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# Title: Leibniz-Handschriften zur Mathematik LH 35, 13, 1
# Folio 172r, page id 00068196:0341
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Ex quadratura Lunulae Hippocratis
AFB ABFA, vel etiam totus quadrans pquadrari possit, licet non defur quadrture tiety= sbv+ EE- sib-
ducta Z vadratura
Trilinei, et examen methodi inveniendi quadraturas
aut eorum impossibilitatem propositae in Actis eruditorum Lipsiensibu
absolvatur quadratum
BR vocetur X et
octobi 1683
Ex invento Hippocratis Chii triangulum ABC
aequatur Lunulae AFCDA. Ergo et similiter du
triangulum AEB, aequatur dimidiae lunulae ALFDH A
sit Gm aequalis respondenti LH, et EN ipsi FD er
et dueatur curva AMMN. erit triliueum AEN MA
aequale semitumilae, ac proinde et triangulo AEB.
AEBg. et producatur Gm, dum occurrat ipsi Bq in R.
RM vocetur y. et QB vel  BE vocetur b.
erit RL_, 12bb = XX, unde si auferas LM (seu GH) hoc est sbb -x
restabit RM seu Y, aequal. 12 bb - XY - Y bb - XX. seu y4 bb- xx aeq. T2 bb - xx
qu ubi quadrando ys + 2yb bb- xx (+ bbF X x) aequ. (2) bb (X . et bb - yy aeq. 2y sbb -x
ubi rursus quadrando,  b - 2bb9y + y aequ. 4bbyy = 4 yyXX. seu 2X aequ. V6bbyy. b-y
y -6bb y 4 yyxX + b aequ. 0. quae est aequatio ad crvum
 arta figuram, cujus area est quadrabilis.
vel
3
orthogonium
Si ergo proponatur problema tale: sit Trilineum AEN M A
cujus a basis NE, sit ad altitudinem AE collocatum intra
quadratum AEBQ. et lateribus quadrati AZ. EB ducantur parallelae
positis
GMR. secantes reliqua duo latera in Get R. curvam in M. ita
ut habeantur abscissae BR quos vocabimus X, et ordinatae RM
quas vocabimus y. sitque ad naturam curvae explicandam aequatio
talis:  y  - 6bb y1 + 4 yyXX + b aequ. 0. quaeritur
Actis Lipsiensibus anni 1694. num. 3. pag. 438 Methodus ab autore
Trilinei quaq
eryditorum
proposita tanquam sufficiens ad indagandas quadraturas aut earum
impossibilitates, qua utendo deberet inveniri quadratura rurus trilinei
aliunde nobis nota, sed non succedit. Nam ut nos accommodemus
formulae in actis propositae, pro nostro y o scribemus X cum autore,
4
aequatio
b scribemus et pro nostro X scribemus Z. erit ergo farmula talis: X - btih XX+ AXXZZ +B
et pro nostro
Er.
a
E+
etee
aequ
quae si quadrabilis est qu (si curva est quadrabilis, secundum nostrum 
gutorem aequari debet comparari posse aequationi seu 12Zoqu.
l
n 6hili XX + X
Z
 aequ. 0 cujus aequationis formula com–
-6tih +
parari debet cum formula aequationis in actis propositae paus. 436 articulu 2
XX
+XX
seu 4Z
erit caz aequ. et 2dxZ aequ. 0 et 2fax aequ. 0. Ergo ea et a et fa sunt nihil. nam
pl. A20, 120
12c
a terrani necesse et ut ex issa compacatant patet b antum est a quia 4h aequ, b2
porro
dam