Scaife ATLAS

Introduction (1.6-2.3)

Refs	{'start': {'reference': '1.6', 'human_reference': 'Chapter 1 Part 6'}, 'end': {'reference': '2.3', 'human_reference': 'Chapter 2 Part 3'}}
Ancestors	[{'reference': '1'}]
Children	[]

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to	27	w	3881
say	4	w	3884
nothing	1	w	3891
of	47	w	3893
the	82	w	3896
lunules	1	w	3903
of	48	w	3905
Hippocrates	1	w	3916
I	20	w	3918
think	1	w	3923
however	2	w	3930
that	13	w	3934
there	1	w	3939
is	48	w	3941
an	39	w	3943
objection	1	w	3952
to	28	w	3954
this	7	w	3958
theory	1	w	3964
so	14	w	3966
far	1	w	3969
as	19	w	3971
regards	1	w	3978
Bryson	2	w	3984
for	8	w	3988
Alexander	2	w	3997
distinctly	1	w	4007
says	3	w	4011
that	14	w	4015
Bryson	3	w	4021
s	255	w	4023
quadrature	2	w	4033
did	2	w	4036
not	6	w	4039
start	3	w	4044
from	9	w	4048
the	85	w	4051
proper	2	w	4057
principles	5	w	4067
of	49	w	4069
geometry	5	w	4077
but	4	w	4081
from	10	w	4085
some	3	w	4089
principles	6	w	4099
more	3	w	4103
general	2	w	4110
2	8	w	4113
The	7	w	4117
Data	1	w	4121
The	8	w	4125
Data	2	w	4129
δεδομένα	1	w	4138
are	2	w	4142
included	1	w	4150
by	12	w	4152
Pappus	1	w	4158
in	68	w	4160
the	86	w	4163
Treasury	1	w	4171
of	50	w	4173
Analysis	1	w	4181
τόπος	1	w	4187
ἀναλυόμενος	1	w	4198
and	25	w	4203
he	106	w	4205
describes	1	w	4214
their	2	w	4219
contents	1	w	4227
Pappus	2	w	4233
VII	2	w	4237
p	87	w	4239
638	1	w	4243
They	1	w	4248
are	3	w	4251
still	1	w	4256
concerned	1	w	4265
with	8	w	4269
elementary	2	w	4279
geometry	6	w	4287
though	1	w	4294
forming	1	w	4301
part	1	w	4305
of	51	w	4307
the	88	w	4310
introduction	1	w	4322
to	29	w	4324
higher	1	w	4330
analysis	1	w	4338
Their	1	w	4344
form	4	w	4348
is	53	w	4350
that	15	w	4354
of	52	w	4356
propositions	1	w	4368
proving	1	w	4375
that	16	w	4379
if	3	w	4382
certain	1	w	4389
things	4	w	4395
in	74	w	4397
a	266	w	4398
figure	3	w	4404
are	4	w	4407
given	2	w	4412
in	75	w	4415
magnitude	1	w	4424
in	76	w	4427
species	1	w	4434
etc	1	w	4438
something	1	w	4450
else	3	w	4454
is	54	w	4456
given	3	w	4461
The	11	w	4465
subjectmatter	1	w	4478
is	55	w	4480
much	2	w	4484
the	89	w	4487
same	2	w	4491
as	21	w	4493
that	17	w	4497
of	53	w	4499
the	90	w	4502
planimetrical	1	w	4515
books	3	w	4520
of	54	w	4522
the	91	w	4525
Elements	7	w	4533
to	30	w	4536
which	11	w	4541
the	92	w	4544
Data	3	w	4548
are	5	w	4551
often	1	w	4556
supplementary	1	w	4569
We	3	w	4572
shall	3	w	4577
see	2	w	4580
this	8	w	4584
later	2	w	4589
when	1	w	4593
we	10	w	4595
come	1	w	4599
to	31	w	4601
compare	1	w	4608
the	93	w	4611
propositions	2	w	4623
in	78	w	4625
the	94	w	4628
Elements	8	w	4636
which	12	w	4641
give	6	w	4645
us	27	w	4647
the	95	w	4650
means	1	w	4655
of	56	w	4657
solving	1	w	4664
