Scaife ATLAS

Introduction (1.1-1.5)

Refs	{'start': {'reference': '1.1', 'human_reference': 'Chapter 1 Part 1'}, 'end': {'reference': '1.5', 'human_reference': 'Chapter 1 Part 5'}}
Ancestors	[{'reference': '1'}]
Children	[]

Tokens

As	1	w	2
in	1	w	4
the	1	w	7
case	1	w	11
of	1	w	13
the	2	w	16
other	1	w	21
great	1	w	26
mathematicians	1	w	40
of	2	w	42
Greece	1	w	48
so	1	w	51
in	2	w	53
Euclid	1	w	59
s	5	w	61
case	2	w	65
we	1	w	68
have	1	w	72
only	1	w	76
the	5	w	79
most	1	w	83
meagre	1	w	89
particulars	1	w	100
of	3	w	102
the	6	w	105
life	1	w	109
and	1	w	112
personality	1	w	123
of	4	w	125
the	7	w	128
man	1	w	131
Most	1	w	136
of	5	w	138
what	1	w	142
we	2	w	144
have	2	w	148
is	1	w	150
contained	1	w	159
in	4	w	161
the	8	w	164
passage	1	w	171
of	6	w	173
Proclus	1	w	180
summary	1	w	188
relating	1	w	196
to	1	w	198
him	1	w	201
which	1	w	207
is	2	w	209
as	4	w	211
follows	1	w	218
Proclus	2	w	225
ed	2	w	228
Friedlein	1	w	238
p	4	w	240
68	1	w	243
6-20	1	w	248
Not	1	w	253
much	1	w	257
younger	1	w	264
than	1	w	268
these	1	w	273
sc	1	w	276
Hermotimus	1	w	287
of	7	w	289
Colophon	1	w	297
and	2	w	300
Philippus	1	w	309
of	8	w	311
Medma	1	w	316
is	3	w	319
Euclid	2	w	325
who	1	w	329
put	1	w	332
together	1	w	340
the	11	w	343
Elements	1	w	351
collecting	1	w	362
many	1	w	366
of	9	w	368
Eudoxus	1	w	375
theorems	1	w	384
perfecting	1	w	395
many	2	w	399
of	10	w	401
Theaetetus	1	w	411
and	3	w	416
also	1	w	420
bringing	1	w	428
to	3	w	430
irrefragable	1	w	442
demonstration	1	w	455
the	13	w	458
things	1	w	464
which	2	w	469
were	1	w	473
only	2	w	477
somewhat	1	w	485
loosely	1	w	492
proved	1	w	498
by	1	w	500
his	1	w	503
predecessors	1	w	515
This	1	w	520
man	4	w	523
lived	1	w	528
The	2	w	531
word	1	w	535
γέγονε	1	w	541
must	1	w	545
apparently	1	w	555
mean	1	w	559
flourished	1	w	569
as	5	w	572
Heiberg	1	w	579
understands	1	w	590
it	2	w	592
Litterargeschichtliche	1	w	615
Studien	1	w	622
über	1	w	626
Euklid	1	w	632
1882	1	w	637
p	14	w	639
26	1	w	642
not	1	w	647
was	1	w	650
born	1	w	654
as	7	w	657
Hankel	1	w	663
took	1	w	667
it	4	w	669
otherwise	1	w	679
part	2	w	683
of	11	w	685
Proclus	3	w	692
argument	1	w	701
would	1	w	706
lose	1	w	710
its	1	w	713
cogency	1	w	720
in	12	w	723
the	15	w	726
time	1	w	730
of	12	w	732
the	16	w	735
first	1	w	740
Ptolemy	1	w	747
For	1	w	751
Archimedes	1	w	761
who	2	w	765
came	1	w	769
immediately	1	w	780
after	1	w	785
the	17	w	788
first	2	w	793
Ptolemy	2	w	801
So	1	w	804
Heiberg	2	w	811
understands	2	w	822
ἐπιβαλὼν	1	w	830
τῷ	1	w	832
πρώτῳ	1	w	837
sc	3	w	840
Πτολεμαίῳ	1	w	850
Friedlein	2	w	861
s	57	w	863
text	1	w	867
has	1	w	870
καὶ	1	w	873
between	1	w	880
ἐπιβαλὼν	2	w	888
and	6	w	891
τῷ	2	w	893
πρώτῳ	2	w	898
and	7	w	902
it	6	w	904
is	8	w	906
right	1	w	911
to	7	w	913
remark	1	w	919
that	1	w	923
another	1	w	930
reading	1	w	937
is	9	w	939
καὶ	2	w	942
ἐν	1	w	944
τῷ	3	w	946
πρώτῳ	3	w	951
without	1	w	959
ἐπιβαλών	1	w	967
which	3	w	973
has	2	w	976
been	1	w	980
translated	1	w	990
in	15	w	992
his	3	w	995
first	3	w	1000
book	1	w	1004
by	2	w	1007
which	4	w	1012
is	11	w	1014
understood	1	w	1024
On	1	w	1026
the	19	w	1029
Sphere	1	w	1035
and	8	w	1038
Cylinder	1	w	1046
I	1	w	1047
where	1	w	1054
1	2	w	1056
in	17	w	1059
Prop	1	w	1063
2	4	w	1065
are	2	w	1068
the	20	w	1071
words	1	w	1076
let	1	w	1079
BC	1	w	1081
be	6	w	1083
made	1	w	1087
equal	1	w	1092
to	9	w	1094
D	1	w	1095
by	3	w	1097
the	21	w	1100
second	1	w	1106
proposition	1	w	1118
of	13	w	1121
the	22	w	1124
first	4	w	1129
of	14	w	1131
Euclid	3	w	1137
s	71	w	1139
books	1	w	1145
and	9	w	1150
2	5	w	1152
in	18	w	1155
Prop	2	w	1159
6	4	w	1161
the	23	w	1164
words	2	w	1169
For	2	w	1172
these	2	w	1177
things	2	w	1183
are	3	w	1186
handed	1	w	1192
down	1	w	1196
in	20	w	1198
the	25	w	1201
Elements	2	w	1209
without	2	w	1217
the	26	w	1220
name	1	w	1224
of	15	w	1226
Euclid	4	w	1232
Heiberg	3	w	1241
thinks	1	w	1247
the	27	w	1250
former	1	w	1256
passage	2	w	1263
is	12	w	1265
referred	1	w	1273
to	10	w	1275
and	11	w	1279
that	2	w	1283
Proclus	4	w	1290
must	2	w	1294
therefore	1	w	1303
have	3	w	1307
had	1	w	1310
before	1	w	1316
him	3	w	1319
the	29	w	1322
words	3	w	1327
by	4	w	1329
the	30	w	1332
second	2	w	1338
of	16	w	1340
the	31	w	1343
first	5	w	1348
of	17	w	1350
Euclid	5	w	1356
a	74	w	1358
fair	1	w	1362
proof	1	w	1367
that	3	w	1371
they	1	w	1375
are	4	w	1378
genuine	1	w	1385
though	1	w	1392
in	23	w	1394
themselves	1	w	1404
they	2	w	1408
would	2	w	1413
be	9	w	1415
somewhat	2	w	1423
suspicious	1	w	1433
makes	1	w	1440
mention	1	w	1447
of	19	w	1449
Euclid	6	w	1455
and	12	w	1459
further	1	w	1467
they	3	w	1472
say	1	w	1475
that	4	w	1479
Ptolemy	3	w	1486
once	1	w	1490
asked	1	w	1495
him	4	w	1498
if	2	w	1500
there	2	w	1505
was	2	w	1508
in	24	w	1510
geometry	1	w	1518
any	3	w	1521
shorter	1	w	1528
way	1	w	1531
than	2	w	1535
that	5	w	1539
of	20	w	1541
the	38	w	1544
elements	1	w	1552
and	13	w	1556
he	45	w	1558
answered	1	w	1566
that	6	w	1570
there	3	w	1575
was	3	w	1578
no	3	w	1580
royal	1	w	1585
road	1	w	1589
to	12	w	1591
geometry	2	w	1599
The	3	w	1602
same	1	w	1606
story	1	w	1611
is	13	w	1613
told	1	w	1617
in	25	w	1619
Stobaeus	1	w	1627
Ecl	1	w	1631
II	1	w	1635
p	24	w	1637
228	1	w	1641
30	1	w	1644
ed	17	w	1647
Wachsmuth	1	w	1657
about	1	w	1663
Alexander	1	w	1672
and	15	w	1675
Menaechmus	1	w	1685
Alexander	2	w	1695
is	14	w	1697
represented	1	w	1708
as	14	w	1710
having	1	w	1716
asked	2	w	1721
Menaechmus	2	w	1731
to	16	w	1733
teach	1	w	1738
him	5	w	1741
geometry	3	w	1749
concisely	1	w	1758
but	1	w	1762
he	48	w	1764
replied	1	w	1771
O	2	w	1773
king	1	w	1777
through	1	w	1785
the	40	w	1788
country	1	w	1795
there	4	w	1800
are	5	w	1803
royal	2	w	1808
roads	1	w	1813
and	17	w	1816
roads	2	w	1821
