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LESSONS IN BOTANY.-X.

The names of his twenty-four classes, including cryptogamic

plants as the twenty-fourth, are as follows:SECTION XX.-FURTHER CLASSIFICATION OF

1. Monandria-one stamen. 2. Diandria-two stamens. 3. VEGETABLES.

Triandria—three stamens. 4. Tetrandria-four stamens. 5. ALL the general principles we have discussed hitherto, and Pentandria-five stamens. 6. Hexandria-six stamens. 7. taken advantage of, have merely furnished us with the means of Heptandria—seven stamens. 8. Octandria-eight stamens. dividing vegetable growths into three sections; the question, 9. Enneandria-nine stamens. 10. Decandria-ten stamens, therefore, presents itself, how we are to continue the division, 11. Dodecandria-eleven to nineteen stamens. 12. Icosandria how arrange the classification of the hundreds of thousands of —twenty or more on the calyx. 13. Polyandria-twenty or plants which exist ? Various methods have been at different more on the receptacle. 14. Didynamia—four, two long, two times proposed for accomplishing this. We shall not mention short. 15. Tetradynamia—six, four long, two short. 16. them in the order of their organisation, nor shall we fully describe Monadelphia-stamens joined by their edges into one body. them, such not being the object with which these papers are | 17. Diadelphia-stamens joined into two bodies. 18. Polywritten. We shall mention the general principles involved in adelphia-stamens joined into many bodies. 19. Syngenesiaeffecting some of these classifica

stamens joined by their anthers tions, and shall point out in what

into a cylinder. 20. Gynandria, respects certain classifications are

stamens adherent to pistil. 21. better than others.

Monacia-flowers bearing pistils Of all the different schemes of

exclusively, and flowers bearing classification which have ever been

stamens exclusively, on the same proposed or carried into execution,

plant. 22. Diccia-flowers bearing that of the celebrated Swede, Linné

· pistils exclusively, and flowers bearor Linnæus, has undoubtedly at

ing stamens exclusively, on different tained to the greatest popularity.

plants. 23. Polygamia — flowers Indeed, so firm is the hold it has

bearing stamens exclusively, or taken of popular appreciation, that

pistils exclusively, or either parno inconsiderable number of those

tially, on one or many plants. 24. who study Botany still fancy they

Cryptogamia. have nothing better to learn than

In the annexed illustration, a rethe number of pistils and stamens

presentation is given of the fleshy which are contained in different

rhizome, leaves and flower of the flowers, totally unconscious of all

Iris Florentina, or White Iris, a natural alliances. Suppose that

· beautiful variety of the family some eccentric ethnologist should

Iridaceæ, and a native of Southern adopt the grotesque idea of classify

Europe. It flowers in May. ACing human faces according to the

cording to the division adopted by number of wives the individuals of

Linnæus, this plant belongs to the each race were in the habit of mar.

first order Monogynia (having one rying. Suppose that in reference

pistil), of the third class Triandria to this master-idea the ethnologist

(having three stamens). should arrive at the conclusion, that

From an inspection of this arinasmuch as Mussulman Turks, and

rangement, we observe that up to Mugsulman negroes, and Mussulman

the eleventh class the number of Kalmues, and Malays, all marry a

stamens alone furnishes the distincgreat many wives, that for this

tive sign, after which other circumreason Turks, and negroes, and

stances are taken cognisance of. Kalmacs, and Malays, must all be

These circumstances are sufficiently similar races of men. Would not

indicated in the list of classes given such a classification awaken a smile

above; but it is desirable to preat its grotesque whimsicality and

sent the reader with the derivation would it not be considered an

of these terms. It will be remememinently false classification, not to

bered that the stamens are the male say absurd ?

organs of the flower, and the names Yet this is almost the parallel case

given to the first eleven classes are to that of Linnæus, when he effected

compounded of the Greek words for his celebrated artificial division of

the numerals, one, two, three, four, plants according to the number and

five, six, seven, eight, nine, ten and portion of the male and female parts

twelve, and the Greek noun avno (stamens and pistils) of flowers.

