#LyX 2.2 created this file. For more info see http://www.lyx.org/
\lyxformat 508
\begin_document
\begin_header
\save_transient_properties true
\origin unavailable
\textclass SimpleTTUThesis
\begin_preamble

\end_preamble
\use_default_options true
\master ThesisTemplate.lyx
\begin_modules
theorems-ams
theorems-ams-extended
\end_modules
\maintain_unincluded_children false
\language english
\language_package default
\inputencoding auto
\fontencoding global
\font_roman "palatino" "default"
\font_sans "default" "default"
\font_typewriter "default" "default"
\font_math "auto" "auto"
\font_default_family default
\use_non_tex_fonts false
\font_sc false
\font_osf false
\font_sf_scale 100 100
\font_tt_scale 100 100
\graphics default
\default_output_format default
\output_sync 0
\bibtex_command default
\index_command default
\paperfontsize 12
\spacing single
\use_hyperref false
\papersize default
\use_geometry true
\use_package amsmath 1
\use_package amssymb 1
\use_package cancel 1
\use_package esint 1
\use_package mathdots 1
\use_package mathtools 1
\use_package mhchem 1
\use_package stackrel 1
\use_package stmaryrd 1
\use_package undertilde 1
\cite_engine basic
\cite_engine_type default
\biblio_style plain
\use_bibtopic false
\use_indices false
\paperorientation portrait
\suppress_date false
\justification true
\use_refstyle 0
\branch answers
\selected 1
\filename_suffix 0
\color #5555ff
\end_branch
\index Index
\shortcut idx
\color #008000
\end_index
\leftmargin 0.9in
\topmargin 0.75in
\rightmargin 0.9in
\bottommargin 0.75in
\secnumdepth 3
\tocdepth 3
\paragraph_separation skip
\defskip medskip
\quotes_language english
\papercolumns 1
\papersides 1
\paperpagestyle default
\tracking_changes false
\output_changes false
\html_math_output 0
\html_css_as_file 0
\html_be_strict false
\end_header

\begin_body

\begin_layout Chapter
Introduction
\end_layout

\begin_layout Standard
Lyx lets you create and view equations like 
\begin_inset Formula $E=mc^{2}$
\end_inset


\begin_inset space ~
\end_inset


\begin_inset CommandInset citation
LatexCommand cite
key "Einstein1905"

\end_inset


\begin_inset space ~
\end_inset

in an almost wysisyg fashion.
 The citation for this equation was input with the Insert/Citation menu
 item.
 The bibliographic information for the paper is in the 
\family typewriter
.bib
\family default
 file.
 
\end_layout

\begin_layout Standard
Naturally you can create displayed equations like
\begin_inset Formula 
\[
K_{ij}=\int_{\Omega}\kappa\left(\mathbf{x}\right)\nabla\phi_{i}\left(\mathbf{x}\right)\cdot\nabla\phi_{j}\left(\mathbf{x}\right)\,d\Omega
\]

\end_inset

as well.
 
\end_layout

\begin_layout Standard
Some nomenclature: a three-letter acronym (
\begin_inset CommandInset nomenclature
LatexCommand nomenclature
symbol "TLA"
description "TLA"

\end_inset

TLA) is an acronym consisting of three letters.
 Examples of TLA include FBI, CIA, ERT, and TLA.
 
\end_layout

\begin_layout Standard
Marginal notes can be used to highlight editing suggestions.
 However, they should be removed before submitting the final draft.
 Other notes can be includes in the text body, but greyed out: 
\begin_inset Note Greyedout
status open

\begin_layout Plain Layout
like this one.
\end_layout

\end_inset

 
\begin_inset Marginal
status open

\begin_layout Plain Layout

\size footnotesize
This margin is too small to contain our simplified proof of Wiles' theorem.
\end_layout

