The compleat surveyor containing the whole art of surveying of land by the plain table, theodolite, circumferentor, and peractor ... : together with the taking of all manner of heights and distances, either by William Leybourn.

CHAP. I. The Elplanation and Ʋse of the Table of SINES.

BEfore I come to the mensuration of Triangles, it will be necessary to explain and shew the use of the Tables of Sines and Logarithms following, by which Tables the sides or angles of right lined Triangles may be readily and exactly measured, so that in any plain Triangle, if there be any three parts thereof gi∣ven, a fourth may be easily discove∣red.

The Table of Sines consisteth of two Rows or Columns, the first whereof sheweth the Degrees and Minutes of the Quadrant, having over the head thereof these two letters, D. M, standing for Degrees and Minutes: In the second Column is the Artificiall Sines answering to every Degree, and 10^th Minute of the Quadrant, having the word Sine over the head thereof. The use of this Ta∣ble will appear by the following Propositions.

PROP. I. Any Degree and Minute being given, to finde the Sine thereof.

FIrst, Seeke the Degree and minute in the first Columne of the Table, under D. M. and right against it, in the next Column towards the right hand, under the word Sine, you shall have your desire.

EXAMPLE. I.

Suppose it were required to finde the Sine of 20 degrees, First, you must seeke 20 in the first Column of the Table under D. M. and right against 20 in the second Column under the word Sine, you shall finde 9,534052, which is the Sine of 20 Degrees.

In the same manner you shall finde the Sine of 50 degrees to be 9,884254, and the Sine of 76 degrees to be 9,986904.

EXAMPLE. II.

Let it be required to finde the Sine of 40 degrees, 30 minutes. First, you must finde 40 30 (which is 40 degrees 30 minutes) in the first Column, under the letters D. M. and against it you shall finde 9,812544, which is the Sine of 40 degrees, 30 minutes.

Also the Sine of 62 degrees 10 minutes, will be found to be 9,946604, and the Sine of 86 degrees 30 minutes will be 9,999189, and in this manner may you finde the artificiall Sine of any number of Degrees and minutes expressed in the Table.

PROP. II. Any Sine being given, to finde the number of de∣grees and minutes thereunto belonging.

EXAMPLE.

LEt 9,866470 be a Sine given, and let it be required to finde the degree and minute of the Quadrant answering thereunto. First, seeke in the second Column amongst the Sines for 9,866470, and against it (on the left hand) you shall finde 47 degrees 20 minutes, which is the arch of the Quadrant answering thereunto.

Again, Let it be required to finde the arch answering to this Sine 9,821264, having found 9,821264 in the second Column under the word Sine, against it you shall finde 41 degrees 30 min. and that is the arch of degree answering thereunto.

¶ But in case you have a number given which you cannot ex∣actly finde in the Table, you must then instead thereof, take the nee∣rest in the Table. As if your number given were 9,675859, if you looke in the Table for this number it cannot be found there, but the neerest thereunto is 9,676328, which is the Sine of 28 degrees 20 minutes, which you must take instead thereof.

The Table of Sines.

D.	M.	Sines
0	0	0,000000
	10	7,463726
	20	7,764754
	30	7,940842
	40	8,065776
	50	8,162681
1	0	8,241855
	10	8,308794
	20	8,366777
	30	8,417919
	40	8,463665
	50	8,505045
2	0	8,542819
	10	8,577566
	20	8,609734
	30	8,639679
	40	8,667689
	50	8,693998
3	0	8,718800
	10	8,742259
	20	8,764511
	30	8,785675
	40	8,805852
	50	8,825130
4	0	8,843584
	10	8,861283
	20	8,878285
	30	8,894643
	40	8,910404
	50	8,925609
5	0	8,940296
	10	8,954499
	20	8,968249
	30	8,981573
	40	8,994497
	50	9,007044
6	0	9,019235
	10	9,031089
	20	9,042625
	30	9,053859
	40	9,064806
	50	9,075480
7	0	9,085894
	10	9,096062
	20	9,105992
	30	9,115698
	40	9,125187
	50	9,134470
8	0	9,143555
	10	9,152451
	20	9,161164
	30	9,169702
	40	9,178072
	50	9,186280
9	0	9,194332
	10	9,202234
	20	9,209992
	30	9,217609
	40	9,225092
	50	9,232444
10	0	9,239670
	10	9,246795
	20	9,253761
	30	9,260633
	40	9,267395
	50	9,274049
11	0	9,280599
	10	9,287048
	20	9,293399
	30	9,299655
	40	9,305819
	50	9,311899
12	0	9,317879
	10	9,323780
	20	9,319599
	30	9,335337
	40	9,340996
	50	9,346579
13	0	9,352088
	10	9,357524
	20	9,362889
	30	9,368185
	40	9,373414
	50	9,378577
14	0	9,383675
	10	9,388711
	20	9,393685
	30	9,398600
	40	9,403455
	50	9,408254
15	0	9,412996
	10	9,417684
	20	9,422317
	30	9,426899
	40	9,431429
	50	9,435918
16	0	9,440338
	10	9,444720
	20	9,449054
	30	9,453342
	40	9,457584
	50	9,461782
17	0	9,465935
	10	9,460446
	20	9,474115
	30	9,478142
	40	9,482128
	50	9,486075
18	0	9,489982
	10	9,493851
	20	9,497682
	30	9,501476
	40	9,505234
	50	9,508955
19	0	9,512642
	10	9,516294
	20	9,519911
	30	9,523495
	40	9,527046
	50	9,530565
20	0	9,534052
	10	9,537507
	20	9,540931
	30	9,544325
	40	9,547689
	50	9,551024
21	0	9,554329
	10	9,557606
	20	9,560855
	30	9,564075
	40	9,567269
	50	9,570435
22	0	9,573575
	10	9,576689
	20	9,579777
	30	9,582840
	40	9,585877
	50	9,588890
23	0	9,591878
	10	9,594842
	20	9,597783
	30	9,600700
	40	9,603594
	50	9,606465

