# Dictionary of National Biography, 1885-1900/Nicholson, Peter

​NICHOLSON, PETER (1765–1844), mathematician and architect, was the son of a stonemason, and was born at Prestonkirk, East Lothian, on 20 July 1765. He was educated at the village school, where he showed considerable talent in mathematics, and studied geometry by himself far in advance of what was taught at the school. At the age of twelve he commenced to assist his father, but, the work proving uncongenial, he was soon after apprenticed to a cabinet-maker at Linton, Haddingtonshire, where he served for four years. His apprenticeship ended, he worked as a journeyman in Edinburgh, at the same time diligently studying mathematics, and at about the age of twenty-four proceeded to London. His fellow workmen, recognising his superior ingenuity, applied to him for instruction, and he accordingly opened an evening school for mechanics in Berwick Street, Soho. Succeeding in his enterprise, he was enabled to produce his first publication, ‘The Carpenter's New Guide,’ for which he engraved his own plates. In it he made known an original method of constructing groins and niches of complex forms. In 1800 he proceeded to Glasgow, where he practised for eight years as an architect. He removed to Carlisle in 1805, and, on the recommendation of Thomas Telford [q. v.], he was appointed architect to the county of Cumberland. He superintended the building of the new court-houses at Carlisle, from designs by Sir Robert Smirke [q. v.] In 1810 he returned to London, and began to give private lessons in mathematics, land surveying, geography, navigation, mechanical drawing, fortification, &c., and produced his ‘Architectural Dictionary.’ He commenced in 1827 a work called ‘The School of Architecture and Engineering,’ designed to be completed in twelve numbers, but the bankruptcy of the publishers prevented more than five numbers appearing. Nicholson lost heavily, and probably on that account went in 1829 to reside at Morpeth, Northumberland, on a small property left to him by a relative. In 1832 he removed to Newcastle-on-Tyne, where he opened a school. But he was apparently not pecuniarily successful, for in July 1834 a subscription was raised in the town and 320l. presented to him. His abilities were also recognised by his election in 1835 as president of the Newcastle Society for the Promotion of the Fine Arts, and many other local honours were bestowed on him. He died at Carlisle on 18 June 1844, and was buried in Christ Church graveyard, where a plain headstone marks the spot. A monument to his memory, by Robert William Billings [q. v.], was erected in the Carlisle cemetery in 1856 (cf. Edinburgh Building Chronicle for 1855, p. 175).
Nicholson was twice married. By his first wife who died at Morpeth on 10 Aug. 1832, he had one son, Michael Angelo (noticed below), and by his second wife a son and daughter, who survived him.
Nicholson's life was devoted to the improvement of the mechanical processes in building. His great ability as a mathematician enabled him to simplify and generalise many old methods, besides inventing new ones. He formulated rules for finding sections of prisms, cylinders, or cylindroids, which enabled workmen to execute handrails with greater facility and from less material than previously. For his improvements in the construction of handrailing the Society of Arts voted him their gold medal in April 1814. He was the first author who treated of the methods of forming the joints, and the hingeing and the hanging of doors and shutters, and was also the first to notice that Grecian mouldings were conic sections, and that the volutes of Ionic capitals ought to be composed of logarithmic spirals. He generalised and enlarged the methods of Philibert de L'Orme and Nicholas Goldmann for describing revolutions between any two given points in a given radius, and was the inventor of the application of orthographical projection to solids in general. His invention of the centrolinead for use in drawing perspective views procured for him the sum of twenty guineas from the Society of Arts in May 1814, and of a silver medal for improvements in the same instrument in the following year.
Nicholson was a claimant to the invention of a method for obtaining the rational roots, and of approximating to the irrational roots, of an equation of any order whatsoever. He ​had been led to the effort by a mathematician of the name of Theophilus Holdred, who showed him a method of his own, which to Nicholson appeared much confused. He then devised a plan on different lines, which the latter agreed to publish at the end of his own tract. Nicholson becoming dissatisfied with Holdred's proceedings, published his own plan in his ‘Rudiments of Algebra’ in 1819. On 1 July 1819 a paper on the same subject by Leonard Horner [q. v.] was read before the Royal Society. Nicholson considered that Horner's paper contained the substance of what he had just published, and wrote an account of the matter in the introduction to his ‘Essay on Involution and Evolution’ in 1820. The question of priority of invention is discussed in the ‘Companion to the British Almanack,’ 1839, pp. 43–6. He invented a new method of extracting the cube root, which is given in the ‘Civil Engineer,’ 1844 (p. 427). Nicholson never succeeded in turning his knowledge to pecuniary advantage. He was too apt to make use of his materials in more than one publication, and was involved in a chancery suit for some years, having violated his promise of making no further use of the plates in his ‘Architectural Dictionary.’ Towards the end of his life he entered into controversy with Sir Charles Fox [q. v.], engineer, as to his claim to having discovered a sure rule for the construction of the oblique arch. But Nicholson's mind was already enfeebled, and he proved unable to defend himself.
As an architect Nicholson did some useful work. The best of his executed designs are those for Castleton House and Corby Castle, both near Carlisle, a coffee-house at Paisley, additions to the university of Glasgow, and he laid out the town of Ardrossan in Ayrshire, intended as a fashionable bathing-place. Plans and elevations of all these are given in his ‘Architectural Dictionary,’ ii. 102–3, 774, 800. He also erected a timber bridge over the Clyde at Glasgow, and several dwelling-houses in the city.
