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# Title: [Francisci Vietae Opera Mathematica] Francisci Vietæ Opera Mathematica (shelfmark Leibn. Marg. 101)
# Folio 308, page id 845634801:0314
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AD A DR. ROMANE PROBLEMA
E OB L E M A
tionalium: data prima, ee rectaae quali lecundx mulciplici pet eLu45.
Etinus quarta mulciplici per numerum 3, 795.
Plus sexta mulciplici per numerum 95, 634.
Minus octaramulripliCi pex MICFUM L, 138, 500.
Plus decima mulciplici per numerum 7, 81I, 375.
Minus duo decima mulciplici per numerum 34, 512,075,
Plus decima quarta multiplici pernumerum 105, 306, 075.
Minus decima sexta mulciplici per nUICrum 232, 676, 280.
Plus decima octara mulciplci pernumerum 384,942, 375.
Mlinusricelima mulciplici per numerum 488, 494, 125.
Plus ricelima secunda mulciplici per numerum 483, 841, 800.
Minus ricelima quarta mulciplici per numerum 378, 658, 800.
Plusricesima sexca mulcip liCI pEFHUMETUI 236, 030, 652.
Ntinus ricelima octara mulciplici peF HUMCFUM FEZ, 679, T00.
Pluscricelima multiplici per numerum 46, 955, 700.
Minuscricelima secunda mulcipliciper numerum 14,945, 040.
Dlustricesima quarca mulciplici per numerum 3, 764, 565.
Minuscricelima Cextamulciplici per numerum 7 40, 259.
Pluscricetima octara MMLEip LICI PeF MLMeFUI HIF, 150.
Minus quadras elima multiplici pCFMUMEFUI 1Z, 300.
Plusquadrarelima lecunda mulciplici pernumerum 945.
Minusquadragelima quarta multiplici per numerum 45.
Plus quadrascha a
Invenire secundam.
cur in Problemate. Oporrer invenire eam secundam puram. Sicilla A. Sanc quadcacu
poreltas est rationis dupla, cubus eriplae, quadraro cubus quincupla. Fxdiola aureme
quadraeorum ec cuborum trequentior reperirio. Sed e porestarisemineniorisrelpecu
interiores dicuncur eradus quibus ad poreltocem Ccandirur, ur in Ia8oxicis eA deliniculu
Secundum quae quarca constimendarum concinue proporrionalium tc A porestas ca
nis criplae adplicara X gradui secundo. Sexta A porestas rarionis quinrupla adplica
Xgradui quarro. Octava A porestasrationis sepruplae a splicara X oradui lexc0. Co
rinueruris ordo ad quadeagelimat usque sextami. Ergo secunda conrinue proporuon
lium, mulcip lex per numerum 45, minus quarra mulciplici per nuerum 3, 795, P lus nt
nulque binis alternis mulciplicibus per numeros in Fheoremare expolicos aquabicur
Omnia ducamur in exanaphoram, seu gradum, qui elariori porestari proxime succect
id eA quadragelimum quaccum. Psicur homoxeneum poceltatis rarionis quadrase qui
cuptae effectum sub A limplici, e X eradu quadrage limo quarco, mulciplici per nunc
rum a5, minus homogenco lub A oradu cerrio, et X ea du quadragehimo lecunco mu
ciplici per numerum 9a5, plusminusque reliquis ordine homogeneis, ita reciproce act
etis sub eradibus binis alternis; ec mulciplicibus secundum numeros conrinue eriane
los a binario suum ducences incremencum in Problemate delignatos, aquabirur da
homogeneo quod sc sub daro larere D e Z gradu quadragelimo guarro.
488, 494, 12) (19) 7 403, 6413800 (21) -378,658,800 (23) + 236, 030,6522
217, 679, 100 (27) + 46, 955, 700 (29) = 14, 945, 040 (37) + 3, 264565 (33
DrODONTa Peric quaAEASIIITB LC L HIICAM rECtATUI CONFIHUE PTOPOE
Sic daca prima X. D vero secunda mulciplex et adtecta prostapheretice, ut expoct
Sit X1. A2 (1). 45 (1) - 3, 795 (3) + 95,634(3) = 1, 130,506 (7) + 7, 812,375
=34,512, 075 (11) -=105, 306,075(13) -232,676, 280 (15) + 384, 942, 375