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# Title: [Ps. 1] (shelfmarks Leibn. Marg. 178, Stück 1; Leibn. Marg. 178)
# Folio 304, page id 175905688X:0326
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304
FR A NCLSCZ a SCHOOTEN
quam diritorem 2, e quidem Aquationem proxolicam v3 8 0
XX - F 8 X = 24 ∞ 0 diridi posse per x = 2 0, e prodire A:gug-
tionem impossibilem XX f 2 X + 12 ∞ 0, qux per x L rel - ai-
quo numero, ultimum cerminum diridence, ulterius dividine.
quic: sequitur radicem qua sitam fore 2, neque ullam aliam extar
re, cum religuae duae in hac formula semper lintimaginarix.
Nec alicer Ht, SIFuerIE X 3 ∞ X -8x -24, qux est AEquatio u-
nam habensradicem Fallam, nempe 2, _ duasimaginarias: cum
producatur ex multiplicatione Equationis impobilis X X = L 2 H
 T2∞ 0 per x = 2 ∞ 0. EIbi obserrandum, quod, licet D. des
Cartes ejulinodi Aquationis formulam inter Cubicas non repo-
suerit, sed cantum eas, in quibus bini polteriorestermini per L
aut per. L e-junctisunt, ipla tamen nihilominus eodem modo,
quo praecedens, relolvi, atque radix ejus exprimi ponic. quod e
de aequatione quadrata ZZ ∞ L aZ -- bb 0 lupra monuimus.
FIinC ( FuCrIE X 3∞ = 3X = 1O, TCUX B OXX L ZX L 10∞O)
qua per x + aliquo numero ultimum terminum dividente dividi
nequie: sequitur radicem ejus esse irrationalem, cam que juxta
primam Cardani regulam, pasin. 93 delcriptam, sic exprimi
x∞ = V C. Y 26 - 5 -L Y C. Y 26= 5. REMPEUTaLIS FAN-
cum signis. + X - utriu(que parcis. Idem incellige de Aquatio.
nibus X 3∞ - 8, auL X 3∞ = 7O, quarum radices TUINEX ∞ - 2,
_ X ∞ - V C. 1O.
Eodem modo operandum erit in Aquatione primi casuS Secun-
dae Formula, puta x 3 ∞ L 8 x F 24, ubi = g q est majus quam
2P3. Duoniam enim dividi nequit per x - p ∞ 0, qui divilor ad
quanticatem radicis proxime accedic, non opus est ut ulterius pro.
Grediamur, siquidem bina reliqua radices hujus casus semper
lunc imaginaria. Ouare radix quaelita eric irrationalis, quae juxta
secundam Cardani regulam, pag. 93 exhibitam, sIC exprimetur:
X ∞ V C. 12 ] V +25 27 -f V C. 12 - V 125.. Adeoutdi-
catur compolita ex duabus lineis, quarum una est prima dua-
rum mediarum proportionalium inter unitatem d lineam 12
L V 12523. ec altera prima duarum mediarum proxortiona.
lium incer unitatem _e lineam 12 = V 125,-. F quibus perspi-
cua Funt illa, qua habentur pag. 92 895. Nocandum vero, me
pouisse quidem accipere a pro r, ica ur p tucura Tuisset 8, e 424: