Who invented Jacob Staff ?

The term Jacob's staff, also cross-staff, a ballastella, a fore-staff, or a balestilha, is used to refer to several things. In its most basic form, a Jacob's staff is a stick or pole with length markings; most staffs are much more complicated than that, and usually contain a number of measurement and stabilization features. 

In navigation the instrument is also called a cross-staff and was used to determine angles, for instance the angle between the horizon and Polaris or the sun to determine a vessel's latitude, or the angle between the top and bottom of an object to determine the distance to said object if its height is known, or the height of the object if its distance is known, or the horizontal angle between two visible locations to determine one's point on a map.

The Jacob's staff, when used for astronomical observations, was also referred to as a radius astronomicus. With the demise of the cross-staff, in the modern era the name "Jacob's staff" is applied primarily to the device used to provide support for surveyor's instruments.

The origin of the name of the instrument is not certain. Some refer to the Biblical patriarch Jacob, specifically Gen 32:11. It may also take its name after its resemblance to Orion, referred to by the name of Jacob on some medieval star charts. Another possible source is the Pilgrim's staff, the symbol of St James (Jacobus in Latin). The name cross staff simply comes from its cruciform shape.

The original Jacob's staff was developed as a single pole device in the 14th century that was used in making astronomical measurements. It was first described by the Jewish mathematician Levi ben Gerson of Provence. However, its invention was likely due to Jacob ben Makir who also lived in Provence in the same period. Attributions to 15th century astronomer Georg Purbach are less likely correct, since Purbach was not born until 1423. Such attributions may refer to a different instrument with the same name. May states that its origins can be traced to the Chaldeans around 400 BC.

Although it has become quite accepted that Levi ben Gerson first described Jacob's staff, the Sinologist Joseph Needham theorizes that the Song Dynasty Chinese scientist Shen Kuo (1031–1095), in his Dream Pool Essays of 1088, described a Jacob's staff. Shen was an antiquarian interested in ancient objects; after he unearthed an ancient crossbow-like device from a home's garden in Jiangsu, he realized it had a sight with a graduated scale that could be used to measure the heights of distant mountains, likening it to how mathematicians measure heights by using right-angle triangles. He wrote that when one viewed the whole breadth of a mountain with it, the distance on the instrument was long; when viewing a small part of the mountainside, the distance was short; this, he wrote, was due to the cross piece that had to be pushed further away from the eye, while the graduation started from the further end. Needham does not mention any practical application of this observation.