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# Title: Leibniz-Handschriften zur Mathematik LH 35, 4, 4
# Folio 2v, page id 00068001:0004
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Restat ut videam pro plena poblenatis propositis solutione possitne effici pot
tam quadrato. quadratus, quam quadratus simul sint dati, quod tiea, si
aequationem hanc V- itq qu +e v  1+ 2l9 - 292 - l
rendemus tatem, ut V pro artituo simita, 4 inveniti.
1+ . l + 1ol + 49.
queat: Fiet + f 2 lV + 1ol v + 4qV p + + 2lq - 25 - 1. poue
V
 et restabet
7 219 - 29. Pone Z5 47.
poterunt omnia dividi per g. et fiet aequatio:
dato
1
1 2l - 29. Esto jam
+ 210
ex  ilem ) ex +) e Namcrg datus, Ent es exempl causa d.
fiet v Xl. per priorem positionem, eoque valore in posteriore substituto, fiet:
(4) X (+) C B d. fier e p X (4) d.  et v
jam vBZ - β., et seu Z H 2 10 Erit 2
hac methado.
Sed hinc jam video rem absolute efficimon
XC
X XI
XC+)d
X()d + 2010I
datus, nisis quia V jam datur Ergo in aequatione initio reperta pen seram
valorem ipsius B. fiet: + F 2xB + 10l X + 4qXl + + 219 X +
s
sive + f2Xt rol x F aqXlp, + F atq L +X ()d
290 
-29.. (4V. 2
f sie. 2qX (+) .9d + + 2lgX (F) +f 21q 5 L+ 2XV + 10V a + CXH)
sive 4 s- 1F . IX q. + O p Ext r 10lX + l X (4) P
5) tra.
1.
(F)4 d
- 2X (+ ) ad
- 2x (4) 2d a erit g+8H S+ DI+ 8.
sunt autem   X et d;  et l. ac per consequens etiam D et C. numeri
dati, quare si 4Dl +. O evenit esse num erum quadratum, tunc effici
potest ut utam quadratus quam quadrato quadratus sunt dati Illud
vero manifestum est, quia in aequatione 8. neque X. neque d. ad quadratum
ascendunt, dinc semper effici posse, ut alterutra earum sit data, item ut datam
ita ut summa eorum sit potestas quaelibet, et summa quadratorum ab
tam summa quadratorum quam summa quadab, udom sit potestas gradu
Videndum tamen superest
habeant rationem inter se. Hinc ettiae posse mani ex hoc uno problemate (16) si ponatur
aTies numeros invenire
ipsis quadrato quadratus. Illud tantum videndum ex an effici queat ut
dati.
tonatur v H Z. (3 fier: + + 21Z + f 2l ( + 10l X - 1ol. ( + 497 + 4487 4 l9 39.  (a) summ hameroni X. Quadratus,  primam conditinem.
Pone ++ 2l  - 10lB p 17 fiet (1
+ +. 1Z  + 101Z + 19Z + 491
10
1+ 2V + 10) + 4 47 + 41
)
4... .
sit
O