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# Title: Leibniz-Handschriften zur Mathematik LH 35, 12, 2
# Folio 142r, page id 00068195:0283
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problema, sive uno sive altero im ajore assunt (66) (B
Batis AC a. (4
 Atitudo BD. B
3 Summa lateii FC. semper enim summa laterum
ALatisrus differentia est major basi
differentia laterum X. . () )  nter Basim &. summam cateru C = (7
5Latus minus C +C = X F37 AB
bLatus majus (t E +X (5)
7. B (5)
a +CFF + 2aC - 2aX - dCX F) AAB
8 (7) - b = D AD F
9. Rg (8) = AD. Fo
10 DC = a = R9(8) Y (
ADC = a + (8) - 2aRg (8)
2 B BC = (11) + b = FI (6) = 1 BC.
B. B6) = a + C +X  + 2ac + 2ax + ZCX. = ( BC. (2
1a Ergo per (12) (19). sequatio plese scripta
(7)- 36
tio cuum ab aus latere sunt munes incogniti, et, forma A d + _ + C + x + 2aC - 2aX - 2 cX-b
aA a
15. Peliatur aequatio in L. abjiciendo a addilum ad Ealitura simplicis
abjiciendo multiplicatorem contra 2. divisorem si  lituras.
abjiciendo in 1. -4b contra + 4b litura 
Dividendo omnia per a.
il 1. (13)
24 Targantur incogniti in vnua
quod rurae felicitatis) no potest deprimi aequa 16. Transponatur aquatio, ut TRq. sit ab uno latere sol.
Mathematica
Et videndum an non hoc semper eveniaa quolus Nata Basi altitudme et summa laterum inveire triangulum
Y - (13 = 4sq LL. Fo7
17 quadretur utrumque aequationis latus fict:
1I - (+ () 17 = 2 + (13)
8. 17. Abjiciantur communia in L et (13) lilura quinlupliti
nempe + a + C + X + 2aC, et ad subtrahendo
utrobique, et 2aX - 2Cx addendo utrabique abjici.
antuo in L. et pro 2. scribatur 8 in 13.)
fiet:
(basiet
Patet ex hujus problematis
solutione:
Utile esse alia quoque theoremata adhibere
prater ea duo quibus solis se utiait Cartesius
Si scilicet in Triangulo rectangulo quadhacum
quadratis, item, in similibus Triangulis
omnia esse proportionalia:) nam
nisiexpertus sum, cum theorema illud:
summam laterum esse majorem basi
Aquod vide hic num 3.) nondum adhiberem
apparuisse. Imo idem hoblema ose
alterius cujusdam Theorematis, pod scilicet
+a- 4ax ∞+ Cx = _T. + Rq 1I. () secd anguli Ga peta. rectangulo ex dasferentia laterum et suma
10 quadretur (17) fict:
ver
(seu quod EC= CF EC AAC. ita enims umenrtatrum
(0) 1b 1b 4. 32 1b 1b 36 2sb 64  b4 12 25b 2
gX+gC X + 18aCN I a + C + X + 2aC - 2aX - 2CX. 4b - a C esta Y tralra x. 2a x
A S
9 arstiplicando ma per a, fat et dicidendo per 16.
a utrume latus
Gumuma talerum posila d. s
ilere minor
1I = 16, aa  iNC 2aX 2Ca X sas + ra  erit ex dicto tcon GC d
AGerit a dX. Ego a Ad eriu
x a. dr. lius eo. unctum )Bd. b
e Apriatur at atre Aequationis (19) latere absinatur. 9a x.
Nam abjiciatur subtrahatur sum a TI. ubi reperituri, sum 9a X, dabit: a= 2a dx + d X + 44b = d- 2d +X
tum a WV, ubi eperitur 1ba x, restabit: Ta
in IV. notata hac mucatione, litura simplicis.
x+2aC-2
Multiplicando utiume
a et dvidinod
16, fiet:
acareni  da
ca + 2ac - 4ab = ex = raX
256+ 512 = 516= 64 + 128
2) Ergo dividendo omn
2ac
2 Et Radicem extrahendo:
+2ac-
per C 4+ 24c
atig a tC + N + 2C -2a2 2CL = (13)
hypotenusae aequami aterorum laterum
difficillimam problimatis hujus solutionem,
Iim a
ad + dX +4ab = d a - 2daX + aX
dx aX= a- 4a6 a
da- 46 a7. 1024-576-256: 19
d- u
182 d 48