Graphometer on:
[Wikipedia]
[Google]
[Amazon]
The graphometer, semicircle or semicircumferentor is a
"Graphometer"
article of the Smithsonian
Le Nôtre's ('The theory and practice of gardening'), published in 1709, described the use of the graphometer in transferring geometric shapes from garden plans onto landscapes at a large scale.
The graphometer, semicircle or semicircumferentor is a surveying
Surveying or land surveying is the technique, profession, art, and science of determining the land, terrestrial Plane (mathematics), two-dimensional or Three-dimensional space#In Euclidean geometry, three-dimensional positions of Point (geom ...
instrument used for angle
In Euclidean geometry, an angle can refer to a number of concepts relating to the intersection of two straight Line (geometry), lines at a Point (geometry), point. Formally, an angle is a figure lying in a Euclidean plane, plane formed by two R ...
measurements. It consists of a semicircular limb
Limb may refer to:
Science and technology
*Limb (anatomy), an appendage of a human or animal
*Limb, a large or main branch of a tree
*Limb, in astronomy, the curved edge of the apparent disk of a celestial body, e.g. lunar limb
*Limb, in botany, t ...
divided into 180 degrees and sometimes subdivided into minutes. The limb is subtended by the diameter with two sights
A sight or sighting device is any device used to assist in precise visual alignment (i.e. ''aiming'') of weapons, surveying instruments, aircraft equipment, optical illumination equipment or larger optical instruments with the intended target. ...
at its ends. In the middle of the diameter a "box and needle" (compass
A compass is a device that shows the cardinal directions used for navigation and geographic orientation. It commonly consists of a magnetized needle or other element, such as a compass card or compass rose, which can pivot to align itself with No ...
) is fixed. On the same middle the alidade
An alidade () (archaic forms include alhidade, alhidad, alidad) or a turning board is a device that allows one to sight a distant object and use the line of sight to perform a task. This task can be, for example, to Triangulation (surveying), tr ...
with two other sights is fitted. The device is mounted on a staff via a ball and socket joint. In effect the device is a half-circumferentor
A circumferentor, or surveyor's compass, is an instrument used in surveying to measure horizontal angles. It was superseded by the theodolite in the early 19th century.
A circumferentor consists of a circular brass box containing a magnetic n ...
. For convenience, sometimes another half-circle from 180 to 360 degrees may be graduated in another line on the limb. Pages: vol. 1 p. 179 for "Graphometer", vol. 2 p. 50 for "Semi-Circle"
The form was introduced in Philippe Danfrie
Philippe Danfrie the elder (about 1532 – 1606) was a designer and maker of mathematical instruments in metal and paper, as well as a type-cutter, engraver, minter of coins and medals, publisher and author. Much is known about Danfrie's life and a ...
's (Paris, 1597) and the term ''graphometer'' was popular with French geodesists
Geodesy or geodetics is the science of measuring and representing the geometry, gravity, and spatial orientation of the Earth in temporally varying 3D. It is called planetary geodesy when studying other astronomical bodies, such as planets ...
. The preferable English-language terms were ''semicircle'' or ''semicircumferentor''. Some 19th-century graphometers had telescopic rather than open sights.J. A. Bennett, "The Divided Circle" (Oxford, 1987), pp. 49-50, as quoted in th"Graphometer"
article of the Smithsonian
Le Nôtre's ('The theory and practice of gardening'), published in 1709, described the use of the graphometer in transferring geometric shapes from garden plans onto landscapes at a large scale.
Usage
To measure an angle, say, EKG, the diameter middle C is placed at the angle apex K using the plummet at point C of the instrument. The diameter is aligned with leg KE of the angle using the sights at the ends of the diameter. The alidade is aligned with the leg KG using another pair of sights, and the angle read off the limb as marked by the alidade. Further uses of the graphometer are the same as those of the circumferentor.References