Huygens, Christiaan
,
Christiani Hugenii opera varia; Bd. 2: Opera geometrica. Opera astronomica. Varia de optica
Text
Text Image
Image
XML
Thumbnail overview
Document information
None
Concordance
Notes
Handwritten
Figures
Content
Thumbnails
Table of Notes
<
1 - 2
[out of range]
>
[Note]
Page: 97
[Note]
Page: 98
[Note]
Page: 99
[Note]
Page: 99
[Note]
Page: 99
[Note]
Page: 100
[Note]
Page: 101
[Note]
Page: 102
[Note]
Page: 102
[Note]
Page: 109
[Note]
Page: 110
[Note]
Page: 110
[Note]
Page: 110
[Note]
Page: 110
[Note]
Page: 110
[Note]
Page: 111
[Note]
Page: 112
[Note]
Page: 113
[Note]
Page: 114
[Note]
Page: 115
[Note]
Page: 115
[Note]
Page: 116
[Note]
Page: 116
[Note]
Page: 116
[Note]
Page: 116
[Note]
Page: 117
[Note]
Page: 117
[Note]
Page: 117
[Note]
Page: 118
[Note]
Page: 118
<
1 - 2
[out of range]
>
page
|<
<
(431)
of 568
>
>|
<
echo
version
="
1.0RC
">
<
text
xml:lang
="
la
"
type
="
free
">
<
div
xml:id
="
echoid-div166
"
type
="
section
"
level
="
1
"
n
="
78
">
<
p
>
<
s
xml:id
="
echoid-s3192
"
xml:space
="
preserve
">
<
pb
o
="
431
"
file
="
0149
"
n
="
158
"
rhead
="
ET HYPERBOLÆ QUADRATURA.
"/>
æqualibus quantitatibus addendo, ſubtrahendo, multiplican-
<
lb
/>
do, dividendo, &</
s
>
<
s
xml:id
="
echoid-s3193
"
xml:space
="
preserve
">c: </
s
>
<
s
xml:id
="
echoid-s3194
"
xml:space
="
preserve
">ſicut ſuperius dictum eſt, ſemper ma-
<
lb
/>
net poteſtas ipſius a in ultimo producto ex termino a
<
emph
style
="
super
">3</
emph
>
+ a
<
emph
style
="
super
">2</
emph
>
b
<
lb
/>
altior poteſtate ulla ipſius a in ultimo producto termini
<
lb
/>
ba
<
emph
style
="
super
">2</
emph
>
+ b
<
emph
style
="
super
">2</
emph
>
a, quoniam illos cum æqualibus quantitatibus ad-
<
lb
/>
dendo, ſubſtrahendo, &</
s
>
<
s
xml:id
="
echoid-s3195
"
xml:space
="
preserve
">c, ſemper manent in factis eædem
<
lb
/>
poteſtates, & </
s
>
<
s
xml:id
="
echoid-s3196
"
xml:space
="
preserve
">illos in ſe eodem modo multiplicando ſemper
<
lb
/>
magis elevatur altior poteſtas in termino a
<
emph
style
="
super
">3</
emph
>
+ a
<
emph
style
="
super
">2</
emph
>
b quam ele-
<
lb
/>
vatur depreſſior poteſtas in termino ba
<
emph
style
="
super
">2</
emph
>
+ b
<
emph
style
="
super
">2</
emph
>
a, & </
s
>
<
s
xml:id
="
echoid-s3197
"
xml:space
="
preserve
">ex illis
<
lb
/>
eaſdem radices extrahendo, ubi a fuerat elevatior in poteſta-
<
lb
/>
te erit etiam elevatior in radice: </
s
>
<
s
xml:id
="
echoid-s3198
"
xml:space
="
preserve
">& </
s
>
<
s
xml:id
="
echoid-s3199
"
xml:space
="
preserve
">quoniam eadem reperitur
<
lb
/>
altiſſima poteſtas ipſius a in termino ab
<
emph
style
="
super
">2</
emph
>
+ b
<
emph
style
="
super
">3</
emph
>
quæ reperitur
<
lb
/>
in termino 2b
<
emph
style
="
super
">2</
emph
>
a, demonſtratur ut antè altiſſimam poteſta-
<
lb
/>
tem ipſius a in ultimo producto ex termino ab
<
emph
style
="
super
">2</
emph
>
+ b
<
emph
style
="
super
