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35. DENTATE LEAF. 36. DELTOID LEAF, 37. DECOMPOSITE LEAF. 38. RENIFORM LEAF, 39. PINNATIPID LEAT. 40. PALMATE LEAY. 41.

DIGITATE LEAT. 42. CAPILLABY LEAF. 43. SPINY LEAF. 44. SESSILE LEAVES. 45. CILIATE LEAF. 46. SERRATS LEAF, 47. OVAL LEAY. 48. PIXXATE LEAF. 49. BIPINNATE LEAF, 50. DISTICHOUS LEAVES. 51. ACUTE LEAVES,

hasta, a spear.

Sagittate Leaf (Fig. 27).—A leaf shaped like the head of an grow on the same level, they are termed verticillate, from the arrow, from the Latin sagitta, an arrow, triangular in form, with Latin verticillus, the whirl of a spindle, derived from verto, to pointed lobes at the base extending backwards. A variety of turn. Leaves growing in this manner, in a ring round the this form is called hastate, or spear-shaped, from the Latin stem, are also said to be whorled.

Pinnate Leaf, with Tendrils (Fig. 30).—Here we have two Spatulate Leaf (Fig. 28).-A leaf formed something like a opposite leaflets, with a tendril issuing from the point of spatula (Latin, spatula), a broad flat knife used by chemists for junction between them. Found in the leaf of the everlastspreading plasters. It is broad and rounded at the end, but ing pea. tapers gradually towards the stalk.

Cordate Leaf (Fig. 31).- A leaf, such as the leaf of the lime. Verticillate Leaves (Fig. 29).-When more than two leaves tree, so called from being shaped like a heart, from the Latin

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cor, cordis, the heart. A cordate leaf is broad at the base, where Pinnate Leaf (another variety). (Fig. 48).—Consisting of it is attached to the petiole, and pointed at the extremity. pairs of leaflets ranged along a common petiole opposite to When a leaf is narrow or pointed at the base and broad at the each other, and attached to the common petiole by leaf-stalks ; end, or shaped something like the figure presented by the so called from the Latin penna, a wing, the attachment of section of a pear, it is called obcordate.

each pair being like the wings of a bird, or the small feathers Confluent Leaves (Fig. 32).- Leaves which are joined together, that branch out on either side of the mid-rib of a complete or which surround the stem in such a way that it appears to feather. pass through the centre of them ; from the Latin con, together, Bipinnate Leaf (Fig. 49).—A leaf consisting of pairs of and fluo, to flow. Leaves of this kind are more often called pinnate leaves arranged along a common petiole opposite to each perfoliate.

other; the leaf, in other words, being pinnately branched, and Lanceolate Leaf (Fig. 33).- A leaf formed like the head of a each branch pinnate with leaflets Leaves are tri-pinnate, or lance, oblong, narrow, and tapering from the broadest part in three times pinnate, when the mib-rib is pinnately branched, the centre towards the base and extremity.

the branches again pinnately branched, and these last furnished Orbiculor Leaf (Fig. 34).- A leaf circular in outline, from the with leaflets pinnately arranged. Latin orbiculus, the diminutive of orbis, a globe or sphere. Distichous Leaves (Fig. 50).-Leaves springing from alter. Leaves of this kind resemble peltate leaves in shape, but differ nate points in two rows, one on the right of the stem, and the from them in being cleft as far as the point of junction with other on the left, from the Greek diotixos (pronounced dis'the petiole. A good example may be found in the leaf of the tick-os) a couplet. common mallow.

Acute Leaves (Fig. 51). —Narrow leaves terminating in a sharp Dentate Leaf (Fig. 35).—When the edge of a leaf is point, from the Latin acutus, sharp. notched or indented it is said to be dentate, from the The above list includes the principal terms applied to leaves. Latin dens, a tooth. When the margin of the leaf is un. Sometimes, however, to describe a leaf correctly, it is necessary broken, as is the leaf of the myrtle, or nasturtium, it is to apply two or three of these terms; as, for example, when à said to be entire.

leaf is long, narrow, and pointed at either end, fringed with Deltoid Leaf (Fig. 36).- A leaf with a broad base and hair-like appendages, and notched with small regular inden. triangular in form, so called from its resemblance to the Greek tations along the margin projecting forwards, it is described as letter A, or capital D, called delta.