for	4	w	1824
common	1	w	1830
citizens	1	w	1838
but	2	w	1842
in	28	w	1844
geometry	4	w	1852
there	5	w	1857
is	16	w	1859
one	1	w	1862
road	4	w	1866
for	5	w	1869
all	1	w	1872
He	5	w	1876
is	17	w	1878
then	1	w	1882
younger	2	w	1889
than	3	w	1893
the	44	w	1896
pupils	1	w	1902
of	21	w	1904
Plato	1	w	1909
but	3	w	1912
older	1	w	1917
than	4	w	1921
Eratosthenes	1	w	1933
and	18	w	1936
Archimedes	2	w	1946
for	6	w	1950
the	46	w	1953
latter	1	w	1959
were	3	w	1963
contemporary	1	w	1975
with	3	w	1979
one	2	w	1982
another	2	w	1989
as	16	w	1992
Eratosthenes	2	w	2004
somewhere	1	w	2013
says	1	w	2017
This	2	w	2022
passage	3	w	2029
shows	1	w	2034
that	7	w	2038
even	1	w	2042
Proclus	5	w	2049
had	2	w	2052
no	5	w	2054
direct	1	w	2060
knowledge	1	w	2069
of	22	w	2071
Euclid	7	w	2077
s	133	w	2079
birthplace	1	w	2089
or	19	w	2091
of	23	w	2093
the	49	w	2096
date	1	w	2100
of	24	w	2102
his	5	w	2105
birth	2	w	2110
or	20	w	2112
death	1	w	2117
He	6	w	2120
proceeds	1	w	2128
by	5	w	2130
inference	1	w	2139
Since	1	w	2145
Archimedes	3	w	2155
lived	2	w	2160
just	1	w	2164
after	2	w	2169
the	50	w	2172
first	6	w	2177
Ptolemy	4	w	2184
and	19	w	2188
Archimedes	4	w	2198
mentions	1	w	2206
Euclid	8	w	2212
while	1	w	2218
there	6	w	2223
is	20	w	2225
an	36	w	2227
anecdote	1	w	2235
about	2	w	2240
some	4	w	2244
Ptolemy	5	w	2251
and	20	w	2254
Euclid	9	w	2260
therefore	2	w	2270
Euclid	10	w	2276
lived	3	w	2281
in	31	w	2283
the	53	w	2286
time	2	w	2290
of	25	w	2292
the	54	w	2295
first	7	w	2300
Ptolemy	6	w	2307
We	1	w	2310
may	1	w	2313
infer	2	w	2318
then	4	w	2322
from	1	w	2326
Proclus	6	w	2333
that	8	w	2337
Euclid	11	w	2343
was	4	w	2346
intermediate	1	w	2358
between	2	w	2365
the	56	w	2368
first	8	w	2373
pupils	2	w	2379
of	26	w	2381
Plato	2	w	2386
and	21	w	2389
Archimedes	5	w	2399
Now	1	w	2403
Plato	3	w	2408
died	1	w	2412
in	34	w	2414
347	1	w	2417
6	5	w	2419
Archimedes	6	w	2430
lived	4	w	2435
287-212	1	w	2442
Eratosthenes	3	w	2455
c	68	w	2456
284-204	1	w	2464
B	2	w	2465
C	4	w	2467
Thus	1	w	2472
Euclid	12	w	2478
must	3	w	2482
have	4	w	2486
flourished	2	w	2496
c	70	w	2497
300	1	w	2501
B	3	w	2502
C	5	w	2504
which	5	w	2511
date	2	w	2515
agrees	1	w	2521
well	1	w	2525
with	4	w	2529
the	58	w	2532
fact	1	w	2536
that	9	w	2540
Ptolemy	7	w	2547
reigned	1	w	2554
from	2	w	2558
306	1	w	2561
to	27	w	2563
283	1	w	2566
B	4	w	2567
C	6	w	2569
It	1	w	2572
is	22	w	2574
most	2	w	2578
probable	1	w	2586
that	10	w	2590
Euclid	13	w	2596
received	1	w	2604
his	6	w	2607
mathematical	1	w	2619
training	1	w	2627
in	37	w	2629
Athens	1	w	2635
from	3	w	2639
the	61	w	2642
pupils	3	w	2648
of	27	w	2650
Plato	4	w	2655
for	8	w	2659
most	3	w	2663
of	28	w	2665
the	62	w	2668
geometers	1	w	2677
who	3	w	2680
could	1	w	2685
have	5	w	2689
taught	1	w	2695
him	11	w	2698
were	4	w	2702
of	29	w	2704
that	11	w	2708
school	1	w	2714
and	22	w	2718
it	13	w	2720
was	5	w	2723
in	38	w	2725
Athens	2	w	2731
that	12	w	2735
the	64	w	2738
older	2	w	2743
writers	1	w	2750
of	30	w	2752
elements	2	w	2760
and	23	w	2764
the	65	w	2767
other	5	w	2772
mathematicians	2	w	2786
on	19	w	2788
whose	1	w	2793
works	1	w	2798
Euclid	14	w	2804
s	171	w	2806
Elements	3	w	2814
depend	1	w	2820
had	3	w	2824
lived	5	w	2829
and	24	w	2832
taught	2	w	2838
He	7	w	2841
may	2	w	2844
himself	1	w	2851
have	6	w	2855
been	2	w	2859
a	174	w	2860
Platonist	1	w	2869
but	4	w	2873
this	1	w	2877
does	1	w	2881
not	4	w	2884
follow	2	w	2890
from	4	w	2894
the	68	w	2897
statements	1	w	2907
of	31	w	2909
Proclus	7	w	2916
on	21	w	2918
the	69	w	2921
subject	1	w	2928
Proclus	8	w	2936
says	2	w	2940
namely	1	w	2946
that	13	w	2950
he	81	w	2952
was	6	w	2955
of	32	w	2957
the	70	w	2960
school	2	w	2966
of	33	w	2968
Plato	6	w	2973
and	25	w	2976
in	39	w	2978
close	1	w	2983
touch	1	w	2988
with	5	w	2992
that	14	w	2996
philosophy	1	w	3006
Proclus	9	w	3013
p	41	w	3015
68	2	w	3018
20	3	w	3021
καὶ	3	w	3025
τῇ	1	w	3027
προαιρέσει	1	w	3037
δὲ	1	w	3039
Πλατωνικός	1	w	3049
ἐστι	1	w	3053
καὶ	4	w	3056
τῇ	2	w	3058
φιλοσοφίᾳ	1	w	3067
ταύτῃ	1	w	3072
οὶκεῖος	1	w	3079
But	1	w	3084
this	2	w	3088
was	7	w	3091
only	3	w	3095
an	45	w	3097
attempt	1	w	3104
of	34	w	3106
a	187	w	3107
New	1	w	3110
Platonist	2	w	3119
to	33	w	3121
connect	1	w	3128
Euclid	15	w	3134
with	6	w	3138
his	9	w	3141
philosophy	2	w	3151
as	22	w	3154
is	29	w	3156
clear	1	w	3161
from	5	w	3165
the	71	w	3168
next	1	w	3172
words	4	w	3177
in	40	w	3179
the	72	w	3182
same	2	w	3186
sentence	1	w	3194
for	9	w	3198
which	6	w	3203
reason	1	w	3209
also	2	w	3213
he	85	w	3215
set	1	w	3218
before	2	w	3224
himself	2	w	3231
as	24	w	3234
the	73	w	3237
end	2	w	3240
of	35	w	3242
the	74	w	3245
whole	1	w	3250
Elements	4	w	3258
the	75	w	3262
construction	1	w	3274
of	36	w	3276
the	76	w	3279
so-called	1	w	3288
Platonic	1	w	3296
figures	1	w	3303
It	2	w	3306
is	30	w	3308
evident	1	w	3315
that	15	w	3319
it	17	w	3321
was	8	w	3324
only	4	w	3328
an	46	w	3330
idea	1	w	3334
of	37	w	3336
Proclus	10	w	3343
own	2	w	3347
to	35	w	3349
infer	3	w	3354
that	16	w	3358
Euclid	16	w	3364
was	9	w	3367
a	203	w	3368
Platonist	3	w	3377
because	1	w	3384
his	10	w	3387
Elements	5	w	3395
end	3	w	3398
with	7	w	3402
the	77	w	3405
investigation	1	w	3418
of	38	w	3420
the	78	w	3423
five	1	w	3427
regular	1	w	3434
solids	1	w	3440
since	1	w	3446
a	208	w	3447
later	1	w	3452
passage	4	w	3459
shows	2	w	3464
him	14	w	3467
hard	1	w	3471
put	2	w	3474
to	37	w	3476
it	19	w	3478
to	38	w	3480
reconcile	1	w	3489
the	79	w	3492
view	1	w	3496
that	17	w	3500
the	80	w	3503
construction	2	w	3515
of	39	w	3517
the	81	w	3520
five	2	w	3524
regular	2	w	3531
solids	2	w	3537
was	10	w	3540
the	82	w	3543
end	4	w	3546
and	26	w	3549
aim	1	w	3552
of	40	w	3554
the	83	w	3557
Elements	6	w	3565
with	8	w	3569
