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Chapter8
The History of Algebra in Mathematics Education
Luis Puig and Teresa Rojano
Universidad de Valencia, Spain, and Centro de Investigación y Estudios Avanzados del Instituto
Politécnico Nacional, Mexico
Abstract: In this chapter, we analyse key issues in algebra history from which some lessons
can be extracted for the future of the teaching and learning of algebra. A
comparative analysis of two types of pre-Vietan languages (before century),
and of the corresponding methods to solve problems, leads to conjecture the
presence of didactic obstacles of an epistemological origin in the transition from
arithmetic to algebraic thinking. This illustrates the value of historic and critical
analysis for basic research design in mathematics education. Analysing the
interrelationship between different evolution stages of the sign system of symbolic
algebra and vernacular language supports the inference that a particular sign system
represents a significant step in the evolution of algebra symbolism when it permits
calculations at a syntactic level. Such analyses provide elements to identify features
of the algebraic in the translation processes from natural language to the algebraic
code. In particular, these elements can be used as a basis to study pupils’ strategies
when they solve word problems, and to conceive didactical routes for the teaching
of solving methods of these problems. The examples discussed emphasise the
importance of speaking of manifestations of the algebraic in the specific, in
contrast to other perspectives that emphasise the nature of algebraic thinking in the
general.
Key words: History of algebra, early algebraic language, didactic obstacles, the algebraic,
Cartesian method, language stratum, mathematical sign system, symbolic algebra,
word problems
8.1 Introduction
Two or three decades ago it was common to find articles that discussed the necessity
or usefulness of knowing about the history of mathematics in order to teach or learn
it or to research its teaching and learning. Hans Freudenthal, for example, called his

190 Chapter 8
famous article Should a mathematics teacher know something about the history of
mathematics? (Freudenthal, 1981), but since then reasons for supporting the
importance of using history in mathematics education have been extensively
provided from a variety of perspectives. ICMI established a group more than 20
years ago to study the relationship between the history and pedagogy of
mathematics, and during the last few years important publications have appeared
that summarise the work done outside and inside this group, especially the ICMI
Study History in Mathematics Education (Fauvel & van Maanen, 2000), but also
Katz (2000), and Jahnke, Knoche, and Otte (1996). These books save us from the
need to review recent work in this chapter, because an extensive account of
everything is included in them. The content of this chapter will therefore focus on
examining some key issues to study in the history of algebraic ideas to be used in
mathematics education, rather than on why to do it or on establishing what has been
done.
The idea is to look at the future of the teaching and learning of algebra in terms
of the lessons that can be extracted from a historical perspective. In turn, our current
knowledge of the difficulties that teachers and students face when learning (and
teaching) algebra should tell us what aspects of the history of algebra are worth
studying in depth. For instance, the present debate on the teaching of the
manipulative aspects of algebra has led us to report on the history of algebraic
symbolism in some depth (see Section 8.3) in order to find arguments to support
decisions concerning the curriculum of algebra. One of the arguments that might be
founded on a historical analysis is that the conceptual development of some
algebraic notions is strongly related to sources of meaning arising from the syntactic
manipulation of symbols.
The history of symbolism in algebra can be regarded as the history of the
development of a system of signs that makes it possible to carry out calculations at a
syntactic level to find the solution of a word problem without having to refer to the
semantic level of the problem statement. In this sense, the evolution of algebraic
symbolism is strongly related to the history of algebraic methods for solving
problems. Relevant interrelations between these two components of the history of
algebra will be discussed (see Section 8.2), and also, especially, the interrelation of
the characteristics of a particular sign system with concepts and methods (Section
8.4), and the use of these analyses in research (Section 8.5).
From a historical point of view, functions are not formally a part of algebra.
Nevertheless, they are a part of the teaching of algebra in many countries (see
Chapter 13 of this book). Furthermore, a promising approach to the teaching of
algebra is the functional one. In connection with this functional approach to the
teaching of algebra it is important, therefore, to study the relationship in history
between algebraic ideas and the idea of variation, the mathematics of change,
variables (that vary), and functions. However, this is a task that we shall not tackle
here.

The History of Algebra in Mathematics Education 191
8.2 Algebraic Problem Solving
8.2.1 The Cartesian Method as a paradigm of algebraic problem
solving
What lies at the heart of algebraic problem solving is the expression of problems in
the language of algebra by means of equations. In order to be able to compare the
ways of writing equations that represent word problems in different historical texts
so that the comparison brings out what is pertinent for teaching, a good strategy is to
take as a reference what is done in the Cartesian Method, which is the algebraic
method par excellence and may be considered as the canon of the methods
traditionally taught in school systems.
Stacey and MacGregor (2001) have pointed out that a major reason for the
difficulty that students have in using algebraic methods for solving problems is not
understanding its basic logic—that is, the logic that underlies the Cartesian Method.
There is a students’ compulsion to calculate, based on their prior experiences with
arithmetic problem solving. This tendency to operate backwards rather than
forwards (Kieran, 1992) prevents students from finding sense in the actions of
analysing the statement of the problem and translating it into equations which
express, in algebraic language, the relations among quantities; actions of analysing
and translating that are the main features of the Cartesian Method. Teaching models
that take into account these tendencies are presented in Filloy, Rojano, and Rubio
(2001). They state that in order to give sense to the Cartesian Method users should
recognise the algebraic expressions, used in the solution of the problem, as
expressions that involve unknowns. Competent use of expressions with unknowns is
achieved when it makes sense to perform operations between the unknown and the
data of the problem. In steps prior to competent use of the Cartesian Method, the
pragmatics of the more concrete sign systems leads to using the letters as variables,
passing through a stage in which the letters are only used as names and
representations of generalised numbers, and a subsequent stage in which they are
only used for representing what is unknown in the problem. These last two stages,
both clearly distinct, are predecessors of the use of letters as unknowns and using
algebraic expressions as relations between magnitudes, in particular as functional
relations.
Furthermore, competent use of the Cartesian Method is linked with the creation
of families of problems that are represented in the mathematical sign system (MSS)
of algebra as canonical forms. This implies an evolution of the use of symbolisation
in which, finally, the competent user can give meaning to a symbolic representation
of the problem that arises from the particular concrete examples given in teaching.
Students will make sense of the Cartesian Method when they become finally aware
that by applying it they can solve families of problems, defined by the same scheme
of solution. The integrated conception of the method needs the confidence of the