lanceolate ciliate serrate. Decomposite Leaf (Fig. 37).—A leaf divided into a great number of leaflets, as in the illustration, in which leaflets are attached on either side to the branches which issue from the

READING AND ELOCUTION.–V. petiole. It should be noted that the meaning of this term is very different to decomposition, which means a state of decay

PUNCTUATION (continued). or dissolution, the word decomposite being derived from the VII. THE PARENTHESIS, CROTCHETS, AND BRACKBTS. Latin compono, to put together, with de prefixed to increase the

( [] force of its signification, and indicating a composition of things already compounded, the leaflets of the compound leaf being 41. A PARENTHESIS is a sentence, or part of a sentence, enclosed also themselves compound.

between two curved lines, thus ( ). Reniform Leaf (Fig. 38).—A leaf shaped like a kidney, and

42. The curved lines in which the parenthesis is enclosed are 80 called from the Latin ren, a kidney.

called Crotchets. Pinnatifid Leaf (Fig. 39).-A leaf indented along the 43. The parenthesis, with the crotchets which enclose it, is margin with deep irregular notches extending about half way generally inserted between the words of another sentence, and into the mid-rib, as in the leaf of the dandelion, or sow

may be omitted without injuring the sense. thistle ; so called from the Latin penna, a feather, and findo, 44. The parenthesis should generally be read in a quicker to split.

and lower tone of voice than the other parts of the sentence in Palmate Leaf (Fig. 40).-A leaf consisting of five leaflets which it stands. attached to a common petiole, so called from its resemblance to 45. Sometimes a sentence is enclosed in marks like these [ ], the extended fingers of the hand, from the Latin palma, a hand. which are called Brackets. Leaves of this kind are sometimes termed quinate.

46. Sentences which are included within crotchets orbrackets, Digitate Leaf (Fig. 41).-A leaf consisting of several leaflets should generally be read in a quicker and lower tono of voice. or lobes proceeding from the same point of a common leaf

47. Although the crotchet and the bracket are sometimes stalk, so called from the Latin digitus, a finger, the lobes being indiscriminately used, the following difference in their use extended like the fingers of a hand. An example may be

may be noticed :-Crotchets are used to encloso a sentence, found in the leaf of the horse-chestnut. Scarcely differs from or part of a sentence, which is inserted between the parts of the last.

another sentence; brackets are generally used to separate two Capillary Leaf (Fig. 42).-A leaf branching out in all direc.subjects, or to enclose an explanation, note, or observation, tions in narrow hair-like divisions, so called from the Latin standing by itself. When a parenthesis occurs within another capillus, hair. Examples of this kind of leaf are found in some parenthesis, brackets enclose the former, and crotchets enclose of the tribe of umbelliferæ.

the latter. Spiny Leaf (Fig. 43).—& leaf with spines or sharp points

Examples. projecting at intervals round the margin, like the leaf of the I asked my eldest son (a boy who never was guilty of a falsehood) holly, so called from the Latin spina, a thorn.

to give me a correct account of the matter. Sessile Leaves (Fig. 44).- When leaves are attached to the

The master told me that the lesson (which was a very difficult one) stem of a plant without any petiole or leaf-stalk, they are

was recited correctly by every pupil in the class. termed sessile, from sessum, a part of the Latin verb sedeo, to

When they were both turned of forty (an age in which, according to sit, because the leaves aro closely attached to the stem as if

Mr. Cowley, there is no dallying with life), they determined to retire, sitting on it.

and pass the remainder of their days in the country.

Notwithstanding all this care of Cicero, history informs us that Ciliate Leaf (Fig. 45).—When a leaf is bordered or edged Marcus proved a mere blockhead ; and that Nature (who, it seems, with short hair-like appendages it is termed ciliate, from the was even with the son for her prodigality to the father) rendered him Latin cilia, eyelashes.

incapable of improving, by all the rules of eloquence, the precepts of Serrate Leaf (Fig. 46).—When the margin of a leaf is toothed philosophy, his own endeavours, and the most refined conversation in sharply, like a saw, the teeth projecting forward, as in the rose

Athens. leaf, it is termed serrate, from the Latin serra, a gaw.

