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# Title: Leibniz-Handschriften zur Mathematik LH 35, 13, 1
# Folio 357r, page id 00068196:0709
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igura segmentorum
prencipim ncum quo ostendo sumncam ocruorentium tangenti aequim dipeo sgmento
nullo negotio constendit dimensionem cyclocidis et omnium tjus partium 8 Mrensionem
etiam segmenti, coclocidalis mei absolutem. Num semper Cd EF sau fisau
y
BDEa
Alo EGA Eet en
segmenta
retao cyiloerdis ad irculu, sed et omnim partium ad circuli
in circulo. du catur
AB, curi tangente
baarrant. produc
EDBACE quarabilis g et etc aequatur quadrato
a r
itur dimidio ertus seu
et EHBsC aequabili
dimidio EC AF H BDE. Hinc facile demconstratur
LH 35, XH, 1, f. 357.
dum occurrant trantro
Ac preducta ps
AL poneum
eit EF B=
raX X
V unde
at- pXt  Ly sive
hvc l cax- x
p
Tam ut EC ad EF, su ut Fq
dea
 ax s 2) ad ax
1-X 
Trax
seu ut a -X ad T2aX = X, seu  sinus complementi ad simum rectum
ita FLZX. FH  b. ad HG
sin comp. 
sive ponendo a = x py. fiet. Va- y
sive a- av
(a- y
Ergo. HG p siv. dest. b b trax- x
sin. ypl.  a = X
D HG. Jam AGp ax +trax- 
V Sa- y
frane a - X
quorum summa peniet exquad.
Cic, quia summa omnium AGp MADM
Hinc ergo et HG pender ex g. circ. Ejus momentum ex busi ND est bra-y. pendet
ex Ellipsi. momentum ex EN, sunt eiu B et fit b a - b  cujus datur dimensio
alsoluta. Ergo et onentum ex EF, seu ba trax X, vel 9. ba   C-yb arip
=X
cnda ex quad cic. haberi pt quod et jam lum patet.
ABB X. eius
GBEpE A172
erit X, 2a2
a2+72
qua datiue qur tangertes
et 7X + a X = 2aZ f0.
sive, axce.
2a -XFI2
DEF Ran -X = YaX B Brax  - ax
Vrax-
A y - Z
Ergo DFH DE +  BE eiit H BC y Z + Z 3CZ
Ergo DFB Trax - x - ; ax F 3ax - X, 3aY - Xt TraX. X
sive 3a
scaxx
Trax -X
2aX - X)
quae lde x2aX - X. Haeesimul sumta quad rabilia.
2a - X ad ex Hyperb
La = X
probleme que Mons. Osannem pue propo Trome
difficale: sit numerus dutus, v.g. 10. dividatur
in pantes duas: 9. 1. et 8. 2. et 7. 3. er 6. 4. erc
ho quaeritar summa rectang ulorum sub ipsis. 9. 16. 21 4 etc.
hoc ait condinere ad solidum sphaerae Ego sic cocipro
sit b. colum erunt partes: y. Bb -1. quae ductae
cu se invicem: by -y. Hoc At summi ergo quaeritur
Omnium . lu st. sed his nihis facili  Et
vedeo a manifestum exhibere adlan sphaeraae,
quia quadrata a 42aX - +V sunt 2aX 
ad est X 2a- X. ubi solum ponitura-
seu diaimeter. Nihil facilius. sed ille in lrve
genere problematum non ita exercitatus est.
ax + x. Ergo
BGB D
AE, EF
besi)
LH. 35, XII, 1, f. 358.