Agricola, Georgius
,
De re metallica
,
1912/1950
Text
Text Image
Image
XML
Thumbnail overview
Document information
None
Concordance
Figures
Thumbnails
List of thumbnails
<
1 - 10
11 - 20
21 - 30
31 - 40
41 - 50
51 - 60
61 - 70
71 - 80
81 - 90
91 - 100
101 - 110
111 - 120
121 - 130
131 - 140
141 - 150
151 - 160
161 - 170
171 - 180
181 - 190
191 - 200
201 - 210
211 - 220
221 - 230
231 - 240
241 - 250
251 - 260
261 - 270
271 - 280
281 - 290
291 - 300
301 - 310
311 - 320
321 - 330
331 - 340
341 - 350
351 - 360
361 - 370
371 - 380
381 - 390
391 - 400
401 - 410
411 - 420
421 - 430
431 - 440
441 - 450
451 - 460
461 - 470
471 - 480
481 - 490
491 - 500
501 - 510
511 - 520
521 - 530
531 - 540
541 - 550
551 - 560
561 - 570
571 - 580
581 - 590
591 - 600
601 - 610
611 - 620
621 - 630
631 - 640
641 - 650
651 - 660
661 - 670
671 - 679
>
31
32
33
34
35
36
37
38
39
40
<
1 - 10
11 - 20
21 - 30
31 - 40
41 - 50
51 - 60
61 - 70
71 - 80
81 - 90
91 - 100
101 - 110
111 - 120
121 - 130
131 - 140
141 - 150
151 - 160
161 - 170
171 - 180
181 - 190
191 - 200
201 - 210
211 - 220
221 - 230
231 - 240
241 - 250
251 - 260
261 - 270
271 - 280
281 - 290
291 - 300
301 - 310
311 - 320
321 - 330
331 - 340
341 - 350
351 - 360
361 - 370
371 - 380
381 - 390
391 - 400
401 - 410
411 - 420
421 - 430
431 - 440
441 - 450
451 - 460
461 - 470
471 - 480
481 - 490
491 - 500
501 - 510
511 - 520
521 - 530
531 - 540
541 - 550
551 - 560
561 - 570
571 - 580
581 - 590
591 - 600
601 - 610
611 - 620
621 - 630
631 - 640
641 - 650
651 - 660
661 - 670
671 - 679
>
page
|<
<
of 679
>
>|
<
archimedes
>
<
text
>
<
body
>
<
chap
>
<
p
type
="
main
">
<
s
>
<
pb
pagenum
="
133
"/>
the length shown by the cord for the side of the major triangle is 101 times
<
lb
/>
seven feet, that is 117 fathoms and five feet, then the intervening space, of
<
lb
/>
course, whether the whole of it has been already driven through or has yet
<
lb
/>
to be driven, will be one hundred times five feet, which makes eighty-three
<
lb
/>
fathoms and two feet. </
s
>
<
s
>Anyone with this example of proportions will be
<
lb
/>
able to construct the major and minor triangles in the same way as I have
<
lb
/>
done, if there be the necessary upright posts and cross-beams. </
s
>
<
s
>When a shaft is
<
lb
/>
vertical the triangle is absolutely upright; when it is inclined and is sunk on
<
lb
/>
the same vein in which the tunnel is driven, it is inclined toward one side. </
s
>
</
p
>
<
figure
number
="
60
"/>
<
p
type
="
caption
">
<
s
>A TRIANGLE HAVING A RIGHT ANGLE AND TWO EQUAL SIDES.
<
lb
/>
Therefore, if a tunnel has been driven into the mountain for sixty fathoms,
<
lb
/>
there remains a space of ground to be penetrated twenty-three fathoms and
<
lb
/>
two feet long; for five feet of the second side of the major triangle, which
<
lb
/>
lies above the mouth of the shaft and corresponds with the first side of the
<
lb
/>
minor triangle, must not be added. </
s
>
<
s
>Therefore, if the shaft has been sunk
<
lb
/>
in the middle of the head meer, a tunnel sixty fathoms long will reach
<
lb
/>
to the boundary of the meer only when the tunnel has been extended a
<
lb
/>
further two fathoms and two feet; but if the shaft is located in the middle of
<
lb
/>
an ordinary meer, then the boundary will be reached when the tunnel has been
<
lb
/>
driven a further length of nine fathoms and two feet. </
s
>
<
s
>Since a tunnel, for
<
lb
/>
every one hundred fathoms of length, rises in grade one fathom, or at all
<
lb
/>
events, ought to rise as it proceeds toward the shaft, one more fathom must
<
lb
/>
always be taken from the depth allowed to the shaft, and one added to the
<
lb
/>
length allowed to the tunnel. </
s
>
<
s
>Proportionately, because a tunnel fifty
<
lb
/>
fathoms long is raised half a fathom, this amount must be taken from the
<
lb
/>
depth of the shaft and added to the length of the tunnel. </
s
>
<
s
>In the same way
<
lb
/>
if a tunnel is one hundred or fifty fathoms shorter or longer, the same proporĀ
<
lb
/>
tion also must be taken from the depth of the one and added to the length
<
lb
/>
of the other. </
s
>
<
s
>For this reason, in the case mentioned above, half a fathom
<
lb
/>
and a little more must be added to the distance to be driven through, so
<
lb
/>
that there remain twenty-three fathoms, five feet, two palms, one and a half
<
lb
/>
digits and a fifth of a digit; that is, if even the minutest proportions are
<
lb
/>
carried out; and surveyors do not neglect these without good cause.
<
lb
/>
</
s
>
<
s
>Similarly, if the shaft is seventy fathoms deep, in order that it may reach to
<
lb
/>
the bottom of the tunnel, it still must be sunk a further depth of thirteen
<
lb
/>
fathoms and two feet, or rather twelve fathoms and a half, one foot, two
<
lb
/>
digits, and four-fifths of half a digit. </
s
>
<
s
>And in this instance five feet must be
<
lb
/>
deducted from the reckoning, because these five feet complete the third side
<
lb
/>
of the minor triangle, which is above the mouth of the shaft, and from its </
s
>
</
p
>
</
chap
>
</
body
>
</
text
>
</
archimedes
>