Natural historians observe (for whilst I am in the country I must Oval Leaf (Fig. 47).- A leaf longer than it is broad, but fetch my allusions from thence) that only the male birds have voices ; equally rounded at the base and extremity, so called from the that their songs begin a little before breeding time, and end a little

after. Latin ovum, an egg. Oval leaves which are broader at the base,

Dr. Clark has observed that Homer is more perspicuous than any where the leaf is attached to the petiole, than at the extremity other author ; but if he is so (which yet may be questioned), the perare called ovaie ; but leaves which are narrower at the base spicuity arises from his subject, and not from the language itself in than at the extremity aro called obovaie.

which he writes.

The many letters which come to me from persons of the best sense 49. The dash is sometimes used to express a sudden stop, or of both sexes (for I may pronounce their characters from their way of change in the subject. writing, do not a little encourage me in the prosecution of this my 50. The dash requires a pause sometimes as short as that of undertaking.

a comma, and sometimes one as long as, if not longer than, that It is this sense which furnishes the imagination with its ideas; so

of a period. that by the pleasures of the imagination, or fancy (terms which I shall use promiscuously), i here mean such as arise from visible

51. The dash is frequently used instead of crotchets or objects.

brackets, and a parenthesis is thus placed between two dashes. The stomach (crammed from every dish, a tomb of boiled and roast,

52. The dash is sometimes used to precede something and flesh and fish, where bile, and wind, and phlegm, and acid, jar, unexpected; as when a sentence beginning seriously ends and all the man is one intestine war) remembers oft the schoolboy's humorously. aimple fare, the temperate sleep, and spirits light as air.

53. In the following examples, the dash is used to express a William Penn was distinguished from his companions by wearing a

sudden stop, or change of the subject. blue sash of silk network (which, it seems, is still preserved by Mr. kett, of Seething Hall, near Norwich), and by having in his hand a

Examples. roll of parchment, on which was engrossed the confirmation of the

If you will give me your attention, I will show you-but stop, I do treaty of purchase and amity.

not know that you wish to see. Again, would your worship a moment suppose (it is a case that has

Alas! that folly and falsehood should be so hard to grapple withhappened, and may be again, that the visage or countenance had not

but he that hopes to make mankind the wiser for his labours, must a nose, pray who would, or who could, wear spectacles then?

not be soon tired. Upon this the dial-plate (if we may credit the fable) changed coun

“Please your honours," quoth Trim, “the inquisition is the vilest—" tenance with alarm.

“Prithee, spare thy description, Trim; I hate the very name of it," said To speak of nothing else, the arrival of the English in her father's

my father. dominions must have appeared (as indeed it turned out to be) a most

The fierce wolf prowls around thee—there he stands listening-not portentous phenomenon.

fearful, for he nothing fears. Surely, in this age of invention, something may be struck out to

The wild stag hears the falling waters' sound, and tremblingly obriate the necessity (if such necessity exists) of so tasking the human

flies forward-o'er his back he bends his stately horns--the noiseintellect.

less ground his hurried feet impress not-and his track is lost amidst I compassionate the unfortunates now (at this very moment, per

the tumult of the breeze, and the leaves falling from the rustling haps) screwed up perpendicularly in the seat of torture, having in the

trees. right hand a fresh-nibbed patent pen, dipped ever and anon into the

The wild horse thee approaches in his turn. His mane stands up ink-bottle, as if to hook up idens, aud under the outspread palm of the left hand a fair sheet of best Bath post (ready to receive thoughts aside.

erect-his nostrils burn-he snorts—he pricks his ears and starts yet unhatched), on which their eres are riveted with a stare of dis

There was silence-not a word was said--their meal was before coasolate perplexity, infinitely touching to a feeling mind.

them -- God had been thanked, and they began to eat. O the unspeakable relief (could such a machine be invented) of

They hear not-see not-know not-for their eyes are covered with haring only to grind an answer to one of one's dear five hundred thick mists - they will not see. friends!

And ye like fading autumn leaves will fall; your throno but dust – Have I not groaned under similar horrors, from the hour when I

your empire but a grave--your martial pomp a black funereal pallFas first shut up (under lock and key, I believe) to indite a dutiful

your palace trampled by your meanest slave. epistle to an honoured aunt?

