It can be divided into elementary number theory ( where the integers are studied without the aid of techniques from other mathematical fields ); analytic number theory ( where calculus and complex analysis are used as tools ); algebraic number theory ( which studies the algebraic numbers-the roots of polynomials with integer coefficients ); geometric number theory ; combinatorial number theory ; transcendental number theory ; and computational number theory.

Diogenes states that Heraclitus ' work was " a continuous treatise On Nature, but was divided into three discourses, one on the universe, another on politics, and a third on theology.

The professors were divided as follows: theology, 7 regular professors, 1 assistant professor, 1 docent ; law, 12 regular professors, 2 assistant professors, 4 docents ; medicine, 15 regular professors, 19 assistant, 30 docents ; philosophy, 30 regular professors, 8 assistant, 19 docents, 7 lecturers.

Christianity divided itself in the East during its early centuries both within and outside of the Roman Empire in disputes about christology and fundamental theology, as well as national divisions ( Roman, Persian, etc .).

( The Gospel of John, which is the only gospel where Nicodemus is mentioned, particularly portrays the sect as divided and willing to debate ) Because of the New Testament's frequent depictions of Pharisees as self-righteous rule-followers ( see also Woes of the Pharisees and Legalism ( theology )), the word " pharisee " ( and its derivatives: " pharisaical ", etc.

Doctors of theology, masters and representatives of chapters, monks and clerks of inferior orders constantly outnumbered the prelates in it, and the influence of the superior clergy had less weight because, instead of being separated into " nations ", as at Constance, the fathers divided themselves according to their tastes or aptitudes into four large committees or " deputations " ( deputationes ).

Protestant theology since the 18th century had been divided in its interpretation of justification by free grace.

In Christian theology, the Christian Church, or Church Universal, is traditionally divided into:

We may divide medieval Jewish theologians into three categories: those primarily concerned with commentary upon Talmud ( who can be further divided into the Genoim and the Rishonim ); those whose main interests were more in the area of philosophical theology ; and those who were part of the Karaite movement that rejected Talmud.

In addition to questions about the efficacy, safety and reliability of TPM, it has also divided Christian observers with regard to the soundness of its theology.

After the execution of Charles I, Scottish Presbyterians and English Anglicans and Congregationalists, despite sharing a common theology, were divided over the place of the Monarchy – the former supported it while the latter were opposed to it.

It is divided into 4 faculties: catholic theology, law, humanities and natural science.

The RCUS was divided on the issue, as the Philadelphia Classis condemned Schaff ’ s theology, while the East Pennsylvania Classis defended it.

Balthasar is well known for his 16 volume systematics ( Trilogy ) which is divided into three parts: The Glory of the Lord, the first 7-volume work on ' theological aesthetics ' ( a theology based upon contemplation of the good, the beautiful, and the true ).

) This, further, seems to hold if ontology itself is divided into political and trans-or supra-or meta-political ontology — i. e., what once was the realm of Christian theology.

The curriculum was divided into several levels (" schools "), including Slavonic and Greek writing, seven liberal arts ( septem artes liberales ), and theology.

The central aspect of Athari theology is its definition of Tawhid, meaning literally unification or asserting the oneness of Allah ( to be the only God who deserves to be worshiped in truth and confirming all attributes with which He has qualified Himself or that are attributed to Him by His Messenger ), whereby it is divided into three tenets of theology ;

His life therefore may be divided into four periods characterized respectively by work on theology and mysticism, medieval universities, the Hundred Years ' War between France and England with its consequences to the Church, and Luther and Lutheranism.

Here in these little rooms -- or stages arched open to the sky and river -- they choose a few lines out of the hundreds they may know and sing them according to one of the modes into which Persian music is divided.

If a work is divided into several large segments, a last-minute drawing of random numbers may determine the order of the segments for any particular performance.

