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his pen by building, by zealous practice, on the foundation that RECORDER : Why do you not pay it then ? we have assisted him to lay, by means of the copy-slips and the PENN: I do. instructions that have been brought under his notice in the RECORDER : Why do you not pull off your hat then ? present series of lessons. In some future Lessons in Writing we Penn: Because I do not believe that to be any respect. will give specimens of the various styles of writing which are RECORDER: Well, the court sets forty marks apiece upon required for commercial purposes and for candidates for the your heads, as a fine for the contempt of the court. Civil Service Examinations, etc.

PENN: I desire it might be observed that we came into the court with our hats off (that is, taken off), and if they have been

put on since it was by order from the bench; and therefore not HISTORIC SKETCHES.—XIII.

we, but the bench, should be fined. HOW A LONDON JURY A TRUE VERDICT GAVE, ACCORDING

After this the prisoners, undoubtedly with much pertinacity

and some show of disrespect to the court, refused to plead to TO THE EVIDENCE.

the indictment, which charged them with having caused a Just as there are many great men in the world who never get tumultuous assembly, until the questions they raised as to the an opportunity of asserting themselves in it, so there are many legality of it in point of form should have been answered. The memorable events in history which are seldom if ever mentioned. Recorder and the Lord Mayor tried in vain to silence them, Some of these are important enough, not merely in a political but resorting to threats, and abuse of a very coarse description, and also in a social sense, and it is well not to suffer them to languish not succeeding, the Recorder did in effect enter a plea of “not in the cold shade of oblivion. Such an event is the subject of guilty” for them, and had them put upon their trial. the present sketch. It has been selected not only because of its Among the jury was one man, Bushell, whose character intrinsic importance, but also as showing how great privileges for conduct displeasing to the court was already well known, may be won and valuable rights established by very humb.e and to whom several unworthy remarks had been made at the

time he was sworn. Under his guidance the jury retired, and In the report books of proceedings in the law courts in 1670 in a short time returned into court with a verdict acquitting is an account of a scene in which the principal actors were Mead, and saying that Penn was "guilty of speaking in Gracethe Recorder of London, King Charles's Attorney-General, church Street.” This verdict angered the court exceedingly. and a citizen, Bushell, member of a jury. The case is called “Is that all ?” they asked the foreman. “That is all I have in * Bushell's Case," and it is one of the most important possible, commission,” was the reply. “You had as good say nothing." for opon it was established once and for ever the grand right of Being further pressed, and also told," the law of England will a juryman "a true verdict to give according to the evidence, not allow you to part till you have given your verdict,” the jury without reference to whether that verdict was or was not accept replied, “We have given in our verdict, and we can give in no able to the court to whom it was returned. Now-a-days, when other.” juries are chosen with the utmost regard to the ends of justice, The Recorder refused to take such a verdict, and sent the and with a single eye to perfect impartiality, and, when chosen, jury back again to reconsider it. In half an hour's time they are treated with the fullest respect, neither being worried into came back into court, and handed in a written verdict to the Ferdicts nor molested after they have given them, we who have same effect as before, and signed by all of them. Upon this never seen a different state of things, are apt to suppose that being received, the Lord Mayor rated the jury in these words: there never was one, and to take it for granted that the thing MAYOR: What, will you be led by such a silly fellow as which is, is the same that hath been. Let us look for a few Bushell ? An impudent, canting fellow. I warrant you, you minutes at " Bashell's case."

