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# Title: Leibniz-Handschriften zur Mathematik LH 35, 5, 3
# Folio 13v, page id 00068021:0026
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quodlibet punctum extra irculum existere intelligi potest.
Iubita
Jam DG. fat investigabitur facilius DE, est enim DE, ad DG, ut BL sinus
rectus ad radium. Ergo  DE e, DG BL, at DGCBL, ax + as + x () dBt
ergo DE ax + af + fX (+) d Trar X
eris C May. X
eris DN
Dp
a-
2
ipsi AHN et in AN demittatur
perpendicularis DP. y AF, f.
 ciro ne 
MLna. ergo DN, as
+
producatur E) in N, dum occurat
a
anx CH. ergo GE) a - X et ENp, ax + af + fx (+) dehar
inventa gautem, ex funte hne
turo ista iisius DN additio ad E, locum tantum habere videtur, cum
D sumta ut in figura extra vert ce diametrum in opposito lingetls late
latrre diametri a sangente averso. Nota hic casum, quo signorum
ambiguorum usus harere videtur aliter enim in quibus dam instituendus erit
Calculus sosit in simistro, quam si sit in dextro tangentus latere, itaque facilitatis
causa uno tantum casu utcmur nunc quadem
Nimorum quia omnia quia catentus per Triangutorum
similium comparaoes peregitur. Alia enim
methodo calculus reddi potest generalis is ergo
praeferendus, minitum
ex date DE et DC,
est enim EG ad DG, ut a x seu BMad ML seu a.
ergo EG DG a- X, et GL id YB, 
ut, 2 M ad BL, seu ut a ad ax-.
seu Gt e an + fa et Et ⊓ 55(+D GL
Pra
quod si unicum exemplum calcusare volum cum punctam
D in simistrolatere ipsius A T  extra circulum, intra langte
e A. (odde surpratius. 1 hunc Exp de Rase axat est d arie at
sin malis NE, uti Ne aqu
AH ax
aux. eut Ap fSra F, addatur Ad sive d, et
vraxrofet: ficax. ∞ + d + ax
s
e
trac. iu
a-x
Y NH. Jum 
Jam EH est ad NH, ut a ad a = x. Ergo EH NH a est autem
NH p
a = X
2fax - fx +ad Trap- x   = dx Srax x + a X - 9F
a -x 2 Sia
So + ad Frax. p - dx rax  + a X - ax cui addatur AL, AH,
a = 2ax + F rax -o
utfier EL. et habebitur
sed quondum calculos tam protixos odi videndum putius an omissa D, les sit facilior
t puncto D in diametro prodcta si opus fig. 3
rg. 3.
(2+
Nimirum TA at
a - X
relatio inter EL et et DE
aufeli  addatur vel adimatur velplusquam
adimatur aD Ad, fiet. D TD + T + Ad
+De = rA + AD
Jam DE ad AC DE
+ YA = AD
-TA + A1
seu
FD Ergo DEp, TDAC. ram eAtC ABB X.
ACr)
Ergo: DE  F ax  7 
TA
ax fF, X. sive DEr = ux + af  = X
Ergo DZ H FSar. 2F X
X
addatur vel adrmatur, etc. a-
jam Dq ad ABf ut rEa-  ad a.
BL ( et Et
nimirum si D sit intra A et T, seu quando TD, FTA- AD perit AEC + CL
quando D intra A et B turc cadit E inter C. et L. et erit EL B. EC + CL. et
item
TDH TA+ AD. quando D ultra B tunc TD etios TA+ AD. sed ELEC-CL
quando D utra _, seu quando TDF -T A + AD tunc E L EC + CL ut ergo