The Elements of Euclid in Greek and Latin

I was trying to parse my way through an edition of The Elements in Greek and Latin:

https://archive.org/details/euclidisoperaomn01eucluoft/page/x

The name of The Elements in Ancient Greek is:

Στοιχει̃a

or, when transliterated:

Stoicheĩa

.

The Ancient-Greek word, τὰ στοιχει̃α or, when transliterated ‘tà stoicheĩa,’ is a plural form of the 2nd-declension neuter verb, τὸ στοιχει̃ον genitive: του̃ στοιχείου or, when transliterated: ‘tò stoicheĩon,’ genitive: ‘toũ stoicheíou.’

The Ancient-Greek word, ‘tò stoicheĩon,’ can mean ‘an element in a set.’

Figure 1: The elements of this set are alpha, beta, gamma and delta.

The Ancient-Greek word, ‘tò stoicheĩon,’ is formed from the Ancient-Greek masculine noun, ὁ στοι̃χος genitive: του̃ στοίχου or, when transliterated, ‘ho stoĩchos,’ genitive: ‘toũ stoíchou,’ which means ‘steps,’ or ‘a flight of stairs;’ and the Ancient-Greek 2nd-declension neuter nominal suffix, ‘-eĩon,’ genitive: ‘-eíou’ which denotes ‘a means (of),’ ‘an instrument of;’ etc.

Figure 2: a ‘stoĩchos’ or ‘series of steps.’

The term, ‘stoĩchos,’ according to Wiktionary, may be traced back to the indo-european word:

*steigʰ

, which means:

‘climb.’

Hence, etymologically, the Ancient-Greek term, ‘stoicheĩa,’ can be said to mean: ‘the means of climbing up;’ ‘the means of stepping up;’ ‘the means of ascent;’ etc.

This is highly instructive, as, in truth, Elements is a book that is a Jacob’s ladder, of sorts, by which one can ascend, element by element, into the heavens of mathematical knowledge.

Figure 3: With The Elements of Euclid, we advance in our mathematical knowledge element by element. Each element is, conceptually, like a rung, heaving us upwards to Mathematical prowess; to an implicit knowledge of Euclidean Geometry.

Operator Precedence in Arithmetic

The Microsoft Word version of this blogpost. (.docx)

The PDF version of this blogpost. (.pdf)

Introduction:

Conventional Arithmetic possesses rules for the order of operations. Which operations ought we to evaluate first? In what order ought we to evaluate operations? This is the topic that this chapter wishes to address. ‘Precedence,’ is also sometimes referred to as ‘the order of operations.’

Body:

The Etymological Definition of ‘Precedence:’

Our English noun, ‘precedence,’ is derived from the Latin substantive participle, ‘praecēdentia.’^[3] ‘Praecēdentia,’ in Latin, means ‘the abstract concept of which things go before [other things].’

Figure 2: The English arithmetical term, ‘precendence,’ is derived from a compund of the Latin verb ‘cēdēre,’ which means ‘to go.’ Go, or Golang, as a language, is—syntactically—very like the C Programming Language.

Within the context of Arithmetic, ‘precedence,’ etymologically, means ‘the science of determining which operations go before [other operations];’ ‘the science of determining which operations should be evaluated before [other operations].

The Acronym, ‘P.E.M.D.A.S:’

The acronym, ‘P.E.M.D.A.S.,’ stands for:

1. Parenthesis;
2. Exponentiation;
3. Multiplication and Division;
4. Addition and Subtraction.

The Acronym, ‘P.E.M.D.A.S.,’ can be easily remembered with the Mnemonic phrase:

‘Please Excuse My Dear Aunt Sally.’^[4]

Levels of Precedence:

As we can observe from the above ordered list, some operations share the same level of precedence. For example, the operation, multiplication, and the operation, division, have the same level of precedence. Multiplication and Division share the third level of precedence, in the above list. When we are confronted with an expression or an equation that contains operations at the same level of precedence, seeing that in Anglophone countries, we read from left to right, then we evaluate operations that possess the same level of precedence from left to right. Hence, when two or more operations—within an equation or an expression—share the same level of precedence, then we evaluate them from left to right. Concerning operations at the same level of precedence, we evaluate from beginning at the leftmost operation, and work our way rightwards.

