# Leibniz Legible — https://leibnizlegible.com
# Page: https://leibnizlegible.com/page/845634801:0322
# Permalink to this reading: https://leibnizlegible.com/page/845634801:0322?run=74
# Title: [Francisci Vietae Opera Mathematica] Francisci Vietæ Opera Mathematica (shelfmark Leibn. Marg. 101)
# Folio 316, page id 845634801:0322
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=845634801&page=322
# Source image: https://digitale-sammlungen.gwlb.de/content/845634801/jpgs/default/00000322.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 66 lines, status machine
# Lines: 66 recognised, mean confidence 0.88
# 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.

316
alta, ex lingulariatacta hiomogenea distribuuntur in duaspartes succellire.
uerobique primum adtirmata, deindenegata, et harumprimx parti limilis
tcbasis secundi, perpendiculum religux.
Sic in ratione duplaitrporenula le cundi Ac limilis quadrato hypotenulae
primis seu aliter adsregato quadratorum à lateribus circa rectum; balis dit
ferentia; perpendiculum duplo sub pra dictis laceribus rectanoulo.
In rarione cripla: lyporenula se cundi sirlimilis cubo hyporenulx primis
baliscubobalis primi, minus (olidorer sub quadrato perpen diculiprimic
balcejuldem; perpendiculum limile solido Ter sub perpendiculo primi et
quadrato balis ejuldem, minus cubo perpendiculi.
In ratione quadrupla; hyporenula se cundi tic similis quadeato. quadrato
hyporenula primisbalis quadraco. quadraco balisprimi minus plano. plano
Sexies sub quadrato perpendiculi primi ec quadrato balis ejusdem, plus
Quadraco. quadraro perpendiculi; perpendiculum simile plano. plano qua
ter sub perpendiculo primi e cubobalisejuldem, minus plano. plano qua
cer sub cubo perpendiculi primi e balc ejuldem.
In ratione quincuplas liyporenula secundi sir similis quadrato. cubolr.
Pocenux primis basis limilis quadrato- cubo balisprimi, minus plano. (ol.
do decies lub cubo perpendiculi primi ex quadraro balis ejusdem, pluspla
n0- solido quinquies sub perpendiculo primi ec quadrato. Quadrato balis
ejuldem; perpendiculum plano solido quinquies lub quadrato- quadrato
perpendiculi primi e basc ejuldem, minus plano:Polido decies sub quadra-
coperpendiculi ee cubo balisejuldem. plus quadrato. cubo balis ejusdem.
Frianguli re Cranguli de angulo acuro enunciandi proponatur hyporenula Z, ba(isD,
perpendiculum B. Er oporrear constiruere rriangula rectangula anguli dupli, cripli, qua
drupli, quincupli, ac.
Aderiangulum anguli dupli sic hyporenu (a similis Z. quadrato. BaLISD quadrato, mL
nus B quadraco. Perpendiculum B in D 2.
Ad eriangulum anguli eripli sc hyporenusa similis Z cubo. BalisD cubo - B quadt
in D3. Perpendiculum B in D quad. Z = B cab0.
Aderiangulum ansuli quadruxli sichyporenusa similis Z quad. - quad. Balis D quadc.
quad. = B quadr. in D quadr. 6 + B quad. quad. Perpendiculum B in D cub. 4
cubo in D 4.
Aderiangulum anguli quincux li sic hyporenula similis Z. quadr. cub o. Balis D quad 
cubo =B quad. in D cub. 10. + B quad. - quad. in D 5. Perpendiculum B in D quacta
quad. 5 - B cub. in D quad 10 + B quad. - cub0.
eroponatur crianeulum rectangulum cujus basis 20. perpendiculum 1. e angulus acurus eju sdetta
telligatur simplus
AD A DR. ROMANE PROBE EM A
Ad trianculum anguli dupli, statuerur basis 99. perpendiculum 20.
Ad triangulum anguli cripli, staruetur basis 970. perpendiculum 299.
Aderiangulum anculi quadrupli, Rtatuetur basis940r. perpenunuuM 3960.
ad triangulum anguli quincupli, scaruerur sufts 9006. perpendiculum 490Or.
Et cum angulus acutus primi erianguli deprehendetur esse
e AR. Sc+
YP.
L anoun abutus scluntat L2
terrii
quarei 22
ed  la
0
Cum aurem factorum nequie fieri suberactio, argumenium est angulum mulciplum esse docu su, C
quinei 28
que casu nihilominus excessus factorum adsienabieur lateri, es angulus subrensus intellicetur exrer
multipu.
A LFFE R.
ditue
Curus (
Cer
sec
ATer
aqu
S(C
IU
PI