Huygens, Christiaan
,
Christiani Hugenii opera varia; Bd. 1: Opera mechanica
Text
Text Image
Image
XML
Thumbnail overview
Document information
None
Concordance
Notes
Handwritten
Figures
Content
Thumbnails
Table of handwritten notes
<
1 - 5
[out of range]
>
<
1 - 5
[out of range]
>
page
|<
<
(139)
of 434
>
>|
<
echo
version
="
1.0RC
">
<
text
xml:lang
="
la
"
type
="
free
">
<
div
xml:id
="
echoid-div274
"
type
="
section
"
level
="
1
"
n
="
102
">
<
p
>
<
s
xml:id
="
echoid-s3143
"
xml:space
="
preserve
">
<
pb
o
="
139
"
file
="
0201
"
n
="
220
"
rhead
="
HOROLOG. OSCILLATOR.
"/>
datorum punctorum multitudinem exprimens, dicatur θ; </
s
>
<
s
xml:id
="
echoid-s3144
"
xml:space
="
preserve
">erit
<
lb
/>
<
note
position
="
right
"
xlink:label
="
note-0201-01
"
xlink:href
="
note-0201-01a
"
xml:space
="
preserve
">
<
emph
style
="
sc
">De centro</
emph
>
<
lb
/>
<
emph
style
="
sc
">OSCILLA-</
emph
>
<
lb
/>
<
emph
style
="
sc
">TIONIS</
emph
>
.</
note
>
E R = {ι/θ}; </
s
>
<
s
xml:id
="
echoid-s3145
"
xml:space
="
preserve
">& </
s
>
<
s
xml:id
="
echoid-s3146
"
xml:space
="
preserve
">R G = {μ/θ}. </
s
>
<
s
xml:id
="
echoid-s3147
"
xml:space
="
preserve
">Cumque G S ſit x, erit R S ſive
<
lb
/>
F T = x - {μ/θ}; </
s
>
<
s
xml:id
="
echoid-s3148
"
xml:space
="
preserve
">vel {μ/θ} - x, ſi G R major quam G S; </
s
>
<
s
xml:id
="
echoid-s3149
"
xml:space
="
preserve
">& </
s
>
<
s
xml:id
="
echoid-s3150
"
xml:space
="
preserve
">ſem-
<
lb
/>
per quadratum F T = xx - 2 {xμ/θ} + {μμ/θθ}. </
s
>
<
s
xml:id
="
echoid-s3151
"
xml:space
="
preserve
">quo ablato ab qua-
<
lb
/>
drato F E = zz, relinquetur quadratum T E = zz - xx
<
lb
/>
+ 2 {xμ/θ} - {μμ/θθ}. </
s
>
<
s
xml:id
="
echoid-s3152
"
xml:space
="
preserve
">Et proinde T E =
<
emph
style
="
red
">zz - xx + 2 {xμ/θ} - {μμ/θθ}</
emph
>
.
<
lb
/>
</
s
>
<
s
xml:id
="
echoid-s3153
"
xml:space
="
preserve
">Erat autem E R = {ι/θ}. </
s
>
<
s
xml:id
="
echoid-s3154
"
xml:space
="
preserve
">Itaque T R = {ι/θ} + vel -
<
emph
style
="
red
">zz - xx
<
lb
/>
+ 2 {xμ/θ} - {μμ/θθ}</
emph
>
. </
s
>
<
s
xml:id
="
echoid-s3155
"
xml:space
="
preserve
">quæ T R, brevitatis gratia, dicatury y. </
s
>
<
s
xml:id
="
echoid-s3156
"
xml:space
="
preserve
">Colli-
<
lb
/>
gamus jam porro ſummam quadratorum omnium F A, F B,
<
lb
/>
F C, F D. </
s
>
<
s
xml:id
="
echoid-s3157
"
xml:space
="
preserve
">Quadratum A F æquatur quadratis A V, V F. </
s
>
<
s
xml:id
="
echoid-s3158
"
xml:space
="
preserve
">
<
lb
/>
Eſt autem A V æqualis differentiæ duarum V K, A K, ſi-
<
lb
/>
ve duarum S G, A K; </
s
>
<
s
xml:id
="
echoid-s3159
"
xml:space
="
preserve
">ac proinde A V = x - e vel e - x; </
s
>
<
s
xml:id
="
echoid-s3160
"
xml:space
="
preserve
">& </
s
>
<
s
xml:id
="
echoid-s3161
"
xml:space
="
preserve
">
<
lb
/>
qu. </
s
>
<
s
xml:id
="
echoid-s3162
"
xml:space
="
preserve
">A V = xx - 2 ex + ee. </
s
>
<
s
xml:id
="
echoid-s3163
"
xml:space
="
preserve
