Arrian's Voyage Round the Euxine Sea/Tables

​

TABLES

OF

THE PROPORTION

WHICH

ANCIENT MEASURES OF LENGTH

BEAR TO

ENGLISH MEASURE.

TO WHICH IS ADDED,

A TABLE

EXTENT OF THE DEGREES OF LONGITUDE,

AT EVERY TEN MINUTES OF LATITUDE,

RECKONED FROM

THE EQUATOR TO THE POLE.

​

TABLE I.

Table of the proportion which Greek Studia bear to Greek Miles, to Englsh Miles, and to Englgish Feet.

Greek
Stadia. 		Greek
Milesand
decimal
parts. 		English
Miles and
decimal
parts. 		English Feet
and
decimal
parts.
1 equal to 0.125 0.114465 604.374[1]
2   0.250 0.228930 1208.748
3   0.375 0.343395 1813.122
4   0.500 0.457860 2417.496
5   0.625 0.572325 3021.870
6   0.750 0.686790 3626.244
7   0.875 0.801255 4230.618
8   1.000 915720 4834.992
9   1.125 1.030185 5439.366
10   1.250 1.144650 6043.747
11   1.375 1.259115 6648.114
12   1.500 1.373570 7252.488
13   1.625 1.488025 7856.862
14   1.750 11.602490 3461.236
15   1.375 11.716955 9065.510
16   2.000 11.831410 9669.984
17   2.125 1.945875 10274.358
18   2.250 2.06034 10878.732
19   2.375 2.174805 11483.106
20   2.500 2.289300 12087.480
21   2.625 2.40376 12691.854
22   2.750 2.518230 13296.228
23   2.875 2.632695 13900.602
24   3.000 2.747150 14504.976
25   3.125 2.861615 15109.250
26   3.258 2.976070 15713.724
27   3.375 3.090535 16318.098
28   3.500 3.205000 16922.472
29   3.625 3.319465 17526.846
30   3.750 3.43395 18131.220
31   3.375 3.543415 18735.594
32   4.000 3.66288 19339.968 ​
33 4.125 3.777345 19944.3420
34   4.250 3.891810 20548.7160
35   4.375 4.006275 21153.0900
36   4.500 4.120740 21757.4640
37   4.625 4.235205 22361.8380
38   4.750 4.34967 22966.2120
39   4.875 4.464135 23571.5860
40   5.000 4.57860 24174.9600
41   5.125 4.695965 24779.3340
42   5.25p 4.807535 25383.7080
43   5.375 4.921995 25988.6820
44   5.500 5.036460 26592.4560
45   5.625 5.150925 27196.8300
46   5.750 5.265390 27801.1204
47   5.875 5.379855 28405.5780
48   6.000 5.494320 29009.9520
49   6.125 5.608785 29614.3260
50   6.250 5.723250 30218.7000
51   6.375 5.837715 30823.0740
52   6.500 5.952180 31427.4480
53   6.625 6.656645 32031.8220
54   6.750 6.17119 32636.1960
55   6.875 6.2955755 3249.5700
56   7.000 6.410040 33844.9444
57   7.125 6.524505 34449.3180
58   7.250 6.3397 35053.6920
59   7.375 5.753435 35658.0650
60   7.500 6.8679 36262.4400
100   12.500 11.4465 60437.4000
200   25.000 22.893 120874.8000
300   37.500 34.3395 18132.2000
400   50.000 45.786 241749.6000
500   62.500 57.2525 302187.0000
600   75.000 68.6789 362024.4000
700   87.500 80.1255 423061.8000
800   100.000 91.572 4883499.2000
900   112.500 103.018515 543936.6000
1000   125.000 114.465 604374.0000
2000   250.000 228.930 1,208748.0000
3000   375.000 343.395 1,813122.0000
4000   500.000 457.86 2,417496.0000
5000   625.000 572.325 3,021870.0000
10,000   1250.000 1144.65 6,043740.0000
20,000   2500.000 2289.3 12,087480.0000
​

TABLE II.

