374 



THE POPULAR EDUCATOR, 



change of masters would prove beneficial the change from the 

 slothful mis-government by provincial governors appointed by 

 the emperor, to the strong, just, and wise government of the 

 K'haliph. 



Prom the death of Omar, who was assassinated in 643, till 

 the invasion of Spain in 710, the Saracen empire had extended 

 its borders with little intermission. Besides establishing itself 

 all along the coast of northern Africa, it had mastered the 

 islands of Sardinia, Sicily, Rhodes, and Crete, and had effected 

 a lodgment on the Italian peninsula. But during that time also 

 divisions had sprung up among chiefs who each claimed the 

 throne, and who appealed to the sword to decide between them. 

 The Arabian simplicity and hardihood became diminished b.v 

 contact with civilisation and refinement, and it was found by 

 the middle of the eighth century that the authority of the 

 Khaliph at Bagdad was practically set at nought, and his 

 dominion confined to the limits of the city itself. Quasi-inde- 

 pendent kingdoms were erected in Tunis, Tripoli, Egypt, 

 Morocco, Damascus, and Spain, each under some successful 

 soldier chief, who owned only a nominal allegiance, if any, to 

 the Commander of the Faithful at Bagdad. 



This decline in power, these splittings up of the unity of the 

 empire, were the salvation for a while of the Greek empire. 

 They were the causes, too, coupled with the establishment of 

 the Christian kingdoms of Leon, Castile, the Asturias, and 

 Navarre, and the continuous bearing down from the north upon 

 the south of the large nationalities of the German and Sclavonic 

 families, why the Saracenic wave of conquest did not sweep 

 northwards after it was first stemmed by Charles the Ham- 

 mer at the battle of Tours. 



There was another and more deadly cause for the break-up 

 of the Saracenic power, at least in the East. In the wars which 

 the Khaliphs waged from time to time upon the barbarous people 

 who dwelt on their north-eastern frontier, there had been cap- 

 tured rnaTiy stalwart men, of large frame and sturdy constitu- 

 tion, who were allowed their freedom from labour and from the 

 other incidents of conquest on condition of entering the military 

 service of their captors. These men were from Turkestan, 

 Tartars of the roughest, strongest kind. They accepted the 

 conditions, and they formed the household troops of the 

 Khaliph about the time when the energetic brethren of their 

 master were establishing themselves in their newly-gained 

 Spanish possessions. From guards they soon learned to become 

 Blasters, and to dispose of the succession when that came in 

 question according to their own liking. The Kaliphate declined 

 visibly. Al Eadi, who died in 940, was the last of the real 

 Khaliphs ; after him there was no head of the empire, and the 

 Turkish soldiers seized for themselves the provinces imme- 

 diately surrounding the capital city of Bagdad. The title of 

 Khaliph was, however, maintained by the Turks for some 

 nominee of their own, in order to give them a sort of title 

 to commit the acts of government they wished. In the year 

 1258 it was finally abolished, the slave-masters having by that 

 time become sufficiently strong to dispense with assistance, aiid 

 to hold their possessions by the help of their own swords. 



Reinforced by large additions from Tartary, the Turks took 

 some time to consolidate their power. They borrowed from the 

 Saracens most of what was valuable in their system, they 

 adopted their religion, and they imported from home certaia 

 hardy principles and practices which gave solidity and robust- 

 ness to tiie state. Now and again they had to endure the 

 attack of some unusually energetic Greek emperor, who 'led hia 

 armies from Constantinople for the purpose of winning back 

 some of the lost ground that had been wrested from feeble 

 governors. But not unfrequently they gained the advantage 

 in this strife, and whether they did or not, they noted down the 

 aggression as a thing to be paid back with interest some day. 

 That day came when Constantinople fell before their assault ; 

 but that event did not happen for more than three centuries 

 after the Turks had become a power in the world. 



