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 handwritten notes
<
1 - 2
[out of range]
>
<
1 - 2
[out of range]
>
page
|<
<
(454)
of 568
>
>|
<
echo
version
="
1.0RC
">
<
text
xml:lang
="
la
"
type
="
free
">
<
div
xml:id
="
echoid-div215
"
type
="
section
"
level
="
1
"
n
="
104
">
<
p
>
<
s
xml:id
="
echoid-s3848
"
xml:space
="
preserve
">
<
pb
o
="
454
"
file
="
0174
"
n
="
184
"
rhead
="
VERA CIRCULI
"/>
(qui exempli gratia ſint G H, E F) in hyperbola aſymptoto
<
lb
/>
O A paralleli; </
s
>
<
s
xml:id
="
echoid-s3849
"
xml:space
="
preserve
">& </
s
>
<
s
xml:id
="
echoid-s3850
"
xml:space
="
preserve
">inveniatur ſpatium hyperbolicum EGHF
<
lb
/>
per hujus 32, quod breviter, fit quoniam G H, E F, parum
<
lb
/>
inter ſe differunt. </
s
>
<
s
xml:id
="
echoid-s3851
"
xml:space
="
preserve
">ex ſuppoſitione, unius numeri, exempli
<
lb
/>
gratia G H, datur logorithmus, & </
s
>
<
s
xml:id
="
echoid-s3852
"
xml:space
="
preserve
">proinde datur ejus logo-
<
lb
/>
rithmi ratio ad logorithmum denarii arbitrarium, quæ ea-
<
lb
/>
dem eſt (ex hactenus demonſtratis) cum ratione ſpatii hyper-
<
lb
/>
bolici G I K H ad ſpatium hyperbolicum L I K M, datur au-
<
lb
/>
tem ex hujus 32 ſpatium L I K M; </
s
>
<
s
xml:id
="
echoid-s3853
"
xml:space
="
preserve
">& </
s
>
<
s
xml:id
="
echoid-s3854
"
xml:space
="
preserve
">ideo innoteſcit quoque
<
lb
/>
ſpatium I K H G, cumque detur ſpatium E G H F, innote-
<
lb
/>
ſcit quoque E I K F; </
s
>
<
s
xml:id
="
echoid-s3855
"
xml:space
="
preserve
">& </
s
>
<
s
xml:id
="
echoid-s3856
"
xml:space
="
preserve
">proinde datur logorithmus numeri
<
lb
/>
compoſiti E F; </
s
>
<
s
xml:id
="
echoid-s3857
"
xml:space
="
preserve
">cumque ex ſuppoſitione dentur logorithmi
<
lb
/>
omnium numerorum numerum E F componentium, exce-
<
lb
/>
pto numero illo primo cujus logorithmus deſideratur, dabi-
<
lb
/>
tur quoque illius numeri primi logorithmus, quem invenire
<
lb
/>
oportuit. </
s
>
<
s
xml:id
="
echoid-s3858
"
xml:space
="
preserve
">Exempli gratia, propoſitum ſit invenire logorith-
<
lb
/>
mum numeri binarii, ſuppoſito arbitrario numeri denariilo-
<
lb
/>
gorithmo, unitate cum 25 cyphris. </
s
>
<
s
xml:id
="
echoid-s3859
"
xml:space
="
preserve
">duo numeri compoſiti
<
lb
/>
parum inter ſe differentes ſunt 1000 & </
s
>
<
s
xml:id
="
echoid-s3860
"
xml:space
="
preserve
">1024; </
s
>
<
s
xml:id
="
echoid-s3861
"
xml:space
="
preserve
">numeri 1000
<
lb
/>
datur logorithmus, nempe triplum ſpatii 23025850929940-
<
lb
/>
456240178700 in antecedente inventi, poſito ſcilicet illo
<
lb
/>
ſpatio numeri denarii logorithmo arbitrario; </
s
>
<
s
xml:id
="
echoid-s3862
"
xml:space
="
preserve
">numeri 1024
<
lb
/>
ignoratur logorithmus, eſt enim compoſitus ex ſolo numero
<
lb
/>
primo 2, nempe ejus decies multiplicatus eſt. </
s
>
<
s
xml:id
="
echoid-s3863
"
xml:space
="
preserve
">applicentur hi
<
lb
/>
numeri compoſiti in hyperbola, ut dictum eſt; </
s
>
<
s
xml:id
="
echoid-s3864
"
xml:space
="
preserve
">ſitque G H
<
lb
/>
1000, E F 1024: </
s
>
<
s
xml:id
="
echoid-s3865
"
xml:space
="
preserve
">ſed quoniam I K unitas eſt 1000000000000,
<
lb
/>
erit G H 1000000000000000 & </
s
>
<
s
xml:id
="
echoid-s3866
"
xml:space
="
preserve
">E F 1024000000000000,
<
lb
/>
& </
s
>
<
s
xml:id
="
echoid-s3867
"
xml:space
="
preserve
">per hujus 32 inveniatur ſpatium E G H F 237165266173-
<
lb
/>
160421183067 (ſeriem convergentem hic appono,</
s
>
</
p
>
</
div
>
</
text
>
</
echo
>