24	0	9,609313
	10	9,612148
	20	9,614944
	30	9,617727
	40	9,620488
	50	9,623229
25	0	9,625948
	10	9,628647
	20	9,631326
	30	9,633984
	40	9,636623
	50	9,639242
26	0	9,641842
	10	9,644423
	20	9,646984
	30	9,649527
	40	9,652052
	50	9,654558
27	0	9,657047
	10	9,659517
	20	9,661970
	30	9,664406
	40	9,666824
	50	9,669225
28	0	9,671609
	10	9,673977
	20	9,676328
	30	9,678663
	40	9,680982
	50	9,683284
29	0	9,685571
	10	9,687842
	20	9,690098
	30	9,692339
	40	9,694564
	50	9,696774
30	0	9,698970
	10	9,701151
	20	9,703317
	30	9,705469
	40	9,707606
	50	9,709730
31	0	9,711839
	10	9,713935
	20	9,716017
	30	9,718085
	40	9,720140
	50	9,722181
32	0	9,724210
	10	9,726225
	20	9,728227
	30	9,730216
	40	9,732193
	50	9,734157
33	0	9,736109
	10	9,738048
	20	9,739975
	30	9,741889
	40	9,743792
	50	9,745683
34	0	9,747562
	10	9,749429
	20	9,751284
	30	9,753128
	40	9,754960
	50	9,756781
35	0	9,758591
	10	9,760390
	20	9,762177
	30	9,763954
	40	9,765720
	50	9,767474
36	0	9,769219
	10	9,770952
	20	9,772675
	30	9,774388
	40	9,776090
	50	9,777781
37	0	9,779463
	10	9,781134
	20	9,782796
	30	9,784447
	40	9,786088
	50	9,787720
38	0	9,789342
	10	9,790954
	20	9,792557
	30	9,794149
	40	9,795733
	50	9,797307
39	0	9,798872
	10	9,800427
	20	9,801973
	30	9,803510
	40	9,805038
	50	9,806557
40	0	9,808067
	10	9,809569
	20	9,810061
	30	9,812544
	40	9,814019
	50	9,815485
41	0	9,816943
	10	9,818392
	20	9,819832
	30	9,821264
	40	9,822688
	50	9,824104
42	0	9,825511
	10	9,826910
	20	9,828301
	30	9,829683
	40	9,831058
	50	9,832425
43	0	9,833783
	10	9,835134
	20	9,836477
	30	9,837812
	40	9,839140
	50	9,840459
44	0	9,841771
	10	9,843079
	20	9,844372
	30	9,845662
	40	9,846944
	50	9,848218
45	0	9,849485
	10	9,850745
	20	9,851997
	30	9,853242
	40	9,854480
	50	9,855710
46	0	9,856934
	10	9,858150
	20	9,859360
	30	9,860562
	40	9,861757
	50	9,862946
47	0	9,864127
	10	9,865302
	20	9,866470
	30	9,867631
	40	9,868785
	50	9,869933

