1. 15 . . , 8/4/2013, . ,[email protected] 2. 15 . 65 ( . 65)
, 15 . .. . , , , . , . , 8/4/2013, . ,[email protected] 3. The
Pythagorean Theorem and its application, according to a Greek
Manuscript of the 15th century Maria Chalkou D.State School Adviser
of MathematicsDr. of Mathematics of NKUA The Code 65 (Codex
Vindobonensis phil. graecus 65) dates fromthe 15th century. In this
Code included are problems of Logisticaeand Geodaesia. This article
contains some chosen problems of the manuscript, which are solved
mainly by the use of the Pythagorean Rule, and their mathematical
comments. I tried an interpretative approach of the authors
methods, as well as acomparison of these with the corresponding
ones of today, which are taught in the secondary education. . ,
8/4/2013, . , [email protected] 4. 65 (Codex Vindbonensis phil.
gr.65), 15 . .. . Augerius von Busbeck, (1555-1562 ..). , J. L.
Heiberg 1899. 2006 , . (. 167-184), , " ", . , , , , . . ,
8/4/2013, . , [email protected] 5. . 167. (). . 22 , 3 1/7= 22/7.
22/(22/7)= 7 . 3 1/7 , = 3,14159... , , . , 22/7, 3 1/7. , , , . ,
3 1/7, , . . , 8/4/2013, . ,[email protected] 6. . 169. (). , 8 3
. =2, =1, =4, =3, : 4.4= 16, 3.3= 9, 1.1= 1, 9+1= 10, 16-10= 6,
2.1= 2, 6/2= 3, 3.3= 9, 9+16= 25, 25 5, 5.2= 10= . : =+ (1) =+ (2)
(1), (2) : -=-, 16-9=(+) -, 16-9=++2..-, 16-9=1+2..1, 16-10=2.,
6=2., =6/2=3, +==, =9+16=25, =5 . , 8/4/2013 , . , 6
[email protected] 7. . , 8/4/2013 , . ,7 [email protected] 8. :
4.4= 16, 16/2= 8, 8+2= 10= , = 10.(3 1/7)= 31 3/7. : /2+= 2., /2=
+, -= 2.+2., -= 2 . , , : = 4+(-2), = 5, = 10, =10. . , 8/4/2013, .
, [email protected] 9. . 170. (). 6 . , . . , 8/4/2013, . ,
[email protected] 10. . 171. (). = 12 , . . = ( ), ===6. ==/2, .
: 6= +(/2), = 144/5, = (144/5). , /5, . . , 8/4/2013 , . , 10
[email protected] 11. . 173. (). 7, . 7. : = 49-49/4=3.49/4, 2=
73. . , . , , = (73)/2= 2, =. . , 8/4/2013, . ,
[email protected] 12. . 174. (). 12 . = (3/4)12= 9, : 81+81/3=
108. 108 10 7/8, . := += (+/2)+= (3/2)+= 9/4+-/4= 3= 108, = 108. =
+(1/3)= +(3/3)= +, = 3/2, , = /2= 3/3. . , 8/4/2013 , . ,12
[email protected] 13. . 176. (). , , 16, 4. 1/4 16 16, 12. , 12 3
8/17. 2/3 3 8/17, 2 16/51. 3 1/7. . , 8/4/2013 , . , 13
[email protected] 14. , : =(-)=12 3 8/17.
2.=(2/3)(3+8/17)=2+16/51, (2+16/51).(3+1/7) = 1/3(43/2)= 23/3,
43/3. , 3/2. . , 8/4/2013 , . ,14 [email protected] 15. . 177. ().