(an'-ear), genitive avopos (an'-dros), The cases are remarkably similar

à man. Icosandria is formed of in all that relates to our argument,

the same Greek noun, and Eikoo for although it is the manner of a

(i'-ko-si), the Greek for twenty; Mussulman gentleman to have several wives, whereas it is the ! polyandria from the same Greek noun arnp and the adjective Wont of a lady flower to have several husbands; yet this col- Tous (pol-use), much or many. The term didynamia means lateral discrepancy does not affect the general deduction. two-powered, from the Greek óvo (du'-o), two, and Suvauis

Nevertheless, the artificial classification of Linnæus has ac- (du-na-mis), power; the reason why the term is applied will be quired a celebrity so great, and is so interwoven with popular seen by referring to the explanation given above. Monadelphia botanical ideas, that it cannot be dismissed with the casual means one brotherhood, from the Greek movos (mon'-os), one, notice we have already afforded it. Let us, therefore, proceed and adenpos (a-del-fos), brother, because all the stamens are conto examine the general principles on which it is based.

nected together. Syngenesia is another term signifying a growIn the first place, Linnæus divided plants into cryptogamic ing together, from the Greek ouv (sune), together, and yeivoua. and flowering, as we have done. The department of crypto- (gi'-no-mi, the g hard), I grow. Gynandria signifies woman-man, gamic Botany was, however, very imperfectly known to Lin- from the Greek yurn (gu'-ne, g hard), woman, and avnp, genitive næus ; it was to the classification of flowering plants that his avapos, a man, because the pistils and stamens are attached. chief efforts were directed, and it is on his mode of effecting Monacia signifies one-housed, from the Greek povos, one, and Oikos this that his botanical fame depends. Linnæus arranged all (oi'-kos), house, for a reason which will be evident. Polygamia flowering plants under twenty-three classes, founded on the num. signifies many-married, from the Greek nolus, many, yauos ber and arrangement of the male parts (stamens) of the flower. (gam'-os), marriage; the meaning of which term will also be VOL. 1.

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THE IRIS, AN EXAMPLE OF THE LINNEAN CLASS TRIANDRIA,

SENT

simile #wt their intermelone. ach properis constitutes that howe Walne delle prime *** Weg

of my all m. llius | Ma t hre" in elotion : although the term is often in Jith Me falha Italy isso prebe pri Mpya habarber sein W Antly final rather an hynonymous with the word "* movement.

na niplined in muale, W tuinw then hallintent Thirimafe mobil, Ibon matinerad mye! Ilm "Blurw" movement differs from the “slowest, in zot Red flowers wat fout i n M ay I would born Hoe winkel! m ining the name extreme prolongation of sound in single # # fit w wiono fare llistel Ilve abonamene Aber want to wawely, or the name length of pause. The slow succession of in the path M amy tu nu trwale wote bere the man mit ****d in, however, & common characteristic in both.

Example of SlowMovement.

2. Before and after an intervening phrase :Thou, who didst put to flight

Talents || without application || are no security for progress in Primeval silence, when the morning stars

learning. Exulting shouted o'er the rising ball;

3. Wherever transposition of phrases may take place :O Thou, whose word from solid darkness struck That spark, the sun, strike wisdom from my soul!

Through dangers the most appalling || he advanced with heroic * Moderate."

intrepidity. There is something nobly simple and pure in a taste for the cultiva

4. Before an adjective following its noun :tion of forest trees. It argues, I think, a sweet and generous nature, Hers was a soul || replete with every noble quality. to have a strong relish for the beauties of vegetation, and a friendship

5. Before relative pronouns, prepositions, conjunctions, or for the hardy and glorious sons of the forest. There is a grandeur of

adverbs used conjunctively, when followed by a clause depending thought connected with this part of rural economy. It is worthy of liberal, and freeborn, and aspiring men. He who plants an oak looks

on them :forward to future ages, and plants for posterity. Nothing can be less A physician was called in ll who prescribed appropriate remedies. selfish than this. He cannot expect to sit in its shade, and enjoy its The traveller began his journey || in the highest spirits , and with Ebelter ; but he exults in the idea that the acorn which he has buried the most delightful anticipations. in the earth shall grow up into a lofty tree, and shall keep on flourish

6. Where ellipsis, or omission of words, takes place :ing, and increasing, and benefiting mankind, long after he shall have

To your elders manifest becoming deference, to your companions || censed to tread his paternal fields.

frankness, to your juniors || condescension. “ Lively.