192 Chapter 8
user that the general application of its steps will necessarily lead to the solution of
these families of problems.
In this section we will present an in-depth analysis of algebraic problem solving
in history bearing in mind that this results from research on its teaching and learning.
We will have to examine the characteristics of the Cartesian Method (Section 8.2.1),
and the search for canonical forms that represent families of problems and its
methods of resolution (Section 8.2.2). In the next section we deal with the history of
symbolisation. First of all we will examine the formulation of the method proposed
by Descartes (1596-1650, France). Indeed, the reason for calling this method
Cartesian is that one part of Descartes’ (1701-original posthumous publication,
1996) Regulæ ad directionem ingenii (Rules for the direction of the mind)1
can be
interpreted as an examination of the nature of the work of translating the verbal
statement of an arithmetic-algebraic problem into the mathematical sign system
(MSS) of algebra and its solution in that MSS.
Broken down into ideal steps, that is, those that would be taken by a competent
user, the first step of the Cartesian Method consists in an analytical reading of the
statement of the problem, which reduces it to a list of quantities and relations
between quantities. The second step consists in choosing a quantity that will be
represented by a letter (or several quantities that will be represented by different
letters), and the third step consists in representing other quantities by means of
algebraic expressions that describe the (arithmetic) relation that these quantities have
with others that have already been represented by a letter or an algebraic expression.
With the MSS of current school algebra this is done by maintaining the
representation of each quantity by a different letter and taking care that each letter
should represent a different quantity and combining the letters with signs for
operations and with delimiters, while also observing certain rules of syntax that
express the order in which the operations represented in the expression are
performed. Descartes (1701) indicates that one makes an abstraction of the fact that
some terms are known and others unknown. Treating known and unknown in the
same way is precisely one of the fundamental features of the method’s algebraic
character, and Descartes himself pointed out that the basic nature of his method
consisted in this [totum huius loci artificium consistet in eo, quod ignota pro cognitis
supponendo possimus facilem & directam quærendi viam nobis proponere, etiam in
difficultatibus quantumcumque intricatis (Descartes, 1701, pp. 61-62)]. The fourth
step consists in establishing an equation (or as many equations as the number of
different letters that it was decided to introduce in the second step) by equating two
of the expressions written in the third step that represent the same quantity. In
Descartes’ rule XIX what gives meaning to the construction of the equation is the
expression of a quantity in two different ways [Per hanc ratiocinandi methodum
quarenda sunt tot magnitudines duobus modis differentibus expressa (Descartes,
1701, p. 66)].

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The news of this great discovery at once made Balboa famous. All
over Europe men talked of the bold man who had been the means
of adding still more glory to the Spanish name, and as a reward for
his services, the king made him Adelantado, or chief ruler, over all
the great sea he had discovered.
But among the Spaniards in Darien, Balboa was very much feared,
and now that he was in such great favor at the Spanish court, every
one dreaded that he would be more cruel and heartless than before,
because he had so much more power. And besides, his companions
were jealous of his fame, and thought that the honor of discovering
the South Sea belonged quite as much to them as to him, quite
forgetting that but for his courage and perseverance they would
have turned back long before the sea came in sight.
The man who disliked and feared Balboa the most was Peter Anias,
the Governor of Darien, and about five years after the great
discovery, he managed to get Balboa into his power, and ordered
him to be beheaded.
This was done, and thus perished one of the greatest of the Spanish
discoverers.

CHAPTER X.
C A B E C A D E V A C A .
And now that Florida had been discovered, and the great South Sea
added to the possessions of the Spanish crown, it was thought it
would be a wise thing to settle as much of the New World as
possible, so that when all its treasures were found they would
already be in the hands of the Spaniards and there would be no
trouble about it. And so many expeditions were sent out from Spain.
These expeditions always had two objects in view. First, to get what
gold and silver might be found in America, and second, to find a
short passage to the East. People had never given up believing that
there must be a short way of getting from the eastern coast of
America to India, and ship after ship was sent to seek the strait
which was supposed to lead across the continent. For, important as
the discovery of a new world seemed, it was considered just as
important to find a short way to the East, and when once the
passage was found, to sail through it with Spanish ships and make
its wealth a part of Spain. Very wonderful stories were told of the
countries in the East—of Cathay, and Mangi, and Cipango—which
had been visited by the great traveller, Marco Polo, and the man who
could find the shortest way thither, would, of all men, receive the
highest honor from the King of Spain. And so every one who sailed
from Spain looked first toward America and then beyond it to the
East. And no wonder, for these countries were richer than Mexico
and Peru, more fertile than Florida, and more beautiful than

