# Leibniz Legible — https://leibnizlegible.com
# Page: https://leibnizlegible.com/page/845634801:0074
# Permalink to this reading: https://leibnizlegible.com/page/845634801:0074?run=74
# Title: [Francisci Vietae Opera Mathematica] Francisci Vietæ Opera Mathematica (shelfmark Leibn. Marg. 101)
# Folio 58, page id 845634801:0074
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=845634801&page=74
# Source image: https://digitale-sammlungen.gwlb.de/content/845634801/jpgs/default/00000074.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 53 lines, status machine
# Lines: 53 recognised, mean confidence 0.91
# 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.

Enimvero,
E TE F LCO R V W
Duplum quadratum hypotenusa, minus quadrato aderezati laterum circa re-
Etum aequatur quadrato differentiae laterum circa rectum.
Velicer interro per ancithelin anrecedenris ordinarionis.
Sit rursus hypotenu sa 13. Summa aurem laterum circa rectum. 17. Differencia eoruidem
LN. 10 aequabicur +9. Et fit LN N 43. Iaque latera circa rectum sunt 8 = + N12 4̀, 8
8= = N 12 =, sive 12885
ZE ZE FTCV H VTI.
Inveniuntur eres proportionales linex rectae numero.
Enimvero.
Adsumptis duobus lateribus se habentibus, utnumerus ad numerum. Major
extremaproportionalium fiet similis, quadrato lateris adsumpri majoris. Mediar
rectangulo sub lateribus. Minor extrema, quadrato minoris lateris adsumpti.
Sincrationalialacera B ec D. Cum B Ratuetur prima proporrionalium, D veco
secunda, certia exir Douadcuum. Omnia pex B duCaNEUE, ee Ceries proporcionalium Aet
B quadrarum.
Sit B2. D3.
11
B in D.
Fiunt proporrionales 4. 6. 9.
D quadrarum.
ZE Y E FTCV H VTTI.
Inrenitur triangulum rectangulum numerO.
Enimmvero,
1I
Constituris tribus proportionalibus numero, hypotenusa fiet similis adgreeato
extremarum, basis differentiae, perpendiculum mediae duplae.
Nempe jam ordinarum est, perpendiculum crianguli proxorrionale esse interdiste
renriam balis e hyporenulae, e adgregatum corumdem.
Exhibentor proporsionales numero 43 6, 9. Abiis constituetur trianguli rectaneuli hypote
nusa 13; basis 5. perpendiculum 12.
A L T F E P
E E Z E YTCV M IZ.
Invenitur eriansulum rectansulum numero.
Enimvero,
adsumpris duobus lateribus rationalibus, hypotenusa fit similis aderegato
quadratorum, basis differentia eorumdem, perpendiculum duplo sub lateribus
rectangulo.
Sine duo larera B dc D. Suneigirur proporrionalia eria laFerA B, D, Dounaraum Om.
nia in B. Sunc eria proportionalia plana Bg. B in D, D9. A quibus proportionalibus
sic per once dicta, hypocenula crianguli similis B9. = D9. balis B9. == D9. Perpendicu
lum B in D 2. Ecalioqui jam ordinacum est. Ouadrarum ab aderesaco quadrarorum;
aequare quadracum a differenria quadracorum, adjunctum quadraco duplirectanguls
Tub laceribus.
Sit B2. D3. Hyporenusa fiet similis 13. basis 5. perpendiculum 12.
E Y E TTCV H Z
Dacoaderesato quadratorum à singuliseribus proporcionalibus, atquo
Ca in seric extremarum una, invenitur altera extrema.
Enimvero.
Adcrecatum illud quadratorum, multatum dodrante quadrati extremae data,
aequale est quadrato composita ex dimidio data extrema, e altera 1ota de qua
quaritur.