An Example of Precedence:

In the expression:

2 ÷ 1 + 3 × 4² – 5 + ( 3 – 2 )

, we first evaluate the operation in parenthesis, i.e.:

( 3 – 2 )

. When we evaluate:

( 3 – 2 )

, then we obtain the difference:

1

.

This renders the original expression as:

2 ÷ 1 + 3 × 4² – 5 + ( 1 )

or as:

2 ÷ 1 + 3 × 4² – 5 + 1

.

Second, we evaluate the exponentiation operation i.e.:

4²

. When we evaluate:

4²

, then this obtains for us the power:

16

. This renders our original expression as:

2 ÷ 1 + 3 × 16 – 5 + 1

.

The operations, Multiplication and Division, share the same level of precedence. However, given that the division operation is further to the left, on the page, than the multiplication operation, then we evaluate the division operation before we evaluate the multiplication operation.

Given that the division operation:

2 ÷ 1

is further to the left, on our page than the multiplication operation:

3 × 16

, then we evaluate:

2 ÷ 1

before we evaluate:

3 × 16

.

When we evaluate:

<!–

2\div1

–>

2 ÷ 1

, then we obtain the quotient:

2

. This renders our original expression as:

2 + 3 × 16 – 5 + 1

. Then we proceed to evaluate:

3 × 16

, and this obtains for us the product:

48

. This renders our original expression as:

2 + 48 – 5 + 1

.

The operations; addition, and subtraction; share the same level of precedence. In the above ordered list, they are at the 4^th level of precedence. We evaluate these operations as we should find them, beginning at the leftmost, and working our way rightward. Hence, we evaluate:

2 + 48

first. This obtains for us the sum:

50

. This renders our original expression as:

50 – 5 + 1

. We then proceed to evaluate the operation:

50 – 5

, which obtains for us the difference:

45

. This renders our original expression as:

45 + 1

. We then proceed to evaluate the expression:

45 + 1

. This obtains for us the sum:

46

.
This renders our original expression as:

46

. We have thus simplified the expression:

2 ÷ 1 + 3 × 4² – 5 + ( 3 – 2 )

to:

46

. We have observed mathematical precedence οr the order of operations in our simplification of the expression:

<!–

2 \div 1 + 3 \times 4² – 5 + \left ( 3 – 2 )

–>

2 ÷ 1 + 3 × 4² – 5 + ( 3 – 2 )

to:

46

.

Conclusion:

In this chapter, we have endeavoured to gain for ourselves an implicit understanding of precedence as it pertains to basic or conventional arithmetic. Boolean arithmetic, an arithmetic of logic employed in Computer Science, also possesses precedence or an order of operations, which we shall examine in a subsequent chapter. In the next chapter, we shall examine precedence or the order of operations as it specifically applies to the C programming language.

---

Footnotes:

^[1] The Etymology of the English mathematical term, ‘arithmetic,’ is as follows. The English adjective, ‘arithmetic,’ is derived from the Latin 1^st-and-2^nd-declension adjective, ‘arithmētica, arithmēticus, arithmēticum.’ Further, the Latin adjective, ‘arithmēticus,’ is derived from the Ancient-Greek phrase, ἀριθμητικὴ τέξνη or, when transliterated, ‘arithmētikḕ téchne,’ which means ‘the art of counting;’ ‘the skill of counting;’ ‘the science of counting.’ ὁ ἀριθμός genitive: τοῦ ἀριθμοῦ, or—when transliterated: ‘ho arithmós,’ genitive: ‘toũ arithmoũ,’—is a 2nd-declension Ancient-Greek noun that means ‘number,’ ‘numeral,’ Cf. ‘ἀριθμός#Ancient_Greek,’ Wiktionary (last modified: 7^th September 2018, at 17:57.), https://en.wiktionary.org/wiki/ἀριθμός#Ancient_Greek , accessed 29th April 2019.^[2] Cf. ‘arithmetic,’ Wiktionary (last modified: 25th April 2019, at 04:45.), https://en.wiktionary.org/wiki/arithmetic, accessed 29th April 2019.

