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# Title: Leibniz-Handschriften zur Mathematik LH 35, 4, 19
# Folio 35r, page id 00068016:0069
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) Ca)
Solutio problemabum
Leida Florentiam missorum
ata differentia segmentorum baseos (q.)
et ratione una cum ratione quam habet
alterutrum  laterum circa rectum verticem
ad differentiam eorundem, datoque alterutro
angulorum ad basin, reperre Triangulum.
BC, y
 v-x n a
CDx
Ad 4
 Cx Z. Z. y.: b: C. seu Z17 bZ - by. seu y
Z: v:: d. C. seu Ze7 du seu e 21
Ex  Ex natura Trianguli  Z. v   3=x
seu Z= y  v= x. jam v x  av + aX per aequ. 1.
ergo per 5 et 6. erit Z- y  ar + ax. et per 2 rt7.
_  5Z+ fZY H avtar. fiet 2 X Sv per 4.
 raeque (ad na et quia 12 s e Z per 3. et  d
SM 
et t (12) lera Ebeque. ideo ex aequ. 9 fiet:
X) 13+6
cet ibe.
bie per 2.
2+45) b+c. ad + C q1 Dip 4 7 7A a
et ex et ex aequ 7. fiet: 22 birc 2ld st
2
b E  tac 2C7+ ax
cy
C
sp
Ergo Z p per sar 7 v XB a =A aZib set a ai ta
In aqu. 8 pro  substituatur valor
per aq ex aequ. 8. per aequ. 2. fiet c
ex
2cb CZpavtx
et EB faciendo ab -c  f. fier sc y
(12) 622
denique ex 3a M 11. fiet fce
J av ex exus et 10.
b24  B ax an +
si ab eo detraratur datus DBE, dubitur et residuns ABE, Ergo Trianguli BAE dabuntur per equ. 1. est  Y qu g  seu  sit fe
seu fier lv lg0 + (d X jam per 1 est ho= hx havthax
addantur 15 et c6 fier + lv - hX s+lgD + lg X + lgX
e in aequ. 17 per _qu. 18. fietroit v
nAn a (24
29- a ponatuo F m. fiet
a et ex a
a et b
et  an
v +X p, mv + mX
constructio elicietur talis circa quadratum ab FG scum
describatur circulus, et in hujus quadrati latere uno F
umatur FH aeqqualis datae a differentiae semmentorum
CCd lyudatu ertioec basis trianguli quaesiti, et per H ducatur recta AHP angulo GHP
ex quibus rectae 
Ecul in puncto p. 
ACEF CO AC semirecto, secans
opus productam demissa perpendiculara
c baseos segmenta, mam v,
itaque erer HB sunt puralle lae
pS est erunt
inus n dems
ex ba
Ergo pro 13 feba
scast9
Ergo 9H sca2
tat feri Nq fot d N 
en 
Vae s fiet ex trper VH9 
Fha. +a +ha
ponatur l +hp - h. seu hp 1. et l - 2 fiet
Siat fet N et 
= q a, v + X B it 3  
fit ee tr sa)
2
eptecbre PVFH
E aqus
Fet Z2 yy aqu av- aa t av
datur y ad 
datur  ad y
Ergone datur
Notu data
ratio dy
v+ 2 at cor
2y aquavtax
Cretle rav. aa
op 2vaa
nac, bb
d, 2bc -cc 
sit ent a et him  habetur b. sit op b
hinc habetur e. fret:
eb y 10Cb aquoradl
2b-a 1 1b. a 2bf-4
 en 10
1. HF seu a ep differenlia P et F5
Summa ER et RF
segrentor
utraque enim est differenti