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# Title: Leibniz-Handschriften zur Mathematik LH 35, 13, 1
# Folio 328r, page id 00068196:0651
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a nax - L = X vay fiet 2as = aXy. seu y et txady
seu Xt = 2aa: ary et ex = raadu 3: atus et X dx = Aa: atque Ergo
du circuliser pit
posito aera 2. pendeti ex quadratura sorculi a saa- aZ: 23 summanda
- - Aiter 2ax =x = XX 9y, fiet ZL x = xyyfiet X= 2a: aa tyu
Iea on e (H Bet dx = 4Gdy,   (aargu) et 2aX - aaXX X
=3aydy. β)(aa + yy) 
2_C. DC B 10 (eu 1). De(ser2
AB X BC, yu. AT, + X AK radius a, seu CK AT =TC
Xi LTC: AD = CK: BC seu +: X =  a: y. seu
srax - XX) =aX seu at b - HtX =X aaX + adeoque t = ax : E ax - XX)
Net X = 2 +), ad + H , se (A dx  se ABBA = bis ACA
Et. siX dt = B D = bis AOAS= XF - bs ACA = La)
Ergo bis ACA= X + - 2a ((tt dF: (aa + H))  + Ergo
ACA= tianqu. B
sia AC- G hilin. AIBA
lineo AYOA
re drc BA T+ trianu B AKC = a sIt d. (aet 1B
ata) aquatur din
seu an ACA La et sector AKCA = trianus
9r
erit
ua
seu sector AKCA = triangs. BAT + trianque. AKC - triliu ATDA
sed trianus BA T = tinanus ATC
. Ergo fiet
dector AKCA = quadrilat.   KA TCF L trilin. ATDA
Ergo rit scob ax est quadallat HATC. sect AKCA = = tritin. AFBA
jam quadrilaterum KATC = rectanus. K AT et fiet sect AHCA= at t sin
seu Trilineum circulare cavum ATCA  L trilin AFBA
fect AKCA = a. AT - L hiliu AFDA. f= at -  Ra saat: (aa + H) t
diffea seu sector ACA est summa omnesm A seu F demta summa omnum
F seu AK, seu A applic ordinatarum ad A
et  dimidium trilin. est summa omnimmatt. (aa + H) ordinatarum ad AT, ergo
jam fa a. AT, est summa omnium
est summa residuorum, si sumum
a prioribus summandis respective detrahandur posteriora, seu summa omnium
residuum prioris summae detractae ex pnore
a dt, a ( a - aH( aatH) =
sect AK CA
dt, a+ aH- a lD n aa  + H seu (d t a: (aa t H) = puo AF, a, et AF C
q
a 
F na udo Fde La sdydy dudx = sector, y = S (ax - XX) et
Htam  conclusionem brevius sic consequi licuisset:
dy = (2 2X) 2 (a - X) dx Eax -XX et dydu = aa - 2aX + XX Adx;, 2aX = X X
it depdus + dxdx = dx dx aa = 2a Xdxx + XX dodx + 2 afdxdx - xx dudx
2aX = XX. sei sector = L aa (dx a C: YhaX-XX) = + aa fix L aa sx t. X
X = 2aH:, aar tt dx = 4 tat (:, aat HC)  2F dt  13(a at t1) seu
ax 2+((44++ 11at 3C ut): ( (it aa + FI
aattt = at. zaa -+tt
aa + +t
et dX l. X dt. H, raa - 4
ax lx = 2aH+ 2aut ratd = ae 2aH + a+ 2abdt- 3at. 24 ta n) t
_ (aa +H)
nat H.
B1) aat et
aa +1t+ 2lt
Ergo dx = +2at dt 11 tdX =
(Cat) t arcus
+2aUdt: (2 (a t H) a + adt.
 Breviter fector iaaflx: teaxn
2aH: (aa +H) 1em n 44 + H eencus
dx: Max -XV) fiat  X - alt 
at. posito Al esse arium
et erit sector Za dare et arcus = aas.
aatu
AB, X; AK, vel RC esse a; et AT vel CT esse t
b 2
32 1aB1 6 sit