shall come no more upon juries in haste. You are a foroman, The circumstances under which Bushell, the juryman, came indeed (addressing Bushell). I thought you had understood your upon the scene wore these :-Two Quakers, Penn and Mead, had place better. thought fit to preach to the people from the steps of a house RECORDER: Gentlemen, you shall not be dismissed till we in Gracechurch Street. In the course of their address they have a verdict that the court will accept; and you shall be had used language which was interpreted as conveying, and locked up, without meat, drink, fire, and tobacco. You shall perhaps was meant to convey, animadversions upon the govern- not think thus to abuso the court. We will have a verdict by ment. For this they were arrested, and, having been committed the help of God; or you shall starve for it. by a city magistrate on the charge of stirring up a riot, wero The jury declined to alter their verdict, and Penn, one of the put upon their trial. Like many of the charges preferred at prisoners, claimed to have it recorded. “ The agreement of that time by the over-zealous agents of the government, the twelve men is the verdict in law; and such a one being given by accusation was an extravagant one, and considerable sympathy the jury, I require the clerk of the peace to record it, as he will was shown by the Londoners in favour of the prisoners. If answer at his peril. And if the jury bring in another verdict what the two men had said amounted to sedition, then, it was contradictory to this, I affirm they are perjured men in law;" felt, no man could safely talk politics even in tho mildest way; and looking upon the jury, he said: “You are Englishmen! and it was further felt that the prosecution was a tyrannical act Mind your privilege ! Give not away your right !" on the part of the government, and people were getting rather The court was adjourned till next morning at seven o'clock, tired of the thing. Notwithstanding such was the case-popular the prisoners were sent back to Newgate, and the jury were sympathy at that time was but a whet to the prosecuting spirit ordered into the custody of those who swore to keep them of the crown lawyers—the trial was urged, and it came on without fire, food, drink, or any other accommodation till the before the Recorder of London at the Old Bailey.

adjourned sitting of the court. The following scene, illustrative of the manner in which While the jury are thus away in their retiring room, making prisoners were treated under Charles II., presented itself on tho up their minds what verdict they shall give-chafing, some of entrance of Penn and Mead into the court :--After the manner of them, at the manner in which they have been treated by the their brethren, the two Friends kept their hats on in the presence court, and, under the guidance of their foreman, resolving that of the judge, as they would have done in the presence of the they will not submit to dictation, but act upon the exordium king himself. The gaoler rudely knocked their hats off, where- delivered to them by the prisoner as they quitted their box apon the Recorder, not with a view to rebuking the man's -let us consider for a moment what right it was for which roughness, but to having a preliminary fling at the prisoners, they were contending, and the way in which that right was ordered him to replace them. Being put in the dock, the acquired. prisoners were thus addressed by their

judge :

Trial by jury was an old-established institution in England, as RECORDER: Do you know where you are ?

old, some think, as the Anglo-Saxon laws. Something like it is PENN: Yes.

certainly to be found in the history which has come down to us RECORDER : Do you not know it is the king's court ?

of those times, but the jury system, as we understand it now, was PENN: I know it to be a court, and I suppose it to be the the creation of a period subsequent to the Norman Conquest, king's court.

1066. Before that date the jury which tried causes consisted of RECORDER : Do you not know there is respect due to the a certain number of "compurgators” as they were called, that court?

is to say, persons who did not give their opinion upon evidence PENN : Yes.

adduced before them on oath, but who merely swore that they believed what the defendant said under sanction of his oath. I would not have back at any price, nor to please any one, but the The form of procedure was simply this. A man accused of judges took upon themselves to revive the wicked old custom of default, on civil or criminal process, was put on his oath if he polluting the very source of justice by intimidating those who chose to be so, and then swore he was innocent of the offence had charge of it. Two Chief Justices of England, Hyde and charged, or that his version of the case between him and the Keeling, were especially guilty of this crime, and made themselves plaintiff was a true one. The compargators, of whom the num- so notorious that the House of Commons came to a resolution to ber varied from twelve to thirty-six, being also sworn, deposed impeach the latter for his misconduct. He was suffered to speak to their belief in what the defendant had said, and, as they were for himself at the bar of the House, and to go free on promise of commonly chosen from among the neighbours and acquaintance amendment. of the man, they were supposed to know something of the facts In the face of this, and in spite of the expressed opinions of connected with his case, as well as to be able to form an esti- most of the legal luminaries of the day, including Lord Chief mate of the truth or falsehood of his statements. It can easily Justice Hale, the Recorder of London, in 1670, ventured, under be imagined that such a tribunal was not one from which the circumstances stated above, to fine the jury which acquitted to expect strict justice, and the shortcomings of the system Penn and Mead, and to commit Mr. Bushell to prison when amounted in many instances to gross miscarriage of right. he refused to pay. Here was what followed when the jury Nevertheless, it continued to be used with other systems till remained obstinate in their simple verdict of “not guilty," Henry II. (1154-1189) introduced the Norman form of trial after having been browbeaten, threatened, and ridiculed, both by jury for civil causes, and Henry III., or rather those by chief magistrate and Recorder, and after having been who represented him, introduced it about 1235 on criminal sent back three times to consider their verdict, which indeed process.