\end_inset


\end_layout

\begin_layout Section
Some good prose
\end_layout

\begin_layout Standard
In the second century of the Christian era, the Empire of Rome comprehended
 the fairest part of the earth, and the most civilised portion of mankind.
 The frontiers of that extensive monarchy were guarded by ancient renown
 and disciplined valour.
 The gentle but powerful influence of laws and manners had gradually cemented
 the union of the provinces.
 Their peaceful inhabitants enjoyed and abused the advantages of wealth
 and luxury.
 The image of a free constitution was preserved with decent reverence: the
 Roman senate appeared to possess the sovereign authority, and devolved
 on the emperors all the executive powers of government.
 During a happy period (A.D.
 98-180) of more than fourscore years, the public administration was conducted
 by the virtue and abilities of Nerva, Trajan, Hadrian, and the two Antonines.
 It is the design of this, and of the two succeeding chapters, to describe
 the prosperous condition of their empire; and afterwards, from the death
 of Marcus Antoninus, to deduce the most important circumstances of its
 decline and fall; a revolution which will ever be remembered, and is still
 felt by the nations of the earth.
\end_layout

\begin_layout Standard
The principal conquests of the Romans were achieved under the republic;
 and the emperors, for the most part, were satisfied with preserving those
 dominions which had been acquired by the policy of the senate, the active
 emulation of the consuls, and the martial enthusiasm of the people.
 The seven first centuries were filled with a rapid succession of triumphs;
 but it was reserved for Augustus to relinquish the ambitious design of
 subduing the whole earth, and to introduce a spirit of moderation into
 the public councils.
 Inclined to peace by his temper and situation, it was easy for him to discover
 that Rome, in her present exalted situation, had much less to hope than
 to fear from the chance of arms; and that, in the prosecution of remote
 wars, the undertaking became every day more difficult, the event more doubtful,
 and the possession more precarious, and less beneficial.
 The experience of Augustus added weight to these salutary reflections,
 and effectually convinced him that, by the prudent vigour of his counsels,
 it would be easy to secure every concession which the safety or the dignity
 of Rome might require from the most formidable Barbarians.
 Instead of exposing his person and his legions to the arrows of the Parthians,
 he obtained, by an honourable treaty, the restitution of the standards
 and prisoners which had been taken in the defeat of Crassus.
 
\end_layout

\begin_layout Standard
His generals, in the early part of his reign, attempted the reduction of
 Ethiopia and Arabia Felix.
 They marched near a thousand miles to the south of the tropic; but the
 heat of the climate soon repelled the invaders, and protected the unwarlike
 natives of those sequestered regions.
 The northern countries of Europe scarcely deserved the expense and labour
 of conquest.
 The forests and morasses of Germany were filled with a hardy race of barbarians
, who despised life when it was separated from freedom; and though, on the
 first attack, they seemed to yield to the weight of the Roman power, they
 soon, by a signal act of despair, regained their independence, and reminded
 Augustus of the vicissitude of fortune.
 On the death of that emperor, his testament was publicly read in the senate.
 He bequeathed, as a valuable legacy to his successors, the advice of confining
 the empire within those limits, which Nature seemed to have placed as its
 permanent bulwarks and boundaries; on the west the Atlantic ocean; the
 Rhine and Danube on the north; the Euphrates on the east; and towards the
 south, the sandy deserts of Arabia and Africa.
\end_layout

\begin_layout Standard
Happily for the repose of mankind, the moderate system recommended by the
 wisdom of Augustus, was adopted by the fears and vices of his immediate
 successors.
 Engaged in the pursuit of pleasure, or in the exercise of tyranny, the
 first Caesars seldom showed themselves to the armies, or to the provinces;
 nor were they disposed to suffer, that those triumphs which their indolence
 neglected should be usurped by the conduct and valour of their lieutenants.
 The military frame of a subject was considered as an insolent invasion
 of the Imperial prerogative; and it became the duty, as well as interest,
 of every Roman general, to guard the frontiers intrusted to his care, without
 aspiring to conquests which might have proved no less fatal to himself
 than to the vanquished barbarians.
\end_layout