7. Before a verb in the infinitive mood, governed by another How does the water come down at Lodore ?

verb: Here it comes sparkling,

The general now commanded his reserve force || to advance to the And there it lies darkling;

aid of the main body.
Here smoking and frothing,

Exercise on Rhetorical" Pauses.
Its tumult and wrath in.
Till in this rapid race

Industry || is the guardian' of innocence.
On which it is bent,

Honour || is the subject of my story.
It reaches the place

The prodigal || lose many opportunities ' for doing good.
Of its steep descent.

Prosperity | gains friends, adversity || tries them.
The cataract strong

• Time I once passed || never returns.
Then plunges along,

He that hath no rule' over his own spirit, is like a city' that is Striking and raging,

broken down, and without walls. As if a war waging,

Better' is a dinner of herbs || where love | is, than a stalled ox || and Its caverns and rocks among ;

hatred therewith. Rising and leaping,

The veil || which covers ' from our sight the events of succeeding Sinking and creeping,

years, is a veil' woven by the hand of Mercy.
Swelling and sweeping,

Blessed || are the poor in spirit.
Showering and springing,

Silver and gold || have I none.
Flying and linging,

Mirth || I consider as an act, cheerfulness || as a habit ' of the
Writhing and ringing,

mind. Mirth || is short and transient, cheerfulness | fixed and Eddying and whisking,

permanent. Mirth || is like a flash of lightning, that glitters' for Spouting and frisking,

a moment: cheerfulness || keeps up a kind of daylight ' in the Turning and twisting

mind.
Around and around,

Some || place the bliss ' in action, some || in ease;
With endless rebound;

Those || call it pleasure, and contentment || these.
Smiting and fighting,
A sight to delight in;

The habitual tendency of young readers being to hurry, in
Confounding, astounding,

reading, their pauses are liable to become too short for distinctDizzying and deafening the ear with its sound.

ness, or to be entirely omitted. In most of the above examples,

the precision, beauty, and force of the sentiment, depend much And so never ending, but always descending,

on the careful observance of the rhetorical pauses. The student Sounds and motions for ever and ever are blending, All at once and all o'er, with a mighty uproar;

may obtain an idea of their effect, by reading each sentence

first, without the rhetorical pauses--secondly, with the pausing And this way the water comes down at Lodore.

as marked. VI.-APPROPRIATE PAUSES.

Rule on the Oratorical" Pause. grammatical punctuation of sentences, by which they are The “ oratorical” pause is introduced into those passages divided into clauses by commas, although sufficiently distinct

which express the deepest and most solemn emotions, such for the purpose of separating the syntactical portions of the structure, are not adequate to the object of marking all the

as naturally arrest and overpower, rather than inspire utter

ance. audible panses, which sense and feeling require, in reading aloud. Hence we find, that intelligible and impressive reading

Examples depends on introducing many short pauses, not indicated by The sentence was-DEATH! There is one sure refuge for the commas or other points, but essential to the meaning of phrases

oppressed, one sure resting-place for the weary-THE GRAVE. and sentences. These shorter pauses are, for the sake of dis

It was the design of Providence, that the infant mind should tinction, termed - rhetorical.”

possess the germ' of every science. If it were not so, the sciences Powerful emotion not unfrequently suggests another species

could hardly be learnt. The care of God || provides for the flower of

the field a place ' wherein it may grow, regale the sense | with its of pause, adapted to the utterance of deep feeling. This pause

fragrance, and delight the soul | with its beauty. Is his providence ! sometimes takes place where there is no grammatical point less active | over those, to whom this flower offers its incense ?-No. bard, and sometimes is added to give length to a grammatical The soil ' which produces the vine || in its most healthy luxuriance, is pause. This pause may be termed the "oratorical,” or the not better adapted to that end, than the world we inhabit, to draw Janse of “effect."

forth the latent energies of the soul, and fill them with life' and The length of the rhetorical pause depends on the length of

vigour. As well might the eye see' without light, or the ear | hear the clause, or the significance of the word which follows it. The

without sound, as the human mind | be healthy and athletic | withTall" rhetorical pause" is marked thus ll, the “half-rhetorical

out descending into the natural world, and breathing the mountain

air. pariae” thus , and the short “rhetorical pause” thus '.