they did alter to a simple verdict of “not guilty" as to both The Norman-English jury was not like ours of to-day. Instead prisoners. of deciding upon the case according to evidence for and against, CLERK : Are you agreed upon your verdict ? and after hearing the summing-up of the judge, the jury included JURY: Yes. all those who under our system would be witnesses, and would CLERK: Who shall speak for you? be rigidly excluded from the jury for the very reason that they JURY: Our foreman. knew most of the facts. Then it was the duty of the sheriff to CLERK: What say you ? Look upon the prisoners at the bar. summon specially on the jury all those who were, or might be is William Penn guilty of the matter whereof he stands indicted supposed to be, acquainted with the material points in the case, in manner and form as aforesaid, or not guilty ? and these persons compared notes with their fellows, but without FOREMAN : William Penn is guilty of speaking in Gracechurch being subjected to any cross-examination, and gave their verdict Street. according to what then appeared to them to be right. Common MAYOR: To an unlawful assembly? rumour, repetitions of what somebody else had said, unsifted BUSHELL (the foreman): No, my lord, we give no other testimony of various kinds, were received by these juries, and verdict than what we gave last night. We have no other verdict sometimes constituted all the evidence they had to guide them. to give. All such would be utterly rejected now, and any person who had MAYOR: You are a factious fellow. I'll take a course with evidence to give would be summoned as a witness—would cer- you. tainly be precluded from sitting on the jury. It was not till the Sie T. BLOODWITH (alderman): I knew Mr. Bushell would twenty-third year of the reign of Edward III. (1327-1377) that not yield. witnesses, though still added to the jury, were not allowed to BUSHELL : Sir Thomas, I have done according to my convote as to the verdict; and it was not till the eleventh year of science. Henry IV. (1399-1413) that they were made to give their evi. MAYOR That conscience of yours would cut my throat. dence in open court, under the scrutiny of the judge, and without BUSHELL: No, my lord, it never shall. being associated in any way with the jury.