\begin_layout Standard
The only accession which the Roman empire received, during the first century
 of the Christian era, was the province of Britain.
 In this single instance the successors of Caesar and Augustus were persuaded
 to follow the example of the former, rather than the precept of the latter.
 The proximity of its situation to the coast of Gaul seemed to invite their
 arms; the pleasing, though doubtful intelligence, of a pearl fishery, attracted
 their avarice; and as Britain was viewed in the light of a distinct and
 insulated world, the conquest scarcely formed any exception to the general
 system of continental measures.
 After a war of about forty years, undertaken by the most stupid, maintained
 by the most dissolute, and terminated by the most timid of all the emperors,
 the far greater part of the island submitted to the Roman yoke.
 The various tribes of Britons possessed valour without conduct, and the
 love of freedom without the spirit of union.
 They took up arms with savage fierceness; they laid them down, or turned
 them against each other with wild inconstancy; and while they fought singly,
 they were successively subdued.
 Neither the fortitude of Caractacus, nor the despair of Boadicea, nor the
 fanaticism of the Druids, could avert the slavery of their country, or
 resist the steady progress of the Imperial generals, who maintained the
 national glory, when the throne was disgraced by the weakest, or the most
 vicious of mankind.
 At the very time when Domitian, confined to his palace, felt the terrors
 which he inspired; his legions, under the command of the virtuous Agricola,
 defeated the collected force of the Caledonians at the foot of the Grampian
 hills; and his fleets, venturing to explore an unknown and dangerous navigation
, displayed the Roman arms round every part of the island.
 The conquest of Britain was considered as already achieved; and it was
 the design of Agricola to complete and ensure his success by the easy reduction
 of Ireland, for which in his opinion, one legion and a few auxiliaries
 were sufficient.
 The western isle might be improved into a valuable possession, and the
 Britons would wear their chains with the less reluctance, if the prospect
 and example of freedom were on every side removed from before their eyes.
\end_layout

\begin_layout Standard
But the superior merit of Agricola soon occasioned his removal from the
 government of Britain; and for ever disappointed this rational, though
 extensive scheme of conquest.
 Before his departure, the prudent general had provided for security as
 well as for dominion.
 He had observed that the island is almost divided into two unequal parts
 by the opposite gulfs, or, as they are now called, the Firths of Scotland.
 Across the narrow interval of about forty miles, he had drawn a line of
 military stations, which was afterwards fortified in the reign of Antoninus
 Pius, by a turf rampart erected on foundations of stone.
 This wall of Antoninus, at a small distance beyond the modern cities of
 Edinburgh and Glasgow, was fixed as the limit of the Roman province.
 The native Caledonians preserved in the northern extremity of the island
 their wild independence, for which they were not less indebted to their
 poverty than to their valour.
 Their incursions were frequently repelled and chastised; but their country
 was never subdued.
 The masters of the fairest and most wealthy climates of the globe turned
 with contempt from gloomy hills assailed by the winter tempest, from lakes
 concealed in a blue mist, and from cold and lonely heaths, over which the
 deer of the forest were chased by a troop of naked barbarians.
\end_layout

\begin_layout Standard
The blue-painted barbarians of pre-Roman Britain were probably more sophisticate
d than Claudius and Nero imagined, and some may have known of the famous
 numbers 
\begin_inset Formula $\pi$
\end_inset

 and 
\begin_inset Formula $\phi$
\end_inset

 listed in table
\begin_inset space ~
\end_inset


\begin_inset CommandInset ref
LatexCommand ref
reference "tab:silly"

\end_inset

.
 I doubt, however, that either they or their Roman conquerors realized the
 relevance of these numbers to the chucking of wood and blowing of wind,
 as that relevance was simply imagined on the spot to give us something
 to put in the table.
 The table is listed in the list of tables.
\begin_inset Separator latexpar
\end_inset


\end_layout

\begin_layout Standard
\noindent
\align center
\begin_inset Float table
placement H
wide false
sideways false
status open

\begin_layout Plain Layout
\noindent
\align center
\begin_inset Caption Standard

\begin_layout Plain Layout
\begin_inset CommandInset label
LatexCommand label
name "tab:silly"

\end_inset

Some questions with important numbers as silly answers.
\end_layout

\end_inset


\begin_inset Tabular
<lyxtabular version="3" rows="3" columns="2">
<features tabularvalignment="middle">
<column alignment="center" valignment="top">
<column alignment="center" valignment="top">
<row>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
Question
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
Answer
\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
Wood chucked by a woodchuck, would that a woodchuck could chuck wood.
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset Formula $\pi$
\end_inset


\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
Roads walked down by a man before we call him a man.
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset Formula $\frac{\sqrt{5}-1}{2}$
\end_inset


