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# Title: Leibniz-Handschriften zur Mathematik LH 35, 2, 1
# Folio 190r, page id 00067993:0381
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Schediasma De Homogeneo aequationum Numericarum
 solutionio habendae causa tellendo:
requaelibet na
Esto aequatio Numerica qlibequadratica duarum ncognitarum, de qua
nunc quidem in specimen Methodi loquemer
Y tsquev + SiII E N C + 2Z 
delonatur Homseneus SIL subtatus esse, sive, nihilo esse qu aequalis, ajo
sononem  roblematis aequatione proposita contenti in promtu esse.
Nam du primuma p suppono quadratum utriusque incognitae extare,
alioquin solutio in Numeris jam tum habetur; deiide vel aliquis
extat ex Terminis sublateratibus, vel denter; si Nenter
ext nenter adest, ac ne homogenens quidem, quod nis obtinuisse
tum
suppono, Aequac
munerum
sive v Z Sh. Ergo q dom  inecesse est esse quadratum
et habetur solutio  ans si non sit quadraons pro certo habendum
est problema in numeris impossibile esse. C Unde illud quoque sequitur
numerum h. esse debere negatirum, sive (uno verbo quadrati ingusdam
numeri negationem. 
fin.  aliquis vel utrque aterque
Terminus Sublateralis sublato homogereo extet, nempe se v
vel 77. problema in Numeris
 quod sic ostendo
(
sculutum censeri debet.
aequatio ad hanc intelligatur rediisse formam:
B n heq C _ + N V + 2Z (0 sive jam  sive 
ponatur nitito aequalis, modo non uterque apparebit solutio neque
haberi, alterutra enim incognitarum ponatur alterius multipla
esse ut e Z 1
B fr Hinc ex aequales rel3, fies.
1
sequers iva (3) 1ol + nola + se Y + 7H 2, 0. Valor ergo
atterius incognitae, quae scilicet explicata non est, habetur
ne et fiet v hat sV  91 C 1 A
a
+ n2
13 + t L quatia  a doctrina Transfor
ini n atio aliqum tta sit: Nimirum
es +5
si qua data
St aequadio ipcognitae ejus ita rexplicandae, methodo praescripta in
schediasmate de Nequationibus Numericis assectis ad puras reducendis,
et inde fiat Nequatio in qua temminus st.
 Te 9 Terminus
Homogeneus vel absit, vel sit negatio numeri quadrati Ut absat
uadratis
esectu nonnipit si se ( Nam si negatio sit numeri potest tolli
cacium
fingamus epim essemd l  =h expeccemus V  _ e + h f
(5) 
+230 et 22
 N ii + ZG
32) Quod si ergo poinns
13 Hoprgeneus ex prodacta
et
cum humen
N. 4. l. n.
sint dati,
 ar
bitrie sum
possit 1
d atro cujuquam termini propositae,
mationum.
es
X
tunc ex aeq. it fiet sequens
3)
130Z+0
fuisse N H0. quod fanite efsici potust, atarit
Erpostuntent eurrse sellas
verte