Protractor and Shadow Square

Protractor and Shadow Square

Usage conditions apply
This brass semicircular protractor is divided by single degrees and marked by fives from 5° to 180°. The letter X is at the 90-degree mark. The upper right side of the protractor contains a shadow square. This is divided on both sides into sets of four units, each approximately 3/8" long and numbered from 1 to 12, for a total of 48 units on each side. The vertical side is marked: OMBRA VERSA. The horizontal side is marked (upside down): OMBRA RETTA.
The scale on the "ombra versa" side measured tangents from 0 to 45°. The scale on the "ombra retta" (or "recta") side measured tangents from 45° to 90°. The lines for degrees and on the shadow square appear to be made by hand, perhaps by placing the instrument next to a pattern. The instrument is decorated with floral and solar motifs. The protractor rests in a brass base that unfolds to form a limb, which is chipped. There are two holes in the limb; the numbers 2 and 1 are scratched next to the holes. There are four holes in the base; the numbers 3 and 1 are scratched next to the outermost holes, which align with the holes on the limb. This instrument is Italian in origin and was likely made before 1800. New York University donated the object in 1963.
Reference: J. A. Bennett, The Divided Circle (Oxford, 1987), 42–43.
Currently not on view
Object Name
protractor and geometric square
date made
18th century
place made
Physical Description
brass (overall material)
overall: 34.8 cm x 13.4 cm x.8 cm; 13 11/16 in x 5 1/4 in x 5/16 in
ID Number
catalog number
accession number
Credit Line
Gift of New York University
See more items in
Medicine and Science: Mathematics
Science & Mathematics
Data Source
National Museum of American History
Nominate this object for photography.   

Our collection database is a work in progress. We may update this record based on further research and review. Learn more about our approach to sharing our collection online.

If you would like to know how you can use content on this page, see the Smithsonian's Terms of Use. If you need to request an image for publication or other use, please visit Rights and Reproductions.


What is the 20C origins of the now common used Solar protractor to determine the angel and azimuth of the sun in order to measure shading devices.

Note: Comment submission is temporarily unavailable while we make improvements to the site. We apologize for the interruption. If you have a question relating to the museum's collections, please first check our Collections FAQ. If you require a personal response, please use our Contact page.