Of the proportion which English Miles bear to Greek Stadia.

English Miles
and
decimal parts 		Greek stadia
and
decimal parts
⅛ or .125 equal to 1.09203925
¼ or .25   2.18407850
⅜ of .375   3.27611775
½ of .5   4.36815700
⅝ of .625   5.46019625
¾ of .75   6.55223550
⅞ of .875   7.64427475
1   8.73631400
2   17.47262800
3   26.20894200
4   34.94525600
5   43.68157000
6   52.41788400
7   61.15419800
8   69.89051200
9   78.62682600
10   87.36314000
11   96.09945400
12   104.83576800
13   113.57208200
14   122.30839600
15   131.04471000
16   139.78102400
17 equal to 148.51733800
18   157.25365200
19   165.98996600
20   174.72628000
21   183.46259100
22   192.19890800
23   209.93522200
24   209.67153600
25   218.43785000
26   227.14416400
27   235.88047800
28   244.61679200
29   253.35210600
30   262.08942000
31   270.82573400
32   279.56204800
33   288.29836200
34   297.03467600
35   305.77099000
36   314.50730100
37   323.24361800
38   331.97993200
39   340.71624600
40   349.45256000
41   358.18887400
42   366.92518800
43   375.66150250
44   384.49781600
45   393.34130000
46   410.87044400
47   410.60675800
48   419.34130720
49   428.45193860
50   436.81570000
51   445.52014000
52   454.28830140
53   463.02464200
54   471.76095600
55   480.45972700
56   489.23358400
57   497.96939800
58   506.70621200
59   515.44252600
60   524.17884000
100   873.63140000
200   1747.26280000 ​
300   2620.89420000
400   3494.52560000
500   4368.15700000
600   5241.78840000
700   6115.41980000
800   6989.01520000
900   7862.68260000
1000   8736.31400000
2000   17472.62800000
3000   26208.94200000
4000   34945.25600000
5000   43681.57000000
10,000   87363.14000000
20,000   174726.28000000
​

TABLE III.

Greek Feet reduced to English Measure.

Greek Feet English Feet, Inches, &c.
    Feet. Inches. Decimals of an Inch.
1 equal to 1   08748
2   2   17496
3   3   26244
4   4   34992
5   5   43740
6   6   52488
7   7   61236
8   8   69984
9   9   78732
10   10   87480
11   11   96228
12   12 1 94976
13   13 1 13724
14   14 1 22472
15   15 1 31220
16   16 1 39968
17   17 1 48716
18   18 1 57464
19   19 1 66212
20   20 1 74960
21   21 1 83708
22   22 1 92456
23   23 2 91204
24   24 2 99952
25   25 2 18700
26   26 2 48716
27   27 2 36196
28   28 2 49444
29   29 2 53692
30   30 2 62440
31   31 2 71188
32   32 2 79936
33   33 2 88684
34   34 2 97432
35   35 3 96180
36   36 3 14928
37   37 3 23678
38   38 3 32424
39   39 3 41172
40   40 3 49920
41   41 3 58668
42   42 3 67416
43   43 3 76164
44   44 3 84912
45   45 3 93660
46   46 4 02408
47   47 4 11156
48   48 4 19904
49   49 4 28652
50   50 4 37400 ​
51 equal to 51 4 46148
52   52 4 54396
53   53 4 63634
54   54 4 72392
55   55 4 81140
56   56 4 89888
57   57 4 98636
58   58 5 07384
59   59 5 16132
60   69 5 24880
100   100 8 74800
200   201 5 49600
300   302 2 24400
400   402 10 99200
500   503 7 74000
600 equal to a stadium 604 4 48800
700   705 1 23600
800   805 9 98400
900   906 6 73200
1000   1007 3 48000
2000   2014 6 96000
3000   3021 10 44000
4000   4029 1 80000
5000   5036 5 40000
6000   6043 8 88000
​

TABLE IV.

Of the proportion which the Minutes upon the Equator, reckoned from one to sixty, bear to English Miles and decimal Parts, to Englis Feet, and to Greek Stadia and decimal Parts.

