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# Title: [Ps. 1] (shelfmarks Leibn. Marg. 178, Stück 1; Leibn. Marg. 178)
# Folio 482, page id 175905688X:0504
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482 IOFT AHNES TTUDDENTL EPTSF. I.
nem Propositam per aliam rationalem, in qua (ve omnes sive
non omnes termini extant, ex sive unius sive plurium est di-
mensionum, penirus esse indivisibilem: Sed praeterea etiam li-
quet, aequationem Propositam nunquam fore divisibilem per
agnationem rationalem, cujus dimensionum numerus non con-
cruit cum dimensionum numero alicujus ex divisoribus ulrimi
Termini vel dicti accrecati. Ouocirca si ae quatione existente
6 dimentionum dirilores non nili x ex 5 dimensionum fuerint,
erit ea indirisibilis per aequationem 2, 3, 8 4 dimentionum; de si
dirilorestantum 2 e 4 dimensionum fuerine, eric ipla indivisi
bilis per aequationem r, 3, d5 dimensionum, aeque ita de omni-
busaliis.
Ita ut per hanc considerationem non tantum multi casus re
secari queant, quando aequatio per aliam rationalem divisibi-
lis est; sed etiam si inquirere velimus, num proposita aliqua
aequatio rationalis per aliam rationalem divisibilis sit, poterit
laexissime parvo admodum labore indivisibilitas, si ea sit IB-
divisibilis, cornosci.
Si enim, exempli causd, proponatur aequario
x5 X = 6 ab X 3- = 3O a a b X X = 24 43 b X  T20 ab + ∞O,
L 10a+
Donaturque x ∞ a, obcinebitur X 5 ∞ L a5.
 6a b ∞ 3 ∞...  6 a b
 30a a b X X ∞- ( 30 a + b
24 a3 b X ∞
0
.  24 a+
 10a + X ∞  1O45
F. 120 ab + ∞ -  F20a b4
ee HIEaGGrCGATUI L IF 45 + 120 ab+.
Cujuscilores Cmns unitate ac ip(0 25
FrCgatO) tantum sunt
La = a, TF aF, F +2O eC  TF a+ = 120 b unius scilicet
e 4 eoun. Sca ropolica aequatio, si per rationalem
unius dimensionis dirisibilis non fuerie, penitus per rarionalem
Futura sic indirilibilis. Ouoniam autem hic X cst ∞ Z = a, ad di
debeta diriloribus - F a, e = a, ad habendos ralores ipsiusX
idcirco tancummodo x  2 a x 0 pro dirisore assumi poser. Sed
pet
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