the	84	w	3572
obvious	1	w	3579
fact	2	w	3583
that	18	w	3587
they	4	w	3591
were	5	w	3595
intended	1	w	3603
to	39	w	3605
supply	1	w	3611
a	220	w	3612
foundation	1	w	3622
for	11	w	3625
the	86	w	3628
study	1	w	3633
of	41	w	3635
geometry	5	w	3643
in	45	w	3645
general	1	w	3652
to	40	w	3655
make	2	w	3659
perfect	2	w	3666
the	87	w	3669
understanding	1	w	3682
of	42	w	3684
the	88	w	3687
learner	1	w	3694
in	47	w	3696
regard	1	w	3702
to	41	w	3704
the	89	w	3707
whole	2	w	3712
of	43	w	3714
geometry	6	w	3722
ibid	1	w	3726
p	50	w	3728
71	1	w	3731
8	9	w	3733
To	1	w	3737
get	2	w	3740
out	5	w	3743
of	44	w	3745
the	90	w	3748
difficulty	1	w	3758
he	104	w	3760
says	3	w	3764
ibid	2	w	3768
p	51	w	3770
70	1	w	3773
19	1	w	3776
sqq	1	w	3779
that	19	w	3784
if	4	w	3787
one	3	w	3790
should	1	w	3796
ask	3	w	3799
him	15	w	3802
what	4	w	3806
was	11	w	3809
the	91	w	3812
aim	2	w	3815
σκοπός	1	w	3822
of	45	w	3825
the	92	w	3828
treatise	1	w	3836
he	107	w	3839
would	3	w	3844
reply	1	w	3849
by	6	w	3851
making	1	w	3857
a	235	w	3858
distinction	1	w	3869
between	3	w	3876
Euclid	17	w	3882
s	241	w	3884
intentions	1	w	3894
1	6	w	3896
as	31	w	3899
regards	1	w	3906
the	93	w	3909
subjects	1	w	3917
with	9	w	3921
which	7	w	3926
his	11	w	3929
investigations	1	w	3943
are	6	w	3946
concerned	1	w	3955
2	15	w	3958
as	32	w	3961
regards	2	w	3968
the	94	w	3971
learner	2	w	3978
and	28	w	3982
would	4	w	3987
say	5	w	3990
as	33	w	3992
regards	3	w	3999
1	7	w	4001
that	20	w	4006
the	95	w	4009
whole	3	w	4014
of	46	w	4016
the	96	w	4019
geometer	2	w	4027
s	255	w	4029
argument	2	w	4037
is	36	w	4039
concerned	2	w	4048
with	10	w	4052
the	97	w	4055
cosmic	1	w	4061
figures	2	w	4068
This	3	w	4073
latter	2	w	4079
statement	2	w	4088
is	38	w	4090
obviously	1	w	4099
incorrect	1	w	4108
It	3	w	4111
is	39	w	4113
true	1	w	4117
that	21	w	4121
Euclid	18	w	4127
s	264	w	4129
Elements	7	w	4137
end	6	w	4140
with	11	w	4144
the	98	w	4147
construction	3	w	4159
of	47	w	4161
the	99	w	4164
five	3	w	4168
regular	3	w	4175
solids	3	w	4181
but	5	w	4185
the	100	w	4188
planimetrical	1	w	4201
portion	1	w	4208
has	3	w	4211
no	8	w	4213
direct	2	w	4219
relation	1	w	4227
to	42	w	4229
them	5	w	4233
and	29	w	4237
the	102	w	4240
arithmetical	1	w	4252
no	9	w	4254
relation	2	w	4262
at	65	w	4264
all	3	w	4267
the	103	w	4271
propositions	1	w	4283
about	3	w	4288
them	6	w	4292
are	7	w	4295
merely	1	w	4301
the	105	w	4304
conclusion	1	w	4314
of	48	w	4316
the	106	w	4319
stereometrical	1	w	4333
division	1	w	4341
of	49	w	4343
the	107	w	4346
work	2	w	4350
One	1	w	4354
thing	3	w	4359
is	41	w	4361
however	1	w	4368
certain	1	w	4375
namely	2	w	4382
that	22	w	4386
Euclid	19	w	4392
taught	3	w	4398
and	30	w	4402
founded	1	w	4409
a	271	w	4410
school	3	w	4416
at	67	w	4419
Alexandria	1	w	4429
This	4	w	4434
is	43	w	4436
clear	2	w	4441
from	6	w	4445
the	108	w	4448
remark	2	w	4454
of	50	w	4456
Pappus	1	w	4462
about	4	w	4467
Apollonius	1	w	4477
Pappus	2	w	4483
VII	1	w	4487
p	62	w	4489
678	1	w	4493
10-12	1	w	4499
συσχολάσας	1	w	4510
τοῖς	1	w	4514
ὑπὸ	1	w	4517
Εὐκλείδου	1	w	4526
μαθηταῖς	1	w	4534
ἐν	2	w	4536
Ἀλεξανδρείᾳ	1	w	4547
πλεῖστον	1	w	4555
χρόνον	1	w	4561
ὅθεν	1	w	4566
ἔσχε	1	w	4570
καὶ	5	w	4573
τὴν	1	w	4576
τοιαύτην	1	w	4584
ἔξιν	1	w	4588
οὐκ	1	w	4591
ἀμαθῆ	1	w	4596
he	124	w	4600
spent	1	w	4605
a	280	w	4606
very	1	w	4610
long	1	w	4614
time	3	w	4618
with	12	w	4622
the	109	w	4625
pupils	4	w	4631
of	51	w	4633
Euclid	20	w	4639
at	68	w	4641
Alexandria	2	w	4651
and	33	w	4655
it	27	w	4657
was	12	w	4660
thus	1	w	4664
that	23	w	4668
he	126	w	4670
acquired	1	w	4678
such	1	w	4682
a	288	w	4683
scientific	1	w	4693
habit	1	w	4698
of	52	w	4700
thought	1	w	4707
It	4	w	4710
is	44	w	4712
in	55	w	4714
the	110	w	4717
same	3	w	4721
passage	5	w	4728
that	24	w	4732
Pappus	3	w	4738
makes	2	w	4743
a	296	w	4744
remark	3	w	4750
which	8	w	4755
might	1	w	4760
to	43	w	4763
an	56	w	4765
unwary	1	w	4771
reader	1	w	4777
seem	1	w	4782
to	44	w	4784
throw	1	w	4789
some	5	w	4793
light	1	w	4798
on	53	w	4800
the	111	w	4803
personality	2	w	4814
of	53	w	4816
Euclid	21	w	4822
He	8	w	4825
is	45	w	4827
speaking	1	w	4835
about	5	w	4840
Apollonius	2	w	4850
preface	1	w	4858
to	45	w	4860
the	112	w	4863
first	9	w	4868
book	3	w	4872
of	54	w	4874
his	14	w	4877
Conics	1	w	4883
where	3	w	4889
he	131	w	4891
says	4	w	4895
that	25	w	4899
Euclid	22	w	4905
had	4	w	4908
not	5	w	4911
completely	1	w	4921
worked	1	w	4927
out	9	w	4930
the	113	w	4933
synthesis	1	w	4942
of	55	w	4944
the	115	w	4947
three-	1	w	4953
and	34	w	4956
four-line	1	w	4965
locus	1	w	4970
which	9	w	4976
in	58	w	4978
fact	3	w	4982
was	13	w	4985
not	6	w	4988
possible	1	w	4996
without	3	w	5003
some	6	w	5007
theorems	2	w	5015
first	10	w	5020
discovered	1	w	5030
by	7	w	5032
himself	3	w	5039
Pappus	4	w	5046
says	5	w	5050
on	57	w	5052
this	3	w	5056
Pappus	5	w	5062
VII	2	w	5066
pp	9	w	5069
676	1	w	5073
25-678	1	w	5080
6	12	w	5082
Hultsch	1	w	5090
it	31	w	5093
is	50	w	5095
true	2	w	5099
brackets	1	w	5108
the	117	w	5111
whole	4	w	5116
passage	6	w	5123
pp	10	w	5125
676	2	w	5129
25-678	2	w	5136
15	1	w	5139
but	6	w	5143
apparently	2	w	5153
on	58	w	5155
the	118	w	5158
ground	1	w	5164
of	56	w	5166
the	119	w	5169
diction	1	w	5176
only	5	w	5180
Now	2	w	5185
Euclid	23	w	5191
regarding	1	w	5201
Aristaeus	1	w	5210
as	39	w	5212
deserving	1	w	5221
credit	1	w	5227
for	12	w	5230
the	120	w	5233
discoveries	1	w	5244
he	140	w	5246
had	5	w	5249
already	1	w	5256
made	2	w	5260
in	61	w	5262
conics	1	w	5268
and	35	w	5272
without	4	w	5279
anticipating	1	w	5291
him	17	w	5294
or	34	w	5296
wishing	1	w	5303
to	46	w	5305
construct	4	w	5314
anew	1	w	5318
the	121	w	5321
same	4	w	5325
system	1	w	5331
such	2	w	5336
was	14	w	5339
his	16	w	5342