His useful publications, most of which went through several editions both before and after his death, include: 1. ‘The Carpenter's New Guide,’ London, 1792, 1797, 1801, 1805, 1808, 1835; Philadelphia, 1848, 1854; London and Philadelphia, 1854, 1856; London, 1857. 2. ‘The Carpenter's and Joiner's Assistant,’ London, 1792, 1793, 1797, 1798, 1810. 3. ‘Principles of Architecture,’ London, 1795–8, 1809, 1836, 1841, 1848 (ed. Joseph Gwilt [q. v.]). 4. ‘The Student's Instructor,’ London, 1804, 1823, 1837, 1845. 5. ‘Mechanical Exercises,’ London, 1811, 1812, 1819, and under the title of ‘The Mechanic's Companion,’ London, 1824; Oxford, 1825; Philadelphia, 1856. 6. ‘Architectural Dictionary,’ London, 1812–19, 1835, 1852–4 (edited and largely rewritten by Lomax and Gunyon, 1855, 1857–62). The titles vary in the several editions; the last three contain portraits from a painting by W. Derby. 7. ‘A Treatise on Practical Perspective,’ London, 1815. 8. ‘An Introduction to the Method of Increments,’ London, 1817. 9. ‘Essays on the Combinatorial Analysis,’ London, 1818. 10. ‘The Rudiments of Algebra,’ London, 1819, 1824, 1837, 1839. 11. ‘Essay on Involution and Evolution,’ London, 1820 (for which Nicholson received the thanks of the Académie des Sciences at Paris). 12. ‘Treatise on the Construction of Staircases and Handrails,’ London, 1820, 1847. 13. ‘Analytical and Arithmetical Essays,’ London, 1820, 1821. 14. ‘Popular Course of Pure and Mixed Mathematics,’ London, 1822, 1823, 1825. 15. ‘Rudiments of Practical Perspective,’ London and Oxford, 1822. 16. ‘The New and Improved Practical Builder and Workman's Companion,’ London, 1823, 1837 (edited by T. Tredgold), 1847, 1848–50, 1853, 1861 (with a portrait by W. Derby). 17. ‘The Builder and Workman's New Director,’ London, 1824 (with portrait by T. Heaphy), 1827, 1834, 1836; Edinburgh, 1843; London, 1848. 18. ‘The Carpenter and Builder's Complete Measurer,’ London, 1827 (with portrait). 19. ‘Popular and Practical Treatise on Masonry and Stone-cutting,’ London, 1827, 1828, 1835, 1838. 20. ‘The School of Architecture and Engineering,’ five parts, London, 1828 (with portrait). 21. ‘Practical Masonry, Bricklaying, and Plastering’ (anon.), London, 1830 (revised by Tredgold. The portion on plastering was supplied by R. Robson, a journeyman plasterer). 22. ‘Treatise on Dialling,’ Newcastle, 1833, 1836. 23. ‘Treatise on Projection, with a Complete System of Isometrical Drawing,’ Newcastle, 1837; London, 1840. 24. ‘Guide to Railway Masonry,’ Newcastle, 1839; London, 1840, 1846; Carlisle, 1846; London, 1860 (with portrait by Edward Train). 25. ‘The Carpenter, Joiner, and Builder's Companion,’ London, 1846. 26. ‘Carpentry’ (anon.), London, 1849, 1857 (edited by Arthur Ashpitel; the book also contains works by other hands). 27. ‘Carpentry, Joining, and Building,’ London, 1851.
With John Rowbotham Nicholson published ‘A Practical System of Algebra,’ London, 1824, 1831, 1837, 1844, 1855, 1858, and a key to the same in 1825; and with his son, Michael Angelo Nicholson, ‘The Practical Cabinet Maker, Upholsterer, and Complete Decorator,’ London, 1826.
Nicholson also wrote articles on ​architecture, carpentry, masonry, perspective, projection, stereography, stereotomy, &c., for Rees's ‘Cyclopædia,’ and on carpentry for Brewster's ‘Edinburgh Encyclopædia.’ For both these works he prepared many of his own plates. He contributed to the ‘Philosophical Magazine’ in 1798 ‘Propositions respecting the Mechanical Power of the Wedge’ (pp. 316–319).
Michael Angelo Nicholson (d. 1842), architectural draughtsman, son of Peter, studied architectural drawing at the school of P. Brown in Wells Street. He engraved plates for his father's works and articles in cyclopædias, and lithographed in 1826 the folio plates for Inwood's ‘Erechtheion.’ Between 1812 and 1828 he exhibited architectural drawings at the Royal Academy. A plan and elevation for a house at Carstairs, Lanarkshire, designed by him, are given in his father's ‘New Practical Builder,’ 1823, p. 566. On the title-page of his ‘Five Orders’ he describes himself as professor of architecture and perspective. He kept a school for architectural drawing in Melton Place, Euston Square. He claims to have improved the centrolinead invented by his father, and to have invented the inverted trammel, an instrument for drawing ellipses. He died in 1842, leaving a large family. Besides ‘The Practical Cabinet Maker’ published with his father, his works include: 1. ‘The Carpenter and Joiner's Companion,’ London, 1826 (with Derby's portrait of his father). 2. ‘The Five Orders, Geometrical and in Perspective,’ London, 1834. 3. ‘The Carpenter's and Joiner's New Practical Work on Handrailing,’ London, 1836.
B. P.