1018:
1754:
582:
1497:
250:
574:
47:
1860:
1749:{\displaystyle F_{\theta }=\mathbf {F} _{A}\cdot {\frac {\partial \mathbf {v} _{A}}{\partial {\dot {\theta }}}}-\mathbf {F} _{B}\cdot {\frac {\partial \mathbf {v} _{B}}{\partial {\dot {\theta }}}}=a(\mathbf {F} _{A}\cdot \mathbf {e} _{A}^{\perp })-b(\mathbf {F} _{B}\cdot \mathbf {e} _{B}^{\perp })=aF_{A}-bF_{B},}
257:
A lever is a beam connected to ground by a hinge, or pivot, called a fulcrum. The ideal lever does not dissipate or store energy, which means there is no friction in the hinge or bending in the beam. In this case, the power into the lever equals the power out, and the ratio of output to input force
589:
Levers are classified by the relative positions of the fulcrum, effort and resistance (or load). It is common to call the input force "effort" and the output force "load" or "resistance". This allows the identification of three classes of levers by the relative locations of the fulcrum, the
556:
This relationship shows that the mechanical advantage can be computed from ratio of the distances from the fulcrum to where the input and output forces are applied to the lever, assuming a weightless lever and no losses due to friction, flexibility or wear. This remains true even though the
793:
As the lever rotates around the fulcrum, points farther from this pivot move faster than points closer to the pivot. Therefore, a force applied to a point farther from the pivot must be less than the force located at a point closer in, because power is the product of force and velocity.
1437:
2163:
4400 B.C. Earliest evidence of the use of a horizontal loom is its depiction on a pottery dish found in Egypt and dated to this time. These first true frame looms are equipped with foot pedals to lift the warp threads, leaving the weaver's hands free to pass and beat the weft
1307:
738:
comprises several levers acting in series: the resistance from one lever in a system of levers acts as effort for the next, and thus the applied force is transferred from one lever to the next. Examples of compound levers include scales, nail clippers and piano keys.
1152:
371:
1324:
1198:
552:
1951:
911:
287:
1855:
1047:
656:– Effort is located between the resistance and the fulcrum: The resistance (or load) is applied on one side of the effort and the fulcrum is located on the other side, e.g. a pair of
2108:
The Genius of
Archimedes -- 23 Centuries of Influence on Mathematics, Science and Engineering: Proceedings of an International Conference held at Syracuse, Italy, June 8-10, 2010
282:
627:– Resistance (or load) is located between the effort and the fulcrum: The effort is applied on one side of the resistance and the fulcrum is located on the other side, e.g. a
480:
597:– Fulcrum is located between the effort and the resistance: The effort is applied on one side of the fulcrum and the resistance (or load) on the other side. For example, a
433:
790:
The lever is a movable bar that pivots on a fulcrum attached to a fixed point. The lever operates by applying forces at different distances from the fulcrum, or a pivot.
676:
of a human skull. Since the effort arm is smaller than the load arm, the lever's mechanical advantage is always less than 1. It is also called a speed multiplier lever.
650:
of a car. Since the load arm is smaller than the effort arm, the lever's mechanical advantage is always greater than 1. It is also called a force multiplier lever.
241:
Autumn
Stanley argues that the digging stick can be considered the first lever, which would position prehistoric women as the inventors of lever technology.
2063:
1978:
where the output force is applied, then the lever amplifies the input force. If the opposite is true that the distance from the fulcrum to the input point
106:. A lever is a rigid body capable of rotating on a point on itself. On the basis of the locations of fulcrum, load and effort, the lever is divided into
51:
Levers can be used to exert a large force over a small distance at one end by exerting only a small force (effort) over a greater distance at the other.
2388:
962:
A lever is modeled as a rigid bar connected to a ground frame by a hinged joint called a fulcrum. The lever is operated by applying an input force
490:
227:, workmen used the lever to move and uplift obelisks weighing more than 100 tons. This is evident from the recesses in the large blocks and the
1890:
850:
2338:
1432:{\displaystyle \mathbf {v} _{A}={\dot {\theta }}a\mathbf {e} _{A}^{\perp },\quad \mathbf {v} _{B}={\dot {\theta }}b\mathbf {e} _{B}^{\perp },}
234:
The earliest remaining writings regarding levers date from the 3rd century BC and were provided, by common belief, by the Greek mathematician
2299:
2269:
2233:
2111:
2313:
2205:
Stanley, Autumn (1983). ""Women Hold Up Two-Thirds of the Sky: Notes for a
Revised History of Technology."". In Rothschild, Joan (ed.).
