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# Title: Leibniz-Handschriften zur Mathematik LH 35, 13, 1
# Folio 426v, page id 00068196:0848
# Scan: One image of two folio pages side by side, registered by the library under both labels (also fol. 425r); this page is its left half.
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sit ∞EBp rectangulum, ejus appositum tifineum BEYB
X centrum commune
M centrum trilinei
juncta CH. cadat in H, punctum re baseos XY, quod sit sit ut se XH minus quam HY
Hea H cadere in medium ipsius xYs quia alicubi supra
L centrum rectanguli,
nempe proxime ad C, cedidit inter medium et Y, t sutrans medum versus 7
sit ABCd rectangulum, huic addatur odE triangulum male a n: m=
centrum ipsius rectanguli sit F, ipsius trianguli G centrum
Commune H, juncta AH occurrat ipsi et producta
occurrat ipsi BE in j (et FHad FGut ECEad veri
F. H est ad Gt, ut BE ad ABCd seu ut L CE ad BC
AB: BI ZAN: NH AN = = AB+FK. VH = EBC+KL
FL = EAB-  AB = = AB
LG= ZBC+3 CE FK AY: FL = ZCE:, BC+ = CE
FK: KH = FL: LG
seu FK = BAB. L CE:, BC + 2CE, Et XH- LB CaL. lE )C
et AB B L 2AB. BC +  AB CE+ L A1B. C23
BC+I ∞
Bi = LBC. BC + 4BC. (E +  BC. C2 + C4 e1( BC13
quod si jam sit BI = iBC+ hCE finet (Bc+ CE = _B Equ + _BC. C2 +  CEqu, :, LBC+  E
senfiet ZBEqu + 2BC. CE + ZBC. CE (+  CEqu) = BCqu + BC. (E (+  C5qu seu fint
EBC + 3 CE = BC + CE, seu C fEBC + L CE = 0 se BC = ECE
seu CE = -  BE entus Esumenda intta B et C. sed suspicor eriore esse in cutculo
sine  cum C endis tendendo versus C, cadit tandem in e, ne tunc quidem tunc etiami cadit
graritur centum figurae per momenta ex duobus axibus AC, et AB, sit centrum partis
B in C. Ergo non in dimidium BC se BE
priaris K accedit novum rectangulum Elemenitare, cijus nebrum g. patet recesse esse  ut K sit utrique
axi propius quamZ. ut possut A, K, q cadere in directum
sit hilineum AXYA, ubi simul crescunt ord inatae et abscissae. sit trilius
aaliuli centum L
ipsius ansungeah X). seu terulundem abest ab axe AX sed M cento vil trilinei est propius Axi AX,
sit i rectaguili circumscirphicentum L., quod imminet medio ipsius
idem est in
ona cujus ordinalae
crescentibus.
crescunt raedenda abscssis a centro A
y = La Max- A∞) hssyax = S, 2 raxdx - 2 XXdx = (x r. - 1 X
sit A X: 29 = sx dex Sem. 21): har . LX
(X dx  (1aX- XC) :, XX = X
Xyax = (Xdx VCrax - X1).
linea centrorum proctatis MM) sit AP, Z et PM, v eit eritus
siu X. y = X: Hrax XY) =
px - 3
fatax) Xax Crap XB) (cx eax XX) = d x Herax- p2) sX ax VCrax XX), :, qu (dx ACrax -XX)
et v =,
AP= Z = SX ax LC Lax - xx)
Ax S(ac XX
de -d (xax =  XX dX) Sdx ICrax XX) = (ZXX = = ) dx SEax X),:, qu Sax MaX - XX
(dx (ax ∞)
Ergo dez ed = X Y(rax- XX) sdx spax- x+) = + (2ax XX) S Xax sCrax XB)
(X = L XX) (dx (Crax - XxX) = (1. xX - L X3) (2ax. XX)
ax -X1)
Xx - X
nan yd  a- X nam : Y Zqu  dy Qu YZ = 4 dy, aa gy 
et summando aau - + eß. Ergo monentur hilinei AXYA ex CB est mon.. ipsius A CZ YA ex CB, dento
momento ipsius rectanguli XZ et CB, quod 1 (a- X) ; (a- X) seu Ly, aa + XX- 2aX seu L’aay - 2 yt
sed datur mom eatu hilinet AX IA ex vasi CB
(dhax. H)
Ergo momenum hrilinei, AXYA ex ape BCest h aay - L est = L aagu + 1 y =  )
ea iyr (yex- ixxca ix9
inde non orctetur aeqi utro
qusesitre d pelitur calcutus
sed Ex summ momenti ex AE + mom ex BC est, ACsis rax Xx) Ergo a (dx M ax - xX) - + G=(Xtx  posito a esse Es, et psat
in Xy syiX - 4y sydx + L et
Ergo lict exprioibus X Rhax XX) Fdx ICan. X) renax x) a (Ex sCrax- ) + sC ax- Xd 3 (ax X∞) Ccap X) Y atd, 0, Di C
(x - 1 XX) (dx 1 (rax - XX)  (1X- 1 p) (C a XF)
asy dx = fy, quod
na a- 3x
et KH: LG= CE:, BC+ Z CE, son XH- EBC C Eide rursus  seu C
seu RH = ZCE, 2BC+ ZCE,:, BC+ ZCE
que
minus
si magis cresca
horforda lis figni
quam recess
CBEYB
Sxdxtuxne et QA = n B: 5 et GA - M-
D Xt Sid s ma
FCrX) sI
seu cadal H versus t. citrca mes portet alicabi inter B et Y