Salusbury, Thomas
,
Mathematical collections and translations (Tome I)
,
1667
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 - 680
681 - 690
691 - 700
701 - 701
>
211
212
213
214
215
216
217
218
219
220
<
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 - 680
681 - 690
691 - 700
701 - 701
>
page
|<
<
of 701
>
>|
<
archimedes
>
<
text
>
<
body
>
<
chap
>
<
p
type
="
main
">
<
s
>
<
pb
xlink:href
="
040/01/281.jpg
"
pagenum
="
261
"/>
which depart from two points marked upon another right line, are
<
lb
/>
then wider above than below, when the angles included between
<
lb
/>
them upon that right line are greater than two right angles; and
<
lb
/>
if theſe angles ſhould be equal to two right angles, the lines would
<
lb
/>
be parallels; but if they were leſs than two right angles, the lines
<
lb
/>
would be concurrent, and being continued out would
<
lb
/>
ly interſect the triangle.</
s
>
</
p
>
<
p
type
="
main
">
<
s
>SIMP. </
s
>
<
s
>Without taking it upon truſt from you, I know the
<
lb
/>
ſame; and am not ſo very naked of
<
emph
type
="
italics
"/>
Geometry,
<
emph.end
type
="
italics
"/>
as not to know a
<
lb
/>
Propoſition, which I have had occaſion of reading very often in
<
lb
/>
<
emph
type
="
italics
"/>
Ariſtotle,
<
emph.end
type
="
italics
"/>
that is, that the three angles of all triangles are equall to
<
lb
/>
two right angles: ſo that if I take in my Figure the triangle ABE,
<
lb
/>
it being ſuppoſed that the line E A is right; I very well conceive,
<
lb
/>
that its three angles A, E, B, are equal to two right angles; and
<
lb
/>
that conſequently the two angles E and A are leſſe than two right
<
lb
/>
angles, ſo much as is the angle B. </
s
>
<
s
>Whereupon widening the lines
<
lb
/>
A B and E B (ſtill keeping them from moving out of the points A
<
lb
/>
and E) untill that the angle conteined by them towards the parts
<
lb
/>
B, diſappear, the two angles beneath ſhall be equal to two right
<
lb
/>
angles, and thoſe lines ſhall be reduced to parallels: and if one
<
lb
/>
ſhould proceed to enlarge them yet more, the angles at the points
<
lb
/>
E and A would become greater than two right angles.</
s
>
</
p
>
<
p
type
="
main
">
<
s
>SALV. </
s
>
<
s
>You are an
<
emph
type
="
italics
"/>
Archimedes,
<
emph.end
type
="
italics
"/>
and have freed me from the
<
lb
/>
expence of more words in declaring to you, that whenſoever the
<
lb
/>
calculations make the two angles A and E to be greater than two
<
lb
/>
right angles, the obſervations without more adoe will prove
<
lb
/>
neous. </
s
>
<
s
>This is that which I had a deſire that you ſhould
<
lb
/>
ly underſtand, and which I doubted that I was not able ſo to make
<
lb
/>
out, as that a meer
<
emph
type
="
italics
"/>
Peripatetick
<
emph.end
type
="
italics
"/>
Philoſopher might attain to the
<
lb
/>
certain knowledg thereof. </
s
>
<
s
>Now let us go on to what remains.
<
lb
/>
</
s
>
<
s
>And re-aſſuming that which even now you granted me, namely,
<
lb
/>
that the new ſtar could not poſſibly be in many places, but in one
<
lb
/>
alone, when ever the ſupputations made upon the obſervations of
<
lb
/>
theſe Aſtronomers do not aſſign it the ſame place, its neceſſary
<
lb
/>
that it be an errour in the obſervations, that is, either in taking the
<
lb
/>
altitudes of the pole, or in taking the elevations of the ſtar, or in
<
lb
/>
the one or other working. </
s
>
<
s
>Now for that in the many workings
<
lb
/>
made with the combinations two by two, there are very few of
<
lb
/>
the obſervations that do agree to place the ſtar in the ſame
<
lb
/>
tion; therefore theſe few onely may happily be the
<
lb
/>
ous, but the others are all abſolutely falſe.</
s
>
</
p
>
<
p
type
="
main
">
<
s
>SAGR. </
s
>
<
s
>It will be neceſſary then to give more credit to theſe
<
lb
/>
few alone, than to all the reſt together, and becauſe you ſay,
<
lb
/>
that theſe which accord are very few, and I amongſt theſe 12,
<
lb
/>
do find two that ſo accord, which both make the diſtance of the </
s
>
</
p
>
</
chap
>
</
body
>
</
text
>
</
archimedes
>