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# Title: [Francisci Vietae Opera Mathematica] Francisci Vietæ Opera Mathematica (shelfmark Leibn. Marg. 101)
# Folio 87, page id 845634801:0103
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=845634801&page=103
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# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 70 lines, status machine
# Lines: 70 recognised, mean confidence 0.81
# Machine transcription. Not an edition. Errors are expected: about 8% character error rate on Latin and French lines, higher on German.
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# After the first blank line: the recognised lines in reading order, one per line.

nire
rei
UI
ex
al
ino.
12
B in
ma
1X.
UIM
UM.
nuC
23
B0r
et
eun
in
10c
ECHII
E1
AE OV A F +O N V Mt.
EtsFC. == 729 N. aequatur 18954. Phma major incer extremas est V 729, id est 27. aggregaruIt
Fundae  quaria i est 26. 8 fit 2 N. secunda ex eadem serie.
H E O R E M A II
AAO_ ATTKII S.
F A cubus =B quadr. in R, aquetur B quad. in D: LuI Gat COn-
tinue proportionales geatum prima minor inter extremas est B, disteren-
Dala prima minore inter extremas, ex differentia secundae ex quartae in se-
rie quaruor continue proportionalium; invenire secundam.
Sic dara B prima minor inter extremas, differentia vero secunda eC GuarEX D. OpOr-
cerinvenire concinue proportionales. Sir le cunda A quarra iDIEUE CrIF A + D, (0ldo 2y-
cem sub guadraco primae de quarta, aequatur cubus e lecunda; quare A cubus aequabicuFB
quad. in A, + B quad. in D, e per ancichetim, A cubus- B quad. In A, xquabitHEB
quad. in D, uc est ordinacum.
Si 1 C. = 64 N aequetur 960. sune quatuor continue proportionales, quarum prima est 64.
id est 3. disserent vero fahia  quarca 3C C id est 15. e fit 1 N. secunda ex serie proporcionalium
T H F O R E M A III.
A N ∞ YB O A O Y.
TB quad. in A = A CubO, EGUCTE B quac. in D: SUINE QLATIOF CONEMUC
proportionales, quarum prima major incer extremas est B. ditterentia
vero secundx _ quartx D, e Ac A lccunda.
Ex LCcCTICO:
Data prima majore inter extremas, es differentia secunda ex quartae in serie
quatuor continue proportionalium in venire secundam.
Sic data B prima maior inter exrremas, differentia vero se cundae _ GuarFa D. O pOrECE
invemre lecundam Sic secunda A, quarca ixicur erir A - D, Colido aurem sub quadeato
DEIIX _E qUArEA, EquaTUT CUbUS C Secunda: quare A cubus aequabieur B quad. in A, -
B quad. in D de per ancirhetin, B quad. in d - A cubo, aequabicur B quad. IN D.
St729N. = 1 C aquentur 7 296. fan qualuor concinue proportionales quarum prima est a 729.
differentia vero secundae e quareae S id est 10. e fic L N. secunda ex serre proporrionalium 27. 18 12. 8.
Pocest antem ea febaum  esse, ut in duplici quaruor commue proportionalium serie quae se-
Guitur.
1
ITT. IV.
N 59319, 195. V 24375 125.
59319. 36. N 624. 8.
Stante eadem prima majore inter extremas V 59319. e eade asperentia secundae ex quarta 30.
secunda hic fic 78. illIc 195. Sic stance eadem prima 36. eademque differentia secundae ex tertia 5. pro-
36. 6. +
36. 30. 25.
 F V
tia secundae d Guaca D, X HE A secunda.
Ex ZCreHICO:
Penitur duplen ser tes tr proporcionalium.
Consticuriva aequationum cubicarum in quibus affectiones sunt
sub quaarato.
Lnes, iildem Fercretmus constane, quibus in affectionibus siblatere,
x aurem cubica aFFectiOHDUS IHD GuACTAL BOVOILIHEIE EGuatO-
elt