the	96	w	4667
general	3	w	4674
quadratic	1	w	4683
equation	1	w	4691
with	9	w	4695
the	97	w	4698
corresponding	1	w	4711
propositions	3	w	4723
of	57	w	4725
the	98	w	4728
Data	4	w	4732
which	13	w	4737
give	7	w	4741
the	99	w	4744
solution	1	w	4752
The	12	w	4756
Data	5	w	4760
may	3	w	4763
in	81	w	4765
fact	2	w	4769
be	25	w	4771
regarded	1	w	4779
as	22	w	4781
elementary	3	w	4791
exercises	1	w	4800
in	82	w	4802
analysis	2	w	4810
It	3	w	4813
is	59	w	4815
not	7	w	4818
necessary	1	w	4827
to	32	w	4829
go	4	w	4831
more	4	w	4835
closely	1	w	4842
into	1	w	4846
the	100	w	4849
contents	2	w	4857
as	23	w	4860
we	11	w	4862
have	8	w	4866
the	101	w	4869
full	2	w	4873
Greek	4	w	4878
text	1	w	4882
and	26	w	4885
the	102	w	4888
commentary	3	w	4898
by	13	w	4900
Marinus	1	w	4907
newly	1	w	4912
edited	1	w	4918
by	14	w	4920
Menge	2	w	4925
and	27	w	4928
therefore	1	w	4937
easily	1	w	4943
accessible	1	w	4953
Vol	2	w	4956
VI	5	w	4959
in	85	w	4962
the	104	w	4965
Teubner	1	w	4972
edition	3	w	4979
of	58	w	4981
Euclidis	2	w	4989
opera	2	w	4994
omnia	2	w	4999
by	15	w	5001
Heiberg	5	w	5008
and	28	w	5011
Menge	3	w	5016
A	24	w	5018
translation	1	w	5029
of	59	w	5031
the	105	w	5034
Data	6	w	5038
is	61	w	5040
also	3	w	5044
included	2	w	5052
in	87	w	5054
Simson	1	w	5060
s	320	w	5062
Euclid	12	w	5068
though	2	w	5075
naturally	1	w	5084
his	17	w	5087
text	2	w	5091
left	1	w	5095
much	3	w	5099
to	34	w	5101
be	27	w	5103
desired	1	w	5110
3	4	w	5114
The	13	w	5118
book	9	w	5122
On	1	w	5124
divisions	1	w	5133
of	60	w	5136
figures	3	w	5143
This	3	w	5149
work	6	w	5153
περὶ	1	w	5158
διαιρέσεων	1	w	5168
βιβλίον	1	w	5175
is	65	w	5178
mentioned	3	w	5187
by	16	w	5189
Proclus	3	w	5196
Proclus	4	w	5203
p	103	w	5205
69	1	w	5208
4	7	w	5210
In	2	w	5214
one	5	w	5217
place	1	w	5222
he	133	w	5224
is	66	w	5226
speaking	1	w	5234
of	61	w	5236
the	106	w	5239
conception	1	w	5249
or	41	w	5251
definition	1	w	5261
λόγος	1	w	5267
of	62	w	5270
figure	5	w	5276
and	29	w	5280
of	63	w	5282
the	107	w	5285
divisibility	1	w	5297
of	64	w	5299
a	320	w	5300
figure	6	w	5306
into	2	w	5310
others	1	w	5316
differing	1	w	5325
from	11	w	5329
it	31	w	5331
in	92	w	5333
kind	2	w	5337
and	30	w	5341
he	137	w	5343
adds	1	w	5347
For	1	w	5351
the	109	w	5354
circle	2	w	5360
is	68	w	5362
divisible	1	w	5371
into	3	w	5375
parts	1	w	5380
unlike	1	w	5386
in	95	w	5388
definition	2	w	5398
or	43	w	5400
notion	2	w	5406
ἀνόμοια	1	w	5414
τῷ	1	w	5416
λόγῳ	1	w	5420
and	31	w	5425
so	23	w	5427
is	70	w	5429
each	2	w	5433
of	65	w	5435
the	110	w	5438
rectilineal	1	w	5449
figures	4	w	5456
this	9	w	5461
is	72	w	5463
in	98	w	5465
fact	3	w	5469
the	111	w	5472
business	1	w	5480
of	66	w	5482
the	112	w	5485
writer	1	w	5491
of	67	w	5493
