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# Title: [Francisci Vietae Opera Mathematica] Francisci Vietæ Opera Mathematica (shelfmark Leibn. Marg. 101)
# Folio 61, page id 845634801:0077
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# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 77 lines, status machine
# Lines: 77 recognised, mean confidence 0.83
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# After the first blank line: the recognised lines in reading order, one per line.

dE
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ate
FBE R T F R F FY3.
lacerum in rectangulum sub laceribus, uc adparer ex genehi cubi d difterentia lacerum.
Duare D in A planum, = B cubo, aequabicur B in A planum 3. Ua L GWasCatC OtOL-
naca; scubu: aequabitur A plano. Daro aurem rectangulo sub lateribus, e differentia eo-
rumdem, dancurlacera.
Daca igitur differentia extremarum, ex differentia mediarum in Perie quaruor continue
proporrionalium, daneur continue proas
Enimveroelt,
diis velesltemis.
Sit D 7. B2. A pranam fit 8 rectangulum sub extremis X es 8 vel mediis 2 s 4
ex serie continue proporcionalium.
1.
TI.
III.
ITFI.
Ouodh ex differentia extremarum, de rectangulo inquireretur de differeneia media-
rum, uchinnocelcac a planum, esse Fplanum. Ac de B esser quaestio, Cc illa A. Ita prO-
cedereraqualitas. n xquobitur F plano. Ordinara vero sequalitare; A cubuS, L P
planorer in A, aequatur F plano in D.
Id est
Cubus differentiae mediarum, plus triplo solido a rectanculo sub lateribus in
differentiam mediarum, aequatur solido à rectanculo sub lateribus in differentiam
extremarum
Ouod adnorasse tuir operxpretium.
ZE TE Z TCV H XVI.
Pursus quoque, Dato adOTESATO EXTTeMaruM _ adlBrCgatO MCdIARUM IN
serie quatIIOF COntinue proportionalium, InVeHITC CONFIHUC PFOPORtO-
nalCS.
Ex istud esse, Daco aderegato laterum et ad gregato cuborum, invenire latera. Fvi-
dens Het perprocessum.
Sic igitur data Z Tumma extremarum, ex C summa mediarum in serie quacuor con-
tinue provortionalium. Oporrer invenire concinue proportionales. Rectanoulum Lub
mediis vel exrremis, eso A planum. Fc vero media majoris cubus, aequatur (olido ab exrre-
mamajore in rectangulum sub exiremis. Eemediaminoriscubus, Colido ab extrema mi-
nore in rectanoulum (ub exeremis. Ouare Z. in A planum aeguabieur adoregato cuborum
a mediis. Si aurem a cubo adgregati lacerum subducarur adorecatum cuborum, quod re-
linguirur xquale est solido criplo ex summa larerum in rectangulum sub laceribus, ucad-
parer ex geneli cubi a duobus laceribus.
Duare C cubus, = Z in Aplanum, xequabicur C in A planum 3. Oua xqualiTaTe OF.
dinaca; 5 cabu xequabitur A plano.
Daro aucem rectanoulo sublaceribus et 2oprepito laterum, dantur latera.
Vacoisituradoregato extremarum de adgresato mediarum in serie quatuor continue
proporcionalium, inveniuntur proporrionales.
mediarum; ita quadratum adgrecati mediarum ad rectanculum sub mediis vel
Ouodhexaderesato extrematu L rectangulo, inquireretur de adgregato media-
cum; uc hinnorelcerer A planuim ese Bplanum, ac de C esfer quaestio, sirilla A. ITa PrO
cederer aequaliras. A elbus Bplanacerin A, xquacur Bplano in L.
+ differentia extremarum, minus crio uifserentia mealarum ad aisseren–
tiam mediarum, ita quadratum differentiae mediarum ad rectanculum sub me-
Lnimrero eA.
Et aderegatum extrematu plus Mpioaata mediarum ad aderecatum
extremis
Sit 2,9. 66. A planam LN. Fit 8 rectaneulum sub extremis 1 es 8, vel mediis 2 8 4.
Id est
Cubus adgrezati mediarun, mssourside eddem adereeato in rectan.
sulum