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# Title: Leibniz-Handschriften zur Mathematik LH 35, 3 B 9
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dul. 1675
LATE RUM
DEBIs 2CTIONI E2
Radices irrationales nova, quibus ad resolvendas aequationes utor, primo statim
aspectu mihi dedere tabulam aequationum quarundam, omnium graduum quae
resolvi possunt per has ipsas irrationales sui gradus. Tabula autem haec est continuabilis in intinition;
2
7
Z
76
e
etcus
A
1 4
1 + p (+3P
N + r (+p L
N. + Y (+) op Z - 5 
1) + qu (4)6 p Z+ - 9p y2
1. 3. 5. 7.. Respondent ergo eotum constrctro, constructioni Tuangul;
1.4. 9. 16
1. 5. 14. 30
1. 6. 20.50
N = X 1f7 p Z - 14p 73 (4Xpd Z
N + Y (48 p Z6 - 20p Z+ (4 16p Z
eK
ete
etc
ete a
2
e -97Z
A er 19 p27. 27pe Z (FBpPZ
Hanc Tabulam initio velut v particularem concerderaverm neglereram, sed
Lattirum
postea re altentius inspecta comperi generalem in ea contineri sectionem Potestatam
Laterum
latere altrens
Sectionem autem Poteotatum appello, expressionem potestatis a Toto, per sotestates
à tata in serieres, aice dente potesate aequate detig rone
partim a toto partim sexis a partibus Latens qua de re non nisi duo habuimus Theoremata, alterum
Euclidis pro Quadrato, alterum sive scixionis Ferrei sive quisquis is est qui regulas invenit
a Cardano sublicatas, pro Cubo.
ACpF AB, (BCB - 2L 11BC
alicubi
Sit linea AB. secta ulivis in C. demonstravit Euclides quadratum ab AB aequari
quadrato ab AC, + quad A CB, +bis rectanus. ACB.
alterutra
alitume
Et idem demonstravit,
quad ratum ab AC, acorutu partium, aequari, quadat ab AB, + quad. a CB. - rectanus ABC
AG BAB-BCB Inventor Regularum Cardani demonstravit cubum ab AB aequari cubo ab AC, + cub. a CB.
A B +B =  cb
ter Rectanu sol
+3 Rectangs. solide ACB A, sive Ccomprehensex sub rectis, AC, CB, B A: et Cubum ab AC aequari Cubo ab AB,
= cub. a CB, - 3 Rectang. solid. ACB A.
Haec Tabula, continuata, pro omnibus aliis potestatibus altioribus similia Theoremata concinnare docet
Nimirum. Surdesolidum ab AC aequatur surdesolid. ab AB, = surdes. a CB, - G Rectanu ACBA in tH C, E AD
quod concidit aequationi Z _ +r - 5p Z3 - 5 pZ, si ponamus Z AC.
a  Daiean D al+ FI soc
modo
si penamus Z ( AC.
IBAC+ L+ ABC
pe= ABC
et 4Y 6I AB. _ CB
est enim - EPZ = sPZ A SPZ in Z + p soiee  est autem pZ e) Rectanus solid. A CB
fitque
E ⊓. + (5) AB. = 5 G G ACBA in ( AC
B
FS ABC
Quod verum esse calculus docebit
sive in literis, sive in
numeris
FCC 1676. Numeu Tabule sic progrediuntur oligu descnsu.
Arithimetici Pascaliani, moda prima series, cujus caecerae
sunt summae aut summarum summae, non ut allic sit
1. 2. 3. 4. sed 1. 3. 5.7 Unde facile hujus Tabulae
uneri ex allipsuo separita catento Mvemur possam si
illi dpicantur
petetatis pue. a qua
tionis purae.
Latus voco radicem
Sed ut seneranter
3H D ACBA
A A ACp