scrupulous	1	w	5352
fairness	1	w	5360
and	36	w	5363
his	17	w	5366
exemplary	1	w	5375
kindliness	1	w	5385
towards	1	w	5392
all	4	w	5395
who	9	w	5398
could	2	w	5403
advance	1	w	5410
mathematical	2	w	5422
science	1	w	5429
to	48	w	5431
however	2	w	5438
small	1	w	5443
an	63	w	5445
extent	1	w	5451
being	1	w	5458
moreover	1	w	5466
in	67	w	5468
no	12	w	5470
wise	2	w	5474
contentious	1	w	5485
and	37	w	5488
though	3	w	5495
exact	1	w	5500
yet	1	w	5504
no	13	w	5506
braggart	1	w	5514
like	1	w	5518
the	123	w	5521
other	6	w	5526
Apollonius	3	w	5537
wrote	1	w	5544
so	20	w	5546
much	2	w	5550
about	6	w	5555
the	125	w	5558
locus	2	w	5563
as	41	w	5565
was	15	w	5568
possible	2	w	5576
by	8	w	5578
means	1	w	5583
of	57	w	5585
the	126	w	5588
conics	2	w	5594
of	58	w	5596
Aristaeus	2	w	5605
without	5	w	5613
claiming	1	w	5621
completeness	1	w	5633
for	13	w	5636
his	18	w	5639
demonstrations	1	w	5653
It	5	w	5656
is	59	w	5658
however	3	w	5665
evident	2	w	5672
when	1	w	5677
the	127	w	5680
passage	7	w	5687
is	60	w	5689
examined	1	w	5697
in	70	w	5699
its	2	w	5702
context	1	w	5709
that	26	w	5714
Pappus	6	w	5720
is	61	w	5722
not	7	w	5725
following	1	w	5734
any	4	w	5737
tradition	1	w	5746
in	72	w	5748
giving	1	w	5754
this	4	w	5758
account	1	w	5765
of	59	w	5767
Euclid	24	w	5773
he	149	w	5776
was	16	w	5779
offended	1	w	5787
by	9	w	5789
the	128	w	5792
terms	1	w	5797
of	61	w	5799
Apollonius	4	w	5809
reference	1	w	5819
to	49	w	5821
Euclid	25	w	5827
which	10	w	5833
seemed	1	w	5839
to	50	w	5841
him	18	w	5844
unjust	1	w	5850
and	38	w	5854
he	151	w	5856
drew	1	w	5860
a	365	w	5861
fancy	1	w	5866
picture	1	w	5873
of	62	w	5875
Euclid	26	w	5881
in	74	w	5883
order	1	w	5888
to	51	w	5890
show	3	w	5894
Apollonius	5	w	5904
in	75	w	5906
a	367	w	5907
relatively	1	w	5917
unfavourable	1	w	5929
light	2	w	5934
Another	1	w	5942
story	2	w	5947
is	63	w	5949
told	2	w	5953
of	63	w	5955
Euclid	27	w	5961
which	11	w	5966
one	4	w	5969
would	5	w	5974
like	2	w	5978
to	54	w	5980
believe	1	w	5987
true	3	w	5991
According	1	w	6001
to	55	w	6003
Stobaeus	2	w	6011
Stobaeus	3	w	6019
l	227	w	6021
c	188	w	6023
some	7	w	6029
one	5	w	6032
who	10	w	6035
had	6	w	6038
begun	1	w	6043
to	58	w	6045
read	4	w	6049
geometry	7	w	6057
with	16	w	6061
Euclid	28	w	6067
when	2	w	6072
he	154	w	6074
had	7	w	6077
learnt	1	w	6083
the	130	w	6086
first	11	w	6091
theorem	3	w	6098
asked	3	w	6104
Euclid	29	w	6110
But	2	w	6114
what	5	w	6118
shall	1	w	6123
I	13	w	6124
get	3	w	6127
by-learning	1	w	6138
these	3	w	6143
things	3	w	6149
Euclid	30	w	6156
called	2	w	6162
his	20	w	6165
slave	1	w	6170
and	39	w	6173
said	1	w	6177
Give	1	w	6181
him	19	w	6184
threepence	1	w	6194
since	2	w	6200
he	158	w	6202
must	4	w	6206
make	4	w	6210
gain	1	w	6214
out	14	w	6217
of	64	w	6219
what	6	w	6223
he	159	w	6225
learns	1	w	6231
In	1	w	6234
the	133	w	6237
middle	1	w	6243
ages	1	w	6247
most	4	w	6251
translators	1	w	6262
and	40	w	6265
editors	1	w	6272
spoke	1	w	6277
of	65	w	6279
Euclid	31	w	6285
as	46	w	6287
Euclid	32	w	6293
of	66	w	6295
Megara	1	w	6301
This	5	w	6306
description	1	w	6317
arose	1	w	6322
out	15	w	6325
of	67	w	6327
a	397	w	6328
confusion	1	w	6337
between	4	w	6344
our	5	w	6347
Euclid	33	w	6353
and	41	w	6356
the	134	w	6359
philosopher	1	w	6370
Euclid	34	w	6376
of	68	w	6378
Megara	2	w	6384
who	11	w	6387
lived	6	w	6392
about	7	w	6397
400	1	w	6400
B	7	w	6401
C	8	w	6403
The	4	w	6407
first	12	w	6412
trace	1	w	6417
of	69	w	6419
this	5	w	6423
confusion	2	w	6432
appears	1	w	6439
in	81	w	6441
Valerius	1	w	6449
Maximus	1	w	6456
in	82	w	6459
the	135	w	6462
time	4	w	6466
of	70	w	6468
Tiberius	1	w	6476
who	12	w	6480
says	6	w	6484
VIII	1	w	6488
12	3	w	6491
ext	5	w	6495
1	12	w	6497
that	27	w	6502
Plato	10	w	6507
on	79	w	6510
being	2	w	6515
appealed	1	w	6523
to	62	w	6525
for	14	w	6528
a	412	w	6529
solution	1	w	6537
of	71	w	6539
the	136	w	6542
problem	1	w	6549
of	72	w	6551
doubling	1	w	6559
the	137	w	6562
cubical	1	w	6569
altar	1	w	6574
sent	3	w	6579
the	138	w	6582
inquirers	1	w	6591
to	63	w	6593
Euclid	35	w	6599
the	139	w	6602
geometer	3	w	6610
There	1	w	6616
is	67	w	6618
no	16	w	6620
doubt	1	w	6625
about	8	w	6630
the	140	w	6633
reading	2	w	6640
although	1	w	6649
an	73	w	6651
early	1	w	6656
commentator	1	w	6667
on	81	w	6669
Valerius	2	w	6677
Maximus	2	w	6684
wanted	1	w	6690
to	65	w	6692
correct	2	w	6699
Eucliden	1	w	6707
into	1	w	6711
Eudoxum	1	w	6718
and	42	w	6722
this	6	w	6726
correction	1	w	6736
is	69	w	6738
clearly	1	w	6745
right	2	w	6750
But	3	w	6754
if	6	w	6757
Valerius	3	w	6765
Maximus	3	w	6772
took	2	w	6776
Euclid	37	w	6782
the	141	w	6785
geometer	4	w	6793
for	15	w	6796
a	429	w	6797
contemporary	2	w	6809
of	73	w	6811
Plato	11	w	6816
it	39	w	6819
could	3	w	6824
only	6	w	6828
be	21	w	6830
through	2	w	6837
confusing	1	w	6846
him	20	w	6849
with	17	w	6853
Euclid	38	w	6859
of	74	w	6861
Megara	3	w	6867
The	6	w	6871
first	13	w	6876
specific	1	w	6884
reference	2	w	6893
to	69	w	6895
Euclid	39	w	6901
as	47	w	6903
Euclid	40	w	6909
of	75	w	6911
Megara	4	w	6917
belongs	1	w	6924
to	70	w	6926
the	142	w	6929
14th	1	w	6933
century	1	w	6940
occurring	1	w	6950
in	90	w	6952
the	143	w	6955
ὑπομνηματισμοί	1	w	6969
of	76	w	6971
Theodorus	1	w	6980
Metochita	1	w	6989
d	243	w	6991
1332	1	w	6996
who	13	w	7000
speaks	1	w	7006
of	77	w	7008
Euclid	41	w	7014
of	78	w	7016
Megara	5	w	7022
the	144	w	7026
Socratic	1	w	7034
philosopher	2	w	7045
contemporary	3	w	7058
of	79	w	7060
Plato	12	w	7065
as	48	w	7068
the	145	w	7071
author	1	w	7077
of	80	w	7079
treatises	1	w	7088
on	88	w	7090
plane	1	w	7095
and	43	w	7098
solid	4	w	7103
geometry	8	w	7111
data	1	w	7116
optics	1	w	7123
etc	1	w	7126
and	44	w	7131
a	452	w	7132
Paris	1	w	7137
MS	1	w	7139
