Long-standing rivalry between Vietnam’s Nguyen and Trinh families had become open warfare in 1620, with hostilities continuing intermittently until 1673.

Both families had accepted a de facto division of the Vietnamese state by that date.

Hien Vuong, a member of the Nguyen family that rules the south, has persecuted European Christian missionaries, expanded the territory under his control, and made notable agricultural reforms.

He has encouraged Vietnamese settlement into southern lands formerly occupied by the Chams and the Cambodians, having acquired these lands at the expense of these groups, but this has been done largely by Chinese refugees fleeing the collapse of the Ming dynasty in 1644.

He has improved the mandarin examination system by which civil-service posts are filled, and established a bureau of agriculture that urges the colonization and development of the newly conquered territories.

He has promulgated needed land reforms, although they failed to alter significantly the social conditions of his lower-class subjects.

Hien Vuong has sought to secure official recognition of his sovereignty from China, but the Chinese continue to uphold the legitimacy of the northern Trinh family.

Akbar had been trying to cajole Sambhaji into joining him and the Rajputs (Hindus) against Agra.

Aurangzeb and the court had therefore come to the Deccan in 1681, living in a vast tent city thirty miles in circumference while Aurangzeb acted as his own commander-in-chief.

Aurangzeb was initially successful, but not against the Marathas, who raid from their forts.

Instead, he has attempted to cut off the Hindu Marathas from Muslim Bijapur and Golconda, which are, as a result of earlier Mughal offensives, similarly predisposed against Aurangzeb.

With the objective of conquering the Marathas outright, he targets the two principal successor states to the Muslim sultanate of Bahmani in the Deccan, seizing the dying Sunnite sultanate of Bijapur in 1686.

The Marathas are the single most important power to have emerged in the long twilight of the Mughal dynasty.

Initially deriving from the western Deccan as a peasant warrior group, the Marathas had risen to prominence during the rule in that region of the sultans of Bijapur and Ahmadnagar.

The most important Maratha warrior clan, the Bhonsles, had held extensive jagirs (land-tax entitlements) under the 'Adil Shahi rulers; these were consolidated in the course of the 1630s and '40s as Bijapur expanded to the south and southwest.

Sahji Bhonsle, the first prominent member of the clan, had drawn substantial revenues from the Karnataka region, in territories that had once been controlled by the rulers of Mysore and other chiefs who derived from the collapsing Vijayanagar kingdom.

One of his children, Sivaji Bhonsle, had emerged as the most powerful figure in the clan to the west, while Sivaji's half-brother Vyamkoji had been able to gain control over the Kaveri delta and the kingdom of Thanjavur in the 1670s.

The death, in 1680, of Shivaji Bhonsle, had brought to the throne his son Sambhagi, whose experience as a Mughal hostage had made him briefly defect to the Muslim side during the Marathan-Mughal War of 1670-80.

It had also brought a new element into the conflict: the defection of Crown Prince Akbar, son of the Mughal emperor Aurangzeb, to the Hindu side during the ongoing Rajput rebellion against his father.

Leibniz, in 1686, first defines the curvature of a curve at each point in terms of the circle that best approximates the curve at that point.

Mathematicians from antiquity had described some curves as curving more than others and straight lines as not curving at all.

 

Religious tension grows from 1686.

James II allows Roman Catholics to occupy the highest offices and receives at his court the papal nuncio, Ferdinando d'Adda,  the first representative from Rome to London since the reign of Mary.

James's Jesuit confessor, Edward Petre, is a particular object of Protestant ire.

When the King's Secretary of State, the Earl of Sunderland, begins replacing officeholders at court with Catholic favorites, James begins to lose the confidence of many of his Anglican supporters.

Sunderland's purge of officeholders even extends to the King's Anglican brothers-in-law and their supporters.

King Charles II had determined in the 1680s to bring the New England colonies under a more centralized administration in order to regulate trade more effectively.

The colonists had fiercely opposed his efforts, resulting in the abrogation of their colonial charter by the Crown.