The separate kingdoms of Saracenic foundation remained in 

 statu quo for long periods of years, excepting that the Sultan of 

 Egypt assumed the lead among them, and, as it fell to pieces, 

 absorbed such provinces of the Bagdad empire as the negli- 

 gence or the impotence of the Turks suffered to drift away. It 

 was with the Sultans of Egypt, most famous of whom was 

 Saladin, that the Crusaders had to reckon when they endea- 

 roured to recover the Holy Land. Syria had fallen to Egypt, 



and the Sultans of Egypt protected it, succeeding, ere they in 

 due time fell before the westward march of the Turks, in 

 driving the Christians out of the whole of Palestine, and in 

 rendering barren of results all the work of the Crusades. 



In Spain the Saracenic, or, as it was called from its 

 identity of interest and from its origin, the Moorish kingdom, 

 long remained in spite of the strenuous efforts of the Christian 

 princes of the north to destroy it. Not until several of the 

 small Christian states had been rolled into one, and made one 

 in interest, one in political purpose, one as a nation, was an im- 

 pression made on the kingdom of Granada, and even then the 

 impression was, so to speak, a slight one. From indolence, in- 

 capacity, from whatever cause, the Christian princes who strove 

 from the year 1100 downwards, with some prospect of ultimate 

 success, to oust the Moors, proved unequal to the task. It was 

 reserved for Ferdinand the Catholic, whose marriage with 

 Isabella of Castile had welded into one the Christian power in 

 Spain, to overthrow without hope of restoration the throne of 

 the Moslem in Cordova. Many strong towns had been gradually 

 won, the bulwarks of the kingdom had been sapped since many 

 years, but on the 2nd of January, 1492, the Spanish king had 

 the satisfaction of receiving as conqueror the keys of Granada, 

 the last stronghold of the Moors. 



Forty years had not elapsed since every echo in Europe had 

 resounded to the crash of the Greek empire as its capital fell tc 

 the Turks. Fresh influxes of men, fresh leaders, new dynasties, 

 had come to swell the might and to develop the resources of 

 those invaders. An irrepressible ardour burned in their hearts 

 to burst their bounds and to achieve conquests, and the weak- 

 ness and the riches of the Greek empire proved an irresistible 

 bait. With a multitudinous army, supplied with everything for 

 the siege of the greatest city of the world with skill, courage, 

 and confidence in himself Mahomet II. pitched his camp 

 around the fated city, and carried it at last by assault. Con- 

 stantinople passed into Turkish hands, by which it has been 

 retained ever since ; and for a while it was feared that the 

 Moslem faith which had been kept out of Europe, save Spain, 

 would be forced upon it by the Turks. Vienna was twice be- 

 sieged by the Turks, the last time in 1683 ; and it was but 

 owing to victories like the naval one of Lepanto in 1571, to 

 those in which the king aud people of Hungary so frequently 

 sacrificed themselves, and to heroic efforts like those which ena- 

 bled John Sobieski, King of Poland, to rescue Vienna in 1683, 

 that the Turkish power was kept from encroaching further 

 westward in Europe. 



LESSONS IN ALGEBRA. XII. 



MULTIPLICATION OP FRACTIONS. 



141. BY the definition of multiplication, to multiply by a 

 fraction is to take a part of the multiplicand as many times as 

 there are like parts of a unit in the multiplier. 



q 



Thus .- Suppose a is to be multiplied by -. Here, a fourth 



4 



part of a is -: and this taken three times is - + - -f- - 

 4 444 



= ; and so of other cases. 

 4 



142. To multiply one fraction by another. 



Multiply their numerators together, and also their denomi- 

 nators ; the products are respectively the numerator and denomi- 

 nator of the answer. 



143. The multiplication may often be shortened, by rejecting 

 the same factors from the numerators and denominators of the 

 given fractions. a h , 



EXAMPLE. Multiply -, -> and - together. 

 "a y 



Here, a being in one of the numerators, and in one of the 



denominators, may be omitted. The answer is then If a 



ry 



be retained, the product will be - ; atad this reduced to lower 



dh 



ary 



terms, will become , the same answer as before. 

 ry 



144. To multiply a fraction and an integer together. 



Rule. Multiply the numerator of the fraction by the integer, 

 and the product with the same denominator is the answer; or 

 divide the denominator by the integer, and the quotient with the 

 same numerator is the answer. * 