of	81	w	7142
the	146	w	7145
14th	2	w	7149
century	2	w	7156
has	4	w	7159
Euclidis	1	w	7167
philosophi	1	w	7177
Socratici	1	w	7186
liber	1	w	7191
elementorum	1	w	7202
The	8	w	7206
misunderstanding	1	w	7222
was	17	w	7225
general	2	w	7232
in	92	w	7234
the	147	w	7237
period	1	w	7243
from	7	w	7247
Campanus	1	w	7255
translation	1	w	7267
Venice	1	w	7274
1482	1	w	7278
to	74	w	7281
those	1	w	7286
of	82	w	7288
Tartaglia	1	w	7297
Venice	2	w	7304
1565	1	w	7308
and	46	w	7312
Candalla	1	w	7320
Paris	2	w	7326
1566	1	w	7330
But	4	w	7335
one	6	w	7338
Constantinus	1	w	7350
Lascaris	1	w	7358
d	255	w	7360
about	9	w	7366
1493	1	w	7370
had	8	w	7374
already	2	w	7381
made	3	w	7385
the	148	w	7388
proper	1	w	7394
distinction	2	w	7405
by	11	w	7407
saying	1	w	7413
of	83	w	7415
our	6	w	7418
Euclid	43	w	7424
that	28	w	7428
he	183	w	7430
was	18	w	7433
different	1	w	7442
from	8	w	7446
him	21	w	7449
of	84	w	7451
Megara	6	w	7457
of	85	w	7459
whom	1	w	7463
Laertius	1	w	7471
wrote	2	w	7476
and	48	w	7480
who	15	w	7483
wrote	3	w	7488
dialogues	1	w	7497
Letter	1	w	7503
to	75	w	7505
Fernandus	1	w	7514
Acuna	1	w	7519
printed	1	w	7527
in	97	w	7529
Maurolycus	1	w	7539
Historia	1	w	7548
Siciliae	1	w	7556
fol	4	w	7560
21	2	w	7563
r	392	w	7564
see	3	w	7569
Heiberg	4	w	7576
Euklid-Studien	1	w	7591
pp	15	w	7594
22-3	1	w	7599
25	3	w	7602
and	50	w	7608
to	77	w	7610
Commandinus	1	w	7621
belongs	2	w	7628
the	149	w	7631
credit	2	w	7637
of	86	w	7639
being	3	w	7644
the	150	w	7647
first	14	w	7652
translator	2	w	7662
Preface	1	w	7669
to	79	w	7671
translation	2	w	7682
Pisauri	1	w	7690
1572	1	w	7695
to	80	w	7699
put	3	w	7702
the	151	w	7705
matter	1	w	7711
beyond	1	w	7717
doubt	2	w	7722
Let	2	w	7726
us	68	w	7728
then	8	w	7732
free	1	w	7736
a	501	w	7737
number	1	w	7743
of	87	w	7745
people	1	w	7751
from	9	w	7755
the	153	w	7758
error	1	w	7763
by	12	w	7765
which	12	w	7770
they	5	w	7774
have	7	w	7778
been	3	w	7782
induced	1	w	7789
to	81	w	7791
believe	2	w	7798
that	29	w	7802
our	7	w	7805
Euclid	44	w	7811
is	79	w	7813
the	155	w	7816
same	5	w	7820
as	53	w	7822
the	156	w	7825
philosopher	3	w	7836
of	88	w	7838
Megara	7	w	7844
etc	2	w	7847
Another	2	w	7855
idea	2	w	7859
that	30	w	7864
Euclid	45	w	7870
was	19	w	7873
born	2	w	7877
at	97	w	7879
Gela	1	w	7883
in	101	w	7885
Sicily	1	w	7891
is	80	w	7894
due	1	w	7897
to	82	w	7899
the	158	w	7902
same	6	w	7906
confusion	3	w	7915
being	4	w	7921
based	1	w	7926
on	98	w	7928
Diogenes	1	w	7936
Laertius	2	w	7944
description	2	w	7956
Diog	2	w	7960
L	7	w	7962
II	6	w	7965
106	1	w	7969
p	131	w	7971
58	1	w	7974
ed	59	w	7976
Cobet	1	w	7982
of	89	w	7985
the	159	w	7988
philosopher	4	w	7999
Euclid	46	w	8005
as	56	w	8007
being	5	w	8012
of	90	w	8014
Megara	8	w	8020
or	57	w	8023
according	1	w	8033
to	83	w	8035
some	8	w	8039
of	91	w	8042
Gela	2	w	8046
as	57	w	8049
Alexander	3	w	8058
says	7	w	8062
in	105	w	8064
the	160	w	8067
Διαδοχαί	1	w	8075
In	2	w	8078
view	2	w	8082
of	92	w	8084
the	161	w	8087
poverty	1	w	8094
of	93	w	8096
Greek	1	w	8101
tradition	2	w	8110
on	101	w	8112
the	162	w	8115
subject	3	w	8122
even	2	w	8126
as	58	w	8128
early	3	w	8133
as	59	w	8135
the	163	w	8138
time	5	w	8142
of	94	w	8144
Proclus	11	w	8151
410-485	1	w	8159
A	26	w	8160
D	4	w	8162
we	16	w	8167
must	5	w	8171
necessarily	1	w	8182
take	1	w	8186
cum	1	w	8189
grano	1	w	8194
the	164	w	8197
apparently	3	w	8207
circumstantial	1	w	8221
accounts	1	w	8229
of	95	w	8231
Euclid	47	w	8237
given	1	w	8242
by	13	w	8244
Arabian	1	w	8251
authors	1	w	8258
and	53	w	8262
indeed	1	w	8268
the	165	w	8271
origin	1	w	8277
of	96	w	8279
their	1	w	8284
stories	1	w	8291
can	1	w	8294
be	34	w	8296
explained	1	w	8305
as	60	w	8307
the	167	w	8310
result	1	w	8316
1	24	w	8318
of	97	w	8321
the	168	w	8324
Arabian	2	w	8331
tendency	1	w	8339
to	85	w	8341
romance	1	w	8348
and	54	w	8352
2	27	w	8354
of	98	w	8357
misunderstandings	1	w	8374
We	2	w	8377
read	7	w	8381
Casiri	1	w	8387
Bibliotheca	1	w	8399
Arabico-Hispana	1	w	8414
Escurialensis	1	w	8427
I	21	w	8429
p	139	w	8431
339	1	w	8435
Casiri	2	w	8442
s	518	w	8444
source	1	w	8450
is	84	w	8452
alQifti	1	w	8459
d	296	w	8461
1248	1	w	8466
the	170	w	8471
author	3	w	8477
of	99	w	8479
the	171	w	8482
Ta	2	w	8484
rīkh	1	w	8489
al-Ḥukamā	1	w	8498
a	561	w	8500
collection	1	w	8510
of	100	w	8512
biographies	1	w	8523
of	101	w	8525
philosophers	1	w	8537
mathematicians	3	w	8552
astronomers	1	w	8564
etc	3	w	8567
that	31	w	8572
Euclid	48	w	8578
son	4	w	8582
of	102	w	8584
Naucrates	1	w	8593
grandson	1	w	8602
of	103	w	8604
Zenarchus	1	w	8613
The	9	w	8616
Fihrist	1	w	8623
says	8	w	8627
son	6	w	8630
of	104	w	8632
Naucrates	2	w	8641
the	173	w	8645
son	7	w	8648
of	105	w	8650
Berenice	1	w	8658
see	4	w	8665
Suter	1	w	8670
s	538	w	8672
translation	3	w	8683
in	110	w	8685
Abhandlungen	1	w	8697
zur	1	w	8700
Gesch	1	w	8705
d	300	w	8707
Math	1	w	8712
VI	4	w	8715
Heft	1	w	8720
1892	1	w	8725
p	143	w	8727
16	1	w	8730
called	3	w	8739
the	174	w	8742
author	4	w	8748
of	106	w	8750
geometry	9	w	8758
a	581	w	8760
philosopher	6	w	8771
of	107	w	8773
somewhat	3	w	8781
ancient	1	w	8788
date	3	w	8792
a	585	w	8794
Greek	2	w	8799
by	14	w	8801
nationality	1	w	8812
domiciled	1	w	8821
at	108	w	8823
Damascus	1	w	8831
born	3	w	8836
at	109	w	8838
Tyre	1	w	8842
most	5	w	8847
learned	1	w	8854
in	111	w	8856
the	175	w	8859
science	2	w	8866
of	108	w	8868
geometry	10	w	8876
published	1	w	8886
a	593	w	8887
most	6	w	8891
excellent	1	w	8900
and	58	w	8903
most	7	w	8907
useful	1	w	8913
work	4	w	8917
entitled	1	w	8925
the	176	w	8928
foundation	2	w	8938
or	66	w	8940
elements	3	w	8948
of	109	w	8950
geometry	11	w	8958
a	596	w	8960
subject	4	w	8967
in	112	w	8969
which	13	w	8974
no	20	w	8976
more	2	w	8980
general	3	w	8987
