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1678 (MDCLXXVIII) was a common year starting on Saturday of the Gregorian calendar and a common year starting on Tuesday of the Julian calendar, the 1678th year of the Common Era (CE) and Anno Domini (AD) designations, the 678th year of the 2nd millennium, the 78th year of the 17th century, and the 9th year of the 1670s decade. As of the start of 1678, the Gregorian calendar was 10 days ahead of the Julian calendar, which remained in localized use until 1923.
|Ab urbe condita||2431|
|Balinese saka calendar||1599–1600|
|English Regnal year||29 Cha. 2 – 30 Cha. 2|
|Chinese calendar||丁巳年 (Fire Snake)|
4374 or 4314
— to —
戊午年 (Earth Horse)
4375 or 4315
|- Vikram Samvat||1734–1735|
|- Shaka Samvat||1599–1600|
|- Kali Yuga||4778–4779|
|Japanese calendar||Enpō 6|
|Julian calendar||Gregorian minus 10 days|
|Minguo calendar||234 before ROC|
|Thai solar calendar||2220–2221|
1804 or 1423 or 651
— to —
1805 or 1424 or 652
- January 27 – The first fire engine company (in what will become the United States) goes into service.
- February 18 – The first part of English nonconformist preacher John Bunyan's Christian allegory, The Pilgrim's Progress, is published in London.
- May 11 – French admiral Jean d'Estrees runs his whole fleet aground in Curaçao.
- June – French buccaneer Michel de Grammont leads 6 pirate ships and 700 men in a daring raid on Spanish-held Venezuela, reaching inland as far as Trujillo.
- June 25 – Elena Lucrezia Cornaro Piscopia becomes the first woman to be awarded a university degree, a doctorate in philosophy from the University of Padua.
- August–December – Kediri campaign: Mataram and Dutch East India Company forces defeat the Trunajaya rebellion in eastern Java.
- August 3 – Robert LaSalle builds the Le Griffon, the first known ship built on the Great Lakes.
- August 10 – The Treaties of Nijmegen end the Franco-Dutch War. The County of Burgundy is ceded to the Kingdom of France.
- August 14–15 – The Battle of Saint-Denis is fought after the peace was signed between France and the Dutch Republic in the Treaties of Nijmegen on 10 August.
- September 6 – Titus Oates begins to present allegations of the Popish Plot, a supposed Roman Catholic conspiracy to assassinate king Charles II of England. Oates applies the term Tory to those who disbelieve his allegations.
- October 17 – English magistrate Sir Edmund Berry Godfrey is found murdered in Primrose Hill, London. Titus Oates claims it as a proof of his allegations.
- December 3 – The Test Act provides that members of both the House of Lords and House of Commons of England must swear an anti-Catholic oath, before taking office.
- Rebellion breaks out in southern China.
- About 1,200 Irish families sail from Barbados, to Virginia and the Carolinas.
- In Ireland, the vacant Bishopric of Leighlin is given to the Bishop of Kildare, to form the Roman Catholic Diocese of Kildare and Leighlin.
- The first chrysanthemums are planted in Europe.
- May 3 – Amaro Pargo, Spanish corsair (d. 1747)
- March 4 – Antonio Vivaldi, Italian composer (d. 1741)
- March 7 – Filippo Juvara, Italian architect (d. 1736)
- April 14 – Abraham Darby I, one of the English fathers of the Industrial Revolution (d. 1717)
- May 16 – Andreas Silbermann, German organ builder (d. 1734)
- July 26 – Joseph I, Holy Roman Emperor (d. 1711)
- September 16 – Henry St John, 1st Viscount Bolingbroke, English statesman and philosopher (d. 1751)
- September 29 – Adrien-Maurice, 3rd duc de Noailles, French soldier (d. 1766)
- October 10 – John Campbell, 2nd Duke of Argyll, Scottish soldier (d. 1743)
- October 16 – Anna Waser, Swiss painter (d. 1714)
- November 26 – Jean Jacques d'Ortous de Mairan, French geophysicist (d. 1771)
- December 8 – Horatio Walpole, 1st Baron Walpole of Wolterton, English diplomat (d. 1757)
