From the book
Stobaeus, Volume I
John Stobaeus · Diotimos Editions · 2026
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At a Glance
- The wordGnōmōn has several uses.
- In StobaeusSuccessive odd numbers can be arranged as borders around a square: adding three to one gives four, and adding five gives nine.
- In this edition“Gnomon” retains the traditional term; “added border” explains its local function.
- A place to beginGnomons explain the relation of successive odd numbers to squares.
- English renderings
- gnomon; added border; figure-preserving addition
Meaning
Gnōmōn has several uses. In this arithmetic setting it is an added arrangement that enlarges a figure while preserving the relevant kind of shape.
Use in the book
Successive odd numbers can be arranged as borders around a square: adding three to one gives four, and adding five gives nine. The account compares this with an even-number construction of oblong figures. Gnomon here belongs to a visual presentation of number, not to the measurement of a shadow.
Places to read
- Arith.10cGnomons explain the relation of successive odd numbers to squares.
Translation in this edition
“Gnomon” retains the traditional term; “added border” explains its local function.
Source note
Wachsmuth, volume I, printed pp. 22. A gnomon can elsewhere be a pointer or sundial component. That sense should not displace the arithmetic construction described here.