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# Title: Leibniz-Handschriften zur Mathematik LH 35, 5, 27
# Folio 14r, page id 00068045:0027
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st
 aequ V2ax -X
1+X ogo 1 + ex + C. C-t X + C. (- 1. C- 2
1.2
1. 2.3
ete aequ Prax x
4
sit e cqu 2. fiet 1+ V CE 2X + XX aequ Prax - XX. ergo 1+ 4X +6X + 4X+ X aeq. 24X- X
47 cqu.
2+2
 - 1 - 27 - 79 aequ F1 - 73
l
in scheda aliqua singulari  plagulae in fol. jun. 84. ubi curvam quoesitam tansentim
a
proprietatem in erset seabentem, nivixinimque ape infiuitarum curvarum bquae in unico
tantum puncto salis faciunt, prodiit pro  o adratura sirculi talis aequatio logari
xI
famice resolvenda:
+Z
= 1
prpilo radio si si sinu verso X. recto siXi
aequ. S2 + 27 = 1- 27- 79 seu 1+Z aego 1 - 7Z et sit Z. sinus complementi sigu sino
fiet 1+3
C AV
Hige qati hanc aequationem entemus resolvere in numeris speciilibus. iti exui potest transcendentaitate
Lar 2
sit: 1+Z aequ 1 + 7 Z + v. v - 74 + r. v- 1. v- 2 73 et. aequ N1 - ZZ. ponamus v aqu. 2. et videam,
21
qualis fuluro sit Z. et quidem senes fit finita et ita stat: 1+ 2Z + Z
4
fit Quadrando fit: 2+ 1+ 4Z +67 + 473+G aequ 1- 72. seu 4 4 +8Z+47+Z3 aeg. 0
e
itaque cum Z(ve X) possit sumi pro arbitrio sumendo talem, ut sit 4+ 72+4Z+ y. 0.
eris a aequ 2. seu eaeque3 Unde haberi posset arcus aliquis circularis per commu-
nem Geometriam. pro _Z  reddendo X
sit
se
fit; X aequ I = 1+ 2X - XX seu aq
seu X  X  X rgo 2. Et poni potest X aequ. 1. sed eo casus X
C
ago 12X- x fit
aequatio identica per se vera. Sed sciendum est hanc radicem plures daci radices.
+X 2+ 
L
eu x
pe
aequ. 1 - XX. fit
A + X = 2 f X + X + 2
+VZ + v. y. 13  etc aequ SZ2
1.L
Z
X + X + aequ
L1 -2
et
fiet X + L aego 1S - 7
si posuissemus voego 1 fieret haequ. 4, et 2
1+ 262+77
et 14 Z aequ  - 77e. seu 142Z+73 coyl
ergo
2
 aequ = . jam 14 7 aequ X
Ergo Xaego 1- 2. seu x aeque 
contra hypolkesiri, utque enim ita est X
mo 12x.X
aequ 27 -79. seu ZZ aeg. = l. quod absundum
2
sidetur se natura  gerum opponere. Solutioni, quantum pote
B. commisus hoc aliquist exer in istis calculis borrectus in s. Eeder 1. Aug. 1664