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# Title: LBr. 943 · Tschirnhaus
# Folio 16r, page id DE-611-HS-867509:0031
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antele
mimum Tisi debeo, quod tantum laborem mea causa sumsisti
et fuas circa Radices aequationum pulchras sane meditationes tam
exacte descripsisti. Statim eas intellexi, et deprehendi superesse difficul
tatem maximam quae et me olim remorata est; imo quam ea cui
Institisti via insuperabilem arbitror; quod TBi quamprimum
scribere volui, ne forte inutiliter labores. Tota res r huc redit
posito Radicem aequationis quaesitam habere partes aliquot, exempli
causa  X+y. vel X +y + Z. etc. observaveram jam olim
et fortasse primus radices irrationales altiores exemplo Cardanicarum invenir
posse. Ex. causa
 sit aequatio
fit R aequ. 5 4 + 9 + p +
s
X +5 pR + 5P R aequ. 9
4- 4+p e aliin
si posito R aequ. X+y.  invenietur enim esse
X aequ. V 4 + Y4 + p6 et y aequ. Yg -Yqu ps. Et haum aequa
tionum hoc modo progressionem in scheda quadam descriptam olim cum
2 StlubEsium
Parisios venires Tibi ostendi. Sed radice in tres quatuor aut ptures
partes secta, quod pro solutionibus aequationum plus quam lubicarum generalibus
necesse est, major est difficultas. Ita autem me jam olim Parisiis pro-
cessisse in schedis illic scriptis, in quarum nonnullis et manus tua est, reperi.
sit R. aegu. X + y +Z. et aequatio data R aegu. PR + 9R + s. 
comparanda huic: R aequ. X + 4 X3Y + 6X
4
324
Hanc posteriorem autem
2
+ 12 X y
2 comparationis gratia
varie exprimi posse constabat, nunc per  potestates, nunc per rectangula
nure ea invicem miscendo. Reperi autem rectangula universalissime et commo-
dissime propter rationem mox dicendam adhiberi adeoque
etionem
posteriorem sic resolvi: R aequ. X 4xyR - 8xyZ R+
quoniam inde comparatione recte instituta
ye
has aequationes comparabitias xy aequ.  P. X
X
e
rest 
ago
ota
et Xt  + E aqu. s+. Comparatio autem recte instituenda  est,  est
c