\end_layout

\end_inset
</cell>
</row>
</lyxtabular>

\end_inset


\end_layout

\end_inset


\end_layout

\begin_layout Section
Yet more good prose
\end_layout

\begin_layout Standard
To understand Plato, and indeed many later philosophers, it is necessary
 to know something of Sparta.
 Sparta had a double effect on Greek thought: through the reality, and through
 the myth.
 Each is important.
 The reality enabled the Spartans to defeat Athens in war; the myth influenced
 Plato's political theory, and that of countless subsequent writers.
 The myth, fully developed, is to be found in Plutarch's Life of Lycurgus
 the ideals that it favours have had a great part in framing the doctrines
 of Rousseau, Nietzsche, and National Socialism.
 1 The myth is of even more importance, historically, than the reality ;
 nevertheless, we will begin with the latter.
 For the reality was the source of the myth.
 
\end_layout

\begin_layout Standard
Laconia, of which Sparta, or Lacedacmon was the capital, occupied the south-east
 of the Peloponnesus.
 The Spartans, who were the ruling race, had conquered the country at the
 time of the Dorian invasion from the north, and had reduced the population
 that they found there to the condition of serfs.
 These serfs were called helots.
 In historical times, all the land belonged to the Spartans, who, however,
 were forbidden by law and custom to cultivate it themselves, both on the
 ground that such labour was degrading, and in order that they might always
 be free for military service.
 The serfs were not bought and sold, but remained attached to the land,
 which was divided into lots, one or more for each adult male Spartan.
 These lots, like the helots, could not be bought or sold, and passed, by
 law, from father to son.
 (They could, however, be bequeathed.) The landowner received from the helot
 who cultivated the lot seventy medirnni (about 105 bushels) of grain for
 himself, twelve for his wife, and a stated portion of wine and fruit annually.
 Anything beyond this amount was the property of the helot.
 The helots were Greeks, like the Spartans, and bitterly resented their
 servile condition.
 When they could, they rebelled.
 The Spartans had a body of secret police to deal with this danger, but
 to supplement this precaution they had another: once a year, they declared
 war on the helots, so that their young men could kill any who seemed insubordin
ate without incurring the legal guilt of homicide.
 Helots could be emancipated by the State, but not by their masters; they
 were emancipated, rather rarely, for exceptional bravery in battle.
 
\end_layout

\begin_layout Standard
At some time during the eighth century B.C.
 the Spartans con- quered the neighbouring country of Messenia, and reduced
 most of its inhabitants to the condition of helots.
 There had been a lack of Lebensraum in Sparta, but the new territory, for
 a time, removed this source of discontent.
 
\end_layout

\begin_layout Standard
Lois were for the common run of Spartans; the aristocracy had estates of
 their own, whereas the lots were portions of common land assigned by the
 State.
 
\end_layout

\begin_layout Standard
The free inhabitants of other parts of Laconia, called 
\begin_inset Quotes eld
\end_inset

prioeci
\begin_inset Quotes erd
\end_inset

 had no share of political power.
 
\end_layout

\begin_layout Standard
The sole business of a Spartan citizen was war, to which he was trained
 from birth.
 Sickly children were exposed after inspection by the heads of the tribe;
 only those judged vigorous were allowed to be reared.
 Up to the age of twenty, all the boys were trained in one big school; the
 purpose of the training was to make them hardy, indifferent to pain, and
 submissive to discipline.
 There was no nonsense about cultural or scientific education; the sole
 aim was to produce good soldiers, wholly devoted to the State.
 
\end_layout

\begin_layout Standard
At the age of twenty, actual military service began.
 Marriage was permitted to anyone over the age of twenty, but until the
 age of thirty a man had to live in the "men's house," and had to manage
 his marriage as if it were an illicit and secret affair.
 After thirty, he was a full-fledged citizen.
 Every citizen belonged to a mess, and dined with the other members; he
 had to make a contribution in kind from the produce of his lot.
 It was the theory of the State that no Spartan citizen should be destitute,
 and none should be rich.
 Each was expected to live on the produce of his lot, which lie could not
 alienate except by free gift.
 None was allowed to own gold or silver, and the money was made of iron.
 Spartan simplicity became proverbial.
 
\end_layout

\end_body
\end_document
