Busacca Gallery

🔥 Note, if any material is found to be questionable after a thorough examination and a determination that it might violate existing legal regulations, it is important to emphasize that Busacca Gallery would be prohibited from selling or distributing such material in compliance with current laws. It should be noted that Busacca Gallery's ability to make such determinations relies on the physical and careful execution of comprehensive testing and meticulous scrutiny by scholarly experts well-versed in the relevant subject matter. The description represents a simple story and opinion with the intention of stimulating conversation and providing education through its historical narrative. Busacca Gallery diligently endeavors to adhere to legal regulations and apologizes for any misrepresentations or confusion. For any inquiries, please do not hesitate to contact us. 415-215-6533 🎯 Very old antique folding sector hand tool. brass and ivory calculation aid sector rule. Signed G.Davis. Leeds. A vintage articulated folding handmade scrimshaw sector ruler measuring 12" inches when completely unfolded in deep old yellow ivory. A sector is an instrument consisting of two rulers of equal length which are joined by a hinge. A number of scales are inscribed upon the instrument which facilitate various mathematical and trigonometrical calculations. Open the instrument fully and examine the long outside edge. This edge is marked with a scale divided into ten equal parts, each of these are further subdivided into ten parts. This scale is known as the scale of decimals. On one flat side, close to the outside edge of the sector in a scale of inches. Typically a small pocket sector will be twelve inches long when opened out. On the other side are three long scales parallel to the long outside edge of the sector. These are marked N , S and T . The line N is a Gunter Line, that is to say, a line marked in a logarithmic scale. The other two lines S and T are the lines of sines and tangents respectively. These three scales are usually referred to as the Lines of Artificial Numbers. The other scales all radiate out from the point where the two rules are hinged and are used with the sector open at an angle. Many of these scales are inscribed twice, once on each leg of the sector are are referred to as double scales. These will be described individually in more detail below. When the compasses are used on a scale to measure a length from the centre it is called a lateral distance. For example distance x in Figure 2. When a measure is taken from any point on the line, to its corresponding point on the line of the same denomination, on the other leg, it is called a transverse distance. For example, the distance y in Figure 2. Calculations possible and the principle involved The sector can be used to perform many different numerical and plane or spherical trigono- metrical calculations. There are two principal modes of operation; • fully open as a straight rule,
• partially open with the scales radiating out from the centre. At all times the sector is used in conjunction with a pair of compasses. Galileo Galilei (1564-1642) Popularized the sector at the very end of the 16th Century. The sector is a graduated ruler that uses trigonometric formulae and a caliper to calculate squares, cubes, reciprocals and tangents of numbers. Galileo's design of the sector as a mathematical tool can be seen as the moment when calculation aids cease to be based upon counting and instead exploit the deeper relationships among numbers. His invention is still in use as a navigation aid in the 20th century 300 years later.(ref: Oughtred Society) Sectors were frequently included in sets of drawing instruments in the eighteenth and nineteenth centuries until made obsolete by the slide rule. There are three types of scale on an English sector: sectoral ones (radiating from the hinge centre), which were used for calculation; plane scales (logarithms, sines, tangents) parallel to the edge; and rules (inches, tenths of feet). Most were six inches in length. Although the sector was a standard component in a set of mathematical instruments there is little evidence that they were ever used for practical calculations. In fact, the smaller pocket sectors would have been little or no use because of the difficulty in accurate use. Compass points damage scales with regular use which reduces the accuracy of the instrument. The number of well preserved sectors that exist would add weight to the school of thought which claims they were of little practical utility. We are committed to enhancing our customer’s lives by discovering creating, and pointing out only the best art we can find in the world today. We Are Taste-Makers, Art Advisers & Consultants.

Link: http://en.wikipedia.org/wiki/Sector_(instrument)

The sector, also known as a proportional compass or military compass, was a major calculating instrument in use from the end of the sixteenth century until the nineteenth century. It is an instrument consisting of two rulers of equal length joined by a hinge. A number of scales are inscribed upon the instrument which facilitate various mathematical calculations. It was used for solving problems in proportion, trigonometry, multiplication and division, and for various functions, such as squares and cube roots. Its several scales permitted easy and direct solutions of problems in gunnery, surveying and navigation. The sector derives its name from the fourth proposition of the sixth book of Euclid, where it is demonstrated that similar triangles have their like sides proportional. It has four parts, two legs with a pivot (the articulation), a quadrant and a clamp (the curved part at the end of the leg) that enables the compass to function as a gunner's quadrant.



The sector was invented, essentially simultaneously and independently, by a number of different people just prior to the start of the 17th century. The credit is usually given to either Thomas Hood, a British mathematician, or to the Italian mathematician and astronomer Galileo Galilei. Galileo, with the help of his personal instrument maker Marc'Antonio Mazzoleni, created more than 100 copies of his military compass design and trained students in its use. Of the two credited inventors, Galileo is certainly the most famous, and earlier studies usually attributed its invention to him.





The instrument can be used to graphically solve questions of proportion, and relies on the principle of similar triangles. Its vital feature is a pair of jointed legs, which carry paired geometrical scales. In use, problems are set up using a pair of dividers to determine the appropriate opening of the jointed legs and the answer is taken off directly as a dimension using the dividers. Specialised scales for area, volume and trigonometrical calculations, as well as simpler arithmetical problems were quickly added to the basic design.

Different versions of the instrument also took different forms and adopted additional features. The type publicised by Hood was intended for use as a surveying instrument, and included not only sights and a mounting socket for attaching the instrument to a pole or post, but also an arc scale and an additional sliding leg. Galileo's earliest examples were intended to be used as gunner's levels as well as calculating devices.

The sector was a very useful instrument at a time when artisans and military men were poorly educated in mathematics and, often, were unable to perform even elementary arithmetical operations. The inaccuracy induced by the analog scales of the sector were usually of no concern to those attempting to find a rapid solution to an approximate problem. It is striking, however, that the disciplines to which these instruments were applied, particularly perspective, music, architecture and fortification, traditionally classed as mechanical sciences, soon emerged as mathematical sciences in the seventeenth century. Indeed there is evidence that the universality of these practical applications helped to make possible the universality of science at a theoretical level. Hence this technology was not simply a consequence of advances in science. Rather, the technology helped make possible the mathematical sciences that led to modern science.