^[3] ‘praecedēntia’ is the nominative neuter plural of the participle, ‘praecedēns,’ which means ‘going before.’ The form, ‘praecedēntia,’ means ‘those things going before;’ ‘the concept of things going before.’ We shall metamorphose ‘praecedēntia’ into a 1st-declension feminine noun that means ‘precedence.’ ‘praecedēntia’ genitive singular: ‘praecēdentiae,’ is a 1st-declension feminine noun that means ‘precedence.’ ‘praecēdentiae,’ can be further broken down into the preposition, ‘prae,’ which means ‘before;’ and the 3rd-conjugation verb, ‘cēdō, cēdere, cessī, cessum,’ which means ‘to go,’ and the Latin 1st-declension feminine nominative nominal suffix, ‘-ia,’ genitive: ‘-iae,’ which, in this instance, denotes ‘a noun formed from a present-participle stem.’ Hence, the etymological definition of ‘precedence’ is ‘the concept of things going before [other things].’ Within the context of arithmetic, the etymological definition of ‘precedence is ‘the concept of operations being evaluated before other operations.’ Cf. ‘praecedentia,’ Wiktionary (last modified on 9^th September 2013, at 02:28.), accessed on 1^st May 2019. Cf. ‘praecedens,’ Wiktionary (last modified on 11^th November 2016, at 16:40.) https://en.wiktionary.org/wiki/praecedens#Latin, accessed on 1^st May 2019.

^[4] Stapel, Elizabeth, ‘The Order of Operations: PEMDAS,’ Purple Math (2019), http://www.purplemath.com/modules/orderops.htm, accessed on the 1^st May 2019.

Wire-Framing Websites and Apps in Inkscape and Scripted SVG:

Figure 1: I drew this HTML logo in Scripted SVG. My development skills, especially my ability to develop web images through code, is really beginning to rise to a professional standard.

Figure 2: I mocked up this old website, phouka.com for an e-book that I am putting the finishing touches to, and hope to release upon Amazon, shortly. This website, developed in 2005, employs a pre-html-5 table layout which is now deprecated. Today, the downloading of fonts by a web-accessor is no longer required thanks to @fontface .

Figure 3: I drew this Swift Logo – the Programming Language employed by Apple – in Vector software such as Vector Magic and Inkscape. Apps can be mocked up in Inkscape so as to give the customer a sense of what his/her app’s user experience/ graphical user interface might look like, prior to the app’s development commencing in earnest.

If anyone should require mockups of apps or websites prior to taking this wireframe to a professional website-developer/app-programmer, let me know. Send me a direct message, or something. The advantage of doing this in SVG, is that one can then employ the SVG code and the CSS code generated by Inkscape in the website/app itself.

The Ancient-Greek word for ‘bone.’

Figure 1: I drew this bone in inkscape.

τὸ οστέον Genitive: τοῦ οστέου ‘tò ostéon’ Genitive: ‘toû ostéou.’ The Ancient-Greek word for ‘bone.’ We derive the medical prefix ‘osteo-‘ from this. ‘osteoarthritis’ for instance is an inflammation of the joints caused by an inflammation of the bones at the joint. Learning Greek makes one better able to understand and remember biological terms.

Oxford

Figure 1:  Oxford University Press.  I drew this logo in inkscape.  You may view the Vector file of the above-depicted image at my at my Codepen Account.

Figure 2:   I drew this book cover in Scripted SVG. Currently, I am learning the Oxford Style. As it is, I have an extremely high daily word-count. Were I to translate what I write already into professional academic papers, then I would be able to obtain a degree without too much effort. I also wish to very shortly begin to publish Epubs on Amazon Kindle. You may view the Vector file of the above-depicted image at my Codepen Account.

Oxford’s motto is

‘Dominus Illuminatio Mea’

. This is Latin for:

‘The Lord is my enlightenment.’

This motto comes from Psalm 26/27^[1]:

‘
1. Psalmus Dāvīd priusquam linīrētur.

Dominus illūminātiō mea et salūs mea, quem timēbō?
Dominus prōtector vītae meae, ā quō trepidābō?’

^[2]

Clementine Vulgate. (1861)

‘{a Pſalme of David.} The Lord is my light, and my ſaluation, whome ſal I feare? the Lord is the ſtrength of my life, of whō^[3] ſall I be afraid?’

King James Version. (1611)

‘{A Psalm of David.} The LORD is my light and my salvation; whom shall I fear? the LORD isthe strength of my life; of whom shall I be afraid?’

King James Version. (1769)

Graduates of Oxford may place the post-nominal suffix, ‘oxon.’ after their names. This is short for ‘Ūniversitās Oxoniēnsis’ or ‘the University of Oxford.’