To-day is thine- improve to-day, nor trust to-morrow's distant To such unhappy persons, then, I would fain offer a few hints (the

ray. frait of long experience), which may prove serviceable in the hour of

For some time the struggle was most amusing—the fish pulling, emergency. li ever you should come to Modena (where, among other relics, you and the other to swim from its invisible enemy—the gunder at one

and the bird screaming with all its might-the one attempting to fly, may see Tassoni's bucket), stop at a palace near the Reggio gate, dwelt

moment losing and the next regaining his centre of gravity. is of old by one of the Donati.

My father and my uncle Toby (clever soul) were sitting by the fire 54. The dash is sometimes to be read as a period, with the with Dr. Slop ; aud Corporal Trim (a brave and honest fellow) was falling inflection of the voice. reading a sermon to them.

E.camples. As the sermon contains many parentheses, and affords an The favoured child of Nature, who combines in herself these united opportunity also of showing you a sentence in brackets (you perfections, may justly be cousidered as the masterpiece of creationwill observe that all the previous parentheses in this lesson are as the most perfect image of the Divinity here below. enclosed in crotchets), I shall insert part of it in the following Now launch the boat upon the wave-the wind is blowing off the paragraph :

shore-I will not live a cowering slave, in these polluted islands To have the fear of God before our eyes, and in our mutual dealings The wind is blowing off the shore, and out to sea the steamers flywith each other, to govern our actions by the eternal measures of my inusic is the dashing roar, my canopy the stainless sky-it bende right and wrong: the first of these will comprehend the duties of above, so fair a blue, that heaven seems opening to my view. religion ; the second those of morality, which are so inseparably con- He had stopped soon after beginning the tale-- he had laid the frag. bected together, that you cannot divide these two tables, even in ment away among his papers, and had never looked at it again. imagination (though the attempt is often made in practice), without The exaltation of his soul left him-he sunk down--and his misery breaking and mutnally destroying them both. [Here my father ob

went over him like a flood. served that Dr. Slop was fast asleep). I said the attempt is often Mr. Playfair was too indulgent, in truth, and favourable to his made; and so it is ; there being nothing more common than to soe a friends and made a kind of liberal allowance for the faults of all man who has no sense at all of religion, and, indeed, has so much mankind-except only faults of baseness or of cruelty ; against which Lonesty as to pretend to none, who would take it as the bitterest he never failed to manifest the most open scorn and detestation. front should you but hint at a suspicion of his moral character, or Towards women he had the most chivalrous feelings of regard and imagine he was not conscientiously just and scrupulous to the utter- attention, and was, beyond almost all men, acceptable and agreeable in

their society-though without the least levity or pretension unbecom. I know the banker I deal with, or the physician I usually call in ing his age or condition. [" There is no need,” cried Dr. Slop (waking) * to call in any physician in this case"], to be neither of them men of much religion.

55. The dash is sometimes to be read like a comma, with the Experienced schoolmasters may quickly make a grammar of boys' voice suspended. zatures, and reduce them all (saving some few exceptions) to certain

Examples. general rules.

“I have always felt that I could meet death with composure ; but I Ingenious boys, who are idle, think, with the hare in the fable, that, did not know," she said, with a tremulous voice, her lips quivering—"I punuing with snails (so they count the rest of their school-fellows), did not know how hard a thing it would be to leave my children, till they shall come soon enough to the post; though sleeping a good now that the hour is come.” while before their starting.

and Babylon shall become-she that was the beauty of kingdoms, VIII. THE DASH.

the glory of the pride of the Chaldeans--as the overthrow of Sodom

and Gomorrah by the hand of God. 48. The Dash is a short straight line which occurs in reading, yet be, the land of the free.

Our land--the first garden of liberty's tree-it has been, and shall and which is placed between the sentences in such a manner as to They shall find that the name which they havo dared to proscribebe parallel to the top or the bottom of the page.

that the name of Mao Gregor is a spell.