2239:
1793:
621:(pulling a nail). With the fulcrum in the middle, the lever's mechanical advantage may be greater than, less than, or even equal to 1.
2457:
2189:
2156:
2119:
114:
identified by
Renaissance scientists. A lever amplifies an input force to provide a greater output force, which is said to provide
1302:{\displaystyle \mathbf {r} _{A}-\mathbf {r} _{P}=a\mathbf {e} _{A},\quad \mathbf {r} _{B}-\mathbf {r} _{P}=b\mathbf {e} _{B}.}
2354:
2082:
258:
is given by the ratio of the distances from the fulcrum to the points of application of these forces. This is known as the
2381:
2472:
2024:
163:
2467:
224:
123:
172:, meaning "light", "easy" or "nimble", among other things. The PIE stem also gave rise to the English word "light".
238:, who famously stated "Give me a lever long enough and a fulcrum on which to place it, and I shall move the world."
2462:
2374:
2007:
2018:
2426:
2002:
1485:
31:
122:
gained in the system, equal to the ratio of the output force to the input force. As such, the lever is a
2012:
1956:
847:, so we have the ratio of the output force to the input force, or mechanical advantage, is given by:
785:
438:
119:
2285:
2181:
397:
1147:{\displaystyle a=|\mathbf {r} _{A}-\mathbf {r} _{P}|,\quad b=|\mathbf {r} _{B}-\mathbf {r} _{P}|,}
2360:
2305:
2295:
2265:
2229:
2185:
2152:
2148:
2115:
1996:
1489:
181:
2289:
2221:
277:, about the fulcrum. If the distance traveled is greater, then the output force is lessened.
950:
The use of velocity in the static analysis of a lever is an application of the principle of
647:
266:
135:
93:
366:{\displaystyle {\begin{aligned}T_{1}&=F_{1}a,\quad \\T_{2}&=F_{2}b\!\end{aligned}}}
2350:
1017:
581:
2436:
2411:
2397:
2137:
2030:
735:
729:
602:
151:
111:
89:
60:
2451:
2144:
2057:
2052:
636:
610:
195:
191:
265:
The mechanical advantage of a lever can be determined by considering the balance of
1785:
951:
228:
2345:
249:
2078:
2021: – Device which converts input forces and motion to output forces and motion
565:
change (diminish) as the lever changes to any position away from the horizontal.
485:
The mechanical advantage of a lever is the ratio of output force to input force.
939:), then the lever amplifies the input force. On the other hand, if the distance
769:
669:
628:
618:
209:
17:
2294:. Harvard University Press (reprinted by Dover Publications 1988). p. 94.
947:
from the fulcrum to the output force, then the lever reduces the input force.
920:
761:
632:
235:
139:
46:
2033: – Mechanical device that changes the direction or magnitude of a force
1776:
are components of the forces that are perpendicular to the radial segments
2309:
102:
673:
657:
606:
2067:. Vol. 16 (11th ed.). Cambridge University Press. p. 510.
573:
162:, meaning "light" (as in "not heavy"). The word's primary origin is the
1859:
773:
765:
744:
220:
2421:
756:
661:
640:
614:
598:
557:"horizontal" distance (perpendicular to the pull of gravity) of both
270:
391:
are the perpendicular distances between the forces and the fulcrum.
223:, a crane-like device that uses a lever mechanism, was invented. In
2015: – Assembly of systems connected to manage forces and movement
764:, connected as compound levers, that transfer sound waves from the
585:
The three classifications of levers with examples of the human body
2431:
1858:
1788:
states that at equilibrium the generalized force is zero, that is
1016:
750:
665:
644:
580:
572:
248:
97:
2366:
231:
which could not be used for any purpose other than for levers.