treatise	3	w	8995
existed	1	w	9002
before	3	w	9008
among	1	w	9013
the	177	w	9016
Greeks	1	w	9022
nay	1	w	9026
there	8	w	9032
was	20	w	9035
no	21	w	9037
one	7	w	9040
even	3	w	9044
of	110	w	9046
later	2	w	9051
date	4	w	9055
who	16	w	9058
did	1	w	9061
not	10	w	9064
walk	1	w	9068
in	113	w	9070
his	24	w	9073
footsteps	1	w	9082
and	59	w	9085
frankly	1	w	9092
profess	1	w	9099
his	25	w	9102
doctrine	1	w	9110
Hence	1	w	9116
also	3	w	9120
Greek	4	w	9125
Roman	1	w	9131
and	60	w	9134
Arabian	3	w	9141
geometers	2	w	9150
not	11	w	9153
a	612	w	9154
few	1	w	9157
who	17	w	9161
undertook	1	w	9170
the	179	w	9173
task	1	w	9177
of	112	w	9179
illustrating	1	w	9191
this	7	w	9195
work	5	w	9199
published	2	w	9209
commentaries	1	w	9221
scholia	1	w	9229
and	61	w	9233
notes	1	w	9238
upon	1	w	9242
it	46	w	9244
and	62	w	9248
made	4	w	9252
an	115	w	9254
abridgment	1	w	9264
of	113	w	9266
the	180	w	9269
work	6	w	9273
itself	1	w	9279
For	3	w	9283
this	8	w	9287
reason	2	w	9293
the	181	w	9296
Greek	5	w	9301
philosophers	2	w	9313
used	1	w	9317
to	87	w	9319
post	1	w	9323
up	8	w	9325
on	115	w	9327
the	182	w	9330
doors	1	w	9335
of	114	w	9337
their	2	w	9342
schools	1	w	9349
the	184	w	9352
well-known	1	w	9362
notice	1	w	9368
Let	3	w	9372
no	27	w	9374
one	8	w	9377
come	1	w	9381
to	88	w	9383
our	9	w	9386
school	5	w	9392
who	18	w	9396
has	5	w	9399
not	14	w	9402
first	15	w	9407
learned	2	w	9414
the	185	w	9417
elements	4	w	9425
of	115	w	9427
Euclid	49	w	9433
The	10	w	9437
details	1	w	9444
at	115	w	9446
the	186	w	9449
beginning	1	w	9458
of	116	w	9460
this	9	w	9464
extract	1	w	9471
cannot	1	w	9477
be	37	w	9479
derived	1	w	9486
from	10	w	9490
Greek	6	w	9495
sources	1	w	9502
for	17	w	9506
even	4	w	9510
Proclus	12	w	9517
did	2	w	9520
not	16	w	9523
know	3	w	9527
anything	1	w	9535
about	10	w	9540
Euclid	50	w	9546
s	591	w	9548
father	1	w	9554
while	2	w	9560
it	48	w	9562
was	21	w	9565
not	17	w	9568
the	188	w	9571
Greek	7	w	9576
habit	2	w	9581
to	89	w	9583
record	1	w	9589
the	189	w	9592
names	1	w	9597
of	117	w	9599
grandfathers	1	w	9611
as	70	w	9614
the	191	w	9617
Arabians	1	w	9625
commonly	1	w	9633
did	3	w	9636
Damascus	2	w	9645
and	64	w	9648
Tyre	2	w	9652
were	6	w	9656
no	33	w	9658
doubt	3	w	9663
brought	1	w	9670
in	119	w	9672
to	90	w	9674
gratify	1	w	9681
a	644	w	9682
desire	1	w	9688
which	14	w	9693
the	192	w	9696
Arabians	2	w	9704
always	1	w	9710
showed	1	w	9716
to	91	w	9718
connect	2	w	9725
famous	1	w	9731
Greeks	2	w	9737
in	120	w	9739
some	10	w	9743
way	3	w	9746
or	75	w	9748
other	9	w	9753
with	18	w	9757
the	194	w	9760
East	1	w	9764
Thus	2	w	9769
Naṣīraddīn	1	w	9779
the	195	w	9783
translator	3	w	9793
of	118	w	9795
the	196	w	9798
Elements	8	w	9806
who	19	w	9810
was	22	w	9813
of	119	w	9815
Ṭūs	1	w	9818
in	121	w	9820
Khurāsān	1	w	9828
actually	1	w	9837
makes	3	w	9842
Euclid	51	w	9848
out	20	w	9851
to	93	w	9853
have	8	w	9857
been	4	w	9861
Thusinus	1	w	9869
also	4	w	9873
The	11	w	9876
same	7	w	9880
predilection	1	w	9892
made	5	w	9896
the	197	w	9899
Arabs	1	w	9904
describe	1	w	9912
Pythagoras	1	w	9922
as	75	w	9924
a	668	w	9925
pupil	5	w	9930
of	120	w	9932
the	198	w	9935
wise	3	w	9939
Salomo	1	w	9945
Hipparchus	1	w	9956
as	76	w	9958
the	199	w	9961
exponent	1	w	9969
of	121	w	9971
Chaldaean	1	w	9980
philosophy	3	w	9990
or	78	w	9992
as	77	w	9994
the	200	w	9997
Chaldaean	2	w	10006
Archimedes	7	w	10017
as	78	w	10019
an	125	w	10021
Egyptian	1	w	10029
etc	4	w	10032
Ḥăjī	1	w	10038
Khalfa	1	w	10044
Lexicon	1	w	10052
Bibliographicum	1	w	10067
and	65	w	10071
Casiri	3	w	10077
The	12	w	10083
readiness	1	w	10092
of	122	w	10094
the	201	w	10097
Arabians	3	w	10105
to	94	w	10107
run	1	w	10110
away	1	w	10114
with	19	w	10118
an	129	w	10120
idea	3	w	10124
is	96	w	10126
illustrated	1	w	10137
by	15	w	10139
the	202	w	10142
last	1	w	10146
words	5	w	10151
of	123	w	10153
the	203	w	10156
extract	2	w	10163
Everyone	1	w	10172
knows	1	w	10177
the	204	w	10180
story	3	w	10185
of	124	w	10187
Plato	13	w	10192
s	639	w	10194
inscription	1	w	10205
over	5	w	10209
the	205	w	10212
porch	1	w	10217
of	125	w	10219
the	206	w	10222
Academy	1	w	10229
let	4	w	10233
no	35	w	10235
one	11	w	10238
unversed	1	w	10246
in	125	w	10248
geometry	12	w	10256
enter	1	w	10261
my	9	w	10263
doors	2	w	10268
the	207	w	10272
Arab	9	w	10276
turned	1	w	10282
geometry	13	w	10290
into	2	w	10294
Euclid	52	w	10300
s	643	w	10302
geometry	14	w	10310
and	66	w	10314
told	3	w	10318
the	208	w	10321
story	4	w	10326
of	126	w	10328
Greek	9	w	10333
philosophers	3	w	10345
in	127	w	10347
general	4	w	10354
and	67	w	10357
their	3	w	10362
Academies	1	w	10371
Equally	1	w	10379
remarkable	1	w	10389
are	10	w	10392
the	210	w	10395
Arabian	7	w	10402
accounts	2	w	10410
of	127	w	10412
the	211	w	10415
relation	3	w	10423
of	128	w	10425
Euclid	53	w	10431
and	68	w	10434
Apollonius	6	w	10444
The	13	w	10447
authorities	1	w	10458
for	18	w	10461
these	4	w	10466
statements	2	w	10476
quoted	1	w	10482
by	16	w	10484
Casiri	4	w	10490
and	69	w	10493
Ḥājī	1	w	10497
Khalfa	2	w	10503
are	11	w	10506
al-Kindi	1	w	10514
s	655	w	10516
tract	3	w	10521
de	54	w	10523
instituto	1	w	10532
libri	1	w	10537
Euclidis	2	w	10545
al-Kindī	1	w	10554
died	2	w	10558
about	11	w	10563
873	1	w	10566
and	70	w	10570
a	725	w	10571
commentary	1	w	10581
by	17	w	10583
Qāḍīzāde	1	w	10591
ar-Rūmī	1	w	10598
d	376	w	10600
about	12	w	10606
1440	1	w	10610
on	127	w	10613
a	729	w	10614
book	4	w	10618
called	4	w	10624
Ashkāl	1	w	10630
at-	1	w	10633
ta	28	w	10635
sīs	1	w	10639
fundamental	1	w	10651
propositions	2	w	10663
by	18	w	10666
Ashraf	1	w	10672
Shamsaddīn	1	w	10682
as-Samarqandī	1	w	10695
c	335	w	10697
1276	1	w	10702
consisting	1	w	10713
of	129	w	10715
elucidations	1	w	10727
