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# Title: Leibniz-Handschriften zur Mathematik LH 35, 12, 1
# Folio 273r, page id 00068194:0545
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problema:
Data trianguli basi altitudine, et summa 2 vel intoloendo in factores incognilorum latus.
laterum invenire Triangulum:
_ Basis AB = a (9)
2. Altitudo DC = b (37
3. Summa Laterum AC + CE = c 1E
4 Latus minus AC (3 j = y vide = (9)
SLatus majus CBC (37 y + X.  vide = (12))
6. Ergo summa laterum c = 2y+X (X = Y, 2ab- ac- a+
7. Item (per 3-5= 4) y = C - y - X.
8 Brgo addendo utrobique y 1) 2y = C.X
controhere in proclivi est Cx
9. Et (Et divitendo per 2. y = C- X fatus Minu AC. sufficit interea inventam aequationem.
10. Ergo sulsituendo pro G m (5) pro y. ejus = ex9)
3t X = c- X 4K
11. Jungeado denominatores: y + X = C- x + 2X
M. abseiendo X inama qqua tionis parte, superflue scriptum 44
7+x = C+ x= Latus Mapes BC
13. differenlia laterum BE = X. (2)
C
Hinc apparet sufficere ex terminis incognitis) ex -ax - 2cxa b a + Cg - 2ca )R9
inveniri X. Quod ita quaeremus: e
56   Y, 1X 2a-. -1 - v 800
a91 _ (9) C+ x = 2CX (9) (256
B. (a)- BB (2) =(11
6400 255 + 44- 216, 220 40
16. fungendo denomeratores c2+   25t 141
286
16.  R9(5) = AD. (7  6400(100 25.
17 (1 - (16) = a - R9 (15) = DB. H)
18 467) = a + (15.) = 2akg (5) C y= DB. Lr
ere
19 (et ) = a+ C+X 2Cx 1 . -bC.
20 se taljiciatur  et +b, litur sinpli
21 ex taur 1dine Dermi t 44 fiet, quod
notitam est litura dupbici
23. Hire gtur (19) (+ BCl eteris majoris =  
23. Scribatur plene aequatio (1) (12) c
a Cart c ag5 +X 2C= C+ X+ 244,
1564 t  mmi
Cxx . 2e- b, + - HBC.)
(20 Poliatur abjiciendo = b et +b litura simplici R9 64 = 8
21. Jungendo iNices unum denominatorem
22. extrahendo, Radicem ex A4. denominatore4. 
23. prit equati 2)
-32 100
Aa + C +X. 2CY ∞ - fa RA C + X = 2 er. 4b = C + f + ECx p257
2.
(2
640f
24 Ponatur in uno latere sola Rq. utrumque dividatur per a ft et multiplicetur per
Anqc Al acX 448, Ca par 2CaC
= A9C +X = 2CX - 4b =  X+ 2CX- 4a-  N + 2CX- 4 cx- 4c
25. Poiatur aequatio auferendo superflua c litura.  X litura dupliciss. jungendi
duo 2CX et ultiplicando utrumque fractionis terminum per 4, liturasse
26. Quadretur utrumque latue, fiet: 15625b
512
=C X + 2CX + 4bV = Cx + a - 2Ca X
27. Multiplicetur ogapia per a fiet
aC
a
1029
a -4cKeK + XX = 
a. X + 2CaZ + 44b =CX + a XaX 1o17
28 junguatim similes incogniti potestates solae, fut ut se.
e elui tallant pro 4ca X subsituendo oeax
(768)4+ C X - 4Ca = - ac- aX + 4a b = X 1024 6+ 5X
ac ax +4ab a4
24 Ergo dividendo utrumque pe e 4C erit. X - X
 imaentur duo similes incogniti Restates: C X + a X a. Aca X X  4a b
equuraidanti p C + a f et X ∞ at 4ca x + a +ab X+4 ca atq a 4a b nin
a.
Xetax
ax = 44 b. ac = d
30. dividantur omnia per C + a. ut X liberatur, fiet.
S compleatur H. fiet: 1t 18
X+Ca
E4
32. Extahatur rad fiet+
X.
162
2
- ....
2C4
2+ a 12 ca
22. Engo habemus aequationem hani quaesil
a
2
rea. Quod in breviorem formam
s
ta CX 2C, Mplic pe
Cta X X, Ha X X
e
(XV= a
102a(64 X
10  u 1os
44
220
+CX - x = cu 2 CX 14
k
=X = RGZCX
= X = 2CX + 4
CX Y aX
asc
44+25
rintisqu
255+
1029
70
sh
356-227
eaie
5X + X= 4b+ +CX C- a
X+  ab + X C a
fa
in
29 7024
a
ib
6400
X ACX= 4 Cx c. a iorg
ac la 45 at 108.
si
id
2
ACX = 2CX 4 46 - cX
s
2
ieat
3s3
10r4
e
13 
256] 128164
100 50 l25
t 36, 1
eta
netax
perax