10. . , 8/4/2013 , . ,15 [email protected] 16. :, : 10.10= 100,
100.3/4= 75, , 75.16= 1200, 75.12= 900, (==, =1200= 34 12/19, 900=
30,=60), =, ==/2,34 12/19-30= 4 12/19= , (, ( ). ). , /=/,
/(103/2)= (5-/2)/5, = 23(10-53). (75.16)- (75.12) , 3. (25.16)-
32(25.4) = 2 3.10-232 25= 2 3(10- 53). . , 8/4/2013, . ,
[email protected] 17. . , . , 1952: (). G. Polya, , 51- 53. , ,
. . , 8/4/2013 , . ,17 [email protected] 18. . 179. (). 3, 4, 5 .
, , 3, 3+4= 7. 5 7 2. 2. = = , = = , == , : 2+2+2= 2, . =
-(+)=(3+4+5)/2-5= (3+4)/2-5/2= 7/2-5/2= 1, 1. . . , 8/4/2013, .
,[email protected] 19. . 182. (). "" ( ) , , = 16, = 12, = 14 ;
16/2= 8, BD= 8, 142 = 196, 196+8= 204, 2.2 = 4 ( 2 ), 204+4= 208,
16.16= 256, 256/4= 64, 208-64 = 144, A 144, 12. , AB= , A= , B= , :
A2 =2 + /2+2.(-)-2 /4. = - 2, A2 = (3.2 14. + 32)/4 = (3.162
14.16+32)/4 = (3.162 12.16)/4 = 144, A=12 . , 8/4/2013 , . , 19
[email protected] 20. A2 = .{1- 2 /(+)2}, A , = -2 = -4, : A2 =
(3.2 12.)/4, A2 = (3.162-12.16)/4=144, = 12. . , = (3.-14.+32)/4, ,
= (3.-12.-2.+2.16)/4, = (3.-12.)/4, ( = 16, -2.+32= 0). , , . . ,
8/4/2013, . ,[email protected] 21. : Codex Vindobonensis phil.
Graecus 65 15 . - (http://hollis.harvard.edu/) ( Chalkou Maria) . ,
8/4/2013, . ,[email protected] 22. Carl B. Boyer, A History of
Mathematics, Princeton UP, 1968/1985.Vogel, Fibonacci.... K. Vogel,
"Leonardo Fibonacci", DSB, IV, 604-613. Heath, Hist. Gr. Math., . -
II..... Th. Heath, A History of Greek Mathematics, Oxford U, .
(1921), (1981). Heron Stereom., . V..... Heronis Alexandrini,
Stereometrica et de mensuris, ed. J. Heiberg, TeubnerStutgard 1976.
Hunger, . ......H. Hunger, . -, . , 1994. (), . . , . , . . , 5
1952. W. R. Knorr, "Archimedes and the Measurement of the circle. A
new interpretation", AHES, V, N2 (1976),115-140. Lefort et al.,
Gom. fisc Byz...... J. Lefort, R. Bondoux, J- Cl. Cheynet, J.- P.
Grlois, V. Kravari, Gometries dufisc Byzantin, P. Lethielleux,
Paris 1991. ioni, . . ..... E. Mioni, , . , 1994. G. Polya, , . , .
, . , 31998. Rose, Ital. Ren. Math..... P. L. Rose, The Italian
Renaissance of Mathematics, Librairie Droz, Genve 1975. , . . , ,
1974, , . . , . . . ...... E. , H. Hunger undKurt Vogel (Ein
byzantinisches Rechenbuch des 15. Jahrhunderts), . , 1965. Smith,
Hist. Math., . I- II..... D. E. Smith, History of Mathematics, . I-
II, Dover, New York 1958. V. d. Waerden, ..... B. L. Van der
Waerden, , . , 2000. Vincent, Gom. prat. gr..... J. H. Vincent, la
Gomtrie Pratique des Grecs. Extrait des notices desManuscrits, .
XIX pt. 2, Imr. Impriale, Paris 1858. , . . 65, , 2001- 2003, . 5,
. 51- 62. , Codex Vindobonensis phil. Gr. 65, , , . , 2006. . ,
8/4/2013 , . ,[email protected]