the	113	w	5496
Elements	9	w	5504
in	100	w	5506
his	20	w	5509
Divisions	1	w	5518
where	3	w	5524
he	144	w	5526
divides	1	w	5533
given	4	w	5538
figures	5	w	5545
in	101	w	5548
one	6	w	5551
case	2	w	5555
into	4	w	5559
like	3	w	5563
figures	6	w	5570
and	32	w	5574
in	103	w	5576
another	1	w	5583
into	5	w	5587
unlike	2	w	5593
ibid	1	w	5597
144	1	w	5601
22-26	1	w	5607
Like	1	w	5613
and	33	w	5616
unlike	3	w	5622
here	6	w	5626
mean	2	w	5630
not	10	w	5634
similar	1	w	5641
and	34	w	5644
dissimilar	1	w	5654
in	105	w	5656
the	115	w	5659
technical	1	w	5668
sense	1	w	5673
but	5	w	5677
like	6	w	5681
or	44	w	5683
unlike	4	w	5689
in	106	w	5691
definition	3	w	5701
or	45	w	5703
notion	3	w	5709
λόγῳ	2	w	5714
thus	1	w	5720
to	39	w	5722
divide	2	w	5728
a	337	w	5729
triangle	1	w	5737
into	6	w	5741
triangles	1	w	5750
would	1	w	5755
be	28	w	5757
to	41	w	5759
divide	3	w	5765
it	35	w	5767
into	7	w	5771
like	8	w	5775
figures	7	w	5782
to	43	w	5785
divide	4	w	5791
a	340	w	5792
triangle	3	w	5800
into	8	w	5804
a	342	w	5805
triangle	4	w	5813
and	35	w	5816
a	345	w	5817
quadrilateral	1	w	5830
would	2	w	5835
be	29	w	5837
to	45	w	5839
divide	5	w	5845
it	36	w	5847
into	9	w	5851
unlike	5	w	5857
figures	8	w	5864
The	14	w	5868
treatise	4	w	5876
is	77	w	5878
lost	2	w	5882
in	112	w	5884
Greek	5	w	5889
but	6	w	5892
has	2	w	5895
been	3	w	5899
discovered	1	w	5909
in	113	w	5911
the	116	w	5914
Arabic	2	w	5920
First	1	w	5926
John	1	w	5930
Dee	1	w	5933
discovered	2	w	5943
a	352	w	5944
treatise	5	w	5952
De	2	w	5954
divisionibus	1	w	5966
by	17	w	5968
one	7	w	5971
Muhammad	1	w	5979
Bagdadinus	1	w	5989
Steinschneider	1	w	6003
places	1	w	6009
him	1	w	6012
in	116	w	6014
the	117	w	6017
10th	1	w	6021
c	181	w	6022
H	16	w	6024
Suter	1	w	6030
Bibliotheca	1	w	6042
Mathematica	1	w	6053
IV_	1	w	6057
3	5	w	6059
1903	1	w	6065
pp	10	w	6068
24	2	w	6071
27	1	w	6074
identifies	1	w	6085
him	2	w	6088
with	10	w	6092
Abū	1	w	6095
Bekr	1	w	6100
Muh	2	w	6104
b	96	w	6106
Abdalbāqī	1	w	6117
al-Baġdādī	1	w	6127
Qād	1	w	6131
ī	3	w	6132
Judge	1	w	6138
of	68	w	6141
Māristān	1	w	6149
circa	1	w	6155
1070-1141	1	w	6164
to	47	w	6168
whom	1	w	6172
he	153	w	6174
also	4	w	6178
attributes	1	w	6188
the	120	w	6191
Liber	1	w	6196
judei	1	w	6201
judicis	1	w	6210
super	2	w	6216
decimum	1	w	6223
Euclidis	3	w	6231
translated	1	w	6241
by	18	w	6243
Gherard	1	w	6250
of	69	w	6252
Cremona	1	w	6259
and	36	w	6263
handed	2	w	6269
over	4	w	6273
a	375	w	6274
copy	1	w	6278
of	70	w	6280
it	38	w	6282
in	117	w	6285
Latin	1	w	6290
in	119	w	6293
1563	1	w	6297
to	48	w	6299
Commandinus	1	w	6310
who	5	w	6314
published	1	w	6323
it	39	w	6325
in	121	w	6328
Dee	2	w	6331
did	3	w	6334
not	12	w	6337
himself	1	w	6344
translate	2	w	6353
the	121	w	6356
