE D vertical or opposite angles are equal. One angle is said to be formed within it. Now, by the 32nd provertical or opposite to another, when the legs of the former position, all the angles of these triangles proceed from the point of intersection or meeting, in directions are equal to twice three right angles, that exactly opposite to those of the latter. Thus in fig. 15 let the is, to six right angles, as before. The same straight lines BE, CD, intersect each other in the point A; then thing could be proved of any other polygon, the angle BAD formed by the production of the legs EA, CA, B C D F G. In like manner, whatever be of the angle CA E, in opposite directions AB, the number of sides in the polygon, it may be shown that the Fig. 15. A D, through the point of intersection a, is truth of the proposition is manifest, for the addition of another said to be vertical or opposite to the side to the figure would only add another pair of right angles to angle CAE. In like manner the angle CAB the number of right angles it previously contained; so that, is said to be opposite or vertical to the whatever was the number of sides, there would always be four c angle DA E. The proof of this proposi- right angles wanting in order to make up twice as many right tion is manifest, for by turning over the angles as the figure has sides. This truth may be exhibited angle B A D upon the angle ca E, they would in another way. By drawing straight lines from any angle in coincide, and they are therefore equal. a polygon to the other angles of the figure, we draw as many Otherwise it is shown that they are equal, straight lines as the figure has sides, wanting two, seeing that, because either of them together with the angle BAC makes in drawing these straight lines, we draw two that must coincide two right angles. with two of its sides already drawn; hence we construct in the interior of the figure as many triangles as the figure has sides, wanting two. It is plain, therefore, that it will then contain only twi e as many right angles as the figure has sides, wanting four right angles.

DEFINITION 1.-When two angles are together equal to two right angles, the one angle is said to be the supplement of the other. Thus, in the preceding figure, the angle B A C is the upplement of either of the angles BAD or CAE. In like manner, the angle B A D is the supplement of either of the angles B A C or DA E. If the angle B AD contained 30°, then the angle B A C must contain 150°.

E

DEFINITION 2.-When two angles are together equal to one right angles, the one angle is said to be the complement of the other. Thus in fig. 16, the three Fig. 16. angles of the triangle E B D are equal to two right angles; but the angle E B D is a right angle by construction; it, therefore, follows that the other two angles B E D, BDE are together equal to a right angle, and the angle BED is the complement of the angle B D E; or the angle BDE is the complement of the angle BED. If the angle B D E contained 40°, then the angle B ED must contain 50°.

D

B

From the propositions above mentioned, it evidently follows, that when two straight lines intersect each other, the four angles thus formed at the point of intersection, are together equal to four right angles; that is, in fig. 15, the four angles BA C, B A D, DAE, and E A C, are together equal to four right angles. It is also evident, that all the angles formed by any number of straight lines meeting together in a point, are together equal to four right angles. Thus, in fig. 17, let any number of straight lines A o, E O, CO, DO, Eo, meet together in the point o; then all the angles, A O B, BO C, CO D, DO E, and

OA, are together equal to four right angles.

D

Fig. 17.
BY

E

From the 32nd proposition, Book I., Euclid, two very important corollaries are deduced, which we now proceed to explain, as they are necessary to be understood in connexion with some practical problems. But first we must explain what is meant by corollary. The Latin word corollarium, from which it is derived, signifies an overplus, or surplus, or something in addition which may be considered as a gratuity. In geometry it means an inference or deduction easily drawn from a proposition just demonstrated. The first corollary which Euclid draws from the 32nd proposition is, that all the interior angles of any convex rectilinear figure or polygon are, together, equal to twice as many right angles as the figure or polygon has sides, wanting four right angles. Thus, in the polygon A B C D E, fig. 18, all the interior angles ABC, BCD, CDE, DEA, and AB, are, together, equal to twice as many right angles as the Agure has sides, wanting four right angles; for this figure has

From this corollary another may be drawn regarding regular polygons. Since all the sides and angles of regular polygons are equal to each other; that is, the sides equal to one another, and the angles equal to one another, it is plain that the value of each of the angles can be determined. Thus : double the number of sides, call them right angles, and subtract four right angles; the remainder will be the number of right angles it contains; divide this remainder by the number of sides, and the quotient will be the value of each angle. Example: In a regular pentagon there are 5 sides; twice five are 10; from 10 right angles, subtract 4 right angles, and 6 right angles remain; divide 6 by 5, and the quotient is one and one-fifth; hence, every angle in a regular pentagon is equal to one right angle and one-fifth of a right angle, or 108°.