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Delightful in his manners-inflexible in his principles—and gene- DBE is a right angle, the straight line B E being at right rous in his affections, he had all that could charm in society, or attach angles to the straight line C D, and making the adjacent in private.

angles D B E, EBC equal to one anoThe joys of life in hurried exile go-till hope's fair smile, and ther. The pupil will remember that the beauty's ray of light, are shrouded in the griefs and storms of night.

measure of an angle is the extent of the Day after day prepares the funeral shroud; the world is grey with age: the striking hour is but an echo of death's summons loud-the opening of the lines or legs of which the jarring of the dark grave's prison door. Into its deep abyss-devour angle is formed. Thus, the sum of the ing all-kings and the friends of kings alike must fall,

openings of the two angles A B C, A B D, She made an effort to put on something like mourning for her son ; or the sum of the openings of the three and nothing could be more touching than this struggle between pious angles C BA, A BE, EBD is equal to the sum Fig. 3. affection and utter poverty: a black ribbon or so-a faded black hand of the openings of the angles C B E, E B D. kerchief, and one or two more such humble attempts to express by

Thus we learn that if any number of straight lines meet in a outward signs that grief that passeth show.

point in another straight line on one side of it, the sum of the

angles which they make with this straight line and with each LESSONS IN GEOMETRY.-V.

other are equal to two right angles; and if any number of

straight lines meet in the same point on the other side of it, the SIMPLE GEOMETRICAL THEOREMS.

angles thus made are also equal to two right angles. Hence BEFORE entering on the consideration of problems in geometry the angles made by any number of lines meetmg together in the which will be found to be practically useful to all who are same point are together equal to four right angles. engaged in any mechanical art, it will be necessary for the As a familiar illustration of this, the spokes of a wheel may learner to become acquainted with a few simple statements or be taken, which radiate from the nave as a common centre. If facts in geometry, the truth of which is so clear and plain that a chalk line were drawn down the middle of each spoke, these they require but little, if any explanation. These are called lines would meet in the centre of the nave, and the angles theorems, or self-evident propositions, from the Greek Dewpnua formed by these lines at their point of meeting would be equal (the-o-re-ma), literally a sight, or something which can be to four right angles. seen, in contradistinction to problems, or propositions which 4. Any angle drawn in a semicircle is a right angle. require something to be done in order to effect their solution. An angle drawn in a semicircle is one which has its top or The word “problem” is derived from the Greek apobanua vertex in the arc, while its legs pass through the extremities of (pro-ble'-ma), which is derived in its turn from a po (pro) before,

the diameter at its points of contact with and Barlw (bal-lo) to cast r throw, while the word “ propo

the arc.

Thus, the angle A C B in the sition” is derived from the Latin pro, before, and pono, to

semicircle ACB is a right angle. The place. Hence the meaning of the words “problem” and “pro

truth of this may be shown by cutting position” is precisely the same, namely, something that is

out a right-angled triangle and applying placed before you to be done or solved.

Fig. 4. it to a semicircle. If large enough, it 1. When one straight line intersects another straight line, the

will be found that the legs of the right vertical or opposite angles are equal to one another.

angle will pass through the ends of the diameter of the semiLet the straight line A B intersect the straight line c D in the circle, no matter at what point in the arc of the semicircle the point E. Now, by the intersection of

vertex of the right angle may be placed. these two straight lines, four angles

5. The greatest side of every triangle is opposite the greatest are formed, namely, CE A, A E D,

angle. D E B, and B E C. Of these the ver

In the triangle A B C in Fig. 5, of the three angles-A B C, BCA, tical or opposite angles are equal,

CAB-ABCis manifestly the greatest; namely, CEA to D E B, and AED

while of the three straight lines to C E B.

Fig. 1.

A B, BC, C A, which form its sides, The truth of this may be shown in

Ac is the greatest. A c, the greatest a very simple and practical manner by copying the figure on a side, is opposite the greatest angle piece of paper, and then cutting out the angles and placing A B C; or, in other words, A c, the them on each other, the greater on the greater and the less on greatest side, subtends the greatest

Fig. 5. the less. This mode of proof will frequently be found useful in angle A B C. similar cases.