tract	1	w	6361
from	12	w	6365
the	122	w	6368
Arabic	3	w	6374
he	159	w	6377
in	122	w	6379
1570	1	w	6383
De	4	w	6385
superficierum	1	w	6398
divisionibus	2	w	6410
liber	1	w	6415
Machometo	1	w	6424
Bagdadino	1	w	6433
adscriptus	1	w	6443
nunc	1	w	6448
primum	1	w	6454
Ioannis	1	w	6461
Dee	3	w	6464
Londinensis	1	w	6475
et	18	w	6477
Federici	1	w	6485
Commandini	1	w	6495
Urbinatis	1	w	6504
opera	3	w	6509
in	127	w	6511
lucem	1	w	6516
editus	1	w	6522
Pisauri	1	w	6530
1570	2	w	6535
afterwards	1	w	6546
included	3	w	6554
in	129	w	6556
Gregory	1	w	6563
s	400	w	6565
Euclid	14	w	6571
Oxford	1	w	6578
1703	1	w	6583
Dee	4	w	6589
did	4	w	6592
not	13	w	6595
himself	2	w	6602
translate	3	w	6611
the	123	w	6614
tract	2	w	6619
from	13	w	6623
the	124	w	6626
Arabic	4	w	6632
he	162	w	6635
found	1	w	6640
it	41	w	6642
in	130	w	6644
Latin	2	w	6649
in	132	w	6651
a	398	w	6652
MS	1	w	6654
which	14	w	6660
was	2	w	6663
then	3	w	6667
in	133	w	6669
his	21	w	6672
own	2	w	6675
possession	1	w	6685
but	8	w	6688
was	3	w	6691
about	3	w	6696
20	1	w	6698
years	1	w	6703
afterwards	2	w	6713
stolen	1	w	6719
or	48	w	6721
destroyed	1	w	6730
in	134	w	6732
an	71	w	6734
attack	1	w	6740
by	19	w	6742
a	408	w	6743
mob	1	w	6746
on	91	w	6748
his	22	w	6751
house	1	w	6756
at	73	w	6758
Mortlake	1	w	6766
R	4	w	6767
C	9	w	6769
Archibald	1	w	6779
Euclid	15	w	6786
s	416	w	6788
Book	2	w	6792
on	92	w	6794
the	126	w	6797
Division	2	w	6805
of	71	w	6807
Figures	1	w	6814
with	11	w	6818
a	412	w	6819
restoration	1	w	6830
based	1	w	6835
on	95	w	6837
Woepck	1	w	6843
s	421	w	6845
text	3	w	6849
and	40	w	6852
on	96	w	6854
the	127	w	6857
Practica	1	w	6865
geometriae	1	w	6875
of	72	w	6877
Leonardo	1	w	6885
Pisano	1	w	6891
Cambridge	1	w	6901
1915	1	w	6906
pp	11	w	6909
4-9	1	w	6913
Dee	5	w	6918
in	135	w	6921
his	23	w	6924
preface	2	w	6931
addressed	1	w	6940
to	52	w	6942
Commandinus	2	w	6953
says	4	w	6958
nothing	2	w	6965
of	73	w	6967
his	24	w	6970
having	1	w	6976
translated	2	w	6986
the	128	w	6989
book	10	w	6993
but	9	w	6997
only	2	w	7001
remarks	2	w	7008
that	18	w	7012
the	129	w	7015
very	3	w	7019
illegible	1	w	7028
MS	2	w	7030
had	2	w	7034
caused	1	w	7040
him	5	w	7043
much	4	w	7047
trouble	1	w	7054
and	42	w	7057
in	139	w	7060
a	434	w	7061
later	4	w	7066
passage	5	w	7073
speaks	1	w	7080
of	74	w	7082
the	130	w	7085
actual	2	w	7091
very	4	w	7096
ancient	1	w	7103
copy	2	w	7108
from	14	w	7112
which	15	w	7117
I	28	w	7118
wrote	3	w	7123
out	8	w	7126
in	140	w	7132
ipso	1	w	7136
unde	5	w	7140
descripsi	1	w	7149
vetustissimo	1	w	7161
exemplari	1	w	7170
The	15	w	7175
Latin	3	w	7180
translation	2	w	7191
of	75	w	7193
this	10	w	7197
tract	3	w	7202
from	15	w	7206
the	131	w	7209
Arabic	5	w	7215
was	4	w	7218
