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# Title: [Francisci Vietae Opera Mathematica] Francisci Vietæ Opera Mathematica (shelfmark Leibn. Marg. 101)
# Folio 363, page id 845634801:0369
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=845634801&page=369
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# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 59 lines, status machine
# Lines: 59 recognised, mean confidence 0.90
# Machine transcription. Not an edition. Errors are expected: about 8% character error rate on Latin and French lines, higher on German.
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# After the first blank line: the recognised lines in reading order, one per line.

AANCHI
BG1
ndit
ILESPONSORVM. LFBER VIII.
liuspranlibic per F, cum
sc angulus Z FB rectuS.
de acta Cemidiametro
AF hecerianoulum ALB
crurunt aequalium AF.
AB. Ouomal aulem
angulus FZ B est sepri
maparsrecti, ideocon-
Airuro angulo recto
ZFB parrium septeM.
carumdé anouIas LL B
IuSF B A leH AFB PaF-
Sulus vero LAB dud-
cumterencis Perpena-
cularis CF abscindens
BI. Friangula igitur
AEI, BE Ixqualium sune lacerum de anoulorum, habencia angulum ad E rectum, et
anoulum IA E anoulo IB E xqualem. Dehnicus est aurem angulus FOTUS PB Z parrium
(ex qualium rectus est seprem. AnguluS VEEOT A F seu LB F earumdem duarum. Cum
itaque ab anoulo FBZ auFerentur parres dux ad anoulnm IBF. Fric anguluS FBL quatHIOE
carumdem parrium qualium etiam sex consticurus est angulus IF. B. Ouare angulus FIB
eric carumdem quoque quatuor partium ur compleantur duo recti, quos eres anguli
crianguli lFB adaequenc. F.sigicureciangulum LF B ae qualium quoque crurum LF, F.B, cum
Cinr anguli FBI; FIB ~qualC5.
Cadat porro in AB perpendicularis FX. Fistisitur FB media proporrionalis inter ZB.
id est AB duplam, e ZB differentiam incer AB ec AX. Ouare quadratum ex FB eguale
eAt duplo quadrato ex AB, minus eo quod Acbis sub AB, AX. Ft consequencer solidum
quodAcsub AL _ quadrATO ex FB, aequabitur Colido duplo sub AI e quadratO ex AB, mi-
nus eo quodErbis sub AI, AB, RX AEverO CAUF AI ad AE, ita AF seu AB ad AX Duplum
ioicur pignum sub AI, AX aequale est quadraro ex AB. Iraque Colidum quod Hc sub A I 8
quadrato ex FB aeguabitur lolido duplo sub A L ex quadraro ex AB, minus cnbO ex AB.
Estaurem AId. Herentia inter AB X IF, Seu FB. Ouare Colidum quod Ac sub AB de qua-
draEO Ex FB, minus cubO ex FB, aequale est cubo ex AB, minus Colido duplo lub FB e
quadrato ex AB. Ouod erar octendendum:
Sie ABF. FB TN. +O = rC, aequaturZ = 2N.
Sit Z. B 200, 000, 000, su E B lacus tessere decasoni circulo insoripsi 44. 504, 187, cujus Z B
est diameter.
PROT ASIS V. THEOR E M A.
Si angulus acurus crianguli rectanguli fuerit dupla sepeima pars recti:
cubus ebale, minus solido sub hyporenusa dimidia e iplius balis quadr2-
co, aequabitur duplo Colido sub balc et hyporenulae dimidix quadrato,
minus ipsius hypocenula dimidixe cubo.
Siceriangulum ZMB, habens angulum ad Mrectum; ad Z vero aequalem duabusse-
Primis recti, de secerur ZB bitariam in A.
Dicocubum ex ZM, minus Colido sub A B ec quadraco ex Z. M, aequari Co lido duplo
CubZM ex quadraco ex AB, minus cubo ex AB.
Centroenim A, incerrallo AB seu AZ describatur circulus. Circumferentia igirur il-
lius cransibie per MI, cum sic angulus Z M B rectus. Secetur aurem bitariam circumte-
rentia
eric pars una, e angu
tium carumdem Pex. an-
TUIM. SCCeEUE auTeM
AB bitariam in F. lca
que in A B cadac e cir-
AF in L. Z Connectacur