Is there aught in Eloquence which warms the heart ? She draws Rules for RhetoricalPauses.

her fire ' from natural imagery. Is there aught in Poetry | to enliven The " rhetorical” pause takes place, as follows:

the imagination? There is the secret of all her power. Is there 1. Before a verb when the nominative is long, or when it is

aught in Science to add strength' and dignity' to the human mi

The natural world || is only the body, of which she is the sou emphatie :

books, Science ' is presented to the eye of the pupil, as it we Life is short, and art \ is long.

dried and preserved 'state. The time may come, when

A

structor' will take him by the hand, and lead him ' by the running triangles only, but for any triangles, whether symmetrical or streams, and teach him all the principles of Science, as she conies not, that are upon the same base and between the same from her Maker; as he would smell the fragrance of the rose, with

parallels. Thus, the triangles LFG, MFG are each of them out gathering it.

equal to the triangle PFG, which is on the same base, F G, and This love of nature; this adaptation of man' to the place assigned him by his heavenly Father; this fulness of the mind | as it des

between the same parallels, D Е, I K, and each of them would cends into the works of God, is something, which has been felt' by be equal to any triangle that may be formed by drawing lines every one, though to an imperfect degree, and therefore needs no

from the points F and G to any point in the straight line I k, explanation. It is the part of science, that this be no longer a blind produced both ways indefinitely. affection; but that the mind ' be opened, to a just perception of Triangles also which stand upon equal bases and between the what it is, which it loves. The affection, which the lover first feels ' same parallels are equal to one another. Thus, the triangles for his future wife, may be attended only by a general sense of her

LNG, MO F, which external beauty ; but his mind 'gradually opens to a perception of

stand on equal the peculiar features of the soul, of which the external appearance

bases, NG, FO, and is only an image. So it is with nature. Do we love to gaze on the sun, the moon, the stars, and the planets? This affection contains

M k between the same ' in its bosom | the whole science of astronomy, as the seed contains

parallels, DE, HK, the future tree. It is the office of the instructor I to give it an

are equal to one existence and a name, by making known the laws which govern the

another, as are also motions of the heavenly bodies, the relation of these bodies to each

the triangles L N F, other, and their uses.

MOG, which are Have we felt delight' in beholding the animal creation,-in watching DN

-OE bet

between the same their pastimes' and their labours? It is the office of the instructor!

Fig. 32

parallels and stand to give birth to this affection, by describing the different classes of

on equal bases N F, animals, with their peculiar characteristics, which inhabit the earth, the air, and the sea. Have we known the inexpressible pleasure of

GO. And this is also as true of unsymmetrical triangles as of beholding the beauties of the vegetable world ? This affection can symmetrical triangles, for if we join the dotted line N P, the only expand ' in the science of botany. Thus it is, that the love of triangles L NF, PNF, are equal to one another, because they nature ' in the mass || may become the love of all the sciences, and are on the same base, NF, and between the same parallels; the mind will grow and bring forth fruit | from its own inherent and since the triangle M Go is equal to the triangle L NF, it power of development.

must also be equal to the triangle PN F.

In Case 3, when two of the angles of the required triangle are

given, it is manifestly necessary only to make at two points in LESSONS IN GEOMETRY.-X.

the same straight line, and on the same side of it, two angles IN our last lesson we considered the various series of data / equal to the given angles, each having its opening turned necessary for the construction of an isosceles triangle: we will towards the apex of the other, and then, if necessary in order to now do the same for any kind of scalene triangle, or triangle of

| complete the triangle, to produce the sides of the angles that are which all three sides are unequal.

inclined to the side that is common to both. The student must A scalene triangle, as it has been stated, may be an acute

notice that when two angles of a required triangle are given angled triangle, an obtuse-angled triangle, or a right-angled

without any special requirement as to their relative position, triangle. To determine any scalene triangle, it is plain that we

an endless number of pairs of symmetrical triangles may be must have one of the following series of data.

drawn, similar in form but of different superficial areas, all I. With regard to the sides without the angles :

satisfying the general requirements set forth in the data.

