gnomon

noun

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.

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.”

   “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.”

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.”

   “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.”

3. The index of the hour circle of a globe.

   “Index of a globe, the little style or gnomon, which being fixed on the pole of the globe, and turning round with it, points out the hours upon the hour circle.”

4. A plane figure formed by removing a parallelogram from a corner of a larger parallelogram.

   “If a Parallelogram be divided into four leſſer ones, by two Lines interſecting each other; and one of theſe Parallelograms be retrench'd, or taken away; the other three will make a Gnomon, ordinarily call'd a Square.”

5. A number representing the increment between two figurate numbers (“numbers equal to the numbers of dots in geometric figures formed of dots”).

   “[page 16] The figurate number's gnomon is therefore 1#43;nb in the general case. A trivial family of numbers, those for which b#61;0, might be called linear. […] [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.”