< lue, is 10; '.' r = 10, and r2 = 100; ., n being = £44, nr2 = 144- · 100=44; 2 r + xXx = 2 × 10 + x Xx=20+xXx is the greatest product in 44; now x < cannot be more than 2, for 20 can be taken from 44 only twice, and 20+ is to be taken x times from 44, and, if it be tried, it will be found, that x is not lefs than 2, for 20+ 2 • X 2 = 22 X 2 = 44 which is contained exactly in n44, and, there being no remainder, the true root is 12; and this is exactly the fame as one of the methods in article 460, and... agreeable to the rule.

n=

2

Again, if the root confifts of three figures, the two first figures of the root may be found by finding the root of the greatcft fquare contained in the two firft periods of the given number, by the method (already proved) for finding a root of two figures; and then, if we put r these two first figures of the root taken in their compleat value, and x for the other figure, and the whole number, then 2r+xXx must be the greatest production in n-2; but in finding the two first <figures of the root, we have found n · r2 (and ·.· need not now fquare r to deduct it from n) it being equal to what remained after the fecond figure of the root was found; for, if we put a to denote the first figure of the root taken in its compleat value, and the fecond figure of the root in its real value, then a+b= the two firft figures in their compleat value=r; now a + b2=a2+2ab+b2= r2; but in finding the two first figures of the root, we first deducted a2, and there < must remain na2; from this again we deducted 2 a+b xb=2ab+b2, and . there must remain n

2

-

2

a

2

2

r2, the re

• a b — b2, or ʼn — -a+b2, or, fince a + b mander muft ben-r2; and we have only to take what remains after the two first figures of the root are found, and to take x fuch a figure, that 2r+xXx may be the greatest product that can poffibly be taken out of that remainder; and this is agreeable to the rule; we will illuftrate it by an example, for inftance, that in article 461. In that example, a in its compleat value is 300, and b, the second figure of the root, in its true value, as yet fuppofed unknown; then na2=119025 -9000029025; now b is to be taken fuch, that 2 a+b • Xb=600+bX b may be the greateft poffible in 29025; ** b= 40 (taken in its true value) for 600 +40 X 40 640 X 40 25600 (and, if b was taken 50 it would be too much for 600 + 50 X 50 = 650 X 50 32500 is greater than 29025, and... cannot be contained in it) now 29025-25600 6 = 3425

=3425"-r2 by the above; hence a = 300, and b = 40, and a+b= 340r; and 2 r 340 X 2 = 680, .. 2r+xxx=680 + xXx is to be the greatest in 3425,

5, for 680 + 5×5 685 × 5 = 3425, which de• ducted from 3425 leaves o, and confequently, r+x=685 is exactly the true root.

6

The fame method of reafoning holds good in any other number of points, but we think it unneceflary to proceed any farther on this head; and therefore fhall only add, that as evolution is the reverfe of involution, an evolution may be proved by involving the root (and adding to the involution the remainder, if any) and the number thus found, if the work be right, must be equal to the given number; and from the nature of multiplication it follows, that (after having fubtracted the remainder, if any, from the given number, as what then remains must be a perfect fquare) if out of the fquare number we caft out the nines, as out of the product in multiplication, and alfo caft the uines out of the root, and the excess multiplied by itself, and the nines being caft out, the excess must be

the excefs after all the nines were caft out of the fquare number. Example, The root of the greatest fquare contained in 150 is 12, and 6 remaining, then 150-6144 the square number, out of which the nines being caft, the remainder is 0; and the nines (or rather the nine) being caft out of 12, the excefs is 3; and 3× 3 = 9, out of which the nine being taken, the excefs is o, the fame as out of the fquare number; • and •.• 12 is the true root of the greateft fquare. And if we prove it by the method of involution, it ftands thus, 12X 12

144 equal to the greatest square, to which adding the remainder 6, the fum is 150, the given number for proof,'

B.

The Parliamentary Hiflory of England, Vols. XIX. and XX.

T

See Review for May.

HIS ufeful and entertaining Hiftory, now leads us to a crifis which affords a melancholy inftance, that the integrity of the human heart is not proof against the intoxications of power. We find the leading men of the nation bravely oppofing the illegal attempts of an arbitrary Monarch; we find them, after a long and bloody conteft, become mafters of his perfon, and ignobly close their triumph with the death of their captive King. The form of government being thus diffolved, we behold thefe Patriots erecting themfelves into a legion of Tyrants, practifing

practicing the fame illegal and unjuftifiable measures they had before fo nobly oppofed; endeavouring to enlarge and perpetuate their own power; and, in one word, purfuing every mode of injuftice and oppreffion, with an infolent prefumption beyond that of the moft flagitious Minifter, or tyrannical King, that ever haraffed this kingdom. So true it is, that all Courts and Judicatories whatever, have a natural longing and tendency to extend their authority even to the very borders of tyranny.

Of the qualifications of our Hiftorians, and the merits of this valuable work, we have delivered our opinion in our review of the eighteen preceding volumes. The nineteenth, which now lies before us, opens with the refolutions of the Commons concerning the burial of the late unhappy King.

The Republican Party was now prevalent in the House of Commons, and they, with the affiftance of the army, having excluded all thofe Members who refufed to concur with their measures, and having abolished both the Monarchy and the Peerage, erected a Council of State for the government of England and Ireland, who were to act under the fole authority of that Houfe. They likewife made alterations in the ftile of the Courtsof Law, and repealed the ftatutes relating to the oaths of Allegiance and Supremacy: In fhort, they induftrioufly devifed every innovation for the establishment of their new, and fhort lived, Commonwealth.

