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# Title: Leibniz-Handschriften zur Mathematik LH 35, 2, 1
# Folio 32r, page id 00067993:0063
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ad propositioniq_C XL VH
n Coroll. 1. s posito areu RiF _a, sinui complementi, D.G posito C,  radio  . r
119r  4u er3 8C.
Nam sinus versus v. aequ. a - at etc. per prop. hanc. est autem C aequ. Y = V, seu D.G aequ. DR - R. G
ergo C aequ.  r- a esc. quemadmodum diximus. vel M. G
1F, G vel D. H. (quia pumita M er F coniceidere seu insinité parr dstare inter villo ponent
3 (oroll. 2. posito arcu R, F, a sinu leretiti s. radio DR, r. erit
3 S. aequ. 4ra 8C.
3 eC. per prop. hares artic. 2. quod spatium A.B. Est aequ. rectangulo Aibst B
seu ar, (posito AIB, aequ.  arc A R. F, aqu. a) demto quadrilineo AB B. C A, id est per artic. 6. hurius prop. hujus demto
rectangulo  R.DH, seu DR in DH seu Yf. ergo spat. A1B, CA, aequ. ar- Ys. seu saequ. ( a- AB. CA
id est Saequ. a -   ec. ut diximus.
circulare
3 Coroll. 3 posito arcu R, F, a, radio  DR, Y, erit segmentum dese R.FR dupticatum
erit aequal.
M eut scilicet segmentum id est per artic. 2. spatio A, B, CA (posita A. B aequ.  arcui RI F) quoniam constat
e Geometris spatiumB A, sinuum ver sorum arculisapplicatorum, a aequari segmento dila R, FR duplicato
idem et sic demonstrari potest. Si segmento R, FR, addas triangulum R D.F, fiet sector RDIFR, Ergo si duplo segmento
R. F R addas duplum triangulum RDIF, id est  rectangulum RDH, id est per artic. 6. sptiuu quadrilin. AB1 B. CA.
fiet duplus sector, RD, FR, duplicatus, so id est rectangulum sub arcu E1F in radium, seu rectanus. A,B. BB,
ergo dupl. segm. R. FR a + quadrilin. Ad. B. CA, aequal. rectanus. A. B, βB.
+ quadrilin. AD, B. (A a qual. rectanus A1B, βD
jam sat. A.BI CA
Ergo duplum segm. R. FR. aequ. spat A. B. CA. Gq dmodum assbatur seu seriei r
Hinc echer expeditissima habetur ratio ex solis datis angulis sive arcubus, (et radio) calculandi
areas segmentorum tamets  dinus phordaeve aut aliae rectae, incalculum non intrest, unde  falite et segutum
quane dectorem dataeenagulitudini, cec cercaloc abscdere. Adde quae suput diximus prop...
a = + - 1 + f-
+35 = 3a - 3a + 18
2a = 2a
H. 2.3 to2. 3. 4. 3
ca = a = a + f. 2. 3. 4a
a optinia fore constructio v sunus versus = aa - a.
est minar quam a
sid areu
BRvel DF, V. RT, +.
unde itsi arcus sit radio aequalis
enit erit minorquam i rac
720 et a - 12aa +36 = 26- 240 et aa = + 2f9-6p +6
et a = et S-2S9. 6∞ +6 Satius constnnctionem Geomnem ur
GF
+ aequ. a + a fra
37
c
1n a X 3273 a ex
19r2 315r6
C aequ. Y- a + a
181440r8
s erc
a = 35: 3- - 1   suu a = 3 5. Etc
ot c  Jos - 4st2t + 2sC+ CC. sin X.
i dec. Aet: Z a aqu. S+  F. seu a aqu 2s + F jesto mnvor, sed dror erit  a d 
corculi dinnctrum habentus a a aqu. 2st nam
sed meler ostrnstuo estusdem
constructio sit arcus datus RF cui quaeritur
aequalis recta. sit sinus versus RG, sinus rectus GF
in BR d
etro producta sumatur  versus R, ipsa GRC
CE aequalis GF, et KH cui juncta BE occurrat
ms + ans =  m a + ma
23.45
-ma
1
n a3 - na + na
123. 4
1. 2. J. F l,. 2. 3. 4. 5.6
= ga 94 + 1ja +4 7 a
= Ah ha n hae aetia
tto
EEtC
(3a-3saqu. a  a
=a
ic
120
uu parado
Dp
2C,  2tC :: 1. C debut este prope vemum
r ip 4. 5Y4 f. 13. sib. 2
Ar d
A5. it
deenor mina
qui
3s
12Y
a.
AF, d.
a aequ. + - 2
1
a
+
+
E
s
12r
5C.
laequ. 4
a aep s+c
a
cujustangen, ex a
sumatur quae producta pea
sic ut sit AV
duplas q labit
crplum arcus
RF, ita an = 2s+F
1+
4ta
Hlarus lxt
aequ
ergo 2a - 35 +t ac = 
ser a.
aequalis ratio, et ad C et A constituantur cormales
ni fit are=
ila lai ope
M, n, p, q tr
tolli possunt qua
termini primi
 arbitrarium
deu a, a, a,
erit AH pertia parsesarcus RF
= pa- pa + pa