MAYOR: But I will cut yours so soon as I can. Under the Plantagenet princes (from Henry II., 1154, to RECORDER : He has inspired the jury. He has the spirit of Richard II., 1399), though the grand provision in Magna Charta- divination. Methinks I feel him. I will have a positive verdict, that no free man should be tried by any but his peers—was con- or you shall starve for it. stantly isregarded, it does not appear that juries as such PENN: I desire to ask the Recorder one question. Do you suffered any violence; but with the Tudor princes came in this, allow of the verdict given of William Mead ? as in other respects, quite another order of things, and that RECORDER : It cannot be a verdict, because you were indicted which the Tudors did the Stuarts did likewise. Juries were for a conspiracy, and one being found not guilty, and not the called to account in the most direct and personal manner for other, it could not be a verdict. verdicts given according to their conscience (some authorities, PENN : If not guilty be not a verdict, then you make of the however, say they were frequently bribed), and were frequently jury and Magna Charta but a mere nose of wax. reprimanded by the judge or the king's council, and sometimes MEAD: How! Is not guilty no verdict ? cited before the Court of Star Chamber, where, if they did not RECORDER : No, it is no verdict. repent, they were heavily fined and also imprisoned. Some of After this fine judicial dictum there were other passages the fines imposed on individual jurymen were as much as £2,000, between the jury and the court, and the jury being once more a ruinous amount in Queen Mary's reign (1553-1558), when asked as to William Penn's guilt, said, as before, that he was such a fine was actually inflicted. Whether there was or was guilty of speaking in Gracechurch Street. not any ground for the interference of the Star Chamber on the RECORDER: What is this to the purpose ? I say I will have & score of bribery of the jurors by the parties to suits, it is evident verdict. (And speaking to Edward Bushell, said) : You are & that the offence might have been punished by more regular factious fellow. I will set a mark upon you ; and whilst I hare means, and that the means actually adopted were liable to be anything to do in the city I will have an eye upon you. grossly abused. As a matter of fact they were grossly abused, MAYOR: Have you no more wit than to be led by such and the tyrannical conduct of the Star Chamber in dealing with pitiful fellow ? I will cut his nose. juries was one of the chief causes which contributed to its down- PENN: It is intolerable that any jury should be thus menaced. fall. When the Star Chamber was abolished by Act of Parlia- Is this according to the fundamental laws ? Are not they my ment in 1641, with an indignant protest against its ever having proper judges by the Great Charter of England ? What hope is existed, and a solemn declaration that nothing of the kind should there of ever having justice done when juries are threatened, and be permitted in the time to come, this evil practice of threatening their verdicts rejected ? I am concerned to speak, and grieved and punishing juries, so as to compel them to give such verdicts to see such arbitrary proceedings. Did not the Lieutenant of as the Crown wished, was abolished also. During the civil war the Tower render one of them worse than a felon? And do you (1642-1648), and during the protectorate of Oliver Cromwell, not plainly seem to condemn such for factious fellows who (1648-1658) it was not heard of ; jurymen were allowed to be answer not your ends ? Unhappy are those juries who are responsible alone to God and their conscience, and gave their threatened to be fined, and starved, and ruined if they give not verdicts freely, no man making them afraid.

in verdicts contrary to their consciences. With the restoration of Charles II., in 1660, some of the old RECORDER: My lord, you must take a course with that same governmental vices were restored also. The Star Chamber men fellow,






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MATOR: Stop his mouth. Gaoler, bring fetters, and stake brought him as her dower Tangier, in Marocco; Bombay, in him to the ground.

Hindostan or India ; and £300,000 in money. The first-named Penn: Do your pleasure. I matter not your fetters. town was abandoned, in 1683, as a place not worth the expenso

of holding by an armed force; while the second, now the capital

of one of the five presidencies of British India, was handed over RECORDER : Gentlemen, we shall not be at this trade always to the East India Company for a small annual quit-rent. with you. You will find the next session of parliament thero will be a law made that those that will not conform shall not Born at St. James's Palace, Declaration of Indulgence in have the protection of the law. Mr. Lee, draw up another

May 29, 1630 favour of the Papists 1672

Crowned at Scone verdict, that they may bring it in special.

1651 ! Test Act passed , March, 1673 LEE: I cannot tell how to do it.

Obliged to retire to Holland Marriage of Mary, daughter after the Battle of Worces.

of the Duke of York (after. JURY: We ought not to be retained, having all agreed, and


wards James II.) to Wil. set our hands to the verdict.