Figure 3: The 1769 Oxford Standard Text is one of the variations of the KJV in use today.

---

^[1] The 1610 Dovvay Rheims numbers this psalm as Psalme 26:

‘Ovr Lord is my illumination, and my ſalvation, whom shall I feare?
Our Lord is the protec͡tour of my life, of whom shal I be afrayd?’

The KJV translation committee criticised the Dovvay Rheims fathers for transliterating too many Latin words, like ‘illuminatio’ into ‘illumination,’ instead of properly translating them into ‘enlightenment’ or ‘light,’ as the King-James translation committee did. Protestants often criticise the use of ‘Our’ as well in this edition of the Bible. In the Hebrew, the Tetragrammaton has no possessive. The KJV translators speak thus of the (1610 and earlier) Dovvay Rheims.:

“…as also on the other side we have shunned the obscurity of the Papists, in their Azimes, Tunike, Rational, Holocausts, Praepuce, Pasche, and a number of such like, whereof their late Translation is full, and that of purpose to darken the sense, that since they must needs translate the Bible, yet by the language thereof, it may be kept from being understood. But we desire that the Scripture may speak like itself, as in the language of Canaan, that it may be understood even of the very vulgar.”

My own view, for what it is worth is that the KJV and the 1610 Dovvay Rheims are both equally charming, but for different reasons. The 1610 Dovvay Rheims, its being a more-or-less formal equivalence translation of the Latin Vulgate, is a great tool for learning Latin.

^[2]Scanned reprint of the Carolus Vercellone edition. BIBLIA SACRA VVLGATAE EDITIONIS SIXTI V. ET CLEMENTIS VIII. PONTT. MAXX. IVSSV RECOGNITA ATQVE EDITA ROMAE TYPIS S. CONGREGATIONIS DE PROPAGANDA FIDE ANNO MDCCCLXI. Psalm 26. p.347

^[3] This scribal abbreviation, a macron placed over the ‘o’ represents an ‘m.’

Esse est Perspicī: to be is to be perceived:

Figure 1:  “Of infinite scope.”  I drew this in Inkscape.

Figure 2:  ‘ho skopós’ in Ancient Greek is whence we derive the programming term, ‘scope.’

At present, I am writing an article on ‘scope’ as it pertains to programming.  I am going to try to explain it with Berkeley’s:

“esse est perspicī;”

which means:

“to be is to be percieved.”

, which some suggest to be a foreshadow of  the scientific phenomenon known as:

“quantum observation.”

How far can the quantum observer, as regards the world or universe of the program see, as regards a variable’s declaration and initialisation?

If the quantum observer can see all things; perceive all things; like the omnivident ^[1] “watcher” portrayed in Figure 1, then the variable is said to be of global scope.

However, as regards the world or universe of the program; should the quantum observer be a little myopic; should his field of perception be limited to a function or an object or some other code block, then the variable in question is said to be of local scope.

---

^[1]  I invented this theological term, as it is convenient.  It describes the ability of a deity to see all things.  From the Latin adjective, ‘omnis,’ which means ‘all;’ and the Latin 2nd-conjugation verb, ‘videō,’ which means ‘I see.’  Incidentally, Goerge Berkely (1685 – 1753) was an Irish Anglican Clergyman.

The Straight Edge:

The better that I know plane and cartesian Geometry, the better that I can both script, and draw (using a free open-source suite like Inkscape) computer Graphics.

In Plane Geometry, a straight edge is used.  A straight edge differs from a ruler, in that:

• whereas rulers possess gradated markings that indicate standard units of measurement, there are no gradated markings that indicate standard units of measurement – such as millimeters centimeters, etc. – on a straight edge.
• the width of the straight edge is deemed infinite, whereas real-life rulers are, it is needless to say, of finite width.

Figure 1:  A collapsible compass and straight edge.  These two instruments are employed in the construction of figures in Euclidean Geometry.  The span of a collapsible compass is deemed to collapse, should both the metallic point, and the graphite point of the compass be removed at the same time from the page.

See the Pen Collapsible Compass and Straight Edge Inkscape SVG by Ciaran Mc Ardle (@Valerius_de_Hib) on CodePen.

 

It is Dangerous to go Alone!

