Newton, Isaac
,
Philosophia naturalis principia mathematica
,
1713
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 - 524
>
Scan
Original
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
<
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 - 524
>
page
|<
<
of 524
>
>|
<
archimedes
>
<
text
>
<
body
>
<
chap
>
<
subchap1
>
<
subchap2
>
<
p
type
="
main
">
<
s
>
<
pb
xlink:href
="
039/01/055.jpg
"
pagenum
="
27
"/>
rallelogramma inter ſe ut partes, ſummæ partium ſemper erunt ut
<
lb
/>
ſummæ parallelogrammorum; atque adeo, ubi partium & paralle
<
lb
/>
logrammorum numerus augetur & magnitudo diminuitur in infiNI
<
lb
/>
tum, in ultima ratione parallelogrammi ad parallelogrammum, id
<
lb
/>
eſt (per hypotheſin) in ultima ratione partis ad partem. </
s
>
</
p
>
<
p
type
="
main
">
<
s
>
<
emph
type
="
center
"/>
LEMMA V.
<
emph.end
type
="
center
"/>
</
s
>
</
p
>
<
p
type
="
main
">
<
s
>
<
emph
type
="
italics
"/>
Similium Figurarum latera omnia, quæ ſibi mutuo reſpondent, ſunt
<
lb
/>
proportionalia, tam curvilinea quam rectilinea; & areæ ſunt in
<
lb
/>
duplicata ratione laterum.
<
emph.end
type
="
italics
"/>
</
s
>
</
p
>
<
p
type
="
main
">
<
s
>
<
emph
type
="
center
"/>
LEMMA VI.
<
emph.end
type
="
center
"/>
</
s
>
</
p
>
<
p
type
="
main
">
<
s
>
<
emph
type
="
italics
"/>
Si arcus quilibet poſitione datus
<
emph.end
type
="
italics
"/>
AB
<
emph
type
="
italics
"/>
ſub-
<
emph.end
type
="
italics
"/>
<
lb
/>
<
figure
id
="
id.039.01.055.1.jpg
"
xlink:href
="
039/01/055/1.jpg
"
number
="
8
"/>
<
lb
/>
<
emph
type
="
italics
"/>
tendatur chorda
<
emph.end
type
="
italics
"/>
AB,
<
emph
type
="
italics
"/>
& in puncto
<
lb
/>
aliquo
<
emph.end
type
="
italics
"/>
A,
<
emph
type
="
italics
"/>
in medio curvaturæ continuæ,
<
lb
/>
tangatur a recta utrinque producta
<
emph.end
type
="
italics
"/>
<
lb
/>
AD;
<
emph
type
="
italics
"/>
dein puncta
<
emph.end
type
="
italics
"/>
A, B
<
emph
type
="
italics
"/>
ad invicem
<
lb
/>
accedant & coëant; dico quod angulus
<
emph.end
type
="
italics
"/>
<
lb
/>
BAD,
<
emph
type
="
italics
"/>
ſub chorda & tangente conten
<
lb
/>
tus, minuetur in infinitum & ultimo e
<
lb
/>
vaneſcet.
<
emph.end
type
="
italics
"/>
</
s
>
</
p
>
<
p
type
="
main
">
<
s
>Nam ſi angulus ille non evaneſcit, continebit arcus
<
emph
type
="
italics
"/>
AB
<
emph.end
type
="
italics
"/>
cum tan
<
lb
/>
gente
<
emph
type
="
italics
"/>
AD
<
emph.end
type
="
italics
"/>
angulum rectilineo æqualem, & propterea curvatura ad
<
lb
/>
ad punctum
<
emph
type
="
italics
"/>
A
<
emph.end
type
="
italics
"/>
non erit continua, contra hypotheſin. </
s
>
</
p
>
<
p
type
="
main
">
<
s
>
<
emph
type
="
center
"/>
LEMMA VII.
<
emph.end
type
="
center
"/>
</
s
>
</
p
>
<
p
type
="
main
">
<
s
>
<
emph
type
="
italics
"/>
Iiſdem poſitis; dico quod ultima ratio arcus, chordæ, & tangentis
<
lb
/>
ad invicem est ratio æqualitatis.
<
emph.end
type
="
italics
"/>
</
s
>
</
p
>
<
p
type
="
main
">
<
s
>Nam dum punctum
<
emph
type
="
italics
"/>
B
<
emph.end
type
="
italics
"/>
ad punctum
<
emph
type
="
italics
"/>
A
<
emph.end
type
="
italics
"/>
accedit, intelligantur ſemper
<
lb
/>
<
emph
type
="
italics
"/>
AB
<
emph.end
type
="
italics
"/>
&
<
emph
type
="
italics
"/>
AD
<
emph.end
type
="
italics
"/>
ad puncta longinqua
<
emph
type
="
italics
"/>
b
<
emph.end
type
="
italics
"/>
ac
<
emph
type
="
italics
"/>
d
<
emph.end
type
="
italics
"/>
produci, & ſecanti
<
emph
type
="
italics
"/>
BD
<
emph.end
type
="
italics
"/>
<
lb
/>
parallela agatur
<
emph
type
="
italics
"/>
bd.
<
emph.end
type
="
italics
"/>
Sitque arcus
<
emph
type
="
italics
"/>
Ab
<
emph.end
type
="
italics
"/>
ſemper ſimilis arcui
<
emph
type
="
italics
"/>
AB.
<
emph.end
type
="
italics
"/>
<
lb
/>
Et punctis
<
emph
type
="
italics
"/>
A, B
<
emph.end
type
="
italics
"/>
coeuntibus, angulus
<
emph
type
="
italics
"/>
dAb,
<
emph.end
type
="
italics
"/>
per Lemma ſuperius,
<
lb
/>
evaneſcet; adeoque rectæ ſemper ſinitæ
<
emph
type
="
italics
"/>
Ab, Ad
<
emph.end
type
="
italics
"/>
& arcus interme
<
lb
/>
dius
<
emph
type
="
italics
"/>
Ab
<
emph.end
type
="
italics
"/>
coincident, & propterea æquales erunt. </
s
>
<
s
>Unde & hiſce
<
lb
/>
ſemper proportionales rectæ
<
emph
type
="
italics
"/>
AB, AD,
<
emph.end
type
="
italics
"/>
& arcus intermedius
<
emph
type
="
italics
"/>
AB
<
emph.end
type
="
italics
"/>
</
s
>
</
p
>
</
subchap2
>
</
subchap1
>
</
chap
>
</
body
>
</
text
>
</
archimedes
>