">V F vero æqualis eſt differen-
<
lb
/>
tiæ duarum F S, V S ſive duarum F S, A L; </
s
>
<
s
xml:id
="
echoid-s3164
"
xml:space
="
preserve
">ac proinde
<
lb
/>
V F = y - a vel a - y; </
s
>
<
s
xml:id
="
echoid-s3165
"
xml:space
="
preserve
">& </
s
>
<
s
xml:id
="
echoid-s3166
"
xml:space
="
preserve
">qu. </
s
>
<
s
xml:id
="
echoid-s3167
"
xml:space
="
preserve
">V F = yy - 2 ay + aa. </
s
>
<
s
xml:id
="
echoid-s3168
"
xml:space
="
preserve
">Ad-
<
lb
/>
ditisque quadratis A V, V F, fit quadratum F A = xx - 2 ex
<
lb
/>
+ ee + yy - 2 ay + aa. </
s
>
<
s
xml:id
="
echoid-s3169
"
xml:space
="
preserve
">Eodemque modo invenientur qua-
<
lb
/>
drata reliquarum F B, F C, F D; </
s
>
<
s
xml:id
="
echoid-s3170
"
xml:space
="
preserve
">atque omnia ordine diſ-
<
lb
/>
poſita erunt hæc; </
s
>
<
s
xml:id
="
echoid-s3171
"
xml:space
="
preserve
">
<
lb
/>
qu. </
s
>
<
s
xml:id
="
echoid-s3172
"
xml:space
="
preserve
">F A = xx - 2 ex + ee + yy - 2 ay + aa. </
s
>
<
s
xml:id
="
echoid-s3173
"
xml:space
="
preserve
">
<
lb
/>
qu. </
s
>
<
s
xml:id
="
echoid-s3174
"
xml:space
="
preserve
">F B = xx - 2 fx + ff + yy - 2 by + bb. </
s
>
<
s
xml:id
="
echoid-s3175
"
xml:space
="
preserve
">
<
lb
/>
qu. </
s
>
<
s
xml:id
="
echoid-s3176
"
xml:space
="
preserve
">F C = xx - 2 gx + gg + yy - 2 cy + cc. </
s
>
<
s
xml:id
="
echoid-s3177
"
xml:space
="
preserve
">
<
lb
/>
qu. </
s
>
<
s
xml:id
="
echoid-s3178
"
xml:space
="
preserve
">F D = xx - 2 hx + hh + yy - 2 dy + dd.</
s
>
<
s
xml:id
="
echoid-s3179
"
xml:space
="
preserve
"/>
</
p
>
<
p
>
<
s
xml:id
="
echoid-s3180
"
xml:space
="
preserve
">Horum vero ſumma; </
s
>
<
s
xml:id
="
echoid-s3181
"
xml:space
="
preserve
">ſi ponamus quadrata ee + ff + gg
<
lb
/>
+ hh = nn; </
s
>
<
s
xml:id
="
echoid-s3182
"
xml:space
="
preserve
">& </
s
>
<
s
xml:id
="
echoid-s3183
"
xml:space
="
preserve
">quadrata aa + bb, + cc + dd = kk;
<
lb
/>
</
s
>
<
s
xml:id
="
echoid-s3184
"
xml:space
="
preserve
">erit iſta, θ x x - 2 mx + nn + θ yy - 2 ly + kk. </
s
>
<
s
xml:id
="
echoid-s3185
"
xml:space
="
preserve
">Siquidem
<
lb
/>
θ erat numerus datorum punctorum ideoque & </
s
>
<
s
xml:id
="
echoid-s3186
"
xml:space
="
preserve
">quadratorum,
<
lb
/>
poſitumque fuerat e + f + g + h = m, & </
s
>
<
s
xml:id
="
echoid-s3187
"
xml:space
="
preserve
">a + b + c + d = l.</
s
>
<
s
xml:id
="
echoid-s3188
"
xml:space
="
preserve
"/>
</
p
>
<
p
>
<
s
xml:id
="
echoid-s3189
"
xml:space
="
preserve
">In iſta vero ſumma, ſi in terminis θ y y & </
s
>
<
s
xml:id
="
echoid-s3190
"
xml:space
="
preserve
">2 l y, pro y,
<
lb
/>
ponatur id cujus loco poſitum erat, nempe {ι/θ} + vel -
<
lb
/>
<
emph
style
="
red
">zz - xx + 2 {xμ/θ} - {μμ/θθ}</
emph
>
<
lb
/>
fiet + θ y y = {ιι/θ} + 2 l
<
emph
style
="
red
">zz - xx + 2 {xμ/θ} - {μμ/θθ}</
emph
>
+ θ zz - θ xx
<
lb
/>
+ 2 x m-{μμ/θ}.</
s
>
<
s
xml:id
="
echoid-s3191
"
xml:space
="
preserve
"/>
</
p
>
</
div
>
</
text
>
</
echo
>