A few weeks later the maps were being divided into squares and a position was described as being `` about lots 239, 247 and 272 with pickets forward as far as 196 ''.

The long-range aspects of this program are divided into four distinct phases: basic mapping, inventory, analysis and plan and policy formation.

This system is divided into a forest highway system, administered by the Secretary of Commerce, and a forest development road and trail system, administered by the Secretary of Agriculture.

The lower number is always divided into the upper number: Af

We divided the country into five regions plus Hawaii and Alaska and in each is included a general description of the area plus specific recommendations of places and events to cover.

`` We, the Subscribers, do agree, that as soon as a convenient Number of Persons have subscribed to this, or a similar Writing, We will present a petition to the Hon'ble General Court of the Commonwealth of Massachusetts, praying for an Act incorporating into a Body politic the subscribers to such Writing with Liberty to build such a Bridge, and a Right to demand a Toll equal to that received at Malden Bridge, and on like Terms, and if such an Act shall be obtained, then we severally agree each with the others, that we will hold in the said Bridge the several shares set against our respective Names, the whole into two hundred shares being divided, and that we will pay such sums of Money at such Times and in such Manners, as by the said proposed Corporation, shall be directed and required ''.

A plug and a tube with holes in its cylindrical walls divided the chamber above the porous plug into two parts.

Also, the dictionary is divided into at least two parts: the list of dictionary forms and the file of information that pertains to these forms.

Instead, all of the total costs are treated as variable costs, although these costs are divided into costs that are deemed to be functions of different variables.

instead they divided the surface into many bands or covered it by all-over patterns into which freehand drawing began to creep.

The open ceiling, with allegorical and classical figures thrown in masses against the sky: the closed frieze, formally divided into historical scenes and tightly tied to the stone walls, belong in their large ordering to the line of Correggio and his Baroque followers.

The compounds are divided according to composition into seven categories.

The book is divided into chapters and in each chapter the material is grouped into Text, Tables, Illustrations, and Bibliography.

he divided humanity into `` right guys '' and `` wrong guys '', and the wrong ones he was always willing to kill and trample under.

But inevitably the border which has divided the ghetto from the rest of the world falls into the hands of the ghetto.

They adopted a program by which Louisiana was divided into five districts.

The savages divided into two factions ; ;

He had assumed that all these buildings had been divided into apartments, but this one, from a glance at the hall furnishings, was obviously still a functioning town house, and its owners were in residence ; ;

Split badly during the recent presidential election into almost equally divided camps of party loyalists and independents, the Democratic party in Mississippi is currently a wreck.

The population of the Congo is 13.5 million, divided into at least seven major `` culture clusters '' and innumerable tribes speaking 400 separate dialects.

The last five chapters are exclusively concerned with land: instructions for the extermination of the Canaanites, the demarcation of the boundaries of the land, how the land is to be divided, holy cities for the Levites and " cities of refuge ", the problem of pollution of the land by blood, and regulations for inheritance when a male heir is lacking.

" In 1982 BJU's then-president Bob Jones III, during interviews in which he defended the school's tax-exempt status, cited nine passages from the Bible-drawn both from the Old and New Testaments-which he claimed demonstrated that God intended races to be segregated: " The Bible clearly teaches, starting in the 10th chapter of Genesis and going all the way through, that God has put differences among people on the earth to keep the earth divided ", he said, adding that inter-racial marriage was " playing into the hands of the antichrist and the one-world system.

Frequently referred to as " Canada's birthday ", particularly in the popular press, the occasion marks the joining of the British North American colonies of Nova Scotia, New Brunswick, and the Province of Canada into a federation of four provinces ( the Province of Canada being divided, in the process, into Ontario and Quebec ) on July 1, 1867.

Thus, living birds were divided into carinates ( keeled ) and ratites ( from ratis, " raft ", referring to the flatness of the sternum ).

