After loosing his post as tutor to the Duke of York (whose father Charles I was still King at this time) Moore went to London where he hoped to make a living as a teacher of mathematics. However, he found it difficult to find sufficiently many pupils so Moore was happy to be appointed as a surveyor in 1649. His task was to work on the draining of the Fens, a natural region of about 40,100 sq km of reclaimed marshland in eastern England between Lincoln and Cambridge. Around the same time as he took up this post as a surveyor, he published a mathematical textbook Arithmetick (1650).
Moore made a reputation for himself in this job and soon was appointed to other surveying jobs. In  Moore's work at this time is described as follows:-
He gained reputation by his success in keeping the sea out of Norfolk, surveyed the coasts, and constructed a map of Cambridgeshire...The Convention Parliament of 1660 declared the restoration of the king and lords. They disbanded the army and established an income for the king, Charles II, by keeping the parliamentary innovation of the excise tax. Charles II returned to London and Moore republished his Arithmetick together with A New Contemplation General upon the Ellipsis and Conical Sections taken from Mydorge. The dedication of the republished work shows that Moore was working hard to find favour with the new regime.
In 1663 Moore was sent to Tangier to conduct a survey and to report on its fortifications. Here he was involved in the ambitious project to build a massive harbour wall. He received a knighthood in 1669 and was appointed to high office as Surveyor-General of the Ordnance.
However Moore is not particularly famous for the mathematics which he did: as a mathematician he is best known as the first to use the notation cot. Rather Moore is famous for his strong support of mathematics and astronomy which made many other mathematical and astronomical advances possible. Perhaps his most important contribution was in his efforts to set up the Royal Observatory at Greenwich and his efforts to support Flamsteed. In 1674 he invited Flamsteed to London, see :-
... with the design of installing him in a small observatory of his own in Chelsea College, but procured from the king instead the foundation of the Royal Observatory. He furnished him, moreover, at his private expense, with a seven foot sextant employed in Flamsteed's observations until 1688 as well as two clocks...These clocks were used by Flamsteed in his work involving finding the longitude. A recent work by Willmoth  goes futher than earlier authors in describing Moore's contribution to the founding of the Royal Observatory claiming, with much supporting evidence, that he was:-
... the sole driving force behind the scheme.Moore, together with the famous diary writer Samuel Pepys, founded the Royal Mathematical School within Christ's Hospital. This School was set up with the specific aim of training boys in navigation techniques so that they could serve the King at sea. Moore became a governor of the school and together with Perkins, a master at the school, he wrote a major mathematical work intended for use at the Royal Mathematical School. Moore died however before the work could be published. The work, A New system of the Mathematicks appeared in 1681. Moore wrote the sections on arithmetic, geometry, trigonometry and cosmography while the sections on algebra, Euclid and navigation were written by Perkins.
Aubrey describes Moore in  as:-
... one of the most accomplished gentlemen of his time: a good mathematician, and a good fellow. ... he was tall and very fat, thin skin, fair, clear grey eyes ...Moore died in 1679 while on a journey from Portsmouth to London. He wrote several books, other than those described above, including Modern Fortification (1673) and A Mathematical Compendium (1674). His Arithmetick was published for a third time in 1698, nearly 20 years after his death.
Article by: J J O'Connor and E F Robertson