Returns to England May 29 1660 liam of Orange

1077 RECORDER : Your verdict is nothing. You play upon the Trial of the Regicides, etc. 1660 Treaty of Nimeguen

1678 coart. I say you shall go together and bring in another verdict, Revision the Common Supposed Conspiracy of the or you shall starve, and I will have you carted about the city as Prayer Book

1661 Papists to assassinate tho in Edward the Third's time.

Act of Uniformity passed 1662 king and restore the RoFOREMAN: We have given in our verdict, and all agreed to Bombay and Tangier added to

Catholic religion it; and if we give in another, it will be a force upon us to save

the British dominions 1662

Aug. 12, 1678 Dunkirk sold to Louis XIV. Murder of Sir Edmondsbury of France for £500,000


Oct. 15, 1678 Finally the jury gave their verdict “not guilty" against

Oct. 17, 1662 Murder of Archbishop Sharpe both prisoners, and each one of them affirmed the same sepa- War with the United Pro

May 3, 1679 rately; whereupon the Recorder fined them forty marks vinces of the Netherlands. 1664 The present Habeas Corpus each, and ordered them to be imprisoned till the fine should be The Great Plague

1665 Act passed May 27, 1079 paid.

The Great Fire of London 1666 Battle of Bothwell Bridge Imprisoned they were accordingly in the common gaol of Ships in the Medway burnt

June 22, 1679 Newgate, a noisome, filthy den, which was a disgrace to any

by the Dutch

1667 Meal Tab Plot. Oct. 23, 1679 Peace of Breda

1667 Persecution of the Covecountry calling itself civilised. From Newgate, however, the

nanters in Seotland. 1680 spirit which had made itself felt in opposition to the oppressive “Triple Alliance" of England,

Holland,and Sweden against conduct of the Recorder's Court made itself heard at the Court France.

Charter of the City of Lon.

Jan, 28, 1668 don declared to be for of King's Bench. A writ of Habeas Corpus* was sued out and Peace of Aix-la-Chapelle 1668


1682 made returnable immediately, and when the governor of Newgate War with Holland

1672 Rye House Plot. June 12, 1683 brought up his prisoners it turned out that they were detained Dutch defeated in the Battle Execution of Algernon Sydney for non-payment of fines imposed upon them on account of their of Solebay or Southwold

and Lord William Russell, 1083 verdict.

May 28, 1672 Death of Charles II. Feb. 6, 1085 Chief Justice Vaughan, in one of the most learned and

SOVEREIGNS CONTEMPORARY WITH CHARLES II. masterly judgments ever delivered, went into the whole matter. What he said may be found in the sixth volume of the State

Denmark, Kings of. Portugal, Kings of. Sweden, King of.

Frederick III. 1648 Alphonso VI. 1656 Charles XI. 1680 Trials, and in the collected judgments of the eminent Chief

Christian V. 1670 Peter II.

1683 Juzstice. The studious who have opportunity will do well to

Turkey, Sultan of.

France, King of. seek the judgment there ; but we have all an interest in the Louis XIV.

Rome, Popes of. Mahomet IV. 1619 1643

Alexander VII. . 1655 gist of what he said, and that can be reproduced without such Germany, Emperor of. Clement IX. .

United Provinces of the

1667 careful search. He laid it down as law that the fines were Leopold I. 1658

Clement x.

Netherlanda, Stadlo

1670 illegal, and that the imprisonment consequent on them was Poland, King of.

Innocent XI.

holders of. 1676

NO Stadholder necessarily illegal also. But he went on still further, and John II. (some

times styled

Russia, Czars of declared in effect that the Recorder had improperly refused to

from 1650 to 1672 Casimir V.) 1649' Alexis .

1655 William Henry regeive the verdict of the jury, and that the jury had an unques

Interregnum 1668 Feodor II.

(afterwards tionable right to give what verdict they pleased, the remedy for

1669 Ivan IV. and Pe-

William III. of 3 stupid verdict being in the discretion of a judge to order a new John III.

ter I. conjointly 1682 England) . . 1672 trial on the ground of the verdict being contrary to the evidence; and for a corrupt verdict, in the power of any one to prosecute a juryinan for perjury if committed wilfully in the course of his duty as a juryman.

