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# Title: Leibniz-Handschriften zur Mathematik LH 35, 5, 23
# Folio 25r, page id 00068041:0049
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es
erit cinuli
Y. tangente BT +, Carcus AB, abe aequ. F- t + L
srruat
rite
-t
3I Spt 7Y
Sit Hyperbola HP, cujus centrum C. demonstratum est alias
abscissis CE, CF, FG existentibus progressionis
Gometricae, seu ut numeros, tunc quadlinea
P, E8, FR, GH, fore progressionis Arithmeticae
sit CE aequ EP aequ Y. et A EF vel ED sit X
et E9 seus
r-X
rex
erdx erit logaritEmus Hy perbolicus de Y- X seu de CD
rax
et dx
Y+x
erit logarithmus Hyperbolicus de Y,4X seu de CF
er ex 4 rrdx 
seu 8 r-X
seu 2sa
dirLXX
1V dx
rrxX
r+X
erit log. Hyp. de
er de est log. de r+ +S-1 d
ret sa
D er- XX
2+X
erit logarithmus. Hyperbolicus de Vrr- XX
quantitates, tunc ita procederemus:
rrdt est log. de r- Fs- 1
Y-t.-1
-
Ergo
rrdt fuet log. de rr+ +
2Srrtet
et serat foret log. de
2t et
arcus AB
Vrr+tt
secante C7
Unde sequeretur dplos arcus fore secantium logarithmis proportionales
et possent inveniri quotcunque mediae proportionales sola sectione arcus
in partes aequales. Quod verum esse, non ausim credere. invitarefutatur
 CB CA, CY, r. C55. SV, (-Y
TV: SV: CB: B5
et Z aequA: DE noqu. m C. ergo IV seu BT: s:: Y: Issa rY. et B, aequ Ys: fs H. Est autem 
erit DN vel F9 aequ , seu DNago  et F9 aequ.
YZX
r-x)
Est autem DP aequ. (rrdx et EQ aequ. Cerda.
Urgo De seu
et DQ
dc
quemadmodum alias demonstravi BF
seu ut Logarilhmos.
uod si liceret honc calculandi modum transferre ad imaginarias
s
CT aequo CB + B72. Ergo CT aequ. rY + rrss: ss- rr seu ex aeqo 2rr1s- F
-r
unde manifestum est CT non esse mediam proportionalem inter ret
quod fanen fieri deveret, si eat cuus ille haberet in migmaris locum g
Be appellato
Radioseistente
eu a aqu. s