# Leibniz Legible — https://leibnizlegible.com
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# Title: [Francisci Vietae Opera Mathematica] Francisci Vietæ Opera Mathematica (shelfmark Leibn. Marg. 101)
# Folio 346, page id 845634801:0352
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=845634801&page=352
# Source image: https://digitale-sammlungen.gwlb.de/content/845634801/jpgs/default/00000352.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 63 lines, status machine
# Lines: 63 recognised, mean confidence 0.85
# 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.

A P OL L O NTVS G A L LY 5.
Adue, cum secaBimr A C in I, uE ST AI ad LC. SICUE L. A AdF C, id est SCUES adR, _C COn
RECICCuT EI, Sectuserir bitariam anguluS AFC. IEAgUE LUMM IM E. A CUIMCTEFeCtA FK ip
E. C aequalis, ec connecterur CK, lecabitur C K bitariam d ad angulosrectos a recta L.t
Secetin L, e connectatur IR. ErgoII, LC crune a GuICS. Ip(I auTeM PG AGATUE Pa
railela kM, sCCanS AB in M. Ouoniam data CUNELAEELL AB, AC, qua secanCUE data F2
tionC SBniS P, L, erBOdANEUE AF, EBSCUFG e AL, LC seu LI. Ec quoniam parallelae sun
FO, MK, quarum data eBratio, cum se habCAF FC Zd MLK, HICUEAC ad AK, id estur dio
ferencia inter S et O ad difterentiam inter S et R, data aliCet est FC, er8o dabitur ML
Ona ratione dabitur eriam AM, CUM SIELICUE AC ad AIE, iid AF data ad AMI. OuadcaB
BUILSICAE AMKC, auE (R Coenne in eandem rectam MK, IEC) crianguli, data erunc hu
Suta aleta, una cum angulo MAC. Ergo data ube erir AK darum angulum M AC
LECaHS; algHC adcDLA 6D dacam rarionem P. A dl LL.
Componetur aurem (IC.
SecetuE A B in F, VE SE AB
adFB, SICHES ad O _ AC sC
cerurint uESE ALad IC, A
CurS ad R. RaESOS AF SecC
CUEINML, VEBE AF ad AMI,
Sicur disferentia inter S et 
ad differentiam interS XR
qua eriam in cariODCBIEF
ad Z. Fx cenero M incerralle
aequali ipsi Z describacur cir
culus, quem cenero l’inter.
vallo IC de(CriptIs sCceF ve
conringarin L, e connecta
THCAK, quae produCaTUEII
E, VESIEAE ad RF, GICUES aC
R. Ajo F punctum esse qua
Sirum, a quo cum ducentus
EB, FCCTITAF ad BF qui
dem SCuFSad O, ad CFvC
SicurS ad R. Ipl enim MH
agneur parallela FG (CCaBS
AE in C, d cOnnectanEUI
BG, CK, EP, EI, iplaqUC EL
secet BO in HI, ec ipla FISC
CeF CR in L. Duoniam isi
tur constructae lunc paralle
IX MK, FB, Cric AH ad AG, _ MR Ad L GHCHEAM ad AF. id est Sicuc difterencia incet
et R ad difterentiam incer S X O. Oua in ratione Facta est MK, id est  ad FB. Suncia
FB, FC aequales, ut eriam CI, IK sumpra sunExquales. FF caproprer rriansula SuWE 
CTUITADFG HIC. Ecquoniam AE ad HE Facta c A, licur AI ad 1C, id eAt. SicuE S ad R, cont
quencer eric AF. ad AK, sicur S ad differentiam inter S et R. Sed AC ad AK, est Acue disla
rencia incer Set O ad diferenciam inter Set R. FrBO AF. ad AC. cA, sicuc S ad diftecenetam
incer S et O. Er componendo AE ad CF. est, sicur S ad Q, id est, sicur AF ad FB. 12 28aC
FL
CN ip( EF parallela, secanS AB in HI. FriL IgITUE AE Ad GF, (ICUE AFadt FN. FrBOFL
ccune xequales, d consequenter aequales BLL, LIC. Prianguli icaq; x quierui BFC. secta ct
balis bitariam in FL. Er80 ad angulos rectos. Iude criangula rectangula BHIF, GFIF aequa
lium sunc lacerum ee angulorum. Ac deniqi criangula rectangula BHIF, CHE aqualu
quogi lacerum et angulorum, ac proinde hypocenula EB hyporenulae L. C. xqualis. L 
Tur AE ad CE, sicur S ad O. A. que ducatur HO ip ( E. L parallela. FriL igituE AF. ad kL
cur Al ad 1O. Sedest licurALad 1C. Duare erune 1C., 10 aequales, de consequenter ae quale
HiL, L. C. Trianguli iraque aequicruri HIC seca est balis KC bitariam in L. F. 1 30 ad an 8
losrectos. Undecriangula rectangula C L. L, H L. laequalium sunc laterum ee angula
rum. Ac denique criangula rectangula C. L. C, H LF, ec proinde hyporenuta C F hypotu
FRAN.
4C
di
S:
XOH