LESSONS IN GEOMETRY.-XIII. As the law was thus settled it has remained ever since, few In the last lesson (page 383) was given the method of drawing occasions having arisen in which the rights of juries have been a triangle equal in superficial area to any regular four-sided imperilled. To Edward Bushell and his fellow-citizens we are directly indebted for the establishment of the law upon this most enterir: on the geometry of the circle, it only remains to show

figures, such as a square, rectangle,or parallelogram; and, before satisfactory footing; and the occasion seemed to us so full of the learner how he may draw a triangle equal in superficial interest, and the principle gaiced so full of importance, that we have thought it to make them the subject of this number of our trapezium or trapezoid (Defs. 31, 32, page 58), or to any roul.

area to any given irregular four-sided figure, whether it be a Historic Sketebes.

tilateral figure or polygon, whether regular or irregular; that

is to say, having its sides and angles equal on the one hand, STXOPEIS OF EVENTS IN THE LIFE AND REIGN OF

or having its sides and angles tinequal on the other (Def. 33, CHARLES II.

page 53). It will be seen that either process is effected Charles II, the second son of Charles I. and Henrietta Maria ' by the aid of the knowledge of certain geometrical facta of France was the trentz-sirth king of England after the in connection with the triangle which have been already exNorman Conquest, and the tzird of the Staart Dynasty. He plained. married a Portaguese prisoess, Catherine of Braganza, who

PROBLEX XXXIII.— To draw a triangle that shall be equal in superficial area to any given irregular quadrilateral,

figure. * A vrit Habeas Corpus is an order which a jndge is obliged, Let ABCD (Fig. 46) be the given irregular quadrilateral figure ; vader a penalty & E, to send a petition of a prisoner, to the it is required to draw a triangle ernal to it in superficial area. eader who detares kim, satisz kim to bring up the body of his pri Draw e D, one of the diagonale of the irregular quartrilateral Sater, and to see who be detaiss him, so that the judge may be figure o trapezium A B C D, ani produce the side c 1), on which satisfied as to the propriety of razit the poscez to entot ce Escharge him as be may see at the figure stenis. indefinitely towards z. Then through a draw This is a sac szigets met zegard against illegal ca tyrannicel Aparalel to the diagonal D. and meeting c E in the print ». isu priscezet. Te she Haters Cargos Act is suspended, the writs Joir: BP; the triangle Brc is equal to the trapezium A B C D. of course do da

| That this is true may be soon seen. After taking away the



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common piece B C D E from the trapezium A B C D and the ABCDEPG (Fig. 48), and proceed to construct a triangle equal triangle B i C, we have the triangle A K B, the remainder of the to it in area. As the figure is complicated, the lines which contrapezium A B C D, and the triangle K F D, the remainder of the tain the heptagon and the triangle equivalent to it in area have triangle B FC.

been drawn thicker than the lines which are necessary in working Bat these triangles are also parts of the triangles A D B, | out the process (as in Fig. 47), that the reader may the more BY D, which are equal in area, since they are on the same base, readily distinguish the relative areas of the figures in question. BD, and between the same parallels A F, B D, and as the triangle The first step is to draw straight lines from a, the apex of * D B is common to both, the triangle A K B is equal to the the polygon, taking D E to represent its base, to the points triangle K F D. In the same manner, by drawing the diagonal C, D, E, F, or to each salient point of the polygon except the two

A c of the tra- immediately on the right and left of the apex. The straight pezium A B C D, lines A C, AD, A E, A F divide the polygon A B C D E F G into producing D c in five unequal triangles, A B C, A C D, A DE, A E F, and a F G. the direction of The reader will note that however many may be the sides of the G; drawing B K polygon, it is divided by this process into a number of triangles parallel to A c,' always less by two than the number of its sides. Thus in the and meeting D G figure below the number of triangles into which it is divided by in H; and lastly, drawing straight lines from its apex to its salient points is five, joining A 1, it i the number of its sides being seven ; & dodecagon, or twelve

may be shown sided figure, would be divided into ten triangles, and so on. Fig. 46.