of	130	w	10729
35	1	w	10731
propositions	3	w	10743
selected	1	w	10751
from	11	w	10755
the	213	w	10758
first	16	w	10763
books	2	w	10768
of	131	w	10770
Euclid	55	w	10776
Naṣīraddīn	2	w	10787
likewise	1	w	10795
says	9	w	10799
that	32	w	10803
Euclid	56	w	10809
cut	1	w	10812
out	23	w	10815
two	1	w	10818
of	132	w	10820
15	5	w	10822
books	3	w	10827
of	133	w	10829
elements	5	w	10837
then	9	w	10841
existing	1	w	10849
and	72	w	10852
published	3	w	10861
the	215	w	10864
rest	1	w	10868
under	8	w	10873
his	29	w	10876
own	4	w	10879
name	5	w	10883
According	2	w	10893
to	101	w	10895
Qāḍīzāde	2	w	10903
the	216	w	10906
king	4	w	10910
heard	1	w	10915
that	33	w	10919
there	9	w	10924
was	23	w	10927
a	752	w	10928
celebrated	1	w	10938
geometer	6	w	10946
named	1	w	10951
Euclid	57	w	10957
at	129	w	10959
Tyre	3	w	10963
Naṣīraddīn	3	w	10974
says	10	w	10978
that	34	w	10982
he	268	w	10984
sent	4	w	10988
for	19	w	10991
Euclid	58	w	10997
of	134	w	10999
Ṭūs	2	w	11002
According	3	w	11013
to	102	w	11015
them	9	w	11019
the	219	w	11022
Elements	9	w	11030
were	7	w	11034
originally	1	w	11044
written	1	w	11051
not	18	w	11055
by	19	w	11057
Euclid	59	w	11063
but	7	w	11067
by	20	w	11069
a	761	w	11070
man	8	w	11073
whose	2	w	11078
name	7	w	11082
was	24	w	11085
Apollonius	7	w	11095
a	765	w	11097
carpenter	1	w	11106
who	21	w	11110
wrote	4	w	11115
the	220	w	11118
work	7	w	11122
in	137	w	11124
15	6	w	11126
books	4	w	11131
or	91	w	11133
sections	1	w	11141
So	4	w	11143
says	11	w	11147
the	221	w	11150
Fihrist	2	w	11157
Suter	2	w	11163
op	23	w	11166
cit	2	w	11170
p	178	w	11172
49	2	w	11175
thinks	2	w	11182
that	35	w	11186
the	222	w	11189
author	6	w	11195
of	135	w	11197
the	223	w	11200
Fihrist	3	w	11207
did	4	w	11210
not	19	w	11213
suppose	1	w	11220
Apollonius	8	w	11230
of	136	w	11232
Perga	1	w	11237
to	103	w	11239
be	40	w	11241
the	224	w	11244
writer	2	w	11250
of	137	w	11252
the	225	w	11255
Elements	10	w	11263
as	85	w	11266
later	3	w	11271
Arabian	8	w	11278
authorities	2	w	11289
did	5	w	11292
but	8	w	11296
that	36	w	11300
he	277	w	11302
distinguished	1	w	11315
another	3	w	11322
Apollonius	9	w	11332
whom	2	w	11336
he	280	w	11338
calls	1	w	11343
a	779	w	11344
carpenter	2	w	11353
Suter	3	w	11359
s	710	w	11361
argument	3	w	11369
is	107	w	11371
based	2	w	11376
on	136	w	11378
the	227	w	11381
fact	4	w	11385
that	37	w	11389
the	228	w	11392
Fihrist	4	w	11399
s	714	w	11401
article	1	w	11408
on	137	w	11410
Apollonius	10	w	11420
of	138	w	11423
Perga	2	w	11428
says	12	w	11433
nothing	1	w	11440
of	139	w	11442
the	229	w	11445
Elements	11	w	11453
and	73	w	11457
that	38	w	11461
it	60	w	11463
gives	1	w	11468
the	230	w	11471
three	3	w	11476
great	2	w	11481
mathematicians	4	w	11495
Euclid	60	w	11502
Archimedes	8	w	11513
and	74	w	11516
Apollonius	11	w	11526
in	141	w	11529
the	232	w	11532
correct	4	w	11539
chronological	1	w	11552
order	2	w	11557
In	3	w	11561
the	233	w	11564
course	1	w	11570
of	140	w	11572
time	6	w	11576
some	11	w	11580
of	141	w	11582
the	234	w	11585
work	8	w	11589
was	25	w	11592
lost	1	w	11596
and	75	w	11599
the	235	w	11602
rest	2	w	11606
became	1	w	11612
disarranged	1	w	11623
so	47	w	11626
that	39	w	11630
one	12	w	11633
of	142	w	11635
the	236	w	11638
kings	1	w	11643
at	140	w	11645
Alexandria	3	w	11655
who	23	w	11658
desired	1	w	11665
to	104	w	11667
study	2	w	11672
geometry	15	w	11680
and	77	w	11683
to	105	w	11685
master	1	w	11691
this	10	w	11695
treatise	4	w	11703
in	143	w	11705
particular	2	w	11715
first	17	w	11720
questioned	1	w	11730
about	13	w	11735
it	61	w	11737
certain	2	w	11744
learned	3	w	11751
men	31	w	11754
who	24	w	11757
visited	1	w	11764
him	24	w	11767
and	78	w	11770
then	10	w	11774
sent	5	w	11778
for	20	w	11781
Euclid	61	w	11787
who	25	w	11790
was	26	w	11793
at	142	w	11795
that	40	w	11799
time	7	w	11803
famous	2	w	11809
as	90	w	11811
a	819	w	11812
geometer	7	w	11820
and	79	w	11824
asked	4	w	11829
him	25	w	11832
to	106	w	11834
revise	1	w	11840
and	80	w	11843
complete	3	w	11851
the	238	w	11854
work	9	w	11858
and	81	w	11861
reduce	1	w	11867
it	63	w	11869
to	107	w	11871
order	3	w	11876
Euclid	62	w	11883
then	11	w	11887
re-wrote	1	w	11895
it	64	w	11897
in	145	w	11899
13	2	w	11901
books	5	w	11906
which	15	w	11911
were	8	w	11915
thereafter	1	w	11925
known	2	w	11930
by	21	w	11932
his	31	w	11935
name	8	w	11939
According	4	w	11950
to	108	w	11952
another	4	w	11959
version	1	w	11966
Euclid	63	w	11972
composed	1	w	11980
the	242	w	11983
13	3	w	11985
books	6	w	11990
out	25	w	11993
of	143	w	11995
commentaries	2	w	12007
which	16	w	12012
he	297	w	12014
had	9	w	12017
published	4	w	12026
on	144	w	12028
two	2	w	12031
books	7	w	12036
of	144	w	12038
Apollonius	12	w	12048
on	146	w	12050
conics	3	w	12056
and	82	w	12059
out	26	w	12062
of	145	w	12064
introductory	1	w	12076
matter	2	w	12082
added	1	w	12087
to	110	w	12089
the	243	w	12092
doctrine	2	w	12100
of	146	w	12102
the	244	w	12105
five	4	w	12109
regular	4	w	12116
solids	4	w	12122
To	2	w	12126
the	245	w	12129
thirteen	1	w	12137
books	8	w	12142
were	9	w	12146
added	2	w	12151
two	3	w	12154
more	3	w	12158
books	9	w	12163
the	246	w	12167
work	10	w	12171
of	147	w	12173
others	1	w	12179
though	5	w	12186
some	12	w	12190
attribute	1	w	12199
these	5	w	12204
also	5	w	12208
to	111	w	12210
Euclid	64	w	12216
which	17	w	12222
contain	2	w	12229
several	1	w	12236
things	4	w	12242
not	23	w	12245
mentioned	1	w	12254
by	22	w	12256
Apollonius	13	w	12266
According	5	w	12276
to	112	w	12278
another	5	w	12285
version	2	w	12292
Hypsicles	1	w	12301
a	839	w	12303
pupil	6	w	12308
of	148	w	12310
Euclid	65	w	12316
at	146	w	12318
Alexandria	4	w	12328
offered	1	w	12336
to	113	w	12338
the	250	w	12341
king	6	w	12345
and	84	w	12348