N. B; A Degree is reckoned to contain 365640 English Feet, according to Mr. Picart's calculation.

Minutes. English Miles. English Feet. Greek Stadia.
1 eq.to 1.154166 6094 10.083127
2   2.303320 12188 20.166254
3   3.462498 18282 30.249381
4   4.616664 24376 40.332508
5   5.776836 30476 50.415633
6   6.924996 36564 60.498762
7   8.079612 42658 70.581889
8   9.233328 48752 80.665116
9   10.387494 54846 90.748143
10   11.541660 60940 100.831270
11   12.695826 67034 110.914397
12   13.849992 73128 120.997524
13   15.064158 79222 131.080651
14   16.158324 85316 141.163778
15   17.312490 91410 151.246905
16   18.466656 97504 161.336032
17   19.620822 103598 171.413150
18   20.774988 109692 181.496286
19   21.929154 115786 191.579418
20   23.083320 121880 201.662540
21   24.237486 127974 211.745667
22   25.391652 134068 221.828794
23   26.545818 140162 231.911911
24   27.699984 146256 241.995048
25   28.854150 152350 252.078175
26   30.008316 158444 262161302
27   31.162482 164538 272.24429
28   32.316648 170632 282.327556
29   33.470814 186726 292.410683
30   34.624980 182820 302.494966
31   35.779146 188914 312.576937
32   36.933312 195008 323.660064
33   38.087478 201162 332.743191
34   39.241644 207196 342.826318
35   46.395816 213290 352.909445
36   41.549976 219384 362.992572
37   42.764142 225478 373.075699
38   43.858308 231572 383.158826
39   45.012474 237666 393.241953
40   46.166640 213760 403.325680
41   47.320806 249854 413.408207
42   48.474972 255948 423.491334 ​
43   49.629000 262042 433.574461
44   50.783594 268156 443.657588
45   51.937470 274230 453.740715
46   53.091636 280324 463.823842
47   54.245802 286418 473.906969
48   55.399968 292512 483.990096
49   56.554134 298606 494.073223
50   57.708396 304700 594.156350
51   58.862466 310794 514.259477
52   60.016632 316888 524.320604
53   61.707980 322982 534.405731
54   62.324964 329076 544.488658
55   63.479130 335170 554.571985
56   64.633296 541264 564.655112
57   65.787462 347358 574.738239
58   66.941628 353452 584.893660
59   68.957940 359546 594.904493
60   69.250000 365640 604.989800
​

TABLE V.