205:
2370:
180:
The earliest evidence of the lever mechanism dates back to the
1970:
where the input force is applied is greater than the distance
943:
from the fulcrum to the input force is less than the distance
30:
This article is about the simple machine. For other uses, see
2056:
1156:
which are the distances from the fulcrum to the input point
927:
from the fulcrum to where the input force is applied (point
27:
Simple machine consisting of a beam pivoted at a fixed hinge
1986:, then the lever reduces the magnitude of the input force.
547:{\displaystyle MA={\frac {F_{2}}{F_{1}}}={\frac {a}{b}}.\!}
2079:"Etymology of the word "lever" in the Online Etymological"
204:, a foot pedal was used for the earliest horizontal frame
1946:{\displaystyle MA={\frac {F_{B}}{F_{A}}}={\frac {a}{b}},}
935:
from fulcrum to where the output force is applied (point
923:
using geometric reasoning. It shows that if the distance
906:{\displaystyle MA={\frac {F_{B}}{F_{A}}}={\frac {a}{b}}.}
2260:
Uicker, John; Pennock, Gordon; Shigley, Joseph (2010).
150:, meaning "to raise". The verb, in turn, goes back to
1893:
1796:
1500:
1488:
that defines the configuration of the lever, and the
1327:
1201:
1050:
853:
835:
is the output, the ratio of the velocities of points
493:
441:
400:
285:
2404:
2207:
74:
66:
56:
39:
2341:at Diracdelta science and engineering encyclopedia
2136:
1982:is less than from the fulcrum to the output point
1945:
1849:
1748:
1431:
1301:
1146:
984:on the bar. The lever then exerts an output force
905:
546:
474:
427:
365:
1846:
543:
471:
424:
358:
1850:{\displaystyle F_{\theta }=aF_{A}-bF_{B}=0.\,\!}
2178:Ancient Egyptian Construction and Architecture
1006:. The rotation of the lever about the fulcrum
394:Since the moments of torque must be balanced,
2382:
2264:(4th ed.). Oxford University Press USA.
167:
8:
2228:(3rd ed.). Academic Press. p. 10.
2176:Clarke, Somers; Engelbach, Reginald (1990).
1492:associated with this coordinate is given by
2135:Bruno, Leonard C.; Olendorf, Donna (1997).
2106:Paipetis, S. A.; Ceccarelli, Marco (2010).
2389:
2375:
2367:
2101:
2099:
1999: – Practical application of mechanics
680:These cases are described by the mnemonic
45:
2027: – Mechanical treatise by Archimedes
1962:This equation shows that if the distance
1930:
1919:
1909:
1903:
1892:
1845:
1833:
1817:
1801:
1795:
1737:
1721:
1702:
1697:
1692:
1682:
1677:
1658:
1653:
1648:
1638:
1633:
1609:
1608:
1597:
1592:
1585:
1576:
1571:
1553:
1552:
1541:
1536:
1529:
1520:
1515:
1505:
1499:
1420:
1415:
1410:
1395:
1394:
1385:
1380:
1369:
1364:
1359:
1344:
1343:
1334:
1329:
1326:
1290:
1285:
1272:
1267:
1257:
1252:
1241:
1236:
1223:
1218:
1208:
1203:
1200:
1136:
1130:
1125:
1115:
1110:
1104:
1089:
1083:
1078:
1068:
1063:
1057:
1049:
890:
879:
869:
863:
852:
805:are distances from the fulcrum to points
530:
519:
509:
503:
492:
462:
446:
440:
418:
405:
399:
349:
332:
311:
294:
286:
284:
1863:Simple lever, fulcrum and vertical posts
146:. This sprang from the stem of the verb
2044:
1029:Let the coordinate vector of the point
126:, trading off force against movement.