Charles' successor James II finalizes these efforts in 1686, establishing the Dominion of New England.

Massachusetts Bay Colony, one of the original English settlements in present Massachusetts, had been settled in 1630 by a group of about a thousand Puritan refugees from England under Governor John Winthrop.

The Massachusetts Bay Company had in 1629 obtained from Charles a charter empowering the company to trade and colonize in New England between the Charles and Merrimack rivers.

Omitted from the charter was the usual clause requiring the company to hold its business meetings in England, a circumstance that the Puritan stockholders used to transfer control of the colony to America.

The Puritans established a theocratic government with the franchise limited to church members.

Increasingly in the 1680s, the English Crown has challenged the institutional discrimination displayed by the Puritans of the United Colonies of New England toward Anglicans.

Growing estrangement between the colony and England resulted in the annulment of the company's charter in 1684.

King James II attempts in 1686 to stem growing colonial independence by imposing on the colonies —the Massachusetts Bay Colony, the Plymouth Colony, the Province of New Hampshire, the Province of Maine, and the Narraganset Country or King's Province—a kind of supercolony, the Dominion of New England, ostensibly as a measure to enforce the Navigation Acts and to coordinate the mutual defense of colonies against the French and hostile Native Americans.

The capital is located in Boston.

The Colony of Rhode Island and Providence Plantations and the Connecticut Colony are added to the Dominion on September 9, 1686.

Sir Edmund Andros, who had grown up as a page in the royal household, had had his fidelity to the crown during its exile after the English Civil Wars rewarded in 1674 by his appointment as governor of New York and New Jersey. (He was also knighted in 1678.)

Although the mother country regarded him as an able and conscientious administrator, the colonists considered him both arrogant and arbitrary, and he had been recalled in 1681 but now returns to America as governor of the Dominion of New England.

Robert Livingston secures a patent in 1686 raising his landholdings to the status of a manor.

The manor and lordship of Livingston, which will be confirmed by royal charter of King George I in 1715, is to last for a century. (The family will continue a portion of the estate into the twenty-first century).

Livingston is the son of a minister of the Church of Scotland, a lineal descendant of the fourth Lord Livingston, ancestor of the earls of Linlithgow and Callendar, who had been sent into exile in 1663 due to his resistance to attempts to turn the Presbyterian national church into an Episcopalian institution.

Raised with his exiled family in Rotterdam, in the Dutch Republic, Robert Livingston had thus become fluent in the Dutch language, which is to help him greatly in his later career in the former Dutch colony of New Netherland, whither Robert had emigrated in 1673, settling in the frontier village of Albany, New York, in 1674.

Serving as an intermediary between speakers of the English and Dutch languages, he had soon been appointed the town clerk and secretary of New York's board of commissioners for Indian affairs.

Marrying advantageously, growing wealthy in the fur trade, and building up influence with successive governors of New York, he has also been able to purchase native claims to large tracts of land along the Hudson River, thereby eventually acquiring an estate of one hundred and sixty thousand acres (sixty-five thousand hectares) in New York, embracing large portions of modern Dutchess and Columbia counties.

New York city adopts an official seal in 1686 that includes the beaver and the flour barrel, images that document this first major phase of Manhattan's economic history.

New Amsterdam had been important to the Dutch because it offered access to the immensely valuable fur trade of an entire continent.

After the English conquest in 1664, the city had won a monopoly to grind and pack grain and now sends its flour to all world markets.

Merchant incomes have soared as commerce, both legitimate and via smuggling, becomes the lifeblood of New York.

Jacques-Rene de Brisay de Denonville, Marquis de Denonville, replaces Joseph Antoine de LaBarre as Governor of New France in 1685, and sets out to make King Louis XIV proud.

The Iroquois Confederation has been a nuisance for half a century, hampering New France's efforts to establish itself as a profitable colony.

A peace treaty was signed in 1667, but the war is renewed in the 1680.

Although France and England are at peace, Denonville sends the newly arrived Pierre de Toyes, the Chevalier de Troyes, north from Montreal with a hundred men (most likely the Troupes de la marine), ...