Of the extent of the Degrees of Longitude in English Miles and decimal Parts, at every ten Minutes of Latitude, reckoned from the Equator to the Pole.
Degrees Minutes Length
of Degrees
of Longitude
in English Miles.
Equator 69.25000
  10 69.24973
  20 69.24885
  30 69.24736
  40 69.24531
  50 69.24271
1   69.23945
1 10 69.23565
1 20 69.23125
1 30 69.22646
1 40 69.22086
1 50 69.21454
2   69.20783
2 10 69.20500
2 20 69.19260
2 30 69.18410
2 40 69.17500
2 50 69.16535
3   69.15510
3 10 69.14426
3 20 69.13285
3 30 69.12085
3 40 69.10825
3 50 69.09510
4   69.0813
4 10 69.06700
4 20 69.05203
4 30 69.03650
4 40 69.02043
4 50 69.00375
5   68.98648
5 10 68.96863
5 20 68.95020
5 30 68.93120
5 40 68.91160
6   68.87600
6 10 68.84915
6 20 68.82740
6 30 68.80486
6 40 68.78173
6 50 68.76600
7   68.73366
7 10 68.70900
7 20 68.68354
7 30 68.65756
7 40 68.63100
7 50 68.60380
8   68.57680
8 10 68.54773
8 20 68.51883
8 30 68.48936
8 40 68.45930
8 50 68.42865
9   58.39740
9 10 68.36563
9 20 68.33323
9 30 98.30360
9 40 68.26675
9 50 68.23263
10   68.19800
10 10 68.16268
10 20 68.12683
10 30 68.09400
10 40 68.05340
10 50 68.01583
11   67.9777O
11 10 67.93880
11 20 67.89966
11 30 67.85980
11 40 67.81935
11 50 67.77837 ​
12   67.73671
12 10 67.69455
12 20 67.65181
12 30 67.60850
12 40 67.56460
12 50 67.52020
13   67.47510
13 10 67.42951
13 20 67.38340
13 30 67.33663
13 40 67.28930
13 50 67.24141
14   67.19300
14 10 57.14409
14 20 67.00436
14 30 67.04423
14 40 65.169350
14 50 66.94220
15   66.89036
15 10 66.83800
15 20 66.78500
15 30 66.73141
15 40 66.67730
15 50 66.61260
16   66.56736
16 10 66.51156
16 20 66.45520
16 30 66.39827
16 40 66.34078
16 50 66.28271
17   66.22410
17 10 667.16493
17 20 66.10520
17 30 66.04500
17 40 65.98460
17 50 65.92263
18   65.86066
18 10 65.79813
18 20 65.73504
18 30 65.67150
18 40 65.60721
18 50 65.54246
19   65.47716
19 10 65.41130
19 20 65.34490
19 30 65.27793
19 40 65.21040
19 50 65.14233
20   65.07371
20 10 65.00453
20 20 64.93480
20 30 54.36454
20 40 64.79373
20 50 64.72370
21   64.65044
21 10 64.57800
21 20 64.50500
21 30 64.43141
21 40 64.35731
21 50 64.25266
22   64.20750
22 10 64.175160
22 20 64.05550
22 30 63.97864
22 40 63.90130
22 50 63.82341
23   63.74494
23 10 63.66600
23 20 63.58646
23 30 63.50640
23 40 63.42583
23 50 63.34470
24   63.26330
24 10 63.18083
24 20 63.09100
24 30 63.01483
24 40 62.93130
24 50 62.84670
25   62.76181
25 10 62.41743
25 20 62.59059
25 30 62.50430
25 40 62.41743
25 50 62.33953
26   62.24150
26 10 62.15293
26 20 62.06383
26 30 61.97420
26 40 61.88460
26 50 61.79340
27   61.70220
27 10 61.61050
27 20 61.51825
27 30 61.42550
27 40 61.33223
27 50 61.23844
28   61.14413
28 10 61.04930
28 20 60.95400
28 30 60.85809
28 40 60.76171
28 50 60.66481
29   60.56741
29 10 60.46950
29 20 60.37107 ​
29 30 60.27214
29 40 60.17270
29 50 60.07274
30   59.97501
30 10 59.88507
30 20 59.76980
30 30 59.96783
30 40 59.56534
30 50 59.46234
31   59.35334
31 10 59.25433
31 20 59.15934
31 30 59.94534
31 40 59.93983
31 50 58.83383
32   58.72732
32 10 58.62032
32 20 58.51279
32 30 58.40487
32 40 58.29538
32 50 58.18740
33   58.98792
33 10 57.96814
33 20 57.85752
33 30 57.74660
33 40 57.63529
33 50 57.52326
34   50.41094
34 10 57.29796
34 20 57.18460
34 30 57.97974
34 40 56.95641
34 50 56.84160
35   56.72628
35 10 56.51050
35 20 56.49425
35 30 56.37750
35 40 56.26027
35 50 56.14260
36   56.02442
36 10 55.90580
36 20 55.78667
36 30 55.66710
36 40 55.54739
36 50 55.42651
37   55.30651
37 10 55.17135
37 20 55.96211
37 30 54.93963
37 40 54.89423
37 50 54.69353
38   54.56972
38 10 54.44559
38 20 54.32080
38 30 54.19562
38 40 54.09820
38 50 53.94390
39   53.81736
39 10 53.69935
39 20 53.56290
39 30 53.43519
39 40 53.39665
39 50 53.175733
40   53.04860
40 10 52.91887
40 20 52.78872
40 30 52.65811
40 40 52.52710
40 50 52.39560
41   52.2366
41 10 52.13126
41 20 51.99845
41 30 51.36513
41 40 51.73150
41 50 51.59735
42   51.46280
42 10 51.32777
42 20 51.19232
42 30 51.95646
42 40 50.91008
42 50 50.78341
43   50.54624
43 10 50.59864
43 20 50.37062
43 30 59.23220
43 40 50.09330