Fairyland itself. There was nothing in the world that one might want
that could not be found within the borders of these lands. For ages
and ages this kingdom had been ruled by the great race of Kublai
Khan, and these monarchs had no other thought than to make their
kingdom the most beautiful and glorious of the whole earth. They
had built great cities, and strong forts, and extensive highways; it
was said that within the Province of Mangi alone were twelve
thousand cities, all within a short distance of one another. Chief of
these cities was Quinsai, which covered a hundred miles of ground.
On one side of it was a river, and on another side a lake, and
through it flowed clear, winding streams spanned by twelve
thousand beautiful bridges, which were so lofty that ships passed
under them with ease. The streets were wide and bordered with
palm trees, and fragrant flowers bloomed all the year round in the
gardens and parks. All the dwellings were of marble, and the
temples and palaces were ornamented with precious stones.
Warehouses of stone stood in different parts of the city, filled with
costly merchandise, silks and velvets, and cloth of gold, and all
manner of rare articles made of gold and silver and mother-of-pearl,
curiously and beautifully beaten and engraved. And crystal fountains
kept the air pure and fresh, and great birds with gold and silver
wings flew lazily from tree to tree, and one could not tell whether
the city was more beautiful by day, when the sun shone down upon
it and brightened the marble roofs and charming gardens, or by
night, when the moon and stars were reflected in the lakes and
rivers, and when the fountains glistened white in the moonlight, and
the great squares and lofty palaces were illumined with a million
crystal lamps.
Most beautiful of all the palaces was that of the king, which stood in
the centre of the city on a hill overlooking all the country round. It
was so large that it covered ten acres, and its wide, lofty corridors,
beautified with groups of magnolia and palm, seemed like
magnificent avenues stretching from one palace to another.

Within the enclosure were groves of pine and oak and many rare
trees, and gardens filled with choicest flowers, and lakes on which
swans floated, and in whose waters rainbow-hued fishes darted
hither and thither. The palace itself was of the purest white marble,
its roof was wrought in gold and supported by hundreds of pillars of
pure gold, wonderfully adorned in azure arabesque, and having the
capitals studded with precious stones; and all the air was sweet with
perfumed fountains, and everywhere it was continual summer from
the abundance of flowers and the songs of birds.
And the king and all his people enjoyed their beautiful city as much
as possible, for they were so rich they had to work very little, and
spent the greater part of every day in pleasant amusements. At any
hour one might see pleasure parties on the lakes and rivers, which
were always covered with gilded boats, and barges with silken
awnings, under which tables were prepared for banquets. And
everywhere through the city were scattered inviting bowers, where
the people sat when tired with walking, and watched the long
procession of elegant chariots, luxuriously fitted up with cushions of
silks and velvet and drawn by richly caparisoned horses. And besides
these every-day amusements there were a great many days held
sacred to the gods, when there were great feasts lasting ten or
twelve days, and when ten thousand guests were entertained at a
time.
And the health and comfort of the people were provided for as well
as their amusement, for there were elegant marble baths, and a
number of fine hospitals for the care of the sick, and a wonderful
system of lighting the houses and palaces, so that the night seemed
almost turned into day again, and a well-trained fire-department,
always ready to act at any moment, and in fact, everything that
could be done to make the people healthy and happy, and to protect
their lives and property, was done. And all the children went to
school in the public parks and gardens, for in that beautiful climate it
never rained or was cold, and so there was no need of school-

houses, and the boys and girls studied botany, and geology, and
astronomy out of doors, and no doubt found it very pleasant.
And Marco Polo, summing up his description of the wonderful place,
says, "And this city, for the excellence thereof, hath the name of the
city of Heaven; for in the world there is not the like, or a place in
which are found so many pleasures, that a man would think he were
in Paradise."
And all the other countries ruled by the great Khan were as rich as
Mangi. In Armenia were tens of thousands of beautiful cities filled
with works of art, and out in the open country were wonderful hot
springs which cured all manner of diseases, and on the top of one of
the high mountains Noah's ark still rested. And Cathay also held
many rich towns. Among them, Cambalu, where the king had a
marble palace with a roof of gold, as in Quinsai. And here, ten
thousand soldiers guarded the palace, and the royal stables, wherein
stood five thousand elephants. Great public roads led out from
Cambalu to all the other cities in the empire, and along these roads
were stationed post-houses where the king's messengers could find
rest and refreshment, and where there were elegant apartments in
which the king himself might rest when on his journey through the
empire. All the king's errands were done by swift messengers, who
ran from one post-house to another. These messengers wore belts
from which hung gold and silver bells, and as soon as one station
was reached, the letters and messages were given to another
messenger and carried on to the next station, and so on, the tinkling
of the bells notifying the waiting messenger to be in readiness. And
so, not a moment was lost; the messengers ran swiftly over the fine
roads, scarcely noticing, in their haste, the beautiful scenery or the
many works of art that adorned the way, which led through deep,
shady forests, and wide, pleasant meadows, and over the numerous
rivers and canals, spanned by lofty bridges built of rare stone and
costly marble, and ornamented with rows of polished columns and
great stone lions, and curiously graven images of gods, and men,
and animals.

