# Leibniz Legible — https://leibnizlegible.com
# Page: https://leibnizlegible.com/page/845634801:0295
# Permalink to this reading: https://leibnizlegible.com/page/845634801:0295?run=74
# Title: [Francisci Vietae Opera Mathematica] Francisci Vietæ Opera Mathematica (shelfmark Leibn. Marg. 101)
# Folio 289, page id 845634801:0295
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=845634801&page=295
# Source image: https://digitale-sammlungen.gwlb.de/content/845634801/jpgs/default/00000295.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 56 lines, status machine
# Lines: 56 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.

Bu5IB, 
0AGII
1e
la
HE. L
CuI
11
AD ANGVZARES SECTEONES.
N R OR EM A IIL
Si fuerine duo eriangula rectangula, quorum angulus acurus primi, lic
lubmulciplus ad angulum acutum secundi.
Lacera secundi, recipiune hanc similicudinem.
LErporenusa Hc similis porestati conduionarix hyporenulx primi: est au-
remporestas conditionaria, qua sequitur gradum proportionis mulcipla,
Quadracum videlicet inratione dupta, cubus in tripla, quadrato- quadra-
cum in quadrupla, quadrato. cubus in quincupla, de eo in infinitum pro-
srestu.
Ad similicudinem aurem laterum circa rectum hrporenusXe conoruen-
tium, eficitur à base d perpendiculo primi ur binomia radice, porestas
aeque alta, ex lingularia Facta homogenea dictribuuntur in duas partes (uc-
Cellire, urobique primum adtirmata, deinde negata, ee harum primae
Parei similis AE balis secundi, perpendiculum religux.
Sicincatione dupla; hyporenusa secundi sic similis quadrato hyporenu-
 prum, seu aliter agoregato quadratorum à lateribus circa rectum; balis
Cuterencix; perpendiculum duplo sub praedictis laceribus rectansulo.
In ratione cripla; lyporenula secundi fic limilis cubo hypotenulx pri-
mi; balis cubobasis primi, minus solido ter lub quadrato perpendiculi pri-
niide bale ejusdem, perpendiculum limile Colido ter sub perpendiculopri-
i e quadraco balis ejuldem, minus cubo perpendiculi.
In ratione quadcupla; hyporenusa secunditic similis quadrato. quadra-
hyporenux primi; balis quadraco- quadraco balis primi, minus plano-
plano sexies lub quadraco perpendiculi primi e quadrato balis ejuldem,
plus quadrato. quadraco perpendiculi; perpendiculum simile plano. p lato
lacer lut perpendiculo primi e cubo balis ejuldem, minus plano. plano
quater sub cubo perpendiculiprimi e bale cjusdem.
Irratione quincupla; hyporenusa lecundi ficlimilis quadrato cubo hy-
Pocenula prunis balis limilis quadrato. cubo balis primi, minus plano. Soli-
ao deciessub cubo perpendiculiprimi et quadrato balisejusdem, plus pla-
40. olido quinquies sub perpendiculo primi et quadrato quadrato balis
Suldem: perpendiculum plano. Colido guinquies sub quadrato. quadrato
expendiculiprimi e bale ejuldem, minus plano. (olido decies sub quadea-
perpendiculie cubo balis ejuldem, plus quadraco. cubo balis ejusdem.
Siccrianoulum rectangulum quodcunque, cujus hyporenula Z. perpendiculum B. ba-
D. Ecicisicur ex demonstracis Theoremate secundo, pro rriangulo anguli dupli, (quan-
ab. quidem duplum difterc à dimidio per ipsum dimidium.)
c29. ad D 9. = B9. ica Z 2d balin anguli dupli: e ex iildem ur Z 9. 2d D in B bis,
ita Z ad pelpendiculum dupli.
ECiterum, uE Z cub. ad D cub. minus D in B q. Cer, ic2 Z. ad ba sin criansuli anguli eri-
e. e indidem Z. cub. ad D9. in B cec, minus B cubo, ur. Z. ad perpendiculum ejuldemeri-
CL99. ad D 99. minus D q. in B9. sexies, plus B 99., ur Z ad balineriansuli anguli
Madrupli. et Z. 49. ad D cub. in B quater, minus B cubo in D quatet, uc Z ad perpendi-
culum ejusdem crianguli anguli quadcupli
em ve Z. 9C. ad D gC. minus D c. in B g. decies, plus D in B99. quinquies, ira Z ad
suum crianguli anguli quincupli. et ut Z gc. ad D 99. in B quinquies, minus D 9. in BC.
ecies, Pus DGC. Ia L. des Petpenarelum ejuldem erianguli anguli quincupli.
Cmili-