published	5	w	12357
Books	1	w	12362
XIV	1	w	12365
and	85	w	12369
XV	1	w	12371
it	65	w	12375
being	6	w	12380
also	6	w	12384
stated	1	w	12390
that	41	w	12394
Hypsicles	2	w	12403
had	10	w	12406
discovered	2	w	12416
the	251	w	12419
books	10	w	12424
by	23	w	12427
which	18	w	12432
it	66	w	12434
appears	2	w	12441
to	114	w	12443
be	43	w	12445
suggested	1	w	12454
that	42	w	12458
Hypsicles	3	w	12467
had	11	w	12470
edited	1	w	12476
them	11	w	12480
from	12	w	12484
materials	1	w	12493
left	1	w	12497
by	24	w	12499
Euclid	66	w	12505
We	3	w	12508
observe	1	w	12515
here	16	w	12519
the	253	w	12522
correct	5	w	12529
statement	4	w	12538
that	43	w	12542
Books	2	w	12547
XIV	2	w	12550
and	86	w	12554
XV	2	w	12556
were	10	w	12561
not	25	w	12564
written	2	w	12571
by	25	w	12573
Euclid	67	w	12579
but	10	w	12583
along	1	w	12588
with	20	w	12592
it	70	w	12594
the	254	w	12597
incorrect	2	w	12606
information	1	w	12617
that	44	w	12621
Hypsicles	4	w	12630
the	255	w	12634
author	8	w	12640
of	150	w	12642
Book	3	w	12646
XIV	3	w	12649
wrote	6	w	12656
Book	4	w	12660
XV	3	w	12662
also	7	w	12667
The	14	w	12671
whole	5	w	12676
of	151	w	12678
the	256	w	12681
fable	1	w	12686
about	14	w	12691
Apollonius	14	w	12701
having	2	w	12707
preceded	1	w	12715
Euclid	68	w	12721
and	87	w	12724
having	3	w	12730
written	3	w	12737
the	257	w	12740
Elements	12	w	12748
appears	3	w	12755
to	115	w	12757
have	9	w	12761
been	5	w	12765
evolved	1	w	12772
out	28	w	12775
of	152	w	12777
the	258	w	12780
preface	2	w	12787
to	116	w	12789
Book	5	w	12793
XIV	4	w	12796
by	26	w	12799
Hypsicles	5	w	12808
and	88	w	12812
in	158	w	12814
this	11	w	12818
way	5	w	12821
the	259	w	12825
Book	6	w	12829
must	6	w	12833
in	159	w	12835
early	4	w	12840
times	1	w	12845
have	10	w	12849
been	6	w	12853
attributed	1	w	12863
to	117	w	12865
Euclid	69	w	12871
and	89	w	12875
the	260	w	12878
inference	2	w	12887
based	3	w	12892
upon	2	w	12896
this	12	w	12900
assumption	1	w	12910
was	27	w	12913
left	2	w	12917
uncorrected	1	w	12928
afterwards	1	w	12938
when	3	w	12942
it	72	w	12944
was	28	w	12947
recognised	1	w	12957
that	45	w	12961
Hypsicles	6	w	12970
was	29	w	12973
the	261	w	12976
author	9	w	12982
The	15	w	12986
preface	3	w	12993
is	121	w	12995
worth	1	w	13000
quoting	1	w	13007
Basilides	1	w	13017
of	153	w	13019
Tyre	4	w	13023
O	4	w	13025
Protarchus	1	w	13035
when	4	w	13040
he	324	w	13042
came	3	w	13046
to	118	w	13048
Alexandria	5	w	13058
and	91	w	13061
met	26	w	13064
my	10	w	13066
father	3	w	13072
spent	2	w	13078
the	263	w	13081
greater	1	w	13088
part	4	w	13092
of	154	w	13094
his	34	w	13097
sojourn	1	w	13104
with	21	w	13108
him	26	w	13111
on	157	w	13113
account	4	w	13120
of	155	w	13122
their	4	w	13127
common	3	w	13133
interest	1	w	13141
in	163	w	13143
mathematics	1	w	13154
And	1	w	13158
once	4	w	13162
when	5	w	13167
examining	1	w	13176
the	266	w	13179
treatise	5	w	13187
written	4	w	13194
by	27	w	13196
Apollonius	15	w	13206
about	15	w	13211
the	267	w	13214
comparison	1	w	13224
between	5	w	13231
the	268	w	13234
dodecahedron	1	w	13246
and	92	w	13249
the	269	w	13252
icosahedron	1	w	13263
inscribed	1	w	13272
in	167	w	13274
the	270	w	13277
same	8	w	13281
sphere	1	w	13287
showing	1	w	13296
what	8	w	13301
ratio	3	w	13306
they	6	w	13310
have	11	w	13314
to	119	w	13316
one	15	w	13319
another	6	w	13326
they	7	w	13331
thought	2	w	13338
that	46	w	13342
Apollonius	16	w	13352
had	12	w	13355
not	27	w	13358
expounded	1	w	13367
this	13	w	13371
matter	3	w	13377
properly	1	w	13385
and	93	w	13389
accordingly	1	w	13400
they	8	w	13404
emended	1	w	13411
the	275	w	13414
exposition	1	w	13424
as	98	w	13427
I	28	w	13428
was	30	w	13431
able	6	w	13435
to	120	w	13437
learn	9	w	13442
from	13	w	13446
my	11	w	13448
father	4	w	13454
And	2	w	13458
I	29	w	13459
myself	1	w	13465
later	4	w	13471
fell	1	w	13476
in	170	w	13478
with	22	w	13482
another	7	w	13489
book	14	w	13493
published	6	w	13502
by	28	w	13504
Apollonius	17	w	13514
containing	1	w	13525
a	925	w	13526
demonstration	3	w	13539
relating	2	w	13547
to	121	w	13549
the	278	w	13552
subject	5	w	13559
and	94	w	13563
I	30	w	13564
was	31	w	13567
greatly	1	w	13574
interested	1	w	13584
in	175	w	13586
the	279	w	13589
investigation	3	w	13602
of	156	w	13604
the	280	w	13607
problem	2	w	13614
The	16	w	13618
book	15	w	13622
published	7	w	13631
by	29	w	13633
Apollonius	18	w	13643
is	128	w	13645
accessible	1	w	13655
to	122	w	13657
all	15	w	13660
for	22	w	13664
it	77	w	13666
has	6	w	13669
a	935	w	13670
large	1	w	13675
circulation	1	w	13686
having	4	w	13693
apparently	4	w	13703
been	7	w	13707
carefully	1	w	13716
written	5	w	13723
out	30	w	13726
later	5	w	13731
but	12	w	13735
I	31	w	13736
decided	1	w	13743
to	123	w	13745
send	1	w	13749
you	3	w	13752
the	281	w	13755
comments	1	w	13763
which	19	w	13768
seem	3	w	13772
to	124	w	13774
me	121	w	13776
to	125	w	13778
be	49	w	13780
necessary	1	w	13789
for	23	w	13793
you	4	w	13796
will	1	w	13800
through	3	w	13807
your	1	w	13811
proficiency	1	w	13822
in	178	w	13824
mathematics	2	w	13835
in	179	w	13837
general	5	w	13844
and	95	w	13847
in	180	w	13849
geometry	16	w	13857
in	181	w	13859
particular	3	w	13869
form	3	w	13873
an	170	w	13875
expert	1	w	13881
judgment	1	w	13889
on	174	w	13891
what	9	w	13895
I	32	w	13896
am	32	w	13898
about	16	w	13903
to	126	w	13905
say	16	w	13908
and	96	w	13912
you	6	w	13915
will	2	w	13919
lend	1	w	13923
a	956	w	13924
kindly	1	w	13930
ear	20	w	13933
to	127	w	13935
my	13	w	13937
disquisition	1	w	13949
for	25	w	13952
the	283	w	13955
sake	1	w	13959
of	158	w	13961
your	2	w	13965
friendship	1	w	13975
to	128	w	13977
my	14	w	13979
father	5	w	13985
and	97	w	13988
your	3	w	13992
goodwill	1	w	14000
to	129	w	14002
me	124	w	14004