107:
36:
2112:Springer Science & Business Media
958:Virtual work and the law of the lever
379:is the input force to the lever and F
190:, when it was first used in a simple
7:
1867:Thus, the ratio of the output force
383:is the output force. The distances
2291:A History of Mechanical Inventions
1605:
1588:
1549:
1532:
1459:are unit vectors perpendicular to
25:
2316:from the original on 26 July 2020
2262:Theory of Machines and Mechanisms
1021:Archimedes lever, Engraving from
1010:is defined by the rotation angle
975:located by the coordinate vector
786:Mechanical advantage § Lever
708:for the 2nd class lever, and the
70:fulcrum or pivot, load and effort
1693:
1678:
1649:
1634:
1593:
1572:
1537:
1516:
1411:
1381:
1360:
1330:
1286:
1268:
1253:
1237:
1219:
1204:
1126:
1111:
1079:
1064:
96:or rigid rod pivoted at a fixed
2242:from the original on 2014-01-03
2226:Physics in Biology and Medicine
2085:from the original on 2015-05-12
1378:
1250:
1167:Now introduce the unit vectors
1097:
931:) is greater than the distance
475:{\displaystyle F_{1}a=F_{2}b\!}
323:
2355:Wolfram Demonstrations Project
1966:from the fulcrum to the point
1708:
1673:
1664:
1629:
1185:from the fulcrum to the point
1137:
1105:
1090:
1058:
1:
2139:Science and technology firsts
1025:, published in London in 1824
696:for the 1st class lever, the
428:{\displaystyle T_{1}=T_{2}\!}
213:
198:
184:
2025:On the Equilibrium of Planes
1042:, and introduce the lengths
1033:that defines the fulcrum be
158:, itself from the adjective
78:see-saw, bottle opener, etc.
1311:The velocity of the points
824:is the input and the force
590:resistance and the effort:
124:mechanical advantage device
2489:
1974:from fulcrum to the point
783:
727:
29:
2405:Classical simple machines
2220:Davidovits, Paul (2008).
720:for the 3rd class lever.
134:The word "lever" entered
44:
2458:Mechanisms (engineering)
2363:at EnchantedLearning.com
1160:and to the output point
2361:Levers: Simple Machines
2064:Encyclopædia Britannica
2019:Mechanism (engineering)
760:are small bones in the
577:Three classes of levers
168:
110:. It is one of the six
2003:Balance lever coupling
1947:
1864:
1851:
1750:
1486:generalized coordinate
1433:
1303:
1148:
1026:
919:, which was proven by
907:
700:resistance is between
586:
578:
548:
476:
429:
367:
254:
155:
143:
32:Lever (disambiguation)
1948:
1862:
1852:
1751:
1434:
1304:
1149:
1020:
908:
584:
576:
549:
477:
430:
368:
252:
2013:Linkage (mechanical)
1957:mechanical advantage
1891:
1794:
1498:
1325:
1199:
1048:
851:
491:
439:
398:
283:
138:around AD 1300 from
120:mechanical advantage
2473:Egyptian inventions
2182:Courier Corporation
1876:to the input force
1784:. The principle of
1707:
1663:
1425:
1374:
688:fulcrum is between
164:Proto-Indo-European
2468:Ancient inventions
2184:. pp. 86–90.
1943:
1865:
1847:
1746:
1691:
1647:
1429:
1409:
1358:
1299:
1144:
1027:
1023:Mechanics Magazine
903:
712:effort is between
587:
579:
544:
472:
425:
363:
361:
255:
253:A lever in balance
2445:
2444:
2301:978-0-486-14359-0
2271:978-0-19-537123-9
2235:978-0-12-369411-9
2209:. Pergamon Press.
1997:Applied mechanics
1938:
1925:
1621:
1617:
1565:
1561:
1490:generalized force
1403:
1352:
898:
885:
780:Law of the lever
569:Classes of levers
538:
525:
182:ancient Near East
82:
81:
16:(Redirected from
2480:
2391:
2384:
2377:
2368:
2326:
2325:
2323:
2321:
2282:
2276:
2275:
2257:
2251:
2250:
2248:
2247:
2217:
2211:
2210:
2202:
2196:
2195:
2173:
2167:
2166:
2142:
2132:
2126:
2125:
2103:
2094:
2093:
2091:
2090:
2075:
2069:
2068:
2060:
2049:
1952:
1950:
1949:
1944:
1939:
1931:
1926:
1924:
1923:
1914:
1913:
1904:
1856:
1854:
1853:
1848:
1838:
1837:
1822:
1821:
1806:
1805:
1755:
1753:
1752:
1747:
1742:
1741:
1726:
1725:
1706:
1701:
1696:
1687:
1686:
1681:
1662:
1657:
1652:
1643:
1642:
1637:
1622:
1620:
1619:
1618:
1610:
1603:
1602:
1601:
1596:
1586:
1581:
1580:
1575:
1566:
1564:
1563:
1562:
1554:
1547:
1546:
1545:
1540:
1530:
1525:
1524:
1519:
1510:
1509:
1477:, respectively.