The roads extended from one great city to another, joining the most
distant places together, and the Khan spent a summer in one place
and a winter in another, and every city tried to outshine the rest. In
the summer months the Khan spent much of his time in his palace at
Ciandu, which was as magnificent as Cambalu. Here the palace
extended over sixteen miles, and ten thousand white horses stood in
the king's stables.
All this country was guarded by soldiers, who were like the sands of
the sea for number, and the great generals were held in such esteem
by the king that they were allowed to live in the most magnificent
style. They all sat in golden chairs, and rode on milk-white horses,
and travelled in gorgeous chariots, or in beautiful barges with silk
and velvet awnings to keep off the heat of the sun. And so mighty
was the Khan, and so great were his generals, that all the other
countries round were very glad to live peaceably, and try in every
way to please such a powerful monarch. The riches of this country
were beyond description; mountains of turquoises reached to the
clouds; the lakes were full of pearls; everywhere were gold and
silver mines; the rivers sparkled with gold, and the valleys were rich
in diamonds. And everywhere, too, there was an abundance of
choice fruits and nuts, and rare spices which grew in the gardens all
the year round, so there was no lack of them summer or winter. And
the people dressed in the richest stuffs, silk and velvet, and cloth of
gold, embroidered with pearls and turquoises and diamonds.
And in Cipango, too, which lay east of Mangi, out in the sea, could
be found the same magnificence. Here were palaces and temples,
with roofs covered with golden plates and floors paved with gold and
silver, and here also the people were rich and prosperous and happy.
And when the news of all this wealth reached Europe it was at once
determined to seek those far lands, and, if possible, to bring the
gold and pearls and diamonds to Spain and France, and other
European countries, and many expeditions were sent out; but none
of them ever reached Cathay, for all the American Continent and the
great Pacific Ocean lay in the way, and the short passage to the East

was never seen except in the dreams of some daring adventurers.
But it was years and years before men gave up searching for it.
France and Spain sent many men to look for it, and if they did not
find Cathay they at least found many curious and wonderful things in
America, and so it came about, after a while, that America itself was
pretty well known, and many attempts were made to settle it. Spain
tried very hard to establish her colonies in the New World, and
expedition after expedition was sent across the sea. With one of
these expeditions sailed Cabeca de Vaca, a Spanish nobleman, and
his account of the trials and misfortunes of the settlers shows how
very difficult it was to establish a Spanish colony in America.
The expedition was commanded by Narvaez, who landed his men at
Tampa Bay, two days before Easter, 1528. They immediately
determined to leave the coast and go into the interior of the country
in search of gold, although De Vaca tried very hard to persuade the
captain to remain near the ships. But here the Indians were not
friendly, and the country farther away was said to be rich in gold;
and so a short time after landing, a part of them started off to find
the gold region which the Indians said was up in the Appalachian
Mountains. But they found travelling through this strange country
very hard work. Soon after their arrival at Tampa Bay they had
angered the Indians by burning the bodies of some chiefs that they
had found in a little village, and the natives now tried in every way
to show their hatred. They refused to act as guides, and the
Spaniards had to toil through swamps and rivers and forests, often
losing their way and always in danger of attack from the Indians. At
length their food gave out, and then they had to depend upon the
fruit that could be found, and so at last, when they reached the little
Indian village of Apalachen, they were quite heart-sick, and glad to
find shelter and rest. They found no one in the village excepting
women and children; all the men had fled to the woods. The village
was built in the midst of a great swamp, and although it held some
maize and other provisions, they soon found there was no gold
there, and that all their long journey had been in vain. And then,
too, the Indians kept lurking around, and not only attacked them

and burned the wigwams in which they were living, but made it very
unsafe for the Spaniards to leave shelter at all. A man could not lead
his horse to water without being in danger of death, and as this kept
growing worse and worse, they decided to leave Apalachen and go
back to the sea. But many days and nights passed, and the sea
seemed as far off as ever. They were without food, and had to
depend upon getting maize from the Indians, and as this could only
be done by force, many battles were fought and many lives were
lost, and besides this trouble many fell sick and died from starvation
and hardship. But, hard as it was to go on, it would have been
harder still to remain, for that would mean certain death at the
hands of the Indians; so they toiled on, discouraged and hopeless,
and at the end of fifteen days found themselves at last at the sea-
coast. But it was not Tampa Bay, and no Spanish ships appeared in
sight on which they might embark and sail back to Spain again. And
the men, quite worn out, laid down on the sands in despair, and
doubted if they should ever see their homes and friends again.
But after a little while their courage came back, and they tried to
think of some way of getting back to the ships or of reaching some
Spanish settlement. It was impossible to think of travelling by land,
and at length they decided that they would have to make boats and
put out to sea with them. But how hard it seemed to undertake
boat-making without tools and materials! It was thought impossible
at first to do more than make some large rafts, but by and by they
discovered that their spurs and cross-bows and stirrups could be
beaten out into nails and axes and saws and other tools, and that
cordage could be made from the manes and tails of the horses, and
that the seams could be caulked with palmetto fibre and pitched
with pine rosin; and, in fact, with time and patience, they managed
to build five very good boats, living in the meantime on horse flesh
and shell-fish and the maize which they could get from the Indians.
When at last they were ready to start, forty of the men had already
died of sickness and hunger besides those that had been killed by
the Indians. They kept along the coast for some weeks, hoping to
reach a Spanish settlement on the western coast of the Gulf of