that the triangle Now-beginning with the triangle A B C, the highest triangle

A D H is also equal on the left side of the apex-by producing D c in the direction in superficial area to the irregular quadrilateral figure A B C D. of P, indefinitely; drawing B n parallel to a c to meet c D pro

It will be useful for the student to repeat this construction as duced in 1; and joining a H; we get a triangle, a u c, equal to an exercise, taking the sides C B, B A, and A D in succession as the triangle A B C, and by adding the polygon A CDEFG to the base of the trapezium A B C D, or the side on which it each of these triangles, we find that we have a hexagon or sixstands.

sided figure, A H D E F G, equal in area to the original sevenPROBLEM XXXIV.—To draw a triangle that shall be equal in sided polygon A B C D ETG. By making the triangle a XD superficial area to any given multilateral figure or polygon. equal to the triangle

First let us take a five-sided figure, as being next in order to A AD by the same a four-sided figure, as far as the number of its sides are con construction, which we cerned, and let A B C D E (Fig. 47) represent the five-sided figure need not repeat, we or pentagon, to which it is required to draw a triangle equal in get a pentagon, or fivesuperficial area. From c, the apex of the pentagon, draw the sided figure, A K E F G, straight lines C A, C E, to the points A, E, the extremities of the equal in area to the base on which it stands. By doing this we divide the pentagon hexagon A H D E F G, ABC D E into three triangles A B C, CA E, and C ED. Produce the and consequently to base E indefinitely both ways in the direction of F and g, and the original heptagon through B and draw the straight lines B H, D K, parallel to A B C D E F G. Con.

Fig. 48. CA, C E respectively, and meeting the base A E produced, in the tinning the process with making the triangle a F Lequal to the tripoints 1 and K. Join C1, CK; the triangle c H K is equal angle A F G, the highest triangle on the right side of the apes, we in superficial area to the pentagon A BC D E. That this is get an irregular quadrilateral figure, A K E L, equal to the pentrue may be seen as follows:-Of the three triangles A B C, tagon A K E F G, the hexagon A H D E F G, and the heptagon C A E, and C E D, into which the pentagon was divided, the A B C DEFG. Once more, by making by a similar construction triangle C A E is common to both the pentagon and the triangle the triangle A E m equal to the triangle A E L, we got at last a CIK. Of the remaining portions of the pentagon and triangle, triangle, A K M, equal in area to the quadrilateral figure as EL

the triangle A B C of the and the above-named pentagon and hexagon and the original
former is equal to the tri. heptagon A B C D E F G.
angle c H A of the latter, The learner will find the value of this geometrical process in
because they are on the same determining the areas of irregular polygons in mensuration. To
base, A C, and between the calculate the area of the heptagon A B C D E F G, it would be
same parallels; and for the divided as in the above figure into five triangles, and by an
same reason the triangle arithmetical process to be explained hereafter the superficial
CED of the pentagon is content of each triangle would be found, and the five results

equal to the triangle C EK added together to obtain the area of the polygon. By reducing
Fig. 47.
of the triangle.

the area of the polygon to a triangle, its area can be found by

The learner will find it one calculation instead of five, and a sum in compound addition; useful to repeat this construction as an exercise, taking the sides or, to ensure accuracy, both processes may be gone through, each A B, BC, C D and D E in succession, as the base on which the proving a test whereby the correctness of the other may be pentagon is supposed to stand.

ascertained. That the learner may thoroughly understand the process of As in the preceding propositions, let the learner repeat the drawing a triangle equal in superficial area to a polygon having above construction as an exercise, taking the sides E F, F G, GA, a great number of sides, and see that it is as easy as it is to A B, BC, and cd in succession, as the base on which the polygon draw a triangle equal in area to a pentagon, which has only five is supposed to stand, and the salient point which happens to be sides, we will take the irregular seven-sided figure, or heptagon immediately opposite the base in each case as the apex.

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