1438:
1436:
1435:
1430:
1424:
1419:
1414:
1405:
1404:
1396:
1390:
1389:
1384:
1373:
1368:
1363:
1354:
1353:
1345:
1339:
1338:
1333:
1319:are obtained as
1308:
1306:
1305:
1300:
1295:
1294:
1289:
1277:
1276:
1271:
1262:
1261:
1256:
1246:
1245:
1240:
1228:
1227:
1222:
1213:
1212:
1207:
1164:, respectively.
1153:
1151:
1150:
1145:
1140:
1135:
1134:
1129:
1120:
1119:
1114:
1108:
1093:
1088:
1087:
1082:
1073:
1072:
1067:
1061:
917:law of the lever
912:
910:
909:
904:
899:
891:
886:
884:
883:
874:
873:
864:
553:
551:
550:
545:
539:
531:
526:
524:
523:
514:
513:
504:
481:
479:
478:
473:
467:
466:
451:
450:
434:
432:
431:
426:
423:
422:
410:
409:
372:
370:
369:
364:
362:
354:
353:
337:
336:
316:
315:
299:
298:
260:law of the lever
245:Force and levers
218:
215:
203:
200:
189:
186:
171:
92:consisting of a
49:
37:
21:
18:Law of the lever
2488:
2487:
2483:
2482:
2481:
2479:
2478:
2477:
2463:Simple machines
2448:
2447:
2446:
2441:
2400:
2395:
2351:Stephen Wolfram
2335:
2330:
2329:
2319:
2317:
2302:
2284:
2283:
2279:
2272:
2259:
2258:
2254:
2245:
2243:
2236:
2219:
2218:
2214:
2204:
2203:
2199:
2192:
2175:
2174:
2170:
2159:
2134:
2133:
2129:
2122:
2114:. p. 416.
2105:
2104:
2097:
2088:
2086:
2077:
2076:
2072:
2051:
2050:
2046:
2041:
2036:
1992:
1915:
1905:
1889:
1888:
1885:is obtained as
1884:
1875:
1829:
1813:
1797:
1792:
1791:
1775:
1766:
1733:
1717:
1676:
1632:
1604:
1591:
1587:
1570:
1548:
1535:
1531:
1514:
1501:
1496:
1495:
1476:
1467:
1458:
1449:
1379:
1328:
1323:
1322:
1284:
1266:
1251:
1235:
1217:
1202:
1197:
1196:
1184:
1175:
1124:
1109:
1077:
1062:
1046:
1045:
1041:
1005:
992:
983:
970:
960:
875:
865:
849:
848:
829:
818:
788:
782:
732:
726:
571:
515:
505:
489:
488:
458:
442:
437:
436:
414:
401:
396:
395:
382:
378:
360:
359:
345:
338:
328:
325:
324:
307:
300:
290:
281:
280:
247:
229:handling bosses
216:
201:
187:
178:
132:
112:simple machines
52:
35:
28:
23:
22:
15:
12:
11:
5:
2486:
2484:
2476:
2475:
2470:
2465:
2460:
2450:
2449:
2443:
2442:
2440:
2439:
2437:Wheel and axle
2434:
2429:
2424:
2419:
2414:
2412:Inclined plane
2408:
2406:
2402:
2401:
2398:Simple machine
2396:
2394:
2393:
2386:
2379:
2371:
2365:
2364:
2358:
2346:A Simple Lever
2342:
2334:
2333:External links
2331:
2328:
2327:
2300:
2277:
2270:
2252:
2234:
2212:
2197:
2190:
2168:
2157:
2127:
2120:
2095:
2070:
2055:, ed. (1911).
2053:Chisholm, Hugh
2043:
2042:
2040:
2037:
2035:
2034:
2031:Simple machine
2028:
2022:
2016:
2010:
2005:
2000:
1993:
1991:
1988:
1959:of the lever.
