gnomon

Etymology

Borrowed from French gnomon, or directly from its etymon Latin gnōmōn, or directly from its etymon Ancient Greek γνώμων (gnṓmōn, “discerner, interpreter; carpenter’s square; gnomon of a sundial; (geometry) gnomon”), from γιγνώσκω (gignṓskō, “to be aware of; to perceive; to know”), ultimately from Proto-Indo-European *ǵneh₃- (“to know”); the word is thus related to know. The geometry sense (sense 4) is from the resemblance of the plane figure to a carpenter’s square. Similarly, a gnomon in mathematics (sense 5) is also shaped like a carpenter’s square when depicted pictorially if the figurate numbers are squares.

noun

1. An object such as a pillar or a rod that is used to tell time by the shadow it casts when the sun shines on it, especially the pointer on a sundial.
   Let a Gnomon, being firſt ſharpened into a Point, be ſhaped, and faſtned in ſuch wiſe, that it no way hinder either the draught of the Horizontal Line, or the Point of the ſhadow from having free access to the Dial at all times of the Year. […] Upon the Superfices of the Dial, obſerve the Point of the Shadow of the Gnomon (making a mark at it) and the Sun's Altitude, both of them at the ſame inſtant of time. 1700, Samuel Foster, “[Projective Dialling: … The Ninth Tractate. Appendix.] Chap. IV. A General and Most Easie Way to Project Hour-lines upon All Kinds of Superfices without any Regard had to Their Standing, either in respect of Declination or Inclination”, in William Leybourn, compiler, Dialling, Plain, Concave, Convex, Projective, Reflective, Refractive. Shewing, how to Make All such Dials, and to Adorn Them with All Useful Furniture Relating to the Course of the Sun;[…], 2nd edition, London: Printed by J. Matthews, for Awnsham and John Churchill[…], →OCLC, page 83
   The moſt celebrated gnomons, for examining the courſe of the ſun, which are exiſting at this time, have been ſuppoſed to be that in the church of St Petronio at Bologna, 89 Engliſh feet high; that of the Chartreux at Rome, about 67 feet; and that of St Sulpice at Paris, 86 feet. […] [T]he gnomon of the cathedral of that city [Florence], erected by [Paolo dal Pozzo] Toscanelli, in the courſe of the 16th century, whoſe height exceeds that of the three before-mentioned, taken all together, being near 300 Engliſh feet, and higher than our London monument by almoſt a third part. 1758 March, “An Account of an Ancient Astronomical Instrument, of Immense Dimensions, lately Restored to Use”, in Sylvanus Urban [pseudonym; Edward Cave], editor, The Gentleman’s Magazine, and Historical Chronicle, volume XXVIII, London: Printed by D[avid] Henry and R. Cave,[…], published January 1755, →OCLC, page 99, column 1
   [T]he gnomon being the upright, and the shadow the side, the square-root of the sum of the squares is the hypotenuse; […] 1817, Brahmegupta [i.e., Brahmagupta], Bháscara [i.e., Bhāskara I], “Shadow of a Gnomon”, in Henry Thomas Colebrooke, transl., Algebra, with Arithmetic and Mensuration, from the Sanscrit of Brahmegupta and Bháscara, London: John Murray,[…], →OCLC, page 108
   Approximate scales can be placed on near-field objects in pictures containing the gnomon by using an ellipse template. The Apollo 16 gnomon […] stands on three legs that, on a hard surface, define a circle 61.7 cm in diameter. 1981, R. M. Batson, V. S. Reed, R. L. Tyner, “Cartographic Procedures”, in George E. Ulrich, Carroll Ann Hodges, and William R[udolf] Muehlberger, editors, Geology of the Apollo 16 Area, Central Lunar Highlands[…] (Geological Survey Professional Paper; 1048), Washington, D.C.: United States Government Printing Office, →OCLC, page 530
2. An object such as a pillar used by an observer to calculate the meridian altitude of the sun (that is, the altitude of the sun when it reaches the observer's meridian), for the purpose of determining the observer's latitude.
   This muſt be performed by help of a Spherick Gnomon, (as Blaew Willem Janszoon Blaeu] calls it,) which is a ſmall Pin or Needle fixed perpendicularly into a ſmal Baſis with an hollow concave bottom, that it may ſtand upon the convexity of the Globe. 1659, Joseph Moxon, “Prob[lem] XVIII. Another Way to Find the Height of the Pole by the Globe; if the Place of the Sun be Given; and also to Find the Hour of the Day, and Azimuth, and Almicantar of the Sun.”, in A Tutor to Astronomie and Geographie: Or An Easie and Speedy Way to Know the Use of Both the Globes, Cœlestial and Terrestrial. In Six Books.[…], London: Printed by Joseph Moxon; […], →OCLC, 2nd book (Shewing the Practical Use of the Globes. Applying Them to the Solution of Astronomical and Geographical Problemes.), page 56
   In order to aſcertain the latitude of any place, the ancients obſerved the meridian altitude of the ſun, either by means of the ſhadow of a perpendicular gnomon, or by means of an aſtrolabe, from which it was eaſy to compute how many degrees and minutes the place of obſervation was diſtant from the Equator. 1791, William Robertson, “Section II. Intercourse with India, from the Establishment of the Roman Dominion in Egypt, to the Conquest of that Kingdom by the Mahomedans”, in An Historical Disquisition Concerning the Knowledge which the Ancients had of India;[…], London: Printed for A[ndrew] Strahan, and T[homas] Cadell[…]; Edinburgh: E. Balfour, →OCLC, pages 78–79
3. The index of the hour circle of a globe.
4. (geometry) A plane figure formed by removing a parallelogram from a corner of a larger parallelogram.
5. (mathematics, by extension) A number representing the increment between two figurate numbers (“numbers equal to the numbers of dots in geometric figures formed of dots”).
   https://books.google.com/books?id=R0d76m-Be10C&pg=PA16 page 16 The figurate number's gnomon is therefore 1+nb in the general case. A trivial family of numbers, those for which b=0, might be called linear. […] https://books.google.com/books?id=R0d76m-Be10C&pg=PA17 page 17 Clearly, a figurate number of rank n is equal to the sum of its first n gnomons, and in particular the sum of the first n odd numbers is equal to n². 1999, Midhat J. Gazalé, “Figurate and m-adic Numbers”, in Gnomon: From Pharaohs to Fractals, Princeton, N.J., Chichester, West Sussex: Princeton University Press, pages 16 and 17