Thus, in Fig. 33, if A and B represent the given angles of the 1. The length of each of the three unequal sides.

triangle required, it is plain that to make a triangle having two 2. The length of two sides and the altitude of the triangle.

angles equal to the given angles A and B, we have only to inake II. With regard to the angles without the sides :

at any point, c, in a straight line, X Y, of indefinite length, the 3. Any two of the angles of the triangle.

anglo Y c E equal to A, and at another point, D, in the same

straight line, the angle x D E equal to B, each angle having its III. With regard to the sides and angles combined :

opening opposite or turned towards the apex of the other, as, in 4. The length of any two of the sides of the triangle and one of its this figure, the opening of the angle at c is opposite the apex D angles.

of the angle at D, and vice versû; and to complete the triangle 5. The length of one side of the triangle and two of its angles.

produce the sides, C E, D Е, of the angles at c and D that are 6. The length of one side of the triangle, its altitude, and one of its

inclined to the common side, CD, until they meet. If we reverse angles adjacent to the given side.

the position of the angles, making the angle at c equal to the As in the construction of the isosceles triangle, the first case angle at B, and the angle at D is met by Problem VIII. (page 191), but the second brings equal to the angle at A, the us to

triangle assusnes the form shown PROBLEM XXIV.- To draw a triangle of which the length of | by the triangle FCD in the two of its sides and the altitude are given.

figure. The triangles ECD, Let A and B (Fig. 32) represent the length of two of the sides F C D, are symmetrical and equal of the triangle required, and c its altitude. In any straight line, / in every respect. The triangles DE, of indefinite length, set off fg equal to B, and by Problem X. KG H, LGH, shown by dotted (page 192), draw the indefinite straight line, k, parallel to lines, are also equal and sym. DE, at a distance from it equal to c, the altitude of the required metrical in every respect, and triangle. Then from F as centre, with a radius equal to a, draw satisfy the general conditions of an arc cutting i k in the point .. Join LF, LG; the triangle the data, although their super. * LFG is a triangle answering the requirements of the data, for ficial area is greater than the

Fig. 33. its sides, LF, F G, are equal to A and B respectively, and its | area of the triangles E C D, F CD, altitude shown by the dotted line L n is equal to the given because the points G and 1, at which the angles necessary for straight line c. The triangle MFG, drawn in the same way, is the construction of the triangle required are made equal to A also a triangle which meets the requirements of the data, for its and B, are taken on the indefinite straight line, XY, at a greater sides, MG, OF, are equal to A and B respectively, and its altitude, distance apart than c and D. shown by the dotted line mo, is equal to c.

PROBLEM XXV.-To draw a triangle of which two sides and The triangles LFG, MFG, are equal to each other in every one of the angles are given. respect, namely, the length of their sides, their altitude, and First, let the given angle be included between the given sides, their wuperficial area. They are upon the same base, FG, and and let the straight lines B, C represent the length of the giren betwoen tho same parallels, DE, A K, and they are what we may sides of the triangle required, and a the given angle included mm kymmetrical triangles. From this we learn that symme between them (Fig. 34). Draw any straight line, x y, of inde

triangles on the same base and between the same parallels finite length, and at any point, D, in x y, make the angle I DE ial to one another; and this is true, not for symmetrical equal to the given angle A. Along D Y set off DF, equal to c,

B

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and along D E set off D G, equal to B. Join G F; the triangle to A. If it be required to have the smaller angle opposite to CD F answers the requirements set forth in the data, as does the given side, the angle Kho must be made equal to the larger also the triangle KDH, obtained by setting off d u along Dy angle B, and the same method of construction followed as indiequal to B, and D K along D E equal to c.

cated by the dotted lines in the figure. The triangles G DF, KDH are symmetrical and equal in every PROBLEM XXVII.—To draw a triangle of which one side, its respect; but if the position of the given angle had been required to be opposite to one of the given sides, instead of being in. cluded between them, a very different result would have been obtained.

DH
We will suppose, firstly, that it is required to place the angle
opposite the shorter of the two given sides. At the point L in the

-B straight line of inde-
-C finite length, X Y,
make the angle x L M

co
equal to the given

Fig. 36. angle A, and as this angle is to be opposite altitude, and one of its angles adjacent to the given side, are to the shorter side, I given. set off along L x thé Let A represent the length of the given side of the required

straight line Ln. | triangle, B its altitude, and c the given angle. Draw any

- equal to c: and from straight line, X Y, of indefinite length, and, by Problem X. Fig. 34.

