Having studied mathematics under John Machin and John Keill, he obtained in 5708 a remarkable solution of the problem of the " centre of oscillation," which, however, remaining unpublished until May 5754 (Phil.
About the same time John Machin calculated it correct to Ioo places, and, what was of more importance, gave for the ratio the rapidly converging expression 4 _ I I 5 I 3152+ 5 1 54 - 7 1 5b?.
On the retirement of Potemkin (q.v.) in 1791, Repnin succeeded him as commander-in-chief, and immediately routed the grand vizier at Machin, a victory which compelled the Turks to accept the truce of Galatz (31st of July 1791).
The following Roman towns have been identified: (i) in the Dobrudja, Cius (Hirsova), Troesmis (Iglitza), Arrubium (Machin), Viodunum (Isakcha), Istrus (Karaharman), Tropaeum (Adam Klissi), Kallatis (Mangalia), Tomi (Constantza); (2) in Moldavia, Dinogetia (Tiglina); (3) in Walachia, Drobetae (Turnu Severin), Malva (Celeiu), Castra Nova (Craiova), Romula (Resca), Sorium (Roshiori de Vede), Pelendava (Bradesci), Acidava (Jenuseshti), Rusidava (Dragasani), Castro Traiana (Ramnicu Valcea), Arutela (Bivolari), Pons Vetus (Caineni), Komidava (Petroasa), Ramidava (Buzeu).
It was soon afterwards translated into English by Raphson; and a second edition of it, with improvements by the author, was published at London in 1712, by Dr Machin, secretary to the Royal Society.
The story of the rediscovery of Madeira by the Englishman Robert Machim or Machin, eloping from Bristol with his lady-love, Anne d'Arfet, in the reign of Edward III.