Mexico, but they could not find this place, and as it was not safe to
land anywhere else on account of the Indians, they had a most
wretched voyage, suffering from cold and hunger and drenched with
rain, and finally separated from one another by a fearful storm which
drove the boats far apart.
De Vaca's boat was thrown upon an island, and so hard was it to get
it off again into the sea that the men had to take off their clothing
and wade into the water to dig the boat out of the sand, and in
doing this many of them lost their lives; for no sooner did the boat
touch the water than it was upset in the surf, and not only were
some of the men drowned, but everything in the boat was lost, and
De Vaca and his friends found themselves on this strange island with
no boat or food or clothing. But, as it happened, the Indians on this
island were kind and pitiful. They built fires to warm the sufferers
and gave them food, and when after a few days, they were joined
by some men from the other boats, they found that their sufferings
had been no worse than their friends', for all had met with the same
hard fate. They stayed here many months, and one after another of
the company died, until only De Vaca and three others were left.
These four remained many years among the Indians, wandering
from one tribe to another, always trying to hear of some Spanish
settlement where they might meet friends. Sometimes the Indians
were kind to them, but oftener they were treated very cruelly.
Several times it happened that they were taken captive and held as
slaves, and then their lives would have been most miserable, had it
not been that the Indians grew to respect them because they knew
so many things that they themselves were ignorant of. De Vaca and
his companions really thought that they had the power of curing
disease by making the sign of the cross, or repeating pater nosters,
and, as in some cases the sick got well, the Indians grew to
reverence the white men and hold them in great esteem. But De
Vaca and his friends could not grow fond enough of the Indians to
be willing to remain among them. Their thoughts were always with
the land of their birth, and so they pushed on through the unknown

country, living on roots and nuts and the fruit of the prickly pear,
suffering from the cold and heat, from which they had no clothing to
protect them, and always in danger of death from hostile Indians. In
this way they travelled through forests and swamps, across prairies
and deserts, over mountains and rivers, for six years, and at last
their courage was rewarded. They came one day to the sea, and
they found there a Spanish settlement. Their countrymen, who had
come there for gold and emeralds, received them with great
kindness, and listened with wonder to the story of their wanderings.
De Vaca learned that they were now on the coast of the Gulf of
California, and that they had travelled from Tampa Bay, through the
country bordering on the Gulf of Mexico, and through Mexico itself to
the sea coast on the other side, having passed over more territory in
North America than any other travellers had yet done.
De Vaca and his three friends returned to Spain as speedily as
possible, where they were received as heroes of adventure, whose
romantic story passed from place to place, and instead of
discouraging others, only made them the more eager to visit those
strange lands themselves, for every one felt sure that if he had been
in De Vaca's place he would surely have discovered the gold and
silver and precious stones that were supposed to be hidden away in
the everglades of Florida, or in the mountains of Apalachen, or in the
rivers and valleys of Mexico.

CHAPTER XI.
H E R N A N D O C O R T E Z A N D T H E C O N Q U E S T O F
M E X I C O .
High on the table-land of Mexico there was once a beautiful city
which was built partly around the shores of a lake and partly on
islands within the lake. It had broad streets and fine buildings, and
its temples were among the most beautiful in the world, the principal
one, that which was devoted to the worship of the sun, being
ornamented with gold and silver and precious stones; here and there
were great public squares around which splendid temples were built,
and in the centre of the city in one of these great squares stood the
temple of the god of war. The people who lived in this city were
Aztecs, a tribe of Indians very different from those of the Atlantic
coast. They worshipped the sun and the moon, and, above all, they
worshipped the terrible god of war, in whose honor they burned the
bodies of the enemies they captured in battle. The temples were
attended by priests, who were held in great honor by the people,
and in every temple there were little boys who were being trained to
the priesthood. On great festival days the priests and boys and all
the people would form a grand procession and march all around the
city, singing and playing on instruments. The lake on which the city
was built was one of the finest in the world, and the Aztecs were
fond of building floating gardens on its waters; these gardens were
very beautiful, with flowers of all kinds, and vegetables were also
cultivated in them. The palaces of the king and nobles were built of

stone and of great size, and very elegant, being ornamented
sometimes with gold and silver. The Aztecs were a very powerful
people, and all the nations around them were afraid of them and
acknowledged the Aztec king as theirs; and everywhere from the
Pacific to the Gulf of Mexico were great roads leading from the city
down to the coasts, so that the king could send messages at any
time from one part of his kingdom to another; all over the country
outside the city were great fields, where cotton, corn, wheat, sugar,
coffee, and other things were raised. The Aztecs did not dress in
skins, as did the Indians farther north, but they wove cotton into
cloth and made garments of that. They also had a written language
and wrote their history down in books. The name of the king was
Montezuma, and all his people loved and worshipped him as a god,
and when he looked over the city and saw the turrets and spires of
the palaces and temples glittering in the sunlight, and the floating
gardens, filling the lakes with beauty and fragrance, and the fields
rich with harvest, and the green forests, stretching away to the base
of the great volcano whose snowy peak shone in the golden light of
the sun, he felt that his was, indeed, a great and fair kingdom,
beautiful and strong and happy.
But the riches of this great city had been heard of across the sea,
and the Spaniards, as ever eager for gold, resolved to make its
wealth their own. So an army was sent from Cuba to conquer
Mexico, and Hernando Cortez was made its leader. Cortez was a
brave soldier, but a cruel and treacherous man. In the year 1519 he
landed his troops at Tabasco on the southern coast of Mexico; he
found the natives prepared for war, but they were soon glad to fly
from the Spaniards, leaving many of their number killed. Cortez then
went on to Vera Cruz, where Montezuma had sent messengers to
meet him; these messengers brought with them magnificent
presents of gold and jewels which they gave to the Spaniards, at the
same time trying to persuade them to go away from their country.
But Cortez would not go away; he said he was going to the City of
Mexico to see Montezuma himself, as the King of Spain had ordered