It is remarkable, however, that the Commons paffed an act for restraining and prohibiting the printing and publishing the paffages and proceedings of the High Court of Justice. Which feems as if they were confcious that the practices of that illegal Judicatory could not abide the teft of open and impartial fcrutiny. Proceedings warranted by the fanction of Law and Juftice, may face the light, and need not be concealed under the mask of obfcurity and oblivion.

The ufurpation of the Commons, however, did not pas unnoticed or uncenfured. Some fenfible and fpirited remonftrances were published, in which their artifices were detected, and their arbitrary views expofed. Thefe they voted to be fcandalous and feditious; and feveral perfons were imprifoned for writing against this new Republic.

Nevertheless they thought proper to publifh a vindication of their proceedings, by way of Declaration of their Reasons for eftablishing a Commonwealth. In this compofition they advance all the fpecious and delufive arguments which fallacy could fuggeft. They begin with recapitulating all the arbitrary acts of the late King; and, after having perverted both reafon and

fcripture

fcripture to justify their putting him to death, they then proceed in the following extraordinary ftrain.

The fame power and authority which firft erected a King, and made him a public Officer for the common good, finding him perverted, to the common calamity, it may juftly be admitted, at the pleafure of thofe whofe Officer he is, whether they will continue that Officer any longer, or change that Government for a better; and, inftead of reftoring tyranny, to refolve into a free ftate.

Herein the Parliament received encouragement, by their • obfervation of the bleffing of God upon other States: the Romans, after their Regifugium, for many hundred years together, profpered far more than under any of their Kings or Emperors: The State of Venice hath flourished for one thou• fand three hundred years: How much do the Commons in • Switzerland, and other free States, exceed those who are not fo, in riches, freedom, peace, and all happiness? Our neighbours in the United Provinces, fince their change of government, have wonderfully increafed in wealth, freedom, trade, and ftrength, both by fea and land.

.

In Commonwealths they find juftice duly adminiftered, the great ones not able to opprefs the poorer, and the poor fufficiently provided for; the feeds of civil war and diffention, by particular ambition, claims of fucceffion, and the like, (wherein this nation hath been in many ages grievously employed) wholly removed; and a juft freedom of their confciences, perfons, and eftates, enjoyed by all forts of men.

On the other fide, looking generally into the times of our • Monarchs, what injuftice, oppreffion, and flavery were the common people kept under; fome great Lords fcarce affording to fome of their fervants, tenants, or peasants, fo good meat, or fo much reft, as to their dogs and horfes? It was long fince warned in Parliament, by a Privy Counsellor to the late King, That we fhould take heed, left, by lofing our Parliaments, it would be with us as with the common people in a Monarchy, where they are contented with canvas cloathing and wooden fhoes, and look more like ghosts than men: This was intended for the fate of England, had our Monarch prevailed over us. To bring this to pass, their beafts of forests must grow fat, by devouring the poor man's corn; for want of which, he and his wife and children must • make many a hungry meal: A Tradefman furnishing a great man with most part of his ftock, or a Creditor with money, and expecting due fatisfaction and payment, is answered with ill words or blows; and the dear bought learning that Lords

' and

f

and King's fervants are privileged from arrefts and procefs of law. Thus many poor Creditors and their families have perifhed by the injuftice and prodigality of their lawless Cre⚫ditors.

A poor Waterman with his boat or barge; a poor Countryman with his team and horfes, and others of other callings, 'muft ferve the King for the King's pay; which, if they can get, is not enough to find themselves bread, when their wives and children have nothing but the hufband's labour to provide 'for them alfo.'

It is worth our while to obferve the Sophiftry which bad men make use of to cover bad defigns. It may be true, that if a King, who is a public Officer for the common good, perverts his truft to the common calamity, then it is at the pleafure of thofe whofe Officer he is, whether they will continue that Officer any longer, or change that government for a better. But this power is not in the Reprefentatives of the people, but in the body of the people at large. The people are Judges, with reverence we fpeak it, both of Kings and Parliaments: But no one branch of the Legiflature has a power over the other, beyond what is particularly limited and afcertained by law. Much less can any one have a right to deftroy or diffolve the other.

As Kings are general Officers for the common good, fo the Reprefentatives of the people are particular Officers for the good of their Conftituents: they are to watch over and protect their Rights and Liberties as eftablished by law. But as their power is limited, they have no right to alter Fundamentals, or to change the Conftitution. That can only be done by the confent of the whole people, for whofe fake it was originally framed. Nor is the fenfe of the whole people fo difficult to be attained as imagined; once in feven years almost every man in the kingdom gives his affent in perfon, and upon an emergency, which may not arife in a century, fure it cannot be impracticable to collect the voice of the nation.

It is the Conftitution, or particular frame of Government, which afcertains and eftablishes the Rights and Liberties of the people: and if their Reprefentatives prefume to change or diffolve the Conftitution, they take away the bafis which fupports thofe Rights and Privileges, and make them to depend on their own abfolute wills, and arbitrary fyftems of Revolution.

It seems evident, therefore, that the proceedings of the Parliament against the King, (we mean the judicial proceedings in the High Court of Juftice) were not warranted by law: much lefs juftifiable was the ufurpation of the Parliament after his death.

8

By