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# Title: Leibniz-Handschriften zur Mathematik LH 35, 3 B 9
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usum autem sectionis potestatum gelier
 patere dubitari non potest, pim enim notavi multa compendia calculi et
pariterine constructionum inde oriri, nec contemnendam hanc videri debere sive Arithmeticae sive
Analyseos accessionem, in qua multa fortasse latent, quae dies deteget. Natura enim rerum
velut ludibunda se non nisi nomento et per partes ostendit, et prensantes inoxina fuga deserit. A
suffocerit interea usum exponere, quem habet ad resolvendas consentientes omnium
graduum aequationes.
Et quanvis alia rem via invenerim, ex ipsis scilicet radicibus
irrationalibus aequationes excitando, quae ad sectionem potestatum observandam occasionem
dedere, nunc tamen, re inventa, per sectionem potestatum, facilior, et ni fallor elegantior
ipsirem radium irrationalim in quas hujusmodi aequationes resolvuntur demonstratio habetur.
sit ergo aequatio surdesolida data
conferatur huic 
Z e
-5p
5pZ
+ Y
N - emu Z3 - end Z + m 1 ponendo Z B n = n
Ubi p. et Y. sunt quantitates datae, m et n quaesitae
Fiet mn B P.
Porro Ypy m - n
et ileo Y P et nEr 
sive re m - P. et tollendo fractionem
habebimus aequationem, mo - Y M r p. et  m F, Y + s X + ps
et m p. 10
+5
Jan cun sit -nE p - n + Y. ideo pro m substituto etus valore invento, fiet
=n . = ∞ X, pF +r. eve c unde extahendo radicem, erit
=n r 16 +Y = SX + p
et Z B m n n O = + Y + p + O= - s2.  p
Idemque in retiquis altiorum graduum hujus exemplo praestare facile est.
Geometriam
ipsas esse quarum extractionem docuit Schotenius in appendice Commenturiorum adCartesis
siquae sunt
Unde radices ejusmodi aequationum rationales, statim invenientur, sine methodo vietae, sine
tentatione divisionum per divisores termini, ultimi
demto culico
Fateor tamen nullum esse gradum, Cin quo aequationes omnes ad format cpri reduci possiat.
Et comperi radices generales quae ad resolutionem totius gradus quinti serviant, ex quinque aut
nov
minimum quatuor irrationalium aggregato constare. Quarum formam cuperto, et multa s
aequationes earum ope resolvere possum, et  spero generalem reddere methodum, et efficere
in surdesolidis, quod in cubicis jam habemus.
obiter adjicio, (in exemplum aliarum regularum) formam aquationis quadrato cubicae valde generalis, quae ose
radicum cubicarum resolvi potest, quod magni potestusus esse: saepe enim cum prublemata sunt d’eprimibilia
id est ope irrationalium sui grat
calculum ita moderari licet, ut ad formae ejus modi deprimittes prodeant. Formula hac est:
X 4PX +9X + _ YX  X + Ps X -
Mi veter qua sui stua ee ea aemum. P. i L. pe c. el s pe g. rdi  cam ce ti reiti s