À moment's reflection will show that the greatest angle of Opposite angles are also called vertical angles, because the any triangle must have the greatest opening between the lines top or vertex of each angle is directly opposite to the vertex of of which it is formed, and that the line which is opposite to or the other.

subtends the greatest opening, must of necessity be greatest of 2. When a straight line intersects two parallel straight lines, the three lines which subtend the three openings of the angles the alternate angles are equal.

of the triangle. Let the straight line E F intersect the parallel straight lines 6. If one side of a triangle be produced, the outer or exterior angle

A B, C D, in the points G H. The angles is equal to the two interior and opposite angles of the triangle.
A G H, G H D are alternate angles, and In the figure that accompanies the preceding theorem let the
are equal to one another, and the angles side A c of the triangle A B C be produced to D. The onter or
CH G, G B are also alternate and exterior angle B C D is equal to the two interior and opposite
equal.

angles C B A, B A C. For if at the point c in the straight line There are eight angles formed by A D the straight line c E be drawn parallel to A B, then the the intersection of the straight lines alternate angles E C B, C B A are equal to one another, and by

A B, C D, E F, in Fig. 2. Of these the Theorem 2, the angle D C E is equal to the angle C A B; but the Fig. 2.

reader will find that there are two sets angles D C E, E C B together make up the angle D C B, which is of four angles that are equal to one

therefore equal to the angles C B A, B A C. another-namely, A GE=BGI=GHC=D HF, and E G B

7. The three interior angles of every triangle are together equal =AGH = G H D=CH F. Let him demonstrate the truth of to two right angles. this practically by drawing the figure on paper, cutting out In Fig. 5 the angle B C D has been shown to be equal to the one of the greater angles and one of the less, and placing them angles C B A, BAC; to each of these equals add the angle B C A. on the remaining angles in each set of four.

Now, by Theorem 3 the angles D C B B C A are equal to two 3. The adjacent angles which are formed when one straight right angles, and C B A, B A C, A C B, the three interior angles line stands on another straight line, are together equal to two of the triangle A B C, which are equal to these two angles, must right angles.

therefore be equal to two right angles. In Fig. 3 the adjacent angles A B C, A B D, which are formed by the straight line A B standing on the straight line

PROBLEMS IN PRACTICAL GEOMETRY. CD, are equal to two right angles. The truth of this is PROBLEM I. – To bisect a given straight line-that is, to diride evident when we consider that each of the angles C B E, it into two equal parts.

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Let A B (Fig. 6) be the straight line to be bisected. From through the point , the angle and the instrument are correct ; the two extremities A and B, with a radius of any length greater if not, they are incorrect, and the instrument must be adjusted. than half of the line, describe or draw arcs of circles, intersecting PROBLEM IV.---To draw a perpendicular to a straight line from or crossing each other at the point c, above the straight line A B, a point without it. and at the point D, below it. Then,

Let A B (Fig. 10) be the straight line, and c the point from from the point of intersection c,

which the perpendicular is to be draw a straight line to the point of

drawn. From the point cas a centre, intersection D; and the straight line

with any radius sufficient to extend A B will be bisected by the straight

beyond the straight line A B, describe line CD, at the point E; that is, A B

an arc of a circle D E, intersecting is divided into two equal parts, A E,

the straight line A B in the points E B, at the point E.

D, E; then, from these points as By this method of construction, a

centres, with any radius greater than straight line may be divided into any

half the straight line D Е, describe number of equal parts, denoted by

arcs intersecting each other in the the series 2, 4, 8, 16, 32, 64, 128, etc.

point F; then join c F; that is, draw It is not necessary in the above

Fig. 6.
a straight line from c to F, cutting

Fig. 10. construction that the two arcs at D

A B in the point G; then c G is perbe drawn with the same radius as the two arcs at c; but it is pendicular to A B, and is drawn from the point c, as required. necessary that each pair be drawn with the same radius; that

PROBLEM V.-To draw a perpendicular to a straight line at or is, practically speaking, without shifting the legs of the com- near one of its extremities, from a point without it. passes.