Figure 1: I drew this Link Sprite Pixel by Pixel in SVG.

I am trying to program without assignment statements for the lulz of it. Modern JavaScript – or ECMA script, as it is increasingly being known – is fully compliant with the functional paradigm. “Uncle Bob” gave a great talk on functional programming. Being able to program without equals signs is like completing Zelda 1 without the Master Sword. It is dangerous to go alone without assignment statements… but I do so anyway as I like to program on the edge. According to Uncle Bob, functional programs are less error prone – no side effects and no changes in state – and more efficient, as there is no need for “garbage collection.”

Figure 2:  Being able to arrive at the value, 0, without the use of an assignment statement was something that I was not able to do… until somebody suggested the bitwise double tilde on Stack  Exchange.

 

Bookcover Design in SVG and Inkscape:

Figure 1: I drew this book-cover in Scripted SVG and Inkscape. You may observe the vector file at my codepen account.

When it comes to the Kindle Store: prospective purchasers really do judge a book by its cover!

That is why a book cover requires its being extremely stylish and appealing to the eye, employing gradients, fonts, contrasting/complementary colours, etc. to this effect.

The Epistemology of Algorithms.

Below is a Word-Document Version of this blog post:

final_epistomology_recovered_algorithms

Below is a pdf Version of this blog post:

final_epistomology_recovered_algorithms

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Figure 1:  The Ancient-Greek word ‘EPISTEME’ which means ‘knowledge’ wrought into the Blacksmith’s monument outside Monaghan Courthouse. Monaghan is such a cultured little burg!

In science and philosophy, Epistemology is the study of knowledge, and what constitutes knowledge.

 

In Computer programming, we have to think epistemologically about knowledge; what constitutes knowledge; and what forms it may take.

 

In Computer programming, knowledge is deemed to have two forms:

1. Declarative,
2. Imperative.

The term, ‘imperative,’ denotes a command. ‘Imperative Knowledge’ is knowledge that instructs one on how to do something by giving him/her a set of commands.

 

If I told you that porridge consisted of oats and heated water, then this would be ‘declarative knowledge.’

 

If, instead, I gave you a set of instructions on how to make porridge such as:

RECIPE:

 

INGREDIENTS:

 

• Oats
• Water

 

METHOD:

 

Measure out 80 grams of oats. Measure out 160 millilitres of water. Combine the oats and water in a pot. Heat the pot over a hob until it reaches boiling point, stirring all the while. Keep the oats-and-water mixture at boiling point for three minutes. Take the porridge off the hob. Serve.

 

then the above would be an example of imperative knowledge.

 

Above, we see the two types of knowledge in action: declarative and imperative. The declarative form of knowledge tells you what porridge is. The imperative form of knowledge consists of a series of instructions that enables you to make porridge.

 

As you can see, the verbs that I use in telling you how to make porridge are, grammatically, in the imperative mood:

 

‘measure…’

‘combine…’

‘heat…’

‘keep…’

‘take…’

‘serve…’

 

In grammar, the imperative mood denotes a verb in its command form.

 

A series of commands that enables one to prepare a foodstuff is termed a ‘recipe.’  Very often, Computer Scientists will refer to algorithms as ‘recipes.’

In cookery, a recipe is a series of commands that allows one to prepare a foodstuff.

In computer science, an algorithm – or recipe – is a series of commands that allows one to solve a computational problem.

In computer science, an algorithm – or recipe – is a series of commands that allows one to accomplish a task computationally.

 

 

Glossary:

declarative

• adjective.

of the nature of or making a declaration: declarative statements.

[GRAMMAR] (of a sentence or phrase) taking the form of a simple statement.

[COMPUTING] denoting high-level programming languages which can be used to solve problems without requiring the programmer to specify an exact procedure to be followed.

noun.

a statement in the form of a declaration.

[GRAMMAR] a declarative sentence or phrase.