probably	1	w	7226
made	3	w	7230
by	20	w	7232
Gherard	2	w	7239
of	76	w	7241
Cremona	2	w	7248
1114-1187	1	w	7258
among	1	w	7265
the	132	w	7268
list	2	w	7272
of	77	w	7274
whose	1	w	7279
numerous	1	w	7287
translations	1	w	7299
a	456	w	7300
liber	2	w	7305
divisionum	1	w	7315
occurs	1	w	7321
The	16	w	7325
Arabic	6	w	7331
original	1	w	7339
cannot	1	w	7345
have	9	w	7349
been	4	w	7353
a	461	w	7354
direct	1	w	7360
translation	4	w	7371
from	16	w	7375
Euclid	16	w	7381
and	43	w	7385
probably	2	w	7393
was	5	w	7396
not	16	w	7399
even	1	w	7403
a	467	w	7404
direct	2	w	7410
adaptation	1	w	7420
of	78	w	7422
it	43	w	7424
it	44	w	7427
contains	1	w	7435
mistakes	1	w	7443
and	44	w	7446
unmathematical	1	w	7460
expressions	1	w	7471
and	45	w	7475
moreover	1	w	7483
does	1	w	7487
not	17	w	7490
contain	3	w	7497
the	134	w	7500
propositions	4	w	7512
about	4	w	7517
the	135	w	7520
division	5	w	7528
of	79	w	7530
a	480	w	7531
circle	3	w	7537
alluded	1	w	7544
to	53	w	7546
by	21	w	7548
Proclus	5	w	7555
Hence	1	w	7561
it	46	w	7563
can	3	w	7566
scarcely	1	w	7574
have	10	w	7578
contained	1	w	7587
more	6	w	7591
than	3	w	7595
a	487	w	7596
fragment	1	w	7604
of	80	w	7606
Euclid	17	w	7612
s	467	w	7614
work	7	w	7618
But	2	w	7622
Woepcke	1	w	7629
found	2	w	7634
in	146	w	7636
a	489	w	7637
MS	3	w	7639
at	85	w	7642
Paris	1	w	7647
a	492	w	7648
treatise	6	w	7656
in	147	w	7658
Arabic	7	w	7664
on	112	w	7666
the	136	w	7669
division	6	w	7677
of	81	w	7679
figures	9	w	7686
which	16	w	7692
he	178	w	7694
translated	3	w	7704
and	46	w	7707
published	2	w	7716
in	148	w	7718
1851	1	w	7722
Fournal	1	w	7729
Asiatique	1	w	7738
1851	2	w	7743
p	137	w	7745
233	1	w	7749
sqq	1	w	7752
It	4	w	7756
is	107	w	7758
expressly	1	w	7767
attributed	1	w	7777
to	54	w	7779
Euclid	18	w	7785
in	149	w	7787
the	137	w	7790
MS	4	w	7792
and	47	w	7796
corresponds	1	w	7807
to	55	w	7809
the	138	w	7812
description	1	w	7823
of	82	w	7825
it	47	w	7827
by	22	w	7829
Proclus	6	w	7836
Generally	1	w	7846
speaking	2	w	7854
the	139	w	7858
divisions	2	w	7867
are	7	w	7870
divisions	3	w	7879
into	10	w	7883
figures	10	w	7890
of	83	w	7892
the	140	w	7895
same	3	w	7899
kind	3	w	7903
as	33	w	7905
the	141	w	7908
original	2	w	7916
figures	11	w	7923
e	875	w	7925
g	115	w	7927
of	84	w	7930
triangles	2	w	7939
into	11	w	7943
triangles	3	w	7952
but	11	w	7956
there	3	w	7961
are	8	w	7964
also	5	w	7968
divisions	4	w	7977
into	12	w	7981
unlike	6	w	7987
figures	12	w	7994
e	883	w	7996
g	119	w	7998
that	19	w	8003
of	85	w	8005
a	513	w	8006
triangle	7	w	8014
by	23	w	8016
a	515	w	8017
straight	1	w	8025
line	2	w	8029
parallel	1	w	8037
to	59	w	8039
the	143	w	8042
base	2	w	8046
The	17	w	8050
missing	1	w	8057
propositions	5	w	8069
about	5	w	8074
the	144	w	8077
