The haidamakas, also haidamaky or haidamaks (singular haidamaka, Ukrainian: Haidamaky, from Turkish haydamak, "to pursue"), are paramilitary bands in eighteenth-century Ukraine.

The haidamak movement is formed mostly of local Cossacks and peasantry (kozaky and holota), against the Polish nobility in right-bank Ukraine, though the movement is not limited to the right bank only.

The equivalent to haidamaka is opryshok in Ukrainian Galicia, and hajduk in the Balkans.

Hajduk is also used in the Polish language.

Unrest against the nobility and the Catholics lead to the haidamaka rebellions (haidamachchyna), the first of which takes place in 1734 during the war for control of the Polish Kingdom after the death of Frederick Augustus II.

Russian troops, brought to remove King Stanisław I (Leszczyński), are initially seen as liberators from Poles and an insurrection develops in Kiev, spreading to Podolia and Volhynia.

After Augustus III gains the throne, the insurrection is defeated by Russian military.

Small raids by haidamakas against Polish nobility will continue in the following years.

Ayuba Suleiman Diallo, captured and sold into slavery in 1732, is an extremely rare exception in the slave trade.

Due to his intelligence and monetary prowess, and Englishmen's desire to use him to increase their own profits in trade on the coast of Africa, he has been able to legally escape the hardships of slavery in Maryland and return to Gambia in July 1734 and later return to his homeland.

His homeland has been ravaged by war, but being a prosperous individual, Ayuba is able to regain his old lifestyle.

His memoirs are published by Bluett in English and French.

Freemasonry is introduced to the Netherlands in 1734.

Lettres philosophiques or Letters Concerning the English Nation, a series of essays written by Voltaire between 1726 and 1729 based on his experiences living in England (from 1707 a constituent nation part Great Britain), had been published first in English in 1733 and in the following year in French.

Seen as an attack on the French system of government, it is rapidly suppressed.

Copies are burned, and a warrant is issued for the author's arrest.

Most modern English language versions are based on a translation of the French text rather than Voltaire's English one.

Voltaire's attitude toward English institutions is generally favorable, but it is by no means as one-sided as generally supposed: he finds plenty of things in England to satirize, including the House of Commons and the moral stringency of the Presbyterians.

William Adam has turned his father's building firm in Kirkcaldy into Scotland's largest construction and contracting enterprise of the time.

Adam uses a wide variety of sources for his designs, often reminiscent of Continental Baroque, as well as Gibbs and Vanbrugh.

The best known of his early works is the extension of Hopetoun House in 1721.

Adam had in 1728 become Clerk and Storekeeper of the King's Works in Scotland, and from 1730 Mason to the Board of Ordnance in North Britain.

The Engraving Copyright Act 1734 (8 Geo.2 c.13) is an Act of the Parliament of Great Britain passed in 1734 to give protections to producers of engravings.

It is sometimes called Hogarth's Act after William Hogarth, whose work had prompted the law.

Historian Mark Rose notes, "The Act protected only those engravings that involved original designs and thus, implicitly, made a distinction between artists and mere craftsmen. Soon, however, Parliament was persuaded to extend protection to all engravings." (Rose, Mark. Technology and Copyright in 1735: The Engraver's Act. The Information Society, Volume 21, Number 1, January-March 2005. pp. 63-66.)

This Act is the first of the Copyright Acts 1734 to 1888.

Oglethorpe returns to England in June 1734 with goodwill ambassadors in the persons of Yamacraw chief Tomochichi, Senauki, his wife, their nephew Toonahowi, and six other Lower Creek tribesmen.

The Indians are regarded as celebrities, feted by the Trustees, interviewed by the king and queen, entertained by the archbishop of Canterbury at Lambeth Palace, and made available to meet the public.

All but two of them pose with a large number of Trustees at the Georgia office for the painter William Verelst.

One of the absent Indians dies of smallpox, despite the ministrations of the eminent physician Sir Hans Sloane, and is buried by his grieving comrades in the burial plot of St. John's in Westminster.

After performing their social obligations, the Indians become tourists, visiting the Tower of London, St. Paul's Cathedral, Oglethorpe's Westbrook Manor, and Egmont's Charlton House, and enjoying a variety of plays, from Shakespearean dramas to comic farces.

The Indians depart on October 31, 1734.

With them go fifty-seven Salzburgers to join the forty-two families already in Georgia at Ebenezer.

George Berkeley is appointed Bishop of Cloyne in Ireland in 1734, a position he is to hold until his death.

In this year, Berkeley publishes The Analyst, subtitled "A DISCOURSE Addressed to an Infidel MATHEMATICIAN. WHEREIN It is examined whether the Object, Principles, and Inferences of the modern Analysis are more distinctly conceived, or more evidently deduced, than Religious Mysteries and Points of Faith".

The mathematician in question is believed to have been either Edmond Halley, or Isaac Newton himself—though if to the latter, then the discourse was posthumously addressed, as Newton had died in 1727.

An empiricist critique of the foundations of infinitesimal calculus, influential in the development of mathematics, The Analyst represents a direct attack on the foundations and principles of Infinitesimal calculus and, in particular, the notion of fluxion or infinitesimal change, which Newton and Leibniz had used to develop the calculus.

Berkeley coins the phrase “Ghosts of departed quantities”, familiar to students of calculus.

He regards his criticism of calculus as part of his broader campaign against the religious implications of Newtonian mechanics—as a defense of traditional Christianity against deism, which tends to distance God from His worshipers.

Spain and Great Britain in the 1730s dispute control over the border between Georgia and La Florida, where the Spanish have several settlements and forts.

Oglethorpe seeks to increase his southern defenses, given a heightened threat of Spanish invasion.

Accompanied by rangers and two Native American guides, he picks St. Simons Island as the site for a new town and fort.

Oglethorpe in 1734, persuades Parliament and the colonial trustees to pay for a new military garrison.

He recruits a company of British settlers to migrate with their families to live at Darien, at the mouth of the Altamaha River.

Salzburgers, Lutherans who had been expelled by the Roman Catholic Bishop of Salzburg, Austria, in October 1731, had set sail on January 8, 1734, for the British Colony of Georgia, in America, and arrive at the mouth of the Savannah River on March 12.

Benjamin Franklin, initiated into the local Masonic Lodge in 1731, becomes Grand Master in 1734, indicating his rapid rise to prominence in Pennsylvania.

This same year, he edits and publishes the first Masonic book in the Americas, a reprint of James Anderson's Constitutions of the Free-Masons.

Franklin will remain a Freemason for the rest of his life.