him to do, and for fear his soldiers would not go with him, he burned
all his ships so they could not go back to Cuba if they wanted to.
THE MESSENGERS OF MONTEZUMA.
The Aztecs returned to Montezuma and told him that the Spaniards
were on their way to his city. Montezuma did not know what to do;
for although he was a good and kind king, he was not a great
soldier. He sent other messengers and more presents, and
commanded Cortez to go back, but Cortez pressed on. Now among
the Aztecs there was a tradition that, hundreds of years before, their
country had been visited by a glorious stranger from the East, a
child of the sun, who had taught them how to till the ground, and all
the arts of peace and war; and he lived with them many years, and
they loved him and worshipped him as a god, and the stranger was
very beautiful to look upon, with hair like the sunlight and eyes as

bright as the stars, and his skin was as white as the snow which
glistened on the tops of the volcanoes. And one day he called the
Indians around him and told them that he must go away forever, but
that some time in the years to come a race would come from the
East, children of the sun like himself, and that they would demand
the Aztec Kingdom for their own, and that it would do no good for
the Indians to fight these strangers, for they were the children of the
sun and could conquer all before them; and so saying, the stranger
from the East vanished from their sight, and they saw him no more,
though they mourned for him many days; for he had gone into the
mysterious West, whence the sun goes at night, for all things that
come from the East find a home at last in the land of the sunsetting,
but save the sun himself, nothing ever comes back from that land,
but all things remain forever hidden by the shadows which lie on its
borders.
And so when Montezuma heard that the Spaniards, who were fair-
skinned and light, compared with the Indians, were resolved to
come on to his city, he thought that perhaps they might be the
children of the sun, and if so, it would be of no use to try and repel
them; and when at last Cortez came up to the city, he went out to
meet him and gave him a courteous welcome.
The Spaniards were rejoiced when they saw the beautiful city, for
they thought that its splendid palaces and treasures would soon be
theirs. Montezuma led Cortez into the city and gave him a large and
elegant building for his quarters, and to every soldier in the army
magnificent presents were made. The army was quartered in the
great central square, near the temple of the god of war; it was in
the winter, and for a month Cortez remained quiet; he and his
soldiers were allowed to go about, and were even permitted to enter
the temples and examine the altars and shrines, where the Mexicans
offered up human beings every day as sacrifices to their gods. But
the thing that interested the Spanish general most were the vast
treasures of gold and silver, the huge storehouses filled with
provisions, and the great arsenals filled with bows and arrows. He

saw that the Aztecs were well prepared for war, and began to grow a
little alarmed for his own safety. He knew that by lifting his finger
Montezuma could fill all the squares with armed soldiers, and
prevent the Spaniards from leaving the city, and he knew also that
the Indian warriors were no longer afraid of his men, as they were
at first, when they thought them immortal; so thinking over all these
things, Cortez resolved upon a bold plan. He knew that if he could
get possession of Montezuma the people would be afraid to make
war on him; so, one day, he asked Montezuma into his quarters, and
then refused to let him go out again, saying that he would kill him if
the people should attack the Spaniards.
Cortez was now obliged to leave Mexico for a short time to oppose a
force that had been sent against him from Cuba. While he was gone,
Alvarado, the general he left in command, attacked the Mexicans
one day when they were celebrating a great feast, and killed five
hundred of their priests and leaders. The Aztecs became furious, and
attacked the palace where Alvarado and his men were, and they
would soon have conquered the Spaniards had not Cortez come
back just in time.
Cortez tried to make peace, but the Mexicans would not listen to
him. In a few days the fighting began all over the city, and the
streets were stained with the blood of tens of thousands. Then
Cortez compelled Montezuma to go upon the top of the palace, in
front of the great square, and ask his people to make peace with the
Spaniards. The Aztecs worshipped Montezuma as a god, and when
they saw him standing on the palace roof, they dropped their
weapons on the ground, and every head was bowed with reverence.
But when he asked them to make peace with the Spaniards, they
grew very angry and immediately began fighting again. Montezuma
was wounded twice by their arrows, which so alarmed the Aztecs,
that they stopped fighting again; but soon the battle re-commenced,
and in a few days Cortez was compelled to leave the city. In the
meantime, Montezuma had died in the Spanish camp; the Spaniards
had treated him kindly toward the end, and had nursed his wounds,

but he refused to take any food, and died at last from a broken
heart. Cortez now saw that there would have to be a great battle
fought, so he made ready his men. On the morning of the battle he
looked out from his camp and saw the Mexican soldiers extending as
far as the eye could reach; he trembled when he saw this great
army of men, knowing that his own troops were few, but he resolved
to conquer or die. Without giving his men time to think, he began to
attack the enemy; at first the Aztecs gave way, but others came in
their stead, for the whole valley was lined with armed Indians. The
Spaniards gave up hope, and prepared to die, but just then, Cortez
advanced to the Mexican standard-bearer and snatched the sacred
standard from his hand. The Mexicans believed that on this standard
depended the fate of every battle, and that if it were captured, there
was no use in fighting any longer. Cortez knew this, and when they
saw it in his hands, they threw down their arms and fled to the
mountains, and thus the Spaniards won the battle.
And so Cortez conquered Mexico, and all its vast wealth passed into
the hands of the Spaniards; its fertile valleys and rich plains, its
beautiful capital and prosperous villages, its great mines of gold and
silver, its thousands and thousands of inhabitants, all became the
property of the King of Spain, a man who cared nothing for the
conquered people, but thought only of the great wealth that had so
unjustly become his. The gold and silver mines of Mexico were then
the richest in the world, and the conquered Aztecs were obliged to
work in these mines as slaves, but the gold and silver was no longer
used to ornament their temples and palaces; it was sent across the
sea to Spain, who thought more of gold than she did of honor or
justice.
It was in the year 1521 that Cortez conquered Mexico, and for three
hundred years it was ruled by Spain; at the end of that time it
became again free. The Mexicans of to-day are partly Indians and
partly Spanish in race, but there are some who remember with pride
that they are the descendants of the ancient Aztecs, and they point
to the ruins of the great temples, which may still be seen in the new

