People in power

Africa
Ashanti Confederacy – Opoku Ware I, Asantehene (1720–1750)
Bunyoro – Duhaga, Omukama of Bunyoro (1731–c.1782)
Dahomey – Tegbesu, King of Dahomey (1732–1774)
Ethiopia – Iyasu II, Emperor of Ethiopia, (1730–1755)
Nkore – Macwa, Omugabe of Nkole, (c.1727–c.1755)
Zulu – Mageba kaPhunga, King of the Zulu (1727–1745)

Asia
China (Qing Dynasty) –
1. Yongzheng, Emperor of China (1723–1735)
2. Qianlong, Emperor of China (1735–1796)
Japan
1. Monarch –
1. Nakamikado, Emperor of Japan (1709–1735)
2. Sakuramachi, Emperor of Japan (1735–1747)
2. Shogun (Tokugawa) – Tokugawa Yoshimune, Shogun of Japan (1716–1745)
3. Ryūkyū Kingdom – Shō Kei, King of Ryūkyū (1713–1751)
Korea (Joseon Dynasty) – Yeongjo, King of Joseon (1724–1776)

Middle East and North Africa
Morocco –
1. Abdallah, Sultan of Morocco (1729–1735)
2. Ali, Sultan of Morocco (1735–1736)
Tunis – Ali I, Bey of Tunis (1735–1756)

Europe
Denmark–Norway –
Monarch – Christian VI, King of Denmark (1730–1746)
Prime Minister –
1. Ivar Eriksen Rosencrantz, Minister of State of Denmark (1730–1735)
2. Johan Ludvig, Minister of State of Denmark (1735–1751)

France – Louis XV, King of France (1715–1774)

Great Britain –
Monarch – George II, King of Great Britain (1727–1760)
Prime Minister – Robert Walpole, Prime Minister of Great Britain (1721–1742)

Holy Roman Empire – Charles VI, Holy Roman Emperor (1711–1740)

Ottoman (Turkish) Empire
Sultan – Mahmud I, Sultan of the Ottoman Empire (1730–1754)
Grand Vizier –
1. Hekimoglu Ali Pasha, Ottoman Grand Vizier (1732–1735)
2. Gürcü Ismail Pasha, Ottoman Grand Vizier (1735)

Portugal – John V, King of Portugal (1706–1750)

Prussia – Frederick William I, King of Prussia (1713–1740)

Russia – Anna Ivanovna, Tsaritsa of Russia (1730–1740)

Spain – Philip V, King of Spain (1700–1724, 1724–1746)

Sweden – Age of Liberty
Monarch – Frederick I, King of ..., also Landgrave of Hesse-Kassel (1720–1751)
Prime Minister – Arvid Horn, President of the Privy Council Chancellery (1710–1738)

Tuscany – Gian Gastone de' Medici, Grand Duke of Tuscany (1723–1737)

United Provinces
Estates of Friesland, Groningen, Guelders, Holland, Overijssel, Utrecht, Zeeland (1581–1795)
Grand Pensionary of Holland – Simon van Slingelandt (1727–1736)
Friesland – Willem IV, Stadtholder of Friesland (1711–1751)
Groningen – Willem IV, Stadtholder of Groningen (1729–1751)
Guelders – Willem IV, Stadtholder of Guelders (1722–1751)

Venice – Alvise Pisani Doge of Venice (1735–1741)

Philadelphia

This is the Pennsylvania State House, Philadelphia, USA, where the Second Continental Congress signed the Declaration of Independence and where, a decade later, delegates to the "Philadelphia Convention" formulated the Constitution. The Pennsylvania Assembly, which had been meeting in homes and taverns, moved into the building in September 1735. It was considered the most ambitious public building in the colonies.

American Politicians

If you check here you will find list of 15 American politicians (with links) born in 1735. John Adams is the most famous.