division	10	w	8085
of	86	w	8087
a	521	w	8088
circle	4	w	8094
are	9	w	8097
also	6	w	8101
here	8	w	8105
to	60	w	8108
divide	6	w	8114
into	13	w	8118
two	3	w	8121
equal	1	w	8126
parts	2	w	8131
a	526	w	8132
given	5	w	8137
figure	16	w	8143
bounded	1	w	8150
by	24	w	8152
an	93	w	8154
arc	2	w	8157
of	87	w	8159
a	529	w	8160
circle	5	w	8166
and	48	w	8169
two	4	w	8172
straight	2	w	8180
lines	1	w	8185
including	1	w	8194
a	532	w	8195
given	6	w	8200
angle	8	w	8205
and	49	w	8208
to	62	w	8210
draw	1	w	8214
in	162	w	8216
a	536	w	8217
given	7	w	8222
circle	6	w	8228
two	5	w	8231
parallel	2	w	8239
straight	3	w	8247
lines	2	w	8252
cutting	1	w	8259
off	1	w	8262
a	540	w	8263
certain	2	w	8270
part	4	w	8274
of	89	w	8276
the	145	w	8279
circle	7	w	8285
Unfortunately	1	w	8299
the	146	w	8302
proofs	1	w	8308
are	10	w	8311
given	8	w	8316
of	91	w	8318
only	3	w	8322
four	1	w	8326
propositions	6	w	8338
including	2	w	8348
the	147	w	8351
two	6	w	8354
last	1	w	8358
mentioned	4	w	8367
out	11	w	8371
of	92	w	8373
36	2	w	8375
because	2	w	8383
the	148	w	8386
Arabic	8	w	8392
translator	1	w	8402
found	3	w	8407
them	7	w	8411
too	2	w	8414
easy	1	w	8418
and	50	w	8421
omitted	1	w	8428
them	8	w	8432
To	1	w	8435
illustrate	1	w	8445
the	151	w	8448
character	1	w	8457
of	93	w	8459
the	152	w	8462
problems	1	w	8470
dealt	1	w	8475
with	12	w	8479
I	30	w	8480
need	1	w	8484
only	4	w	8488
take	3	w	8492
one	9	w	8495
more	7	w	8499
example	2	w	8506
To	2	w	8509
cut	2	w	8512
off	2	w	8515
a	558	w	8516
certain	3	w	8523
fraction	1	w	8531
from	17	w	8535
a	561	w	8536
parallel-	1	w	8546
trapezium	1	w	8556
by	25	w	8558
a	565	w	8559
straight	4	w	8567
line	5	w	8571
which	17	w	8576
passes	1	w	8582
through	2	w	8589
a	568	w	8590
given	9	w	8595
point	2	w	8600
lying	1	w	8605
inside	1	w	8611
or	60	w	8613
outside	2	w	8620
the	153	w	8623
trapezium	2	w	8632
but	12	w	8635
so	28	w	8637
that	20	w	8641
a	571	w	8642
straight	5	w	8650
line	6	w	8654
can	4	w	8657
be	36	w	8659
drawn	1	w	8664
through	3	w	8671
it	52	w	8673
cutting	2	w	8680
both	1	w	8684
the	154	w	8687
parallel	4	w	8695
sides	2	w	8700
of	95	w	8702
the	155	w	8705
trapezium	3	w	8714
The	18	w	8718
genuineness	1	w	8729
of	96	w	8731
the	156	w	8734
treatise	7	w	8742
edited	2	w	8748
by	26	w	8750
Woepcke	2	w	8757
is	114	w	8759
attested	1	w	8767
by	27	w	8769
the	157	w	8772
facts	1	w	8777
that	21	w	8781
the	158	w	8784
four	2	w	8788
proofs	2	w	8794
which	18	w	8799
remain	1	w	8805
are	11	w	8808
elegant	1	w	8815
and	51	w	8818
depend	1	w	8824
on	127	w	8826
propositions	7	w	8838
in	177	w	8840
the	159	w	8843
Elements	10	w	8851
and	52	w	8855
that	22	w	8859
there	4	w	8864
is	115	w	8866
a	588	w	8867
lemma	1	w	8872
with	13	w	8876
a	590	w	8877
true	2	w	8881