Capital, as an instance of the wealth and power of their nation when
the Aztecs ruled from ocean to gulf, and when from mountain peak
to lowest valley every heart beat with pride in thinking of the glory
of the kingdom which Montezuma called his own.

CHAPTER XII.
P I Z A R R O A N D T H E C O N Q U E S T O F P E R U .
Francisco Pizarro was a little Spanish boy who was very poor and
very miserable. Living in a beautiful valley where the climate was
agreeable, and where one might gather grapes and chestnuts and
oranges at will, it might have been quite possible for him to be poor
and happy, too, but there were many things about Francisco's lot
that were harder to bear than poverty. Many other children dwelt in
this pleasant valley, some of them as poor and wretched and ragged
as Francisco, and others who were rich and well clothed and happy.
Not far from the little hut that was Francisco's home was a stately
castle, where a great duke lived, and the little boy would often go
and stand by the stone wall that enclosed the grounds, and wonder
how it would seem to live in that splendid mansion, and be allowed
to walk in its beautiful parks. Once in a while, when the gates were
opened to let in a crowd of gaily-dressed visitors, or when the duke,
at the head of a laughing party, went forth on a merry hunting
expedition, he would catch a glimpse of the velvet lawns and shady
trees and gorgeous flowers, and could see children dressed in dainty
garments, and sometimes wearing beautiful jewels, playing on the
grass or swinging under the trees. And Francisco would look and
look with eyes big with wonder till the gay party had passed and the
gates swung back in his face, and he was left out there in the dusty
road alone. And then he would turn and watch the hunting party
until the brilliant scene faded quite away in the distance, and he was

once more left alone. It always seemed to him that no matter how
gay or happy this bit of the world might seem, it always ended in his
being left outside of that gray stone wall, alone and hungry and
ragged, and that in fact these glimpses of another, happier life were
only after all just like his dreams, which were sure to fade away
when morning came. He could not help sighing sometimes and
wishing that the dream would go on for him just as it did for the
other children inside the stone wall. Once it did go on just a moment
or two, for one day as he stood dejectedly by the gates, they
opened, and a beautiful child came out who spoke to him kindly. He
was dressed in a suit of velvet, and his long hair fell in curls over his
shoulders, and in his cap was a little pearl ornament which fastened
a bird's wing. And Francisco, as he looked at the wing, thought he
had never in his life seen anything so wonderful, for the feathers
were soft like velvet, but glowed and burned in the sunlight like the
rubies in the ring on the child's hand.
He raised his hand and touched the lovely object, and the wearer of
the cap, being as kind-hearted as he was beautiful, began to tell
Francisco the story of the wing—how it had been given to him by a
great soldier, who had brought it from a long way off, farther than
he himself had ever been; farther than the mountains or the sea
even.
Francisco wondered at this, and when the child passed on he stood
still thinking a long time; it seemed so strange to hear that there
were other places and countries besides this quiet little valley where
he had always lived. Then he went back to his work, disagreeable
work it was, very, for he had to watch the swine and keep them
from straying off; but that night his dreams were brighter than ever,
for he dreamed that he had visited those strange lands that he had
heard of from the child, and that he had found enough treasures
there to make him rich and great. The morning came and the dream
was gone, but it left behind a thought that did not go away. And
always after the boy Francisco carried with him the resolve to make
his dream come true. But for many years there seemed no hope of

anything beyond the mean life he was living, and sometimes he
quite despaired. He was very proud and ambitious, too, and his
lowly lot in life seemed all the more bitter when he compared it with
that of the more fortunate boys who had good comfortable homes
and could go to school. He thought that he should have a good
home and go to school too, for his father was a man of wealth and
of good birth; but his mother was only a peasant, and it was with
her he had always lived, and the poor woman could not afford to
bring up her child in comfort, or even to have him taught to read
and write. And so Francisco grew to be a big boy, and still watched
the pigs from morning till night, and still sighed restlessly to get
away from his distasteful life, and find one fairer and nobler.
One day, when he was quite a big lad, a stranger came to the little
valley; he was an old, weather-beaten sailor, and had sailed across
distant seas and journeyed through many strange lands, and at
night, when the peasant boys were through with their day's work,
they all gathered around him and listened to his tales of the great
world that lay beyond the mountains that shut in their quiet little
valley, just as the stone wall shut in the duke's palace.
Francisco listened with the others, but his heart beat wildly, for, as
the old man talked, it seemed that he was again in the land of his
dreams. And no wonder, for the sailor's stories were very wonderful
and quite true, for he was one of the men that sailed across the
ocean with Columbus on his first great voyage. He had seen with his
own eyes that far-off, beautiful land, where the air was always soft
as the spring in the valleys, and where the flowers bloomed forever,
and the trees bore delicious fruits; he had heard the reports of its
mountains of gold and mines of precious stones, and rivers whose
waves tossed gleaming pearls upon the beach. And it was all true,
and all this wealth and beauty lay there waiting for bold hearts and
brave hands to claim and keep, for the people of that far country
were only poor savages, knowing nothing of the value of the gold
and gems they wore, and were so ignorant that they thought the