1942:
1937:
1934:
1929:
1922:
1918:
1912:
1908:
1902:
1899:
1896:
1880:
1871:
1844:
1841:
1836:
1832:
1828:
1825:
1820:
1816:
1812:
1809:
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1800:
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1732:
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1595:
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1472:
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1096:
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868:
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859:
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827:
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813:and the force
781:
778:
736:compound lever
730:Compound lever
728:Main article:
725:
724:Compound lever
722:
678:
677:
651:
622:
570:
567:
542:
537:
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217: 3000 BC
212:(modern Iraq)
202: 4400 BC
188: 5000 BC
177:
174:
131:
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90:simple machine
80:
79:
76:
72:
71:
68:
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61:Simple machine
58:
57:Classification
54:
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50:
42:
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26:
24:
14:
13:
10:
9:
6:
4:
3:
2:
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2191:9780486264851
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2158:9780787602567
2154:
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2146:
2145:Gale Research
2141:
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2121:9789048190911
2117:
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2096:
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2058:"Lever"
2054:
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2017:
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1955:which is the
1953:
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993:at the point
991:
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225:ancient Egypt
222:
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193:
192:balance scale
183:
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55:
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43:
38:
33:
19:
2416:
2344:
2318:. Retrieved
2290:
2286:Usher, A. P.
2280:
2261:
2255:
2244:. Retrieved
2225:
2215:
2206:
2200:
2177:
2171:
2162:
2138:
2130:
2107:
2087:. Retrieved
2073:
2062:
2047:
1983:
1979:
1975:
1971:
1967:
1963:
1961:
1954:
1887:
1881:
1877:
1872:
1868:
1866:
1790:
1786:virtual work
1781:
1777:
1772:
1768:
1763:
1759:
1757:
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1481:
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1473:
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1440:
1321:
1316:
1312:
1310:
1195:
1190:
1186:
1181:
1177:
1172:
1168:
1166:
1161:
1157:
1155:
1044:
1038:
1034:
1030:
1028:
1022:
1014:in radians.
1011:
1007:
1002:
998:
994:
989:
985:
980:
976:
972:
967:
963:
961:
952:virtual work
949:
944:
940:
936:
932:
928:
924:
916:
915:This is the
914:
844:
843:is given by
840:
836:
832:
825:
821:
814:
810:
806:
802:
798:
796:
792:
789:
755:
749:
743:
741:
733:
717:
713:
709:
705:
701:
697:
693:
689:
685:
681:
679:
664:, a pair of
653:
624:
613:, a pair of
605:, a pair of
594:
588:
562:
558:
555:
487:
484:
393:
388:
384:
374:
279:
274:
264:
259:
256:
240:
233:
179:
159:
147:
133:
115:
101:
85:
83:
2222:"Chapter 1"
997:located by
971:at a point
831:applied at
820:applied to
770:oval window
670:fishing rod
629:wheelbarrow
619:claw hammer
210:Mesopotamia
118:, which is
108:three types
2452:Categories
2246:2016-02-23
2147:. p.
2089:2015-04-29
2039:References
1480:The angle
921:Archimedes
784:See also:
762:middle ear
684:where the
672:, and the
643:, and the
633:nutcracker
236:Archimedes
140:Old French
67:Components
1824:−
1803:θ
1728:−
1704:⊥
1689:⋅
1668:−
1660:⊥
1645:⋅
1615:˙
1612:θ
1606:∂
1589:∂
1583:⋅
1568:−
1559:˙
1556:θ
1550:∂
1533:∂
1527:⋅
1507:θ
1422:⊥
1401:˙
1398:θ
1371:⊥
1350:˙
1347:θ
1264:−
1215:−
1122:−
1075:−
654:Class III
130:Etymology
2314:Archived
2288:(1929).
2240:Archived
2083:Archived
1990:See also
674:mandible
658:tweezers
625:Class II
617:, and a
607:scissors
116:leverage
75:Examples
2320:7 April
2164:thread.
