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68:"rectilinear", since they can only be represented on a one-dimensional line. Non-prime numbers, on the other hand, can be represented on a two-dimensional plane as a rectangle with sides that, when multiplied, produce the non-prime number in question. He further called the number
112:
557:
unknown quantities. The rule was evidently well known, for it was called by the special name the 'flower' or 'bloom' of
Thymaridas. The rule is very obscurely worded, but it states in effect that, if we have the following
81:
states that
Thymaridas also worked with simultaneous linear equations. In particular, he created the then famous rule that was known as the "bloom of Thymaridas" or as the "flower of Thymaridas", which states that:
451:
594:, namely Iamblichus, our informant on this subject, goes on to show that other types of equations can be reduced to this, so that the rule does not 'leave us in the lurch' in those cases either.
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697:
54:
Although little is known about the life of
Thymaridas, it is believed that he was a rich man who fell into poverty. It is said that Thestor of Poseidonia traveled to
337:{\displaystyle {\begin{aligned}x+x_{1}+x_{2}+\cdots +x_{n-1}&=s,\\x+x_{1}&=m_{1},\\x+x_{2}&=m_{2},\\&~~\vdots \\x+x_{n-1}&=m_{n-1}\end{aligned}}}
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quantities be given, and also the sum of every pair containing a particular quantity, then this particular quantity is equal to 1/(
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quantities be given, and also the sum of every pair containing a particular quantity, then this particular quantity is equal to 1/(
1970:
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Thymaridas of Paros, an ancient
Pythagorean already mentioned (p. 69), was the author of a rule for solving a certain set of
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Iamblichus goes on to describe how some systems of linear equations that are not in this form can be placed into this form.
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Thymaridas (fourth century) is said to have had this rule for solving a particular set of
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in order to help
Thymaridas with the money that was collected for him.
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or using modern notation, the solution of the following system of
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446:{\displaystyle x={\frac {(m_{1}+m_{2}+\cdots +m_{n-1})-s}{n-2}}.}
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535:(1981). "The ('Bloom') of Thymaridas".
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1727:Latin translations of the 12th century
30:; c. 400 – c. 350 BCE) was an ancient
1457:Straightedge and compass construction
671:The mac-tutor biography of Thymaridas
7:
1422:Incircle and excircles of a triangle
16:4th-century BCE Greek mathematician
613:Numbers: Their History and Meaning
497:Numbers: Their History and Meaning
14:
1991:4th-century BC Greek philosophers
1939:
1926:
1759:A History of Greek Mathematics
1272:The Quadrature of the Parabola
539:A History of Greek Mathematics
473:A History of Greek Mathematics
417:
366:
75:Iamblichus in his comments to
64:states that Thymaridas called
1:
1981:4th-century BC mathematicians
44:simultaneous linear equations
1966:Ancient Greek mathematicians
1540:Intersecting secants theorem
1535:Intersecting chords theorem
1402:Doctrine of proportionality
609:(1983). "Unknown Numbers".
2007:
1231:On the Sphere and Cylinder
1184:On the Sizes and Distances
1933:Ancient Greece portal
1922:
1737:Philosophy of mathematics
1707:
1652:Ptolemy's table of chords
707:Ancient Greek mathematics
27:
1604:Aristarchus's inequality
1177:On Conoids and Spheroids
1712:Ancient Greek astronomy
1525:Inscribed angle theorem
1515:Greek geometric algebra
1170:Measurement of a Circle
515:Citations and footnotes
78:Introductio arithmetica
72:a "limiting quantity".
1946:Mathematics portal
1732:Non-Euclidean geometry
1687:Mouseion of Alexandria
1560:Tangent-secant theorem
1510:Geometric mean theorem
1495:Exterior angle theorem
1490:Angle bisector theorem
1194:On Sizes and Distances
499:. Dover publications.
477:. Dover publications.
447:
338:
96:
38:noted for his work on
1971:4th-century BC deaths
1634:Pappus's area theorem
1570:Theorem of the gnomon
1447:Quadratrix of Hippias
1370:Circles of Apollonius
1318:Problem of Apollonius
1296:Constructible numbers
1120:Archimedes Palimpsest
562:equations connecting
448:
339:
84:
1850:prehistoric counting
1647:Ptolemy's inequality
1588:Apollonius's theorem
1427:Method of exhaustion
1397:Diophantine equation
1387:Circumscribed circle
1204:On the Moving Sphere
637:linear equations in
467:Heath, Thomas Little
354:
113:
102:linear equations in