48	0	9,871073
	10	9,872208
	20	9,873335
	30	9,874456
	40	9,875571
	50	9,876678
49	0	9,877780
	10	9,878875
	20	9,879963
	30	9,881045
	40	9,882121
	50	9,883191
50	0	9,884254
	10	9,885311
	20	9,886361
	30	9,887406
	40	9,888444
	50	9,889476
51	0	9,890503
	10	9,891522
	20	9,892536
	30	9,893544
	40	9,894546
	50	9,865542
52	0	9,896532
	10	9,897516
	20	9,898494
	30	9,899467
	40	9,900433
	50	9,901391
53	0	9,902349
	10	9,903298
	20	9,90424
	30	9,905179
	40	9,906111
	50	9,907037
54	0	9,907958
	10	9,908873
	20	9,909782
	30	9,910686
	40	9,911584
	50	9,912477
55	0	9,913364
	10	9,914246
	20	9,915123
	30	9,915994
	40	9,916859
	50	9,917719
56	0	9,918574
	10	9,919424
	20	9,920268
	30	9,921107
	40	9,921940
	50	9,922768
57	0	9,923591
	10	9,924409
	20	9,925222
	30	9,926029
	40	9,926831
	50	9,927628
58	0	9,928420
	10	9,929207
	20	9,929989
	30	9,930766
	40	9,931537
	50	9,932304
59	0	9,933066
	10	9,933822
	20	9,934574
	30	9,935320
	40	9,936062
	50	9,936799
60	0	9,937531
	10	9,938257
	20	9,938980
	30	9,939697
	40	9,940409
	50	9,941116
61	0	9,941819
	10	9,942517
	20	9,943210
	30	9,943898
	40	9,944582
	50	9,945261
62	0	9,945935
	10	9,946604
	20	9,947269
	30	9,947929
	40	9,948584
	50	9,949235
63	0	9,949881
	10	9,950522
	20	9,951159
	30	9,951791
	40	9,952419
	50	9,953042
64	0	9,953660
	10	9,954274
	20	9,954883
	30	9,955488
	40	9,956088
	50	9,956684
65	0	9,957276
	10	9,957862
	20	9,958445
	30	9,959023
	40	9,959596
	50	9,960165
66	0	9,960730
	10	9,961290
	20	9,961846
	30	9,962398
	40	9,962945
	50	9,963488
67	0	9,964026
	10	9,964560
	20	9,965090
	30	9,965615
	40	9,966136
	50	9,966653
68	0	9,967166
	10	9,967674
	20	9,968178
	30	9,968678
	40	9,969173
	50	9,969665
69	0	9,970152
	10	9,970634
	20	9,971112
	30	9,971588
	40	9,972058
	50	9,972524
70	0	9,972986
	10	9,973443
	20	9,973897
	30	9,974346
	40	9,974792
	50	9,975233
71	0	9,975670
	10	9,976103
	20	9,976532
	30	9,977956
	40	9,977377
	50	9,977794

72	0	9,978206
	10	9,978615
	20	9,979019
	30	9,979419
	40	9,979816
	50	9,980208
73	0	9,980596
	10	9,980980
	20	9,981361
	30	9,981737
	40	9,982109
	50	9,982477
74	0	9,982842
	10	9,983202
	20	9,983558
	30	9,983910
	40	9,984259
	50	9,984603
75	0	9,984943
	10	9,985280
	20	9,985613
	30	9,985942
	40	9,986266
	50	9,986587
76	0	9,986904
	10	9,987217
	20	9,987526
	30	9,987832
	40	9,988133
	50	9,988430
77	0	9,988724
	10	9,989014
	20	9,989299
	30	9,989581
	40	9,989860
	50	9,990134
78	0	9,990404
	10	9,990671
	20	9,990934
	30	9,991193
	40	9,991448
	50	9,991699
79	0	9,991947
	10	9,992190
	20	9,992430
	30	9,992666
	40	9,992898
	50	9,993127
80	0	9,993351
	10	9,993572
	20	9,993789
	30	9,994003
	40	9,994212
	50	9,994418
81	0	9,994620
	10	9,994818
	20	9,995012
	30	9,995203
	40	9,995390
	50	9,995573
82	0	9,995753
	10	9,995928
	20	9,996100
	30	9,996269
	40	9,996433
	50	9,996594
83	0	9,996751
	10	9,996904
	20	9,997053
	30	9,997199
	40	9,997341
	50	9,999998
84	0	9,997614
	10	9,997732
	20	9,997873
	30	9,997996
	40	9,998106
	50	9,998232
85	0	9,998344
	10	9,998453
	20	9,998558
	30	9,998659
	40	9,998757
	50	9,998851
86	0	9,998941
	10	9,999927
	20	9,999110
	30	9,999189
	40	9,999265
	50	9,999336
87	0	9,999404
	10	9,999469
	20	9,999529
	30	9,999586
	40	9,999640
	50	9,999689
88	0	9,999735
	10	9,999778
	20	9,999816
	30	9,999851
	40	9,999882
	50	9,999910
89	0	9,999934
	10	9,999954
	20	9,999971
	30	9,999983
	40	9,999993
	50	9,999998