2008:bascule
1484:is the
774:cochlea
772:of the
768:to the
766:eardrum
745:malleus
682:fre 123
603:crowbar
595:Class I
375:where F
267:moments
221:shadouf
176:History
136:English
103:fulcrum
2422:Pulley
2310:514178
2308:
2298:
2268:
2232:
2188:
2155:
2118:
1758:where
1441:where
757:stapes
662:hammer
641:wrench
615:pliers
599:seesaw
435:. So,
271:torque
219:, the
169:legwh-
156:levare
144:levier
2432:Wedge
2427:Screw
2417:Lever
2339:Lever
1193:, so
751:incus
666:tongs
648:pedal
645:brake
208:. In
194:. In
166:stem
160:levis
152:Latin
148:lever
100:, or
98:hinge
88:is a
86:lever
40:Lever
2322:2013
2306:OCLC
2296:ISBN
2266:ISBN
2230:ISBN
2186:ISBN
2153:ISBN
2116:ISBN
1780:and
1767:and
1468:and
1450:and
1315:and
1189:and
1176:and
839:and
809:and
801:and
754:and
742:The
716:and
704:and
692:and
668:, a
660:, a
639:, a
635:, a
631:, a
609:, a
601:, a
561:and
387:and
206:loom
94:beam
2349:by
845:a/b
797:If
269:or
2454::
2353:,
2312:.
2304:.
2238:.
2224:.
2180:.
2161:.
2151:.
2143:.
2110:.
2098:^
2081:.
2061:.
1843:0.
1782:PB
1778:PA
954:.
776:.
748:,
734:A
482:.
273:,
262:.
214:c.
199:c.
185:c.
154::
142::
84:A
2390:e
2383:t
2376:v
2357:.
2324:.
2274:.
2249:.
2194:.
2149:2
2124:.
2092:.
1984:B
1980:A
1976:B
1972:b
1968:A
1964:a
1941:,
1936:b
1933:a
1928:=
1921:A
1917:F
1911:B
1907:F
1901:=
1898:A
1895:M
1882:A
1878:F
1873:B
1869:F
1840:=
1835:B
1831:F
1827:b
1819:A
1815:F
1811:a
1808:=
1799:F
1773:B
1769:F
1764:A
1760:F
1744:,
1739:B
1735:F
1731:b
1723:A
1719:F
1715:a
1712:=
1709:)
1699:B
1694:e
1684:B
1679:F
1674:(
1671:b
1665:)
1655:A
1650:e
1640:A
1635:F
1630:(
1627:a
1624:=
1599:B
1594:v
1578:B
1573:F
1543:A
1538:v
1522:A
1517:F
1512:=
1503:F
1482:θ
1474:B
1470:e
1465:A
1461:e
1456:B
1452:e
1447:A
1443:e
1427:,
1417:B
1412:e
1407:b
1392:=
1387:B
1382:v
1376:,
1366:A
1361:e
1356:a
1341:=
1336:A
1331:v
1317:B
1313:A
1297:.
1292:B
1287:e
1282:b
1279:=
1274:P
1269:r
1259:B
1254:r
1248:,
1243:A
1238:e
1233:a
1230:=
1225:P
1220:r
1210:A
1205:r
1191:B
1187:A
1182:B
1178:e
1173:A
1169:e
1162:B
1158:A
1142:,
1138:|
1132:P
1127:r
1117:B
1112:r
1106:|
1102:=
1099:b
1095:,
1091:|
1085:P
1080:r
1070:A
1065:r
1059:|
1055:=
1052:a
1039:P
1035:r
1031:P
1012:θ
1008:P
1003:B
999:r
995:B
990:B
986:F
981:A
977:r
973:A
968:A
964:F
945:b
941:a
937:B
933:b
929:A
925:a
901:.
896:b
893:a
888:=
881:A
877:F
871:B
867:F
861:=
858:A
855:M
841:B
837:A
833:B
828:B
826:F
822:A
817:A
815:F
811:B
807:A
803:b
799:a
718:r
714:f
710:e
706:e
702:f
698:r
694:e
690:r
686:f
563:b
559:a
541:.
536:b
533:a
528:=
521:1
517:F
511:2
507:F
501:=
498:A
495:M
469:b
464:2
460:F
456:=
453:a
448:1
444:F
420:2
416:T
412:=
407:1
403:T
389:b
385:a
381:2
377:1
356:b
351:2
347:F
343:=
334:2
330:T
321:,
318:a
313:1
309:F
305:=
296:1
292:T
275:T
34:.
20:)
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