1936: •
1742:Neusis construction
1662:Spiral of Theodorus
1555:Pythagorean theorem
1500:Euclidean algorithm
1442:Lune of Hippocrates
1311:Squaring the circle
1067:Theon of Alexandria
742:Aristaeus the Elder
666:Thymaridas of Paros
566:unknown quantities
32:Greek mathematician
20:Thymaridas of Paros
1629:Menelaus's theorem
1619:Irrational numbers
1432:Parallel postulate
1407:Euclidean geometry
1375:Apollonian circles
917:Isidore of Miletus
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1530:Intercept theorem
1380:Apollonian gasket
1306:Doubling the cube
1279:The Sand Reckoner
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1639:Problem II.8 of
1609:Crossbar theorem
1565:Thales's theorem
1505:Euclid's theorem
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1392:Commensurability
1353:Axiomatic system
1301:Angle trisection
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681:
678:
672:
669:
667:
664:
663:
659:
652:
650:
646:
640:
636:
630:
628:9780805238471
624:
620:
615:
614:
608:
602:
599:
595:
591:
587:
580:
573:
569:
565:
561:
556:
552:
546:
541:
540:
534:
528:
526:
524:
520:
514:
508:
506:0-486-42165-1
502:
498:
494:
493:Flegg, Graham
490:
486:
484:0-486-24073-8
480:
475:
474:
468:
464:
463:
459:
457:
440:
434:
431:
428:
423:
420:
412:
409:
406:
402:
398:
395:
392:
387:
383:
379:
374:
370:
360:
357:
350:
349:
348:
325:
322:
319:
315:
311:
309:
302:
299:
296:
292:
288:
285:
278:
264:
259:
255:
251:
249:
242:
238:
234:
231:
224:
219:
215:
211:
209:
202:
198:
194:
191:
184:
181:
178:
176:
169:
166:
163:
159:
155:
152:
149:
144:
140:
136:
131:
127:
123:
120:
109:
108:
107:
105:
101:
95:
93:
89:
83:
80:
79:
73:
71:
67:
66:prime numbers
63:
59:
57:
50:Life and work
49:
47:
45:
41:
40:prime numbers
37:
33:
25:
21:
1986:Pythagoreans
1937:
1924:
1766:Thomas Heath
1757:
1640:
1624:Law of sines
1480:
1412:Golden ratio
1277:
1270:
1261:
1255:(Theodosius)
1251:
1243:
1236:
1229:
1222:
1213:
1203:
1197:(Hipparchus)
1193:
1183:
1175:
1168:
1159:
1149:
1141:
1136:(Apollonius)
1132:
1124:
1112:
1087:Zeno of Elea
1076:
847:Eratosthenes
837:Dionysodorus
648:
644:
638:
634:
632:
612:
601:
589:
585:
578:
571:
567:
563:
559:
554:
550:
548:
538:
496:
472:
455:
347:is given by
346:
103:
99:
97:
91:
87:
85:
76:
74:
60:
53:
19:
18:
1833:mathematics
1641:Arithmetica
1238:Ostomachion
1207:(Autolycus)
1126:Arithmetica
902:Hippocrates
832:Dinostratus
817:Dicaearchus
747:Aristarchus
617:. pp.
543:. pp.
36:Pythagorean
1960:Categories
1885:Babylonian
1785:arithmetic
1751:History of
1580:Apollonius
1265:(Menelaus)
1224:On Spirals
1143:Catoptrics
1082:Xenocrates
1077:Thymaridas
1062:Theodosius
1047:Theaetetus
1027:Simplicius
1017:Pythagoras
1002:Posidonius
987:Philonides
947:Nicomachus
942:Metrodorus
932:Menaechmus
887:Hipparchus
877:Heliodorus
827:Diophantus
812:Democritus
792:Chrysippus
762:Archimedes
757:Apollonius
727:Anaxagoras
719:(timeline)
460:References
106:unknowns:
62:Iamblichus
1346:Inscribed
1106:Treatises
1097:Zenodorus
1057:Theodorus
1032:Sosigenes
977:Philolaus
962:Oenopides
957:Nicoteles
952:Nicomedes
912:Hypsicles
807:Ctesibius
797:Cleomedes
782:Callippus
767:Autolycus
752:Aristotle
732:Anthemius
641:unknowns:
432:−
421:−
410:−
396:⋯
323:−
300:−
279:⋮
167:−
153:⋯
28:Θυμαρίδας
1910:Japanese
1895:Egyptian
1838:timeline
1826:timeline
1814:timeline
1809:geometry
1802:timeline
1797:calculus
1790:timeline
1778:timeline
1481:Elements
1327:Concepts
1289:Problems
1262:Spherics
1252:Spherics
1217:(Euclid)
1163:(Euclid)
1160:Elements
1153:(Euclid)
1114:Almagest
1022:Serenus
997:Porphyry
937:Menelaus
892:Hippasus
867:Eutocius
842:Domninus
737:Archytas
495:(1983).
469:(1981).
1890:Chinese
1845:numbers
1773:algebra
1701:Related
1675:Centers
1471:Results
1341:Central
1012:Ptolemy
1007:Proclus
972:Perseus
927:Marinus
907:Hypatia
897:Hippias
872:Geminus
862:Eudoxus
852:Eudemus
822:Diocles
1905:Indian
1682:Cyrene
1214:Optics
1133:Conics
1052:Theano
1042:Thales
1037:Sporus
982:Philon
967:Pappus
857:Euclid
787:Carpus
777:Bryson
625:
503:
481:
276:
273:
1900:Incan
1821:logic
1597:Other
1365:Chord
1358:Axiom
1336:Angle
992:Plato
882:Heron
802:Conon
607:Flegg
545:94–96
533:Heath
56:Paros
24:Greek
1862:list
1150:Data
922:Leon
772:Bion
623:ISBN
584:...
501:ISBN
479:ISBN
42:and
34:and
1764:by
1478:In
619:205
70:one
1962::
631:.
621:.
592:−1
577:,
570:,
547:.
522:^
46:.
26::
699:e
692:t
685:v
649:n
645:n
639:n
635:n
590:n
586:x
582:2
579:x
575:1
572:x
568:x
564:n
560:n
555:n
551:n
509:.
487:.
441:.
435:2
429:n
424:s
418:)
413:1
407:n
403:m
399:+
393:+
388:2
384:m
380:+
375:1
371:m
367:(
361:=
358:x
326:1
320:n
316:m
312:=
303:1
297:n
293:x
289:+
286:x
265:,
260:2
256:m
252:=
243:2
239:x
235:+
232:x
225:,
220:1
216:m
212:=
203:1
199:x
195:+
192:x
185:,
182:s
179:=
170:1
164:n
160:x
156:+
150:+
145:2
141:x
137:+
132:1
128:x
124:+
121:x
104:n
100:n
92:n
88:n
22:(
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