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# Title: [Francisci Vietae Opera Mathematica] Francisci Vietæ Opera Mathematica (shelfmark Leibn. Marg. 101)
# Folio 274, page id 845634801:0280
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# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 57 lines, status machine
# Lines: 57 recognised, mean confidence 0.89
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non eran(eaE per Veran(eaF per Z, proximius remorius ve ip(o V a R puncto. Ouoniau
iditur inleriprae circulo OR, Z X sese secanr in R, Ideo ei quod Ac (ub ZIE, R X erIL aequa
leid quod Ar (ub OK, R R. Id aurem est ineptum cum id quod Ar (uD QR, XR (CX
quale ex hypoche ei quod sic sub R V, KX, id eAt lub P, G. F. s aurem K Z majorminoc
aurem fuir constirurio proporrionalium K O. R V, H X, H R, id eAtE, F, C, II. In qua
cumque ixirur sectione inscriprae e diamerri, an guli qui tiunc lunt xequales. Ouod ctat
demonstrandum.
Elenchus aovMozistas.
liud quam V punctum, quoniam adlumotrantire per Z. hoc enim concesso d illud con
cedinccesse est, ex contra, ex Theoremare Fuclideo xxxv. libri cerrii. Sed cum parodos, I
vepeE V (IVCPeF Z nesetur, una ex alcera non poruit interri. Ouare capriosa est e impet.
Eecta cacis rdaedivaror a narcoi.
E8donsoBnqua.
Datis duabus lincisrectis, invenire duas meciaS COnFIHUCPFOPOKEOla
Sint datx dua rectae Z, X. OpOr-
tet invenire inter dacasZ, X duas
medias continue proportionales.
Exponacur circulus in quo diame
ter ita secet inscripeam, ur segmen
ta inscripeae sine in continua pro-
Portione inter legmenca diametri.
Sit itaque diameter AB, inlcripea
CD, Cele muruo sccanres in F, ita uE
Teomenta sine in Continua prOPOE
cionc, Cemtrum verOF. Ec eodem
Fcenero incervallo dimidiae com-
Policae ex Z, X describatur circulus
quem diamerer A B lecerin C, II.
_c absG HI abscindatur GI, ip (1 7
dara aequalis. Ieaque LII sic alce
ra daca, e per l’agatur ipA C V
Parallela, lecans circulum OHI in
K, L. OuOnIaM IgITUE AF, F. C
ED, E B sUNE In CONTINUR PEOPOE.
tione exhypochesi, angulo aurem
CF. A consticurus est aequalis R 1C.
Frgo C L, LK, IL, TEI Cuntincon-
cinua proporrione. Ad datasigitur
ZyZ, Id est G I, LEI inveNEX TunE
II, IL dux medix in continua
proporrione. Quod crac Facien-
dum.
Sed illud est angulum anoulo
daco rexuincos sumere aequalem.
Mesolaba aurem organa (UInE, e
acopemata acopematis placet cu-
mulare. Organum (ane ABC D
exleri ex dura materia, imO verO
ex aere perenni construito, et eo
eanquam alceromunimine iis qui
in vereres Machemaricos remere
insurgume, obll.
PSE V DO-M E SOL A BVM.
diamerer CR. Ajo circumterenta erelipri circuli O R transireper V, Z. Si enim
ve L V. Travlicisitur per V, ee ideoangulus V K O idem est cum angulo MI K Q libera
A’aeyco cis rd a duvaror circum terentiam circuli, cujus diamerer est OR, trantire Per a
Ilar