43 50 49.95400
44   49.81430
44 10 49.67414
44 20 49.53358
44 30 49.39261
44 40 43.25115
44 50 49.10938
45   48.96714
45 10 48.83878
45 20 48.68143
45 30 48.53796
45 40 48.39410
45 50 48.24980
46   48.10510
46 10 47.96000
46 20 47.81448
46 30 47.66855
46 40 47.52224
46 50 47.37551 ​
47   47.22840
47 10 47.88553
47 20 46.93294
47 30 45.73462
47 40 46.63599
47 50 46.48680
48   46.33730
48 10 46.18740
48 20 46.03712
48 30 45.33644
48 40 45.73534
48 50 45.58391
49   45.43209
49 10 45.27992
49 20 45.12726
49 30 44.97428
49 40 44.82093
49 50 44.66716
50   44.51304
50 10 44.35854
50 20 44.20327
50 30 44.04842
50 40 43.89280
50 50 43.73671
51   43.53944
51 10 43.42371
51 20 43.26661
51 30 43.10915
51 40 42.95131
51 50 42.79312
52   42.63456
52 10 42.47565
52 20 42.31549
52 30 42.15673
52 40 41.99676
52 50 41.83640
53   41.57571
53 10 41.51464
53 20 41.35324
53 30 41.19149
53 40 41.62946
53 50 40.86693
54   40.70412
54 10 40.54100
54 20 40.37750
54 30 40.21357
54 40 40.04952
54 50 39.88561
55   39.72903
55 10 39.56410
55 20 39.38947
55 30 39.22362
55 40 39.05746
55 50 38.89094
56   38.72411
56 10 38.55694
56 20 38.38945
56 30 38.22164
56 40 38.05350
56 50 37.38534
57   37.71629
57 10 37.54715
57 20 37.36913
57 30 37.29500
57 40 37.03795
57 50 36.86759
58   36.69692
58 10 36.52593
58 20 36.35463
58 30 36.18325
58 40 36.01112
58 50 35.83390
59   35.66939
59 10 35.49357
59 20 35.32045
59 30 35.14732
59 40 34.97331
59 50 35.14732
60   34.62500
60 10 34.52961
60 20 34.27551
60 30 34.10033
60 40 33.92136
60 50 33.74911
61   33.57306
61 10 33.39674
61 20 33.22014
61 30 33.04324
61 40 33.86608
61 50 32.68863
62   32.51090
62 10 32.33290
62 20 32.15463
62 30 31.97610
62 40 31.79724
62 50 31.61820
63   31.43812
63 10 31.25922
63 20 31.07934
63 30 30.89920
63 40 30.718868
63 50 30.53813
64   30.35720
64 10 30.17602
64 20 29.99458 ​
64 30 29.81290
64 40 29.63095
64 50 29.44874
65   29.26631
65 10 29.08362
65 20 28.90071
65 30 28.71751
65 40 28.53410
65 50 28.35041
66   28.10172
66 10 27.98231
66 20 27.79800
66 30 27.61331
66 40 27.42852
66 50 27.24344
67   27.05813
67 10 26.87251
67 20 26.68682
67 30 26.50084
67 40 26.31461
67 50 26.13820
68   25.94150
68 10 25.75463
68 20 25.56752
68 30 25.38021
68 40 25.19261
68 50 25.00431
69   24.81700
69 10 24.62881
69 20 24.44044
69 30 24.25181
69 40 24.06308
69 50 23.87409
70   23.68490
70 20 23.30591
70 30 23.11613
70 40 22.92614
70 50 22.73531
71   22.54.551
71 10 22.35504
71 20 22.16521
71 30 21.97335
71 40 21.78222
71 50 21.59092
72   21.39941
72 10 21.20771
72 20 21.01590
72 30 20.82340
72 40 20.63162
72 50 20.43930
73   20.24674
73 10 20.05402
73 20 19.86112
73 30 19.66806
73 40 19.47428
73 50 19.28144
74   19.08790
74 10 13.89417
74 20 18.70030
74 30 18.50621
74 40 18.31207
74 50 18.11772
75   17.92322
75 10 17.72858
75 20 17.53380
75 30 17.33882
75 40 17.14372
75 50 16.94847
76   16.75310
76 10 16.55751
76 20 16.36190
76 30 16.16610
76 40 15.97015
76 50 15.77407
77   15.57785
77 10 15.33152
77 20 15.18505
77 30 14.98840
77 40 14.79170
77 50 14.59490
78   14.89760
78 10 14.22050
78 20 14.00350
78 30 13.80623
78 40 13.60878
78 50 13.40120
79   13.21323
79 10 13.03540
79 20 12.81782
79 30 12.61981
79 40 12.42170
79 50 12.22343
80   11.02510
80 10 11.82670
80 20 11.62820
80 30 11.43951
80 40 11.23081
80 50 11.03200
81   10.83308
81 10 10.63408
81 20 10.43500
81 30 10.23580
81 40 10.03650
81 50 9.81455 ​
82   9.63774
82 10 9.43822
82 20 9.23802
82 30 9.03894
82 40 8.83919
82 50 8.63935
83   8.43945
83 10 8.23942
83 20 8.03943
83 30 7.83932
83 40 7.63915
83 50 7.43890
84   7.23860
84 10 7.03823
84 20 3.83780
84 30 6.63732
84 40 6.43678
84 50 6.23618
85   6.03554
85 10 5.83484
85 20 5.53409
85 30 5.43329
85 40 5.23245
85 50 5.03156
86   4.83064
86 10 4.62967
86 20 4.42866
86 30 4.22761
86 40 4.02653
86 50 3.82541
87   3.64277
87 10 3.42301
87 20 3.22188
87 30 3.02064
87 40 2.81238
87 50 2.61809
88   2.41673
88 10 2.21546
88 20 2.01412
88 30 1.81275
88 40 1.61138
88 50 1.40998
89   1.20858
89 10 1.00716
89 20 0.80574
89 30 0.60431
89 40 0.40288
89 50 0.20144
90   0.0000
​

