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# Title: Leibniz-Handschriften zur Mathematik LH 35, 13, 1
# Folio 348v, page id 00068196:0692
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8
Inoestigatio chordarum aequalium e curvam datam dividenti
tit curva HAd HAK, in qua sit arcus ABD arcus cujus chorda AB. jam
centro B radio BA, describatur areus circuli, secans curvam in C. fungatur AB AC
jam pro calculo referentur puncta A, BC, ad Rectam indefinitam 1 Ar demuis
rectis cormalibus Axi. Ob data puncta A ob dator puncta A, B dantur LG, LN
abhictae, et ob naturam curae resario inter LG, GA, et inter L1, 1B. ob naturam
sirculo excentro B radio BAde scripti erit  B0 qu +Co qu= ABqu. et quia B0 = LN - LI
2LN. 21 + Negut 1Bqu - Z. NC. 1P4 ABqu.
ek NC = 1B, fiet. L LNqu.  Lqu
Alimnendo datu qua exhibet Ex naturi curvae relationem
inter LNoet NC, habebitur utraque halum rectarum. Rursus AC, GNqu + (NC- BA) qu, seu
comper pro
AC qu = (LN - LG) qu + (NC=GA qu).
exprimenda curvae natura scribamus GA = LG et IB - L1
et NC = LN fiet LNqu. ( LI qu) - 2 LN. 11 + L 4 4 ( 21. 
et (0- 
pea- du. VG a thldect
N- 1G) qu + (LN = GA) qu
Habemus valorem AC, et duos ralores AB, C
et ACeju. =
valores ABqu. cum qua Regu
tres literas LG, C LI, IN et harum trium
aequationum ope tollendo LN, LI, LN
prodibit aequatio inter LG, AB, AC, vel
Itaque hinc vicissim datis punctis A et C datur B
qualem ipsi BC vel AB) habebitur relatio
datur ex LG et AB, et BC est aequ. ipsi AB
 et posset tollendo LG relatu
LGe. D tG + LIqu en  G. La) C . 2. 15) - (15 - 1A) (2E1 4 7 + C)
C1. FC
(si quis id maltet inter LA, AB,  AC
n
illodem
BV
Et quia L1
dabitur relatio inter LG, A
Sed sufficiet paucis assum deseripto r
inter AB, AC, Bd. postremo quarendo Ad, poterit relatio haberi inter LG, AB,
vel et prsse
inter LB, B
vel inter AB
Dqu=
DE qu =
et
ep+ Nequ+
P1
1. c
50
2G
Hsc
determinari D, et hinc duci AD, atque unde sublatis reliquis quaeri
+
 circulo centro eira
1y
3
23
en
quaryquti
lationem inter A in Ellipsi or 
dio
qudud
AB = LGqu + L1 qu - 2(G. L9 + GA qu + 1B4
BCm = ABju = LIqu + CNqu - 2 L1. LN = 1Bqu + XC qu = 2i B. NC
LPqu -2
tL
u
He quesqu LAqu
Dqu=
ed
Z
in = 2 dB
ZN+ GA u  Nc
2
l. L
In Hyperbola H Aequilatera sit ubi y = aa : X
1, 2X LN, EX. LP, AX. LQ sX
Aqu
GA Gu 4)
sit RGiX.
quabesa
qu BC qu
123X
 2X - 1X) + qu aa - a)
2) ju (Ex - 2X) + qus au- aa
qu. CD= qu AB - qu aX. 3X) + qu a - au
M
In AE = qu ( 5X 1
ess (5X aX) + qu (aa- aa
 a
-0a)
porre
17
a
NC, a
qui d E= qu
IX)+ qua
(AX- IX)
AB qu = L
 s
Ju Ad