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# Title: [Francisci Vietae Opera Mathematica] Francisci Vietæ Opera Mathematica (shelfmark Leibn. Marg. 101)
# Folio 139, page id 845634801:0145
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A, OY A Y Z O N Y et.
(i aequalia per aequalia multiplicentur vel divictantur, Facta vel orta esse
aequalia.
Ita enim fecisse ilomaeriam in summa nihil aliud est, quam propolitx
equaliratis porestatem, e adfectionum d comparationis HOMOSCHCA PEF
cundem cerminummulciplicasse, auc divisisse, mulciplicationis autem P2-
ratior ulus est quam divitionis.
Proponamr siquidem, A cubus- Bcoidoma; aquari Z Colido. Oporrerjam equalica-
tem a Fcactionibus quibus laborac, liberare. D in A esto F planum, ergo Ertanum erit A.
Ouare Extmicabus + Bcodoin Bine vianum, aequabicur Z Colido. Omnia per D cubum duCRNEUE,
ergo E plani cnbus  B Colido in D in E. planum, aquabicur Z Colido in D cubum.
C + 3. N, aequetur 2 25. IBItUT NaE iouOIpiaNZ C = 6N, aequabitur 1800. E radix pra
Paratae ad radicem propositae se habet ut 2 ad L. Itaque quum sit hic 12, illic erit 6.
EFGPEOxOnatuE A cubus +Boldoima aquari Z mno viano. Ipsilnet vestigiis E plani Cu-
bus- = B Colido in D in P. planum, aquabitur Z. plano. plano in D quadratum.
2C + 2 N, aquetur 2 53. Igitur nar ioouorplaer, rC. = 6 N, ae quabicur 1060. es quum sis hic
XN 10, illicerit 5.
Echipcoponacur Acubus Formonios:, aequari Z. Solido. sildem velligiis E planiea-
bus = B plano in E. plani quad, aequabitur Z Colido in D cubum.
2C + = 9, aequetur 270. Ieitur nar ioouorpiar, LC = 39, aequabieur 2160. ex quum sit hI6
2N X2, illic erit 6.
ECLIPTOPONATUE A cubuS FBvimo ina quas: Xquari Z mnopluno: Tisdem vestixiis F plani cu-
bus. F B plano in F plani quad., aequabirur Z plano. plano in D quadracum.
1C. + 3 9, aquetur 3 25. Tgitur nar ioquoiplar, 1C + 3 9, aequabieur 1300. ex quum sit hib
2N 10, illic erit 5
Sed proxonatur A cubus FBcolisoma, aequari Zo dido. D in Hplanum in A, eAtos;
Plano- planUI, exg Eplnotanum exit A.
Ouare F. plano plani cubus Fvinarrmo mommindconsommestinorum xequabicur Zoluo coldo.
Omnia per D cubum in EI plano. plano. planum ducancur, erso F. plano plani cubus. +
B Colido in D in HI plano. planum in F plauo. planum, aequabirur Z plano. Solido in D cu-
bum in EI plano- planum.
2C. + 2= N, aquetur = 2. Tgitur nar ioquoplar L C + ZIT2N, aequabitur 525312. ex radix prae
Paracae ad radicem proposita se habet ue 48 ad 1. Ieaque quum sit hic L N 72, illib erit 3..
Poterit aurem ad eandem fractionem quoque reduci.
TC + == N, aequetur ? 2. Vnde per opus ioouorplaer, Y C + 13Z N, aequabitur 8208. e radix prae
Paratae ad radicem proposita, se habet uF 12 ad I. Teaque quum sit hic L N 18; illic erit Z. Ouod est
Praeparatam primum aequalitarem divisisse ioouoipinco 5 per 4.
2C. + 2IIZN, aguecur 5253 12. isicur isomaerica divisione, 1C + 2  d 2 N, aequabieur 3 25 3 12
id est 1 C + 132 W, aquabitur 3208, es quum si illic 1 N 72, hiccrie 18. quia radixisomarica divi-
sionis est 4
Opus ilomaericae divitionis ica evidens HiE.
ProponatuE E plani- cubus = C in D in E plani. quad. f B plano in D quad. in F pla
num, _q Z Col. in D cub. E plum esto A. isicur D in A exic F planum. Ouare D cubus in
acubum L. C in D in D quad. in A quad. + B plano in D quad. in D in A, aequabitur L
olido in D cubum. Omnia atsidaneur per D cubum, ergo A cubus. + C in A quad.  + B
12 9 - + 8N, aequetur 2280. ex sit L N 10. Dividaneur omnia ioouoipInc 5 per 2. 8 con
orua ab ea radice scansilia, ergo 1 C - 2 = Q -1. B. N, aequabicur =2 d e fit L N. , id est 1C
diempocestacibus non adsectis + C, aquetur 1728. 8 fi LN12. 1 C aquabitur  2 . 33 fiet 1N
6Q. + 2N, aequabitur 285. 8 fiet LH 5
F. Id est 2C, aequabieur 8. e siet LN 2.
Est aucem in analysibus opus illud magni incerdum compendii.
A P Y