">3</
emph
>
eandem
<
lb
/>
eſſe cum altiſſima poteſtate ipſius a in ultimo producto ex
<
lb
/>
termino 2b
<
emph
style
="
super
">2</
emph
>
a: </
s
>
<
s
xml:id
="
echoid-s3200
"
xml:space
="
preserve
">in ultimo igitur producto termini a
<
emph
style
="
super
">3</
emph
>
+ a
<
emph
style
="
super
">2</
emph
>
b
<
lb
/>
reperitur altior poteſtas ipſius a quam in ultimo producto
<
lb
/>
termini ba
<
emph
style
="
super
">2</
emph
>
+ b
<
emph
style
="
super
">2</
emph
>
a, & </
s
>
<
s
xml:id
="
echoid-s3201
"
xml:space
="
preserve
">in ultimo producto termini ab
<
emph
style
="
super
">2</
emph
>
+ b
<
emph
style
="
super
">3</
emph
>
<
lb
/>
altiſſima poteſtas ipſius a eadem eſt cum altiſſima poteſtate
<
lb
/>
ipſius a in ultimo producto termini 2b
<
emph
style
="
super
">2</
emph
>
a; </
s
>
<
s
xml:id
="
echoid-s3202
"
xml:space
="
preserve
">& </
s
>
<
s
xml:id
="
echoid-s3203
"
xml:space
="
preserve
">igitur ultima
<
lb
/>
producta ex terminis a
<
emph
style
="
super
">3</
emph
>
+ a
<
emph
style
="
super
">2</
emph
>
b, ab
<
emph
style
="
super
">2</
emph
>
+ b
<
emph
style
="
super
">3</
emph
>
, eodem modo inter
<
lb
/>
ſe addita, ſubducta, multiplicata, diviſa, &</
s
>
<
s
xml:id
="
echoid-s3204
"
xml:space
="
preserve
">c. </
s
>
<
s
xml:id
="
echoid-s3205
"
xml:space
="
preserve
">ſemper effi-
<
lb
/>
cient quantitatem, in qua reperitur altior poteſtas ipſius a
<
lb
/>
quam ulla quæ reperiri poteſt in quantitate facta ex eadem
<
lb
/>
prorſus additione, ſubductione, multiplicatione, diviſione,
<
lb
/>
&</
s
>
<
s
xml:id
="
echoid-s3206
"
xml:space
="
preserve
">c, productorum à terminis ba
<
emph
style
="
super
">2</
emph
>
+ b
<
emph
style
="
super
">2</
emph
>
a, 2b
<
emph
style
="
super
">2</
emph
>
a; </
s
>
<
s
xml:id
="
echoid-s3207
"
xml:space
="
preserve
">quoniam al-
<
lb
/>
tior poteſtas cum altera poteſtate ſemper altiorem facit po-
<
lb
/>
teſtatem quam depreſſior poteſtas cum eadem altera poteſta-
<
lb
/>
te; </
s
>
<
s
xml:id
="
echoid-s3208
"
xml:space
="
preserve
">& </
s
>
<
s
xml:id
="
echoid-s3209
"
xml:space
="
preserve
">igitur iſtæ duæ quantitates non poſſunt eſſe indefini-
<
lb
/>
tè æquales, cum reperiatur altior poteſtas ipſius a in una
<
lb
/>
quam in altera: </
s
>
<
s
xml:id
="
echoid-s3210
"
xml:space
="
preserve
">atque hinc evidens eſt quod ſector circuli,
<
lb
/>
ellipſeos vel hyperbolæ A B I P non poſſit componi analy-
<
lb
/>
ticè à triangulo A B P & </
s
>
<
s
xml:id
="
echoid-s3211
"
xml:space
="
preserve
">trapezio A B F P, quod demon-
<
lb
/>
ſtrandum erat.</
s
>
<
s
xml:id
="
echoid-s3212
"
xml:space
="
preserve
"/>
</
p
>
<
p
>
<
s
xml:id
="
echoid-s3213
"
xml:space
="
preserve
">Ut autem evidentius fiat propoſitum, aliam demonſtratio-
<
lb
/>
nem treviorem faciliorem & </
s
>
<
s
xml:id
="
echoid-s3214
"
xml:space
="
preserve
">ex alio medio petitam hic </
s
>
</
p
>
</
div
>
</
text
>
</
echo
>