* This story forms the first serial in the Dalek Empire arc, a storyline that begins here with the Seventh Doctor, continues with the Sixth Doctor ( The Apocalypse Element ) and Fifth ( The Mutant Phase ) and concludes with the Eighth ( The Time of the Daleks ) Elements from these stories tie in the Dalek Empire series.

Euclid ’ s algorithm appears as Proposition II in Book VII (" Elementary Number Theory ") of his Elements.

* Proclus, A commentary on the First Book of Euclid's Elements, translated by Glenn Raymond Morrow, Princeton University Press, 1992.

Book VII, propositions 30 and 32 of Euclid's Elements is essentially the statement and proof of the fundamental theorem.

( Book X of Euclid's Elements is described by Pappus as being largely based on Theaetetus's work.

A summary of Proclus ' Elements of Theology circulated under the name Liber de Causis ( the Book of Causes ).

* A Commentary on the First Book of Euclid's Elements

The Liber de Causis ( Book of Causes ) is not a work by Proclus, but a summary of his work the Elements of Theology, likely written by an Arabic interpreter.

This proof appears in Euclid's Elements, Book 1, Proposition 20.

However, by Proposition 2 of Book 1 of Euclid's Elements, no computational power is lost by using such a collapsing compass ; there is no need to transfer a distance from one location to another.

The exposition of the theory of proportions that appears in Book VII of The Elements reflects the earlier theory of ratios of commensurables.

Book V of Euclid's Elements has 18 definitions, all of which relate to ratios.

For example, in Book I of Euclid's Elements, a line is defined as a " breadthless length " ( Def.

The Five Elements or Forces ( wu xing ) – which, according to the Chinese, are metal, earth, fire, water, and wood – are first mentioned in Chinese literature in a chapter of the classic Book of History.

The direct theorem was Proposition 22 in Book 3 of Euclid's Elements.

The Book frontispiece | frontispiece of Sir Henry Billingsley's first English version of Euclid's Elements, 1570

The diagram accompanies Proposition 5 of Book II of the Elements.

The Archimedean property appears in Book V of Euclid's Elements as Definition 4:

Knowledge of the golden mean goes back at least as far as 300BC, when Euclid described the method of geometric construction in Book 6, Proposition 30 of his book the Elements.

Euclid introduced the term in his Elements in Book I, Definition 22,

Euclid's Elements Book 10 is dedicated to classification of irrational magnitudes.

His proof is in Euclid's Elements Book X Proposition 9.

See Aristotle, Metaphysics, 1020a14 and Euclid, Elements, Book VII, Definition 1 and 2.

Book IX, Proposition 36 of Elements proves that if the sum of the first terms of this progression is a prime number ( means, a Mersenne prime mentioned above ), then this sum times the th term is a perfect number.

The Elements of Color: A Treatise on the Color System of Johannes Itten Based on His Book The Art of Color.

The basic properties of inscribed angles are discussed in Book 3, Propositions 20-22 of Euclid's Elements.

*" The Elements ", a mnemonic song of the periodic table by Tom Lehrer

There is no mention of Euclid in the earliest remaining copies of the Elements, and most of the copies say they are " from the edition of Theon " or the " lectures of Theon ", while the text considered to be primary, held by the Vatican, mentions no author.

* Heath, Thomas L. ( 1908 ), " Euclid and the Traditions About Him ", in Euclid, Elements ( Thomas L. Heath, ed.

* " The Elements: Fire ", a 1966 song by The Beach Boys

Following the French committee's findings, in his Elements of the Philosophy of the Human Mind ( 1818 ), Dugald Stewart, an influential academic philosopher of the " Scottish School of Common Sense ", encouraged physicians to salvage elements of Mesmerism by replacing the supernatural theory of " animal magnetism " with a new interpretation based upon " common sense " laws of physiology and psychology.

Elements from the Spanish language were also integrated into the Palauan lexicon ; the Palauan word for hammer, " martiliong ", is derived from the Spanish " martillo ".

" On the Elements of Being ", Review of Metaphysics, vol.

A notable exception is his song " The Elements ", where he sets the names of the chemical elements to the tune of the " Major-General's Song " from Gilbert and Sullivan's Pirates of Penzance.

" On the Elements of Being ", Review of Metaphysics, vol.

" Discrete Elements and Nonlinearity in Design of Structural Concrete Walls ", Section 1. 3 Historical Overview of Structural Concrete Modelling, ISBN 90-901184-3-8.

The third edition of The Elements of Style ( 1979 ) features 54 points: a list of common word-usage errors ; 11 rules of punctuation and grammar ; 11 principles of writing ; 11 matters of form, and 21 reminders for a better style, in Chapter V. The final reminder, the 21st, " Prefer the standard to the offbeat ", is thematically integral to the subject of The Elements of Style, yet does stand as a discrete essay about writing lucid prose.

Note: Elements of the original text of this article are taken from the NIH Fact Sheet " Group A Streptococcal Infections ", dated March 1999.

* Julio E. Rubio & Ntumbua Tshipamba, " Elements of the public policy of science, technology and innovation ", Canadian Social Science, 6 ( 6 ), 61-80.

Elements from several Asimov robot stories were woven into the overall storyline, including " Little Lost Robot ", " The Evitable Conflict " and " Robot Dreams ".

* De Elementen (" The Elements ", 1988 ; novel )

Elements of popular culture that appear as backdrops to the main story include the song " If I Were a Rich Man ", from Fiddler on the Roof ; a recorded orchestral performance of The Beatles ' song " Yesterday "; The Tonight Show Starring Johnny Carson ; and televised boxing matches.

* " The Synthesis of Ammonia from its Elements ", Nobel Lecture, 2 June 1920

Playfair's contributions to pure mathematics were not considerable, his papers " On the Arithmetic of Impossible Quantities " and " On the Causes which Affect the Accuracy of Barometrical Measurements ", and his Elements of Geometry, all already referred to, being the most important.

Watercolor tutorials were first published in this period by Varley, Cox and others, innovating the step-by-step painting instructions that still characterizes the genre today ; " The Elements of Drawing ", a watercolor tutorial by the English art critic John Ruskin, has been out of print only once since it was first published in 1857.

Between 1922 – 1924, Orozco painted the murals: " The Elements ", " Man in Battle Against Nature ", " Christ Destroys His Cross ", " Destruction of the Old Order ", " The Aristocrats ", and " The Trench and the Trinity " at the National Preparatory School.