As archaeological discoveries revealed the scale of the Hittite kingdom in the second half of the 19th Century, Archibald Henry Sayce postulated, rather than to be compared to Judah, the Anatolian civilization " worthy of comparison to the divided Kingdom of Egypt ", and was " infinitely more powerful than that of Judah ".

The Histories, otherwise known as The Researches or The Inquiries, were divided by later Alexandrian editors into nine books, named after the nine Muses: the " Muse of History ", Clio, representing the first book, then Euterpe, Thaleia, Melpomene, Terpsichore, Erato, Polymnia, Ourania and Calliope for books 2 to 9, respectively.

For a decade, the nation was divided between " dreyfusards " and " anti-dreyfusards ", and far-right Catholic agitators inflamed the situation even when proofs of Dreyfus's innocence came to light.

Strategies can be divided into those in which investments can be selected by managers, known as " discretionary / qualitative ", or those in which investments are selected using a computerized system, known as " systematic / quantitative ".

The Fianna of the story are divided into the Clann Baiscne, led by Fionn mac Cumhaill ( often rendered as " Finn MacCool ", Finn Son of Cumhall ), and the Clann Morna, led by his enemy, Goll mac Morna.

Invoking " science " and " realism ", the two men derided their " philanthropic " predecessors for believing in human equality and for not recognizing that mankind was divided into superior and inferior races.

Even Julian's intellectual friends and fellow pagans were of a divided mind about this habit of talking to his subjects on an equal footing: Ammianus Marcellinus saw in that only the foolish vanity of someone " excessively anxious for empty distinction ", whose " desire for popularity often led him to converse with unworthy persons ".

These unions are often divided into " locals ", and united in national federations.

Medieval theologians, in western Europe, described the underworld (" hell ", " hades ", " infernum ") as divided into four distinct parts: Hell of the Damned ( which some call Gehenna ), Purgatory, Limbo of the Fathers or Patriarchs, and Limbo of the Infants.

Inhabitants (" Mountaineers ") are divided into two rigid hereditary castes, the " crew " and the " colonists ", depending on whether their ancestors piloted the colonizing vessel.

Alfonso also describes a game entitled " astronomical chess ", played on a board of seven concentric circles, divided radially into twelve areas, each associated with a constellation of the Zodiac.

Nights into Dreams ... is split into seven levels or " Dreams ", each divided further into four " Mares " and a boss battle.

Old Turkic being a synharmonic language, a number of consonant signs are divided into two " synharmonic sets ", one for front vowels and the other for back vowels.

Puppis was originally part of an over-large constellation, the ship of " Jason and the Argonauts ", Argo Navis, which was centuries later divided into three parts, the other two being Carina ( the keel and hull ), and Vela ( the sails of the ship ).

Like the English poll tax, the French capitation tax was assessed on rank – for taxation persons, French society was divided in twenty-two " classes ", with the Dauphin ( a class by himself ) paying 2, 000 livres, princes of the blood paying 1500 livres, and so on down to the lowest class, composed of day laborers and servants, who paid 1 livre each.

An " S ", by contrast, is assumed to be guided more by the judgment / perception axis, and thus divided into the " SJ " ( guardian, traditionalist ) or " SP " ( performer, artisan ) temperament.

Bede makes the claim that Oswald " brought under his dominion all the nations and provinces of Britain ", which, as Bede notes, was divided by language between the English, Britons, Scots, and Picts ; however, he seems to undermine his own claim when he mentions at another point in his history that it was Oswald's brother Oswiu who made tributary the Picts and Scots.

The incorrupt arm was divided among European royalty, but the Holy Right of King Saint Stephen was placed in a town built solely for the purpose of keeping it, the town in Transylvania called " Szent Jobb ", or Holy Right.

Following the example of the Buddhist Tripiṭaka, it is divided into three dong (, " caves ", " grottoes ").

Tool substitution may be divided broadly into two classes: substitution " by-design ", or " multi-purpose " use, and substitution as makeshift.