Spaniards were the children of some great god, and were ready to
fall down and worship their beauty and strength and courage.
And the old man talked till the stars came out, and the moon had
climbed far up the sky, for never before had there been told such
wonderful news as this, for all the stories of the fabulous wealth of
the East had come true at last, and no one could doubt any more.
By and by, as the days passed, the sailor told other stories of other
countries, where the soldiers of Spain were winning great victories,
and although his words were forgotten by most of the boys, yet
Francisco and one or two others thought of them often and
pondered over them, and thought what a fine thing it must be to be
a soldier fighting for honor and glory. And as time went on they
talked more and more about this, and at last they resolved to leave
their old miserable life behind them forever, and go out into the
world and seek their fortune. But they had to be very careful and
secret, for they meant to run away; the summer was gone and the
autumn had come to the valley before the three boys found a
chance to carry out their plan, and one morning when Francisco and
his friends were called to go to their distasteful work, they did not
answer, for they were far on their way up the mountains, and had
said farewell to the valley forever. It was pleasant travelling through
the hospitable country roads, and after they had gone so far that
they had no fear of being overtaken, they went on merrily enough.
Francisco's heart was the lightest and bravest. He had most detested
his old life, and now he most rejoiced that it was past.
So the boys journeyed on and crossed the mountains and passed
through the fertile valleys and then climbed other mountains, and
everywhere the kind country folk gave them food and drink and
shelter, and the young travellers thought they had never had grapes
and chestnuts and goat's milk taste as good before, as they ate and
drank under the trees by the road-side or in some peasant's cottage;
and by and by the journey was over, and they were in Seville. And
now the runaways found they were out in the world indeed. No one
in all that great, splendid city cared in the least whether they lived or

died, whether they suffered from hunger or thirst, or whether they
had a place to lay their heads at night. But they kept brave hearts,
got what they could to eat, slept where they could at night, and
spent the days in wandering through the streets and getting
acquainted with the life of a great city. And although they were not
sure where bread and cheese were to come from and where they
were to lie down at night, still the wonderful sights of this new life,
the magnificent houses, splendid palaces, costly dresses, and, above
all, the companies of mounted soldiers that were continually
parading the streets, all drove thoughts of home from their minds,
and they did not regret in the least that they had exchanged the
village of Truxillo for the glitter and show of Seville.
In a few days Francisco decided that he would join the army and go
to Italy, where the Spaniards were then fighting, and as the king
wanted all the soldiers he could get, and as he was large and well
developed for his age, he had no trouble in enlisting in one of the
regiments, and when he put on the gaudy uniform and began to live
in camp, he felt, indeed, that his old life was over and that Francisco
Pizarro was quite a different person from the ragged little urchin that
tended pigs at Truxillo.
But there was one sad thing about it, and that was the parting from
his two friends, for Pizarro's regiment sailed very soon for Italy, and
it was with great sorrow that he said farewell to the two companions
who had shared the excitement and danger of his escape from
home. However, the noise of war soon drove sad thoughts from his
mind, and so eagerly did he enter into his new life that he soon
became one of the best soldiers in the regiment, and so renowned
for bravery that by the time the war was over and the army ready to
return to Spain he had been made a lieutenant. This only made him
more ambitious, and as he found life in the city very stupid for the
next few years, because there was no fighting to be done, he was
very glad when he heard one day that a great expedition was to be
sent out to America, and that any one who was brave and daring
might join it and so have a chance of gaining riches and fame. He

hastened to Cadiz at once, and as his courage and bravery were well
known, had no trouble in being made one of the company; and
when, in a few days, the ships left Cadiz and started on their long
voyage across the Atlantic, Pizarro thought with great joy that he
was on his way to those strange lands at last, and that perhaps his
old dreams might come true.
The voyage was a stormy one, but at last they came safely to
Hispaniola, and there Pizarro learned, what all newly-arrived
Spaniards were not slow to learn, that of all restless, roving lives,
those of Spanish adventurers were the most so. They were never
content to remain in one place, but went hither and thither in their
mad search for gold, always hoping to find something better, and
always ready to risk their lives for the sake of bettering their
fortunes. And so, no sooner had Pizarro become a little acquainted
with the country at Hispaniola than he straightway caught the mad
fever for moving on to some new place; and as there were constant
reports of the wealth of the countries of Central America and Mexico,
he decided that those places would suit him better than Hispaniola,
and he accepted an offer to go to Darien, meaning to explore the
country and see for himself what riches it contained.
At that time Balboa was also living in Darien, and Pizarro was one of
the company who went with him across the isthmus to discover the
Pacific. In this expedition Pizarro noted the country well, and was
rejoiced to see the gold and gems which were bestowed upon him
by the friendly chiefs, and when he returned to Darien he was very
willing to become the leader of an expedition that the governor of
the colony was fitting out, to conquer lands on the Pacific. The party
reached the ocean in safety, and Pizarro immediately resolved to get
all the treasure he could before any other Spaniards should have a
chance to come there. On his former visit he had heard from the
natives that there were great quantities of pearls to be found on
some islands lying out from the land, and now he at once called part
of his men together, and leaving the rest on the shore, started out in
canoes to reach the islands. The sea was heavy, and the canoes

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