The second corollary which Euclid draws from the 32nd proposition, is that all the exterior angles of any rectilineal figure or polygon are together equal to four right angles. By the exterior angles here, is meant those which arise from producing each of the sides of the figure in one direction only, say from right to left, in going round the figure. The truth of this proposition is manifest, from the consideration that through any point external to the polygon straight lines can be drawn parallel to the productions of the sides, and forming with each other angles equal to those formed by the production of each side, and the adjacent side; now all the angles which can be formed by any number of straight lines meeting in a point are equal to four right angles; therefore, all the angles formed by the production of each side, and the adjacent side,-that is, all the exterior angles of any polygon, are together equal to four right angles. This might also be inferred from another consideration,-viz., that as the magnitudes of the exterior angles would not be altered by the size of the figure, provided its interior angles remained of the same value, neither would they be altered if the figure were ever so small, say reduced to a point; and the exterior angles would then be the angles about a point, and therefore equal to four right angles.

QUESTIONS ON THE PRECEDING LESSON.

How many right angles are equal to all the angles of any triangle taken together? How is it proved mechanically that all the angles of any triangle are together equal to two right angles? If one straight line makes angles with another on one side of it, how many right angles are they equal to? If on both sides of it how many? What is the supplement of an angle? What the complement? What is the meaning of the word corollary? What are the two very important corollaries which Euclid has drawn from the 32nd Prop of his 1st Book? How are they demonstrated? What is the value of each angle of a regular hexagon ?

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coincide with each other.

Fig. 1.

B

At the point a, in the straight line c D, fig. 1, let the straight line A B make the two angles B A C, B A D, on opposite sides of it, equal to two right angles, then a C, A D, are in the same straight line. For if A D is not in the same straight line with a C, let A E be in the same straight line with it. Then, by the 13th proposition of Book I., the two angles, BA C, EBA E, are equal to two right angles; but the angles BA C, B A D, are, by hypothesis (i.e., supposition), equal to two right angles; therefore the two angles BA C, BA E, are, by Axiom I., Book I., equal to the two angles B A C, B AD; take away from these equals the common angle BA C, and by Axiom III., Book I., the remaining angle B A E is equal to the remaining angle B A D; that is, the less equal to the greater, which is impossible; therefore A E is not in the same straight line with a c. In the same manner it may be shown that no other straight line can be in the same straight line with A c but a D; therefore A D is in the same straight line

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with a C.

D

A

curse, became, by the ever-merciful goodness of God, "the
It is the source of the
mother and nurse of the human race.'
most solid wealth, and of the most exhaustless treasure. For
nearly six thousand years has this little earth of ours been
tilled, and sown, and reaped, and yet never was its produce
richer or more abundant than at this moment. "Though mines
of gold and silver should be exhausted, and the moneys made
of them lost; though pearls and diamonds should remain hid
in the womb of the earth and sea; though commerce should
be prohibited; though all arts, which have no other object
than embellishment and splendour, should be abolished; the
fertility of the earth alone would afford an abundant supply"
for every possible condition of the world and of society.
Hence it is that agriculture was held in such esteem among
the ancients. It was the earliest employment of man; and
before the flood, could not be other than favourable to the
the wonderful length of life which those enjoyed who lived
progress and improvement of this interesting art. Nor is there
anything very extravagant in the conjecture, that, as Noah
laid up food in the Ark for himself and those who were with
him, he was also careful to preserve various seeds of corn and
Vegetable with which to sow the earth when the waters should
subside; whilst his knowledge of reaping, sifting, and grinding
the grain, would be made the common property of his family
and their posterity.

