# Leibniz Legible — https://leibnizlegible.com
# Page: https://leibnizlegible.com/page/845634801:0132
# Permalink to this reading: https://leibnizlegible.com/page/845634801:0132?run=74
# Title: [Francisci Vietae Opera Mathematica] Francisci Vietæ Opera Mathematica (shelfmark Leibn. Marg. 101)
# Folio 126, page id 845634801:0132
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=845634801&page=132
# Source image: https://digitale-sammlungen.gwlb.de/content/845634801/jpgs/default/00000132.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 43 lines, status machine
# Lines: 43 recognised, mean confidence 0.87
# Machine transcription. Not an edition. Errors are expected: about 8% character error rate on Latin and French lines, higher on German.
# Licence: CC BY 4.0, Leibniz Legible. Machine output: do not ingest it as verified text; keep this provenance with the text.
# Wording rule: say "the machine reads it as …", never "Leibniz wrote".
# After the first blank line: the recognised lines in reading order, one per line.

126
Suntoproporrionales 1.
220 211. 11. 1.
1o
2. 4. 8. 16, 32. 23IC- F1OC, aequatur 96040. C
sit 2N7. Et rursus 231C- 79C, aequatur 96040. 8s fit IN 14.
E E O R E M A VI.
CFB Colidum in A quad. + A quadrato. cubo, aequetur Z plano- Colido.
e rurlius B lolidum in E quad. - P quadrato- cubo, aeguetur Z plano- soli
do: lunt lex proportionales continue, quarum exeremx ducte in guadra-
tum a differentia tertiae e prima, taciunt B Colidum. Fit autem Z plano- pla-
num a B Colido plus cubo a differentia certie e prime in quadricum diste-
rentie ejuldem; vel a BIolido minus cubo a ditterentia secundae _ quarta
in quadratum dicterentix illius inter se cundam de quartam: d quum prima
intelligitur minor inter extremas, tir A cercia minus prima. E quarta minus
secunda.
I. II. III. IV. V. VT.
Sunco proportionales r.
20
4. 8. 16, 32. 297Q = 1OC, aguatur 2916.
e fit LN3. Et rur sus 2978- 19C, aquatur 2916. 8 fit 1N 6.
C A P Y F ZXT.
alia rursus aequalicarum inversarum consticuriva.
T E E O R E M a I
EFB planum in A = A cubO, XGuCTE Z Colido, _E PUKSUS E cubrs =B
plano in E, aquCtUE Z Colido: SunE treSpropOxtionales, quarum quade2-
ta juncta, conticiune B planum, Cumma aucem exrremarum ducta in me-
dix quadratum, vel altera extremarum in aggregatuM QUadrATOTUM a
duabus reliquis, Facic Z. Colidum. _ AE A alFCFUITa CxTTeMaTUIM, P vero ea
rundem lumma.
Sunco proporcionales r. 2. 4. 21 N = 1C, aequatur 20. 8 sit L N L vel 4. EF rursis
LC - 21 N, aequatur 20. 85 fit 1N5.
E H E OR F M A II.
CTB in A quad. = A cubo, aequetur Z Colido, e rurlus Bin F qurad. p L
cubo, xquetur Z. Colido: lunteres proportionales radices, quarum Cum-
ma est B, compolita aurem c duabus prunis adjecta compoliex a duabus
reliquis, dum ducitur in medix quadratum, vel altera extremarum in qua-
dracum compoliex a duabus reliquis, Facic Z. Colidum. X HE A AlFCFIIEE A
praedictarum compolicarum. P MCdiA InFEF CXECMaS.
Suneo proportionales T. 2. 4.
Q FIC, aquatur 36. 8 fit LN 2.
78 = 2C, aquatur 36. 8 sit L N 3 vel 6. Et rur sus
DE R E COCHFFTONE A OV A FF ON VH.