TABLE VI.

Of the Greek Numerals, and of the Characters used by PTOLEMY to exprese Minutes of and Latitude.

GREEK NUMERALS.

α β γ δ ε ϛ ζ η θ
1 2 3 4 5 6 7 8 9
ι κ λ μ ν ξ ο ϖ ϟ
10 20 30 40 50 60 70 80 90
ρ σ τ υ φ χ ψ ω ϡ
100 200 300 400 500 600 700 800 900
α̣ β̣ γ̣ ι̣ κ̣ ρ̣      
1000 2000 300 10,000 20,000 100,000      

Charcters used by Ptolemy to express Minutes

ιβ ϛ δ γ γιβ ∠' ∠'ιβ γο ∠'δ ∠'γ ∠'γιβ α
5 10 15 20 25 30 35 40 45 50 55 60

THE END.

​

S. Colling wood, Printer, Oxford.

  1. ↑ The length of the Greek stadium, expressed as here laid down in English feet, is correct according to the numbers given by Mr. Greaves, who has employed only two places of decimal figures. If we extend these to six figures, (and it may be done indefinitely,) the proportion will be as below stated.

    34: 25:: 967: 1007.291666
    Again, 1007.491666 x 12 ÷ 1000 =12.087509992
    Again, 12087509992 x 600 = 72525059952
    Again, 7252.25059952 ÷ 12 = 604.3754933

    which differs from the calculation used in the Tables less than .018 decimals of an inch, or considerably less than ⁠1/50⁠ part of an inch in the extent of a stadium.

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