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# Title: Leibniz-Handschriften zur Mathematik LH 35, 4, 19
# Folio 36r, page id 00068016:0071
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millena
Problemata primum secundum tertium
quartum una constructione complecti licet
Datis leteribus summit
p
sint Z y. latera circa verticem
aegmanta baseos a perpendiculo in ipsademip
differentia seqmentorum v- XFa.
e
bZ +c n BZ + Vy + 9: d2 +8y + t:: b: c
(2) 4b
et Z. v  seu CBZ+ 6p9+ Cq 7 d Z+ bdy + bt. seu yp- bn
et Z: v:: d: e. seu CZ7 dv. seu 2p 2b. _
Ex natura trianguli Z. y n X. seu (ob aequ.
5se
fiet et Z. y ax  ax.   aqu2 erit yp
(6)
ob aequ 2 erit 3 77y1 +  r AZ- p. Unde
est
run et- p
A 
2 + r12Y  py (5)
E rax
et in aqu8 proy ponendo et pro yr. et Z. ponendo
in aequ. 5. vatores ex aequ. 2. et 3. fiet.
6
pr non render-p reavtrear
ubi si posset fieri  conticusat esse nr. problema
solo ductu redtarum sobo solvetur. sed quia
nos generalem solutionem volumus compendii causa ponatur
vocetur Y d+ na (7), 4
1S
tsit: v renden, ext r’eavtreax
(10)
cOmpendii causa v7 O set lvF l0
(9
jam
aequatio 1. exaltata fat multiplicata per hvthx
dabit hV = hX Y ha+ ho. Quam addendo subtrahendo ab
11)
aequatione 10. fiet + tB quam addendo aequationi 10.
fiet +lr = hx (12) MeI O +haB+ haX Quae aequatio
(14)
ut fiat ad circulum; faciamus +l + h  - t. fiet lp - 2h.
h.
(16
et ponendo nF- 1. erit l+ +2 et ex aequ. 12.
fiet sequens _ +v + X  (2O - ab - aX. sive ex aequ. 8. 9.
fiet vex
2ld
617
+rend p V +re a X + C p
+ rea
 sa a
-
(19
- 5a a.
v. x a
vel per compendium v +X  +v + 1X + g. quae est ad ciiculumus
sui si conjungatur aequatio v- x ri a quae est ad
lineam rectam habebitur pmoblematis solutio
si novissimam aequationem quaeramus et pro X
substituamus v- a. et pro x ponamus v2+ a- 2Da turce ex aequ. 19
fiet 2V + a - 2av7 tv + Y v- Y a + g2. et
20
ordinando fiet habetur aequatio plana: 
v- alv +a 10. Unde constrnctionem
- 1- t - va
reperire facillimum est
Eadem constucte idem calculus eadem constrictio mutatis signis
serviet etiam si perpendicularis ed ex triangulo
in basiu demissa cadat extra triangulum AB(C)
quo casu V etx non erunt segmenta seu partes baseos
sed basis erit una ex A(C) erit pars major
et minor X eunt segme sive (cId. erunt partes vel segmenta
najoris V. sive AD
et alia ad huc rem numero
infinita
LC
vel per com
-bt vel percmpendium
b c
y(2+
nt1
nernao
arculus genecalis
no on
v ez vuille
2. 3 av+ ax
n aer
i2
ts
2. 7 12ac20 a
2
2ez- a
yA.
2v- vta
+Y
ex-ap