Nas a centre. with (page 192), draw the straight line D E, also of indefinite length.

a radius equal to B. | parallel to it, at a distance from it equal to B. Set off rain describe the arc OP, cutting the straight line L M in the points x y equal to A, and at the point F in the straight line G F make 0, P. Join on and on. Either of the triangles ONL, PNL, the angle GF H equal to the given angle c. Let Fl meet D E will satisfy the requirements of the data, for in the triangle in H. Join GH. The triangle F G H answers the requirements ONL the sides o N, NL are equal to B and c respectively, of the data, for it has a side F G equal to A, an angle G FH while the angle OL N is opposite to the shorter side on; and equal to C, and it is of the altitude H K, which is equal to the in the triangle PNL, the sides PN, NL are equal to B and c given altitude B. A triangle equal to the triangle G F H in respectively, while the angle PLN is opposite to the shorter every respect, and symmetrical with it, may be obtained by side Pn.

making an angle at G, in the straight line F G, equal to c, and If it be required to place the angle opposite to the longer of following the same process of construction. the two given sides, it is manifest that we must set off l Q along

If the given angle be an obtuse angle, as c, the line which LX equal to B: and from o as centre, with a radius equal to c, represents the altitude of the triangle required will fall on a describe an arc cutting the straight line L M in R. By joining point in X Y without the line which is set off upon it equal to RQ, we get a triangle, RQL, that satisfies the requirements of the given side. If it be an acute angle, as the angle z, the the data, the sides L Q, QR being equal to B and c respectively, line representing the altitude of the triangle may fall between and the angle QLR, which is equal to the angle A, opposite to the extremities of the line set off equal to the given side, as the longer side R Q.

No in the triangle NLM, which is drawn having the side. L M The learner may make an endless variety of practical exercises equal to A, and the angle ML N equal to the given angle z; on this problem, by varying the length of the given sides and but whether this be the case or not depends entirely on the the opening of the given angle. Practice of this kind will be size of the angle and the relative proportions of the altitude and found to ensure neatness and accuracy in geometrical or

side. mechanical drawing, and will tend to render the draughtsman

In the construction of right-angled triangles, as one angle is skilfal in the use of his compasses and parallel ruler.

always necessarily known, less data are required than in the PROBLEM XXVI.-To draw a triangle of which one side and construction of obtuse-angled and acute-angled triangles ; thus tico of the angles are given.

any right-angled triangle may be constructed if we knowLet A represent the length of the given side of the required 1. The length of either of the sides containing the right angle (as triangle, and B and c the given angles, and first let both of the A B and ac in Fig. 37).

given angles be ad. 2. The length of either of the sides containing the right angle, and jacent to the given the side which subtends the right angle (as a B and Bc, or a c and BC, side, or in other

in Fig. 37). words, let them be

3. The side which subtends the right angle, and the perpendicular at its opposite ex

let fall on it from the right angle (as A D and b c in Fig. 37). tremities, on the Thus, if the sides that contain the right angle be equal to p same side of it. and R, draw at right angles to each other A B and A c, and

Draw any straight make A B equal to P, and Ac equal to R, and join BC: ABC line, x y, of indefinite will be the triangle required.

y length, and in it take Again, if one of the sides containing the right angle be given Ε Η

DE equal to A. At equal to P, and the side that sub-
Fig. 35.

the point d make the tends the right angle equal to s,

angle E D F equal to draw Bc equal to s; bisect it in the angle B, and at the point E make the angle D E F equal to c. E, and from E as centre, with the Let the sides D F, EF meet in the point F; the triangle F D E distance E B or EC, describe the satisfies the requirements of the data; as will also the triangle semicircle Bac. Then from B as GDE, constructed by making the angle G D E equal to c, and centre, with a radius equal to P, the angle GED equal to B.

draw an arc cutting the semicircle Next, let one of the given angles be opposite to the given BAC in A. Join A B, AC; the side, as, for example, when the angle equal to the larger angle B triangle ABC will be the triangle is required to be in this position. Take I k, in the straight required.

Fig. 37. line of indefinite length, x Y, and at the point u make the angle If the side which subtends the KHL equal to the angle c. Through K draw KM parallel to right angle be given equal to s, and the perpendicular let fall I L, and at the point k in the straight line MK make the angle on it from the right angle equal to Q, draw B C equal to s, bisect NK N equal to the angle B, and let the straight line in meet it in E, and draw the semicircle BAC as before; through E draw the straight line IL in . The triangle NHK has the angle EF perpendicular to B C, and along it set off Eg equal to Q. II N equal to C, and the angle I N K equal to B (for it is equal Through a draw G A parallel to Bc, cutting the circumference to its alternate angle N KM, which was made equal to B), and the in a, and from a draw A B, AC, to the points B and c. The larger angle H NK is opposite to the side u k, which is equal altitude, A D, of the triangle A B C is equal to Q.

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