- December 13 – Yongzheng Emperor of China (d. 1735)
- December 14 – Daniel Neal, English historian (d. 1743)
- December 30 – William Croft, English composer (d. 1727)
- date unknown
- George Farquhar, Irish dramatist (d. 1707)
- Maria Faxell, Swedish vicar's wife and war heroine (d. 1738)
- Joachim Ludwig Schultheiss von Unfriedt, German architect (d. 1753)
- Pierre Fauchard, French physician and author, considered The father of modern dentistry (d. 1761)
- John Senex, British geographer (d. 1740)
- January 11 – Ferrante III Gonzaga, Duke of Guastalla, Italian noble (b. 1618)
- January 12 – Robert Ellison, English politician (b. 1614)
- January 23 – Sir William Curtius FRS, German magistrate and English baronet b. (1599)
- January 24 – Joan Maetsuycker, Governor-General of the Dutch East Indies (b. 1606)
- January 27 – Maria Overlander van Purmerland, Dutch noble (b. 1603)
- January 29 – Jeronimo Lobo, Portuguese Jesuit missionary (b. 1593)
- February 7 – Sir Philip Musgrave, 2nd Baronet, English politician (b. 1607)
- November 20 – Daniel Clasen, German academic (b. 1622)
- March 3 – Philip Bell, British colonial governor (b. 1590)
- March 10 – Jean de Launoy, French historian (b. 1603)
- March 27 – Juan de Leyva de la Cerda, conde de Baños, Spanish noble (b. 1604)
- April 12 – Mary Rich, Countess of Warwick, 7th daughter of Richard Boyle (b. 1625)
- April 23 – Walter Aston, 2nd Lord Aston of Forfar, second and eldest surviving son of Walter Aston (b. 1609)
- April 24 – Louis VI, Landgrave of Hesse-Darmstadt (1661–1678) (b. 1630)
- April 27 – Nicolas Roland, French priest and founder (b. 1642)
- May 2 – Willem Nieupoort, Dutch politician, and diplomat (b. 1607)
- May 3 – Bernhard II, Duke of Saxe-Jena, German noble (b. 1638)
- May 4 or May 14 – Anna Maria van Schurman, Dutch poet and scholar (b. 1607)
- May 16 – Tamura Muneyoshi, Japanese daimyō of the Iwanuma Domain (b. 1637)
- May 18 – Miyamoto Iori, Japanese samurai (b. 1612)
- June 2 – Pieter de Groot, Dutch diplomat (b. 1615)
- June 17 – Giacomo Torelli, Italian stage designer, engineer, and architect (b. 1608)
- June 19 – Benedict Arnold, Rhode Island colonial governor (b. 1615)
- August 5 – Juan García de Zéspedes, Mexican musician and composer (b. 1619)
- August 16 – Andrew Marvell, English writer (b. 1621)
- August 17 – Guillaume Herincx, Flemish theologian, Bishop of Ypres (b. 1621)
- August 28 – John Berkeley, 1st Baron Berkeley of Stratton, English soldier (b. 1602)
- August 31 – Louis VII, Landgrave of Hesse-Darmstadt (b. 1658)
- September 1 – Jan Brueghel the Younger, Flemish painter (b. 1601)
- September 8 – Pietro della Vecchia, Italian painter (b. 1603)
- September 19 – Christoph Bernhard von Galen, German Catholic bishop (b. 1606)
- September 28 – Maurizio Cazzati, Italian composer (b. 1616)
- October 5 – Hedevig Ulfeldt, daughter of King Christian IV of Denmark and Kirsten Munk (b. 1626)
- October 11 – Sir Peter Leycester, 1st Baronet, British historian (b. 1614)
- October 12
- October 14 – Sir Richard Newdigate, 1st Baronet, English politician (b. 1602)
- October 16 – Cornelis HrR Ridder de Graeff, Dutch nobleman and chief landholder of the Zijpe and Haze Polder (b. 1650)
- October 18 – Jacob Jordaens, Flemish painter (b. 1593)
- October 19 – Samuel Dirksz van Hoogstraten, Dutch painter (b. c. 1627)
- November 1 – William Coddington, first Governor of Rhode Island (b. 1601)
- November 4 – Solomon Swale, English politician (b. 1610)
- November 5 – Giovan Battista Nani, Italian historian and diplomat (b. 1616)
- November 10 – Daniel Zwicker, German physician (b. 1612)
- November 30 – Andries de Graeff, Dutch politician (b. 1611)
- December 3 – Edward Colman, English Catholic courtier under Charles II (b. 1636)
- December 20 – Matthew Marvin, Sr., Connecticut settler (b. 1600)
- December 31 – Charles de Lorme, French physician (b. 1584)