The Egyptians, the most ancient people on earth who have
a history and an historical life, seem to have been well ac-
quainted with agriculture. Not only was the population very
numerous, but the land was so well cultivated as to be able to
support its own inhabitants, and to export large quanti-
Its wonderful fertility
ties of grain to other countries.
was owing chiefly to the overflowing of the Nile, that largest
and noblest river in the old world, and the only one that flowed
from ten to twelve hundred miles without receiving a single
tributary stream. A distinguished traveller has thus described
the phenomena connected with the overflow of this great
river:-"The air is so much rarefied by the sun during the
time that he remains almost stationary over the tropic of
Capricorn, that the winds, loaded with vapours, rush in upon
the land from the Atlantic Ocean on the west, the Indian
Ocean on the east, and the cold Southern Ocean beyond the
Cape. Thus a great quantity of vapour is gathered, as it
were, into a focus; and, as the same causes continue to
operate during the progress of the sun northward, a vast train
extended much farther than at other times. In April, all the
of clouds proceeds from south to north, which are sometimes
rivers in the south of Abyssinia begin to swell; in the begin-

Again, at the point a in the straight line CD, let the straight line A B make the two angles B A E, BA D, on the same side of it, two right angles, then AD, A E, coincide with each other. For, if possible, let them not coincide with each other. Produce A D to c; then, by the 13th proposition of Book I., the two angles BAD, BAC, are equal to two right angles; but the angle BAD is, by hypothesis, a right angle; therefore, the angle B A C is a right angle; now, by hypothesis, the angle B A E is also a right angle; therefore, the two angles BAE, BAC, are equal to two right angles; wherefore, by what was demonstrated above, AC, AE, are in the same straight line; but, by construction, AC, A D, are also in the same straight line; therefore, the straight line A Ening of June they are all full, and continue so while the sun coincides with the straight line A D; for if A E, A D, do not coincide, they have a common segment a c, which, by Euclid's corollary to the 13th proposition of Book I., is impossible; wherefore the straight lines A, AD, coincide with each

other.

Remarks.-That the latter case of the preceding proposition is absolutely necessary for the clear understanding of the various cases of the Pythagorean theorem, we hold to be undeniable. Otherwise, how are we to know that the sides of the two smaller squares AC, AG, fig. 2, page 110, No. 7, coincide with each other. It might be stated indeed as a sufficient reason for this, that all right angles are equal to another; for if the one angle did not coincide with the other, then, of course, one of them must be greater than the other, which is contrary to the hypothesis. This to many would appear a sufficient

demonstration.

LESSONS IN ANCIENT HISTORY.-No. V.
By ROBERT FERGUSON, LL.D.

By the conquest of Cambyses, the far-famed land of Egypt
became a province of the Persian empire. But, before we
pursue the history of conquest any farther, it will be both in-
teresting and instructive to turn our thoughts to the state of
the arts and sciences at this earliest period of human and
earthly development.

Among those arts the first place must be given to AGRICULTURE. This is the most ancient as well as the most useful. After his fall, man was sent forth TO TILL THE GROUND; and thus what in itself bore the nature of a punishment and a

The rise of

remains stationary in the tropic of Cancer. This excessive
rain, which would sweep off the whole soil of Egypt into the
sea were it to continue without intermission, begins to abate
as the sun turns southward; and, on his arrival at the zenith
of each place, on his passage towards that quarter, they cease
entirely. Immediately after the sun has passed the line,
he begins the rainy season to the southward.
the Nile at Cairo, does not commence till June, the green
colour produced either by the influx of corrupt or stagnant
water, or by the action of the hot south winds on the sluggish
stream, appearing about the twelfth day of that month. The
red appearance, occasioned by the arrival of the Abyssinian
waters, takes place early in July, from which the rise of the
river may property be dated, as it then begins to increase
rapidly. By the middle of August, it reaches half its greatest
height, and it attains its maximum towards the end of Septem-
ber. From the twenty-fourth of that month, the waters are
supposed to decline, but maintain nearly the same level till
the middle of October. By the tenth day of November, they
have sunk about half, and from that period continue to sub-
side very slowly till they reach their minimum in April."

Some writers have fallen into the error that this periodical
inundation is the only means which the greater part of the
country po-sesses for irrigation or being watered; but when
it is said that no rain falls in Egypt, it must be understood of
Upper Egypt, or the Thebaid;-in Lower Egypt, and on the
sea-coast, the rains are frequent and heavy. The land is not
destitute of water, and the dews fall rich and copiously. Dr.
Clarke says-" The vegetation of Egypt-even the redundant
produce of the Delta-is not owing solely to partial inundation

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