Sectors - Italian Style
Galileo became so associated with the sector that many people incorrectly believed he was the instrument's only inventor. Even though the collection is small, the Museum's holdings suggest there was little consensus in seventeenth-century Italy about which arrangement of scales was most essential to mathematical practitioners' activities. Indeed, Galileo himself experimented with several different scales during the decade he spent working on the instrument before he formally published Operations of the Geometric and Military Compass. One reason for the variety is he started out thinking only about military applications but gradually decided to develop a general-purpose device. The Italian sectors in the collection might have been used for tasks ranging from positioning a cannon and designing fortifications to converting between systems of currency.
"Sectors - Italian Style" showing 4 items.
Italian-Style Sector
- Description
- This small brass instrument has two hinged arms, each with a steel point at the end. On one side, both arms have a single scale that runs from 8 (near the hinge) to 1 and is labeled Lin. Recta. If 1 is the full length of the line, 2 represents 1/2 the length, 3 is 1/3 the length, and so on. One arm on this side also has a scale marked with the number 3 at both ends. It is 1/3 the length of the instrument. The single scale on the other side runs from 15 to 6 and is labeled Lin. Circularis. It is used to indicate the length of arcs of a circle. If the points are set at opposite ends of the radius of a circle (the distance marked "6"), a polygon inscribed in the circle with sides equal to that distance will have six sides. A polygon inscribed in the circle at the separation marked "7" will have seven sides, and so on.
- Instruments of this type were introduced in Italy, probably by Guidobaldo del Monte, and first described by G. P. Gallucci in a book about mathematical instruments published in Venice in 1598. They were used into the seventeenth century, but they were superseded by more complicated sectors. In particular, Galileo expanded on and publicized the arrangement of scales in 1606, and his form became known as the Italian style.
- Reference: Galileo Galilei, Operations of the Geometric and Military Compass, trans. and intro. Stillman Drake (Washington, D.C.: Smithsonian Institution Press, 1978), 12.
- Location
- Currently not on view
- date made
- early 17th century
- ID Number
- MA*321678
- catalog number
- 321678
- accession number
- 245711
- Data Source
- National Museum of American History, Kenneth E. Behring Center
Italian-Style Sector by Jacobus Lusuerg
- Description
- The two arms on this brass hinged sector have decorative curves at one end. An acanthus scroll motif is on the hinge. Five double scales (i.e., the scales on one arm are identical to those on the other arm) are on one side. The scales are labeled on both legs. The outermost scale is labeled Metallorum and marked with the letters: Aur, Mer, Plu, Arg, Cup, Fer, Sta, Mar, Sax. These correspond to the specific weights of different metals. The second scale runs from 4 to 40 and is labeled Quadratrix Segmentorum. The third scale is marked with engravings of various polyhedra and the letters: D, I, C, S, O, T. It is labeled Solidorum Regularum. The fourth scale runs from 20 to 3. The letters D and R are on either side of the number 7. The scale is labeled Planorum AEqualium. The innermost scale runs from 10 to 180 and is labeled Graduum Circuli.
- The reverse side has four double scales. The outermost runs from 20 to 3 and is labeled Figurarum Regularium. The second runs from 1 to 100 and is labeled Planorum. The third runs from 1 to 125 and is labeled Solidorum. The innermost scale runs from 20 to 300 and is labeled Partium AEqualium. One arm has a scaled diagram, labeled Orthographia Munimentorum, for dividing various heights, lengths, and depths of military fortifications into sections. The other arm has a table labeled Tabula Ignographia Munimentorum that gives the proportional dimensions for areas of fortifications that have between four and ten sides.
- The outer edges of the arms have scales that run from 1/4 to 64. One is labeled Poids des boulets, and the other is labeled Calibre des pieces. Although most of the scales on this instrument reflect the Italian style of sector, these scales are typical of sectors made for the French market. See, for example, MA*321676 and MA*333929.
- In the closed position, the front of the sector reads: Iacobus Lusuerg (/) Mutinensis Faciebat (/) Roma Ao. 1683. Jacob Lusuerg and his son, Dominicus, made mathematical instruments in Rome and Modena from 1674 until 1719. Henry Russell Wray, the previous owner of this instrument, graduated from the University of Pennsylvania and was a businessman in Colorado Springs, Colo., in the early 20th century.
- References: Jim Bennett and Stephen Johnston, The Geometry of War, 1500–1750 (Oxford: Museum of the History of Science, 1996); Maya Hambly, Drawing Instruments, 1580–1980 (London: Sotheby's Publications, 1988), 25.
