In the early 18th century, the second frame was eliminated, and the Russian abacus acquired its present appearance. The introduction of Arabic numerals and a new taxation system entailed the loss of the rows for fractions in the late 17th century. If, for example, the sokha is equal to 48 monetary units, then the above fraction is equal to 12 + 8 + 3 = 23 monetary units. Sometimes operations on fractions were performed as operations on whole numbers by setting the sokha equal to a certain amount of money. Fractions were added without reduction to a common denominator an example of a typical sum is 1/4 + 1/6 + 1/16. For example, the counter under the row with three counters represented one-half of one-third, and the counter under this counter represented one-half of one-half of one-third. Located under these fraction rows were rows containing one counter each: each counter represented one-half of the fraction it was under. Doshchanyi schet (from a 17th century drawing) the number represented on the left is ¼ + ⅙ +, and the amount shown on the right is 30 rubles 18 altyny 2¼ den’giĬounters represented four fourths. Operations on fractions were performed on incomplete rows: a row of three counters represented three thirds, and a row of four Since the decimal number system was used, each whole-number row had nine or ten counters (Figure 2). Counters were strung on taut strings or wires running across the frame. The second frame was needed because of the nature of the monetary system. Each frame was divided into two sections (in later types only the lower part of the frame was so divided). The doshchanyi schet consisted of two frames that could be folded together. This system required the addition, subtraction, multiplication, and division not only of whole numbers but also of fractions, since the unit of taxation, the sokha, was divisible into parts. The development of the doshchanyi schet was greatly influenced by the system of taxation used in Russia from the 15th to 17th centuries ( see SOSHNOE PIS’MO). The forerunner of the modern Russian abacus was the doshchanyi schet (counting board), which first appeared in Russia in the 16th century. Russian abacus the number represented is 401.28 Pullan, The History of the Abacus (1968) P. Another type of abacus includes a board covered with sand or wax to facilitate making and erasing marks. A special merit of the abacus was that it simplified the addition and subtraction of numbers written in Roman numerals. An apparatus of pebbles or other movable counters was known in antiquity to the Egyptians, Greeks, Romans, and Chinese. The abacus is used for calculating in the Middle East, Asia, and Russia and for teaching children the elements of arithmetic in many countries. More elaborate processes are used to perform multiplication and division. Subtraction can be performed by separating groups of beads. The number 398 is now represented on the abacus. To add 243 to 155, three more beads on the units wire are slid over to join the group of five, four more beads on the tens wire join the five there, and two more beads on the hundreds wire join the one there. To represent 155, five beads on the units wire are separated from the others on that wire, five beads on the tens wire, and one bead on the hundreds wire. Numbers are represented and added together on the abacus by grouping beads together. For example, all of the beads on a particular wire may have a value of 1, making this the units wire, or 10, making this wire the tens wire. Each bead on a given wire has the same value: either ten or some multiple or submultiple of ten. An elementary abacus might have ten parallel wires strung between two boards on a frame, with nine beads on each wire. The type of abacus now best known is represented by a frame with sliding counters. In Gothic work the form varies, appearing in square, circular, and octagonal forms with molded members.Ībacus (ăbˈəkəs, əbăkˈ–), in mathematics, simple device for performing arithmetic calculations. In Romanesque work the abacus is heavier in proportion, projects less, and is generally molded and decorated. In classical orders it varies from a square form having unmolded sides in the Greek Doric, to thinner proportions and ovolo molding in the Greek Ionic, and to sides incurving and corners cut in Roman Ionic and Corinthian examples. Abacus (ăbˈəkəs), in architecture, flat slab forming the top member of a capital.
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