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# Title: Leibniz-Handschriften zur Mathematik LH 35, 2, 1
# Folio 194r, page id 00067993:0389
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In crculo aCf ducta chorda ec. et ab extremis dianetu f. g. junctis rectis gc. fe
et ex centro a. recta ab. ducta, perpendiculari ad gc. ajo Triangula rectansula:
Di = =D GF - C1.
abc. et sdc vel dgc) esse similia. Nam ang. efc = ang. gac. ergo
et unu fec angu vel fce angulo agc vel acgaequalis Tuangula ergo efc.
gac similia, ergo c. 4ofe et barfdc, abc. Z. E. d.
rrgo D abc. simile Triansulo Characteristico Cyclocidis. Sed hocperse
A febet hfC et ifc. sinilia sunt seu hf -Cf =
patet
Di- FD1G5 2
H
f 1c = cfc3C
porre quodr. fit = Aq 7L -LH, a et LH = +q LA + Rad . - LA
Ergo FH = Ra, FL. - LA Rad + L A sed FL = PA Rad + L A - 2 F ALB.
Ergo FH. Bq 2L A = 2TA L
G2+LF GL
GF 2 Gt.
in circulo L 1 sinu ess A4, a- 4. β3, B a 4 (3, 19 a 
idem LH sinus = EgF, GL L F, R4, = . β ha - β3. -
Mulliplicetur, per a - β. fiet vel R9 a + (3 = 2a β.
fiit: + a + B - 2 a (3
+ 2a B
4a B
+2a (3 + 2aβ
=B a + 2425
FH- R9 GF = GFGL.
R9 GF- GFGL
FH.
GF + GF GV - a G1GD - (F 1. GF + G1 91 - - GF G1
GFD = GFGL _
Ergo FI GF + GV - 2GF, GD,
GF
GF -GL.
GF - GL.
Fi
p sG0
GF - GD
YGF- GL.
vel FI GF+ GD = 2GF, G). Ego FI, GF- GD = rD
tq 2a (3 - , = Rq 4 aβ - 4( = Ag, 6a (3 - 9 (
Ag +a B- 4 p = R4. 2a(. ( summum pener a Z. C.
FC = R9 GF = GF GD.
Ego GF - GFGd FI
V, = e + +a β3 + 24- 3a  et hocum quidem
Si jam diffientiae sinuum sumantuer:
Sit a 1( 2aβ,
erit d diamenter in
f a X = b. Ergo b = X.
GL. LF
ob Plum rectangulum AL H. a. +3 - 2a (3) = Aq, 2 a B - (
R9, 2 a β - (..
1
GH = GL + LH, gergo GFI = GF GL.. Ego FH = GF = GFGA = GF- GLGF.
FH2
CI = CFHC. Ergo FDGF4E CF. HC L DC.
FH
e
lono ex his colligi posse puto fi, quod quaerimus. Eto fh - (a) fc = (b) fi fX).
es ic = ifehC.
erit
DEi - GF 4B L FD FI = FDGF
ZH
c
crgo hf If = CfB. Ergo si f sha sit diametca fg. et hc sit gc. et 12 sit de.
GLGL +GL LF. =GL LF GL
ad + ab = a +b, a
AI= EC
HF
FH
GF - GLGF
GF AgGF - GFGL, = FH
cylinder Ergo parattolicus = sum cylindio omnium FI, demto
demtae ducta omnium gd. in f1
FI
5G0
GF- GP
 Ergo FI =
rGF- GL
FI FH = GF = GD, GF= ACHCF
Ergo summa quadratorum, CF pendet a summa quadralox diametri
et summa omnium Gd. ductam B diametrum
FD. FI, seu FD = FDeGF. Ergo FL = FH
FL
FH
FL
FH
FH
Iuspiciatur figura 2d deductibus in ea demittatur ex H. puncto exhemo rectae Ak. sinus compiti perpendi culari in
AE rad E
Ergo XV AEB. (gradrab.) = sin. compl. E Tanus.
pro K). ejus aequationem: erit:
Sncypl.
AE H. rad.
sinesii. Sim. Singpl.  rad e
AE d +0
Bosins A A0 sin ypL. Ergo XJ. AEB AOBD
radium AE. cam appellem esto XY. ne literas multiplicemus nami testum XY
datur autem quadratura summae omnium AD. quia K), quia H cylinder
XV. aequalis momento sinuum et ided quadrabilia
HElan AH sc.
ra
sF
ino Fd = Bd GF - F1. Ego F8 EF - F1
4
AO. AE
RY a rad= momentum sinus. Ergo cylinder omnum
rad.
Ergo XVAED = mom. Tangs.
ey
Ara Bosin C Aad E mom. Tangs. seu Radi cubus in vinum momitanus
mdto compl.
= mon. Tanus su compl.
rad
sin compl. 1.
bupaditus cubus in Tangenlem, aequatur sinus complement cubo in
sinum.
siri
294
Aade rad. suni rad suum
horum idee differntiarum inter sec. B Tanus summa quadcabilis seu boum rad. D - sinrad. Erosi quadiari possent sut rad fricopla
in copl.
Sin. opl
suuicgpl. C
sin compl.
sii. copl.
summa quadrar
potest, puto ertiam
radicem extrahi poe
Imio dubito de radice
G) -GD
18GF - GL
Y 9