Greek	6	w	8886
ring	4	w	8890
to	65	w	8893
apply	1	w	8898
to	66	w	8900
a	592	w	8901
straight	6	w	8909
line	7	w	8913
a	594	w	8914
rectangle	1	w	8923
equal	2	w	8928
to	67	w	8930
the	161	w	8933
rectangle	2	w	8942
contained	2	w	8951
by	28	w	8953
AB	1	w	8955
AC	1	w	8958
and	53	w	8961
deficient	1	w	8970
by	29	w	8972
a	600	w	8973
square	1	w	8979
Moreover	1	w	8988
the	162	w	8991
treatise	8	w	8999
is	117	w	9001
no	28	w	9003
fragment	2	w	9011
but	13	w	9015
finishes	1	w	9023
with	14	w	9027
the	163	w	9030
words	1	w	9035
end	3	w	9038
of	98	w	9040
the	164	w	9043
treatise	9	w	9051
and	54	w	9055
is	120	w	9057
a	606	w	9058
well-ordered	1	w	9070
and	55	w	9073
compact	1	w	9080
whole	1	w	9085
Hence	2	w	9091
we	13	w	9093
may	4	w	9096
safely	1	w	9102
conclude	2	w	9110
that	23	w	9114
Woepcke	3	w	9121
s	551	w	9123
is	121	w	9125
not	18	w	9128
only	5	w	9132
Euclid	19	w	9138
s	553	w	9140
own	3	w	9143
work	8	w	9147
but	14	w	9150
the	165	w	9153
whole	2	w	9158
of	99	w	9160
it	57	w	9162
A	38	w	9164
restoration	2	w	9175
of	100	w	9177
the	166	w	9180
work	9	w	9184
with	15	w	9189
proofs	3	w	9195
was	6	w	9199
attempted	1	w	9208
by	30	w	9210
Ofterdinger	1	w	9221
L	14	w	9222
F	6	w	9224
Ofterdinger	2	w	9236
Beiträge	1	w	9245
zur	1	w	9248
Wiederherstellung	1	w	9265
der	12	w	9268
Schrift	1	w	9275
des	14	w	9278
Euklides	1	w	9286
über	2	w	9290
die	2	w	9293
Theilung	1	w	9301
der	13	w	9304
Figuren	1	w	9311
Ulm	1	w	9315
1853	1	w	9320
Who	1	w	9325
however	3	w	9332
does	2	w	9336
not	19	w	9339
give	14	w	9343
Woepcke	4	w	9350
s	561	w	9352
props	1	w	9357
30	1	w	9360
31	1	w	9363
34	1	w	9366
35	1	w	9369
36	3	w	9372
We	4	w	9375
have	11	w	9379
now	3	w	9382
a	616	w	9383
satisfactory	1	w	9395
restoration	3	w	9406
with	16	w	9411
ample	3	w	9416
notes	1	w	9421
and	56	w	9424
an	109	w	9426
introduction	2	w	9438
by	31	w	9441
R	5	w	9442
C	14	w	9444
Archibald	2	w	9454
who	9	w	9458
used	3	w	9462
for	14	w	9465
the	167	w	9468
purpose	1	w	9475
Woepcke	5	w	9482
s	569	w	9484
text	4	w	9488
and	57	w	9491
a	625	w	9492
section	1	w	9499
of	102	w	9501
Leonardo	2	w	9509
of	103	w	9511
Pisa	3	w	9515
s	572	w	9517
Practica	2	w	9525
geometriae	2	w	9535
1220	1	w	9540
There	1	w	9547
is	124	w	9549
a	631	w	9550
remarkable	1	w	9560
similarity	1	w	9570
between	1	w	9577
the	168	w	9580
propositions	8	w	9592
of	104	w	9594
Woepcke	6	w	9601
s	577	w	9603
text	5	w	9607
and	58	w	9610
those	4	w	9615
of	105	w	9617
Leonardo	3	w	9625
suggesting	1	w	9636
that	24	w	9640
Leonardo	4	w	9648
may	5	w	9651
have	12	w	9655
had	3	w	9658
before	1	w	9664
him	6	w	9667
a	642	w	9668
translation	5	w	9679
perhaps	1	w	9687
by	32	w	9689
Gherard	3	w	9696
of	106	w	9698
Cremona	3	w	9705
of	107	w	9708
the	169	w	9711
Arabic	9	w	9717
tract	4	w	9722