<DERIVATIVES> declaratively adverb. [1]

<ETYMOLOGY> from the Latin 1st-and-2nd-declension adjective, ‘dēclārātīva, dēclārātīvus, dēclārātīvum,’ which means ‘pertaining to the making quite clear.’ From the Latin 1st-conjugation verb, ‘dēclārō, dēclārāre, dēclārāvī, dēclārātum,’ which means ‘to explain,’ ‘to make quite clear,’ and the Latin 1st-and-2nd-declension adjectival suffix ‘-īva,    -īvus, -īvum,’ which means ‘of,’ ‘concerning,’ ‘pertaining to.’ From the Latin prefix ‘dē-’ which expresses intensive force, and the Latin 1st-conjugation verb, ‘clārō, clārāre, clārāvī, clārātum,’ which means ‘to brighten,’ ‘to illuminate,’ ‘to clarify.’

epistemology

[mass noun] [PHILOSOPHY] the theory of knowledge, especially with regard to its methods, validity, and scope, and the distinction between justified belief and opinion.

< DERIVATIVES> epistemological adjective. epistemologically adverb. epistemologist noun.

         < ORIGIN> mid 19th century: from Greek episteme ‘knowledge’, from epistathai ‘know, know how to do’.[2]

<ETYMOLOGY> From the Ancient-Greek Feminine noun, ‘hē épistḗmē,’ which means ‘knowledge,’ and the Ancient-Greek Masculine noun, ‘ho lógos,’ which denotes a ‘study.’ Therefore, the English term, ‘epistemology’ can be said, etymologically, to mean ‘the study of knowledge. The Ancient-Greek Feminine noun, ‘hē épistḗmē,’ which means ‘knowledge’ can be broken down, a little further, into the Ancient-Greek preposition, ‘epí,’ which means ‘above,’ or ‘over,’ and the Ancient-Greek verb, ‘hístēmi,’ which means ‘to stand.’ Hence, ‘hē épistḗmē,’ at root, means ‘above-standing,’ ‘over-standing.’ In English, the term ‘knowledge’ is more-or-less synonymous with the term, ‘understanding.’ The Ancient-Greeks did not “understand:” instead they were inclined to “above-stand;” they were inclined to “over-stand.” Etymologically, therefore, the English term, ‘epistemology’ can be said to mean ‘the study of over-standing,’ ‘the study of above-standing.’

 

 

 

 

imperative[3]

• adjective.

1. of vital importance; crucial: immediate action was imperative | [with clause] it is imperative that standards are maintained.
2. giving an authoritative command; peremptory: the bell pealed again, a final imperative call.
   • [GRAMMAR] denoting the mood of a verb that expresses a command or exhortation, as in come here!

• noun.
  1. an essential or urgent thing: free movement of labour was an economic imperative.
     • a factor or influence making something necessary: the biological imperatives which guide male and female behaviour.
  2. [GRAMMAR] a verb or phrase in the imperative mood.
     • (the imperative) the imperative mood.

<DERIVATIVES> imperatival adjective. imperatively adverb. imperativeness noun.

<ORIGIN> late Middle English (as a grammatical term): from Late Latin imperativus (literally ‘specially ordered’, translating Greek prostatikē enklisis ‘imperative mood’), from imperare ‘to command’, from in- ‘towards’ + parare ‘make ready’.[4]

<ETYMOLOGY> from the Latin 1st-and-2nd-declension adjective, ‘impĕrātīva, impĕrātīvus, impĕrātīvum,’ which means ‘pertaining to the command;’ ‘of the command.’ From the Latin 1st-conjugation verb, ‘imperō, imperāre, imperāvī, imperātum,’ which means ‘to command,’ ‘to order,’ and the Latin 1st-and-2nd-declension adjectival suffix ‘-īva, -īvus,              -īvum,’ which means ‘of,’ ‘concerning,’ ‘pertaining to.’ From the Latin prefix ‘in-’ which expresses the concept of ‘unto,’ ‘toward,’ and the Latin 1st-conjugation verb, ‘parō, parāre, parāvī, parātum,’ which means ‘to make ready,’ ‘to prepare.’ The etymological sense, therefore, of the English adjective, ‘imperative’ is: ‘concerning the command;’ ‘pertaining to the command;’ ‘of the command;’ ‘concerning the order;’ ‘pertaining to the order;’ ‘of the order;’ ‘concerning the making ready of;’ ‘pertaining to the making ready of;’ ‘of the making ready of;’ etc.

 

 

 

 

[1] Oxford University Press. Oxford Dictionary of English (Electronic Edition). Oxford. 2010. Loc178909.

[2] Oxford University Press. Oxford Dictionary of English (Electronic Edition). Oxford. 2010. Loc 234206

[3] ibid. Loc 345797