Agricola, Georgius
,
De re metallica
,
1912/1950
Text
Text Image
Image
XML
Thumbnail overview
Document information
None
Concordance
Figures
Thumbnails
Page concordance
<
1 - 30
31 - 60
61 - 90
91 - 120
121 - 150
151 - 180
181 - 210
211 - 240
241 - 270
271 - 300
301 - 330
331 - 360
361 - 390
391 - 420
421 - 450
451 - 480
481 - 510
511 - 540
541 - 570
571 - 600
601 - 630
631 - 660
661 - 679
>
Scan
Original
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
<
1 - 30
31 - 60
61 - 90
91 - 120
121 - 150
151 - 180
181 - 210
211 - 240
241 - 270
271 - 300
301 - 330
331 - 360
361 - 390
391 - 420
421 - 450
451 - 480
481 - 510
511 - 540
541 - 570
571 - 600
601 - 630
631 - 660
661 - 679
>
page
|<
<
of 679
>
>|
<
archimedes
>
<
text
>
<
body
>
<
chap
>
<
p
type
="
caption
">
<
s
>
<
pb
pagenum
="
132
"/>
the first cord, and makes a note of this first side of the minor triangle
<
emph
type
="
sup
"/>
17
<
emph.end
type
="
sup
"/>
.
<
lb
/>
</
s
>
<
s
>Afterward, starting again from that point where the third cord intersects the
<
lb
/>
second cord, he measures the straight space which lies between that point
<
lb
/>
and the opposite point on the first cord, and in that way forms the minor
<
lb
/>
triangle, and he notes this second side of the minor triangle in the same way as
<
lb
/>
before. </
s
>
<
s
>Then, if it is necessary, from the angle formed by the first cord and
<
lb
/>
the second side of the minor triangle, he measures upward to the end of the
<
lb
/>
first cord and also makes a note of this third side of the minor triangle. </
s
>
<
s
>The
<
lb
/>
third side of the minor triangle, if the shaft is vertical or inclined and is sunk
<
lb
/>
on the same vein in which the tunnel is driven, will necessarily be the same
<
lb
/>
length as the third cord above the point where it intersects the second cord;
<
lb
/>
and so, as often as the first side of the minor triangle is contained in the
<
lb
/>
length of the whole cord which descends obliquely, so many times the length
<
lb
/>
of the second side of the minor triangle indicates the distance between the
<
lb
/>
mouth of the tunnel and the point to which the shaft must be sunk; and
<
lb
/>
similarly, so many times the length of the third side of the minor triangle
<
lb
/>
gives the distance between the mouth of the shaft and the bottom of the
<
lb
/>
tunnel.</
s
>
</
p
>
<
p
type
="
main
">
<
s
>When there is a level bench on the mountain slope, the surveyor first
<
lb
/>
measures across this with a measuring-rod; then at the edges of this bench
<
lb
/>
he sets up forked posts, and applies the principle of the triangle to the two
<
lb
/>
sloping parts of the mountain; and to the fathoms which are the length of
<
lb
/>
that part of the tunnel determined by the triangles, he adds the number
<
lb
/>
of fathoms which are the width of the bench. </
s
>
<
s
>But if sometimes the
<
lb
/>
mountain side stands up, so that a cord cannot run down from the shaft to
<
lb
/>
the mouth of the tunnel, or, on the other hand, cannot run up from the
<
lb
/>
mouth of the tunnel to the shaft, and, therefore, one cannot connect them in
<
lb
/>
a straight line, the surveyor, in order to fix an accurate triangle, measures the
<
lb
/>
mountain; and going downward he substitutes for the first part of the cord
<
lb
/>
a pole one fathom long, and for the second part a pole half a fathom
<
lb
/>
long. </
s
>
<
s
>Going upward, on the contrary, for the first part of the cord he subĀ
<
lb
/>
stitutes a pole half a fathom long, and for the next part, one a whole fathom
<
lb
/>
long; then where he requires to fix his triangle he adds a straight line to
<
lb
/>
these angles.</
s
>
</
p
>
<
p
type
="
main
">
<
s
>To make this system of measuring clear and more explicit, I will proceed
<
lb
/>
by describing each separate kind of triangle. </
s
>
<
s
>When a shaft is vertical or
<
lb
/>
inclined, and is sunk in the same vein on which the tunnel is driven, there
<
lb
/>
is created, as I said, a triangle containing a right angle. </
s
>
<
s
>Now if the minor
<
lb
/>
triangle has the two sides equal, which, in accordance with the numbering
<
lb
/>
used by surveyors, are the second and third sides, then the second and third
<
lb
/>
sides of the major triangle will be equal; and so also the intervening
<
lb
/>
distances will be equal which lie between the mouth of the tunnel and the
<
lb
/>
bottom of the shaft, and which lie between the mouth of the shaft and the
<
lb
/>
bottom of the tunnel. </
s
>
<
s
>For example, if the first side of the minor triangle is
<
lb
/>
seven feet long and the second and likewise the third sides are five feet, and </
s
>
</
p
>
</
chap
>
</
body
>
</
text
>
</
archimedes
>