- Location
- Currently not on view
- Currently not on view
- date made
- 1683
- maker
- Lusuerg, Jacobus
- ID Number
- MA*316915
- accession number
- 228694
- catalog number
- 316915
- Data Source
- National Museum of American History, Kenneth E. Behring Center
Italian-Style Sector
- Description
- This brass instrument has two hinged arms, each with three curves at the end. Six double scales (i.e., the scales on one arm are identical to those on the other arm) are on one side. The outermost runs from 1 to 12 and is labeled "Forti" on one arm. The second scale is labeled "Lin : Metali :" on the other arm and marked with the letters: I, T, C, S, L, Q, G. These correspond to the specific weights of different metals. The third scale runs from 30 to 3 and is labeled "Div Cir" on the first arm. The fourth scale runs from 10 to 180 and is not labeled. The fifth scale runs from 5 to 100. The sixth scale is located where the two arms meet and is marked with engravings of various polyhedra. Two short single scales are on the lower arm near the hinge; one is marked L and the other is marked I.
- The reverse side also has six double scales. The outermost is marked with polyhedra. The second runs from 3 to 30 and is labeled sub poli on one arm. The third is a scale of equal parts that runs from 10 to 200. The fourth runs from 15 to 3 and is labeled Tetrag : on one arm. This is a scale of tetragonic lines, for squaring regular areas and the circle. The fifth runs from 10 to 100 and is labeled Qua on one arm. The innermost scale is marked 1/6 of the distance from the hinge with a 6, 1/5 of the way with a 5, and so on to halfway down the instrument with a 2. The scale is labeled "Divid :" on the lower arm.
- Galileo outlined this arrangement of scales in 1606, which is why this example is considered to be in the Italian style. The previous owner believed it was made in the 18th century. The inside edge of one arm is marked with the letters I S, but nothing else is known about the maker.
- Reference: Galileo Galilei, Operations of the Geometric and Military Compass, trans. and intro. Stillman Drake (Washington, D.C.: Smithsonian Institution Press, 1978).
- Location
- Currently not on view
- date made
- 18th century
- ID Number
- MA*317352
- catalog number
- 317352
- accession number
- 230279
- Data Source
- National Museum of American History, Kenneth E. Behring Center
Italian-Style Sector
- Description
- This copper-colored metal instrument has scrolling at the ends of both arms. The hinge is decorated with a floral pattern and is held together with a screw shaped like a flower. On one side, the sector has four unlabeled double scales. From the fold line out, these appear to be a scale of equal parts, running from 20 to [2]50 with the interval from 20 to 30 shorter than the rest of the intervals; a scale of unequal parts, running from 1 to 50; a scale for the quadrature of circle sections, running from 1 to 40; and a scale for the specific weights of metals, which is marked O, P, A, R, F, S, M, and P. Around the hinge reads: IN LEVITATE GRAVIS ("in lightness, seriousness"). The arms are engraved with two stars, floral designs, a bee, a bird, a hand holding dividers, a globe, and a carpentry square.
- The other side has four unlabeled double scales. The innermost scale runs from 3 to 15 and is presumably for tetragonic lines, although the numbers increase from the hinge out on this instrument but decrease from the hinge out on most sectors. The second scale runs from 13 to 3 and is probably for the sides of inscribed regular polygons. The "3" on the top arm is incorrectly engraved on the first scale. The third is evenly divided and runs from 18 to 1. The fourth scale is on the same line as the third scale. It is unevenly divided and runs from 17 to 1. The letter D is engraved below the fourth scale. Around the hinge reads: HISQVO[illegible] FINEM ("having end"). The arms are engraved with clouds, a sailing ship, castle towers above and below water, a bird, a dragon, and an inscription in Hebrew. According to Bernard Goldstein, who examined photograph P-64-112E of the object on 21 March 1973, the Hebrew inscription reads, "Keep your tongue from evil and your lips from saying deceits."
- The Smithsonian received this sector from New York University in 1963. It has similarities to the arrangement of scales typical of the Italian style of the instrument, but it is also quite different from surviving instruments known to have been made in Italy, France, or England in the 17th and 18th centuries. For another unusual mathematical instrument that may not be authentic, see MA*316861.
- Reference: Anthony Turner, "Sector," in Instruments of Science: An Historical Encyclopedia, ed. Robert Bud and Deborah Jean Warner (New York and London: Garland Publishing, 1998), 526–528.
- Location
- Currently not on view
- ID Number
- 1990.0646.03
- catalog number
- 326977
- accession number
- 1990.0646
- Data Source
- National Museum of American History, Kenneth E. Behring Center