Let A G (Fig. 9) be the straight line, G one of its extremities, It is self-evident that in Fig. 6 the straight lino c D is bisected and c the point without it, from which the perpendicular is to by the straight line A B at the point E; and that A B and CD

be drawn. Take any point d in A G, and join D c; bisect it intersect each other at right angles. The problem therefore in E; and from the point E, as a centre, with radius E D or E C, teaches us how to draw two straight lines at right angles to describe the semicircle D G C; then join a c, and it will be pereach other.

pendicular to A G. It is evident, from the remarks made on PROBLEM II.—To draw a perpendicular to a straight line from Problem III., that c G is perpendicular to A G, and it is drawn a point in it.

from the point c, as required.
Let A F (Fig. 7) be the straight line Observe, that unless the point happens to be exactly in the
to which the perpendicular is to be vertical line above the point G, the semicircle will not pass
drawn, and B the point in it. From exactly through g, but will pass through a point either nearer
the point B, with any convenient to or farther from the point A. In the latter case, the stra ht
radius, less than B A or B F, cut off, line A G must be produced till it meets the arc of the semi-
or measure off equal parts of the circle. This problem is considered as merely a case of the
straight lines B A, B F-namely, BC, preceding problem, although the construction be different.
BE; and from the points C, E, with
any radius greater than a B or E B,
describe arcs of circles intersecting

HISTORIC SKETCHES.–V.
Fig. 7.
each other at the point D. Then

THE RISING OF THE LABOURERS UNDER RICHARD II. join D B, that is, draw a straight line from the point to the point B, and B D will be perpendicular On Whit Monday, 1382, Sir Simon Burley, who is called by one

historian "a favourite of King Richard II.," and by another, "a PROBLEM III.—To draw a perpendicular to a straight line Knight of the King's Household,” rode into Gravesend, and from one of its extremities.

seeing one of the townsmen, claimed him as his slave. There Let AB (Fig. 8) be the straight line, and B one of its was great dissatisfaction and open murmuring among the extremities, from which the perpendicular is to be drawn. Take people, with whom the man was a favourite, and they protested any point c, at a convenient distance from B, and nearly over against his removal. The townsman himself loudly declared the middle of the straight line A B;

that he never was slave to any one, to Sir Simon or another, then with c as a centre, at the dis.

and seeing the sympathy the crowd had with him, he appealed tance C B as radius, describe the

to them for help. Sir Simon claimed the man as the son of one arc D B E, so that it shall be greater

of his female slaves, called niefs, and disregarding the earnest than a semicircle; from the point D,

entreaty of the crowd, would not abate his claim unless he were draw throngh the point c, the

paid three hundred pounds of silver-a price he well knew the straight line D C E, to meet the arc

friends of the bondman could not possibly raise. Some disorder in the point E; and join E B, that is,

ensuing, Sir Simon, who was attended by two serjeants of law draw a straight line from the point E

and a following of armed men, pushed on through the crowd, to the point B, and B E will be per

and gave orders tha the prisoner should be taken to Rochester pendicular to A B, at the extremity of

Fig. 8.

Castle. B, as required.

As soon as the great man's train had left, the awe inspired by The demonstration of this proposition is founded on the fact its presence died away, and the people, whom the seizure of that the angle contained in a semicircle is a right angle. This their fellow had taken completely by surprise, and had also fast, indeed, is well known to intelligent workmen, who are deprived of their power to act, recovered their self-possession, and accustomed to make use of the For the T square ; for they try the began to cry out with one voice, “ Down with the tyrants ! Let

accuracy of that instrument by this us go to Rochester! Let us join our brethren of Essex!” property of the circle. Thus, if in The Essex men had already risen in arms, and were vowing Fig. 9 A G C were an angle drawn by vengeance on all the lords and owners of land, and especially means of an F or T square, in order against lawyers, whom they hated as the ministers of the law to test its accuracy, and consequently that crushed them. Norfolk, Suffolk, Cambridgeshire, and some that of the instrument, they join any of the other home counties, had been infected with the same two points in the legs of the angle, spirit. In them the bubbles of rebellion were beginning to rise say Dc, by drawing the straight line to the surface and to break, though as yet there was nothing DC; they bisect it in E by means of like united action. The above-mentioned claim of Sir Simon

the arcs shown in the figure on either Burley, made in spite of the ferment which was going on only on Fig. 9.

side of the straight line c D, and the opposite bank of the river, was the spark which fired the

drawn by the method explained in train of the Kentish men's anger. Problem I.; and then, with radius E c or E D, they describe the Before time enough had elapsed to throw cold water on the semicircle DG C; if the arc of this semicircle passes exactly fire, another and more serious offenco had been given to the

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