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# Title: [Francisci Vietae Opera Mathematica] Francisci Vietæ Opera Mathematica (shelfmark Leibn. Marg. 101)
# Folio 392, page id 845634801:0398
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=845634801&page=398
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# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 53 lines, status machine
# Lines: 53 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.
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# After the first blank line: the recognised lines in reading order, one per line.

392
prima diametri, LC MsC CI de cuparriente septuagelimas primas
diamerri, id est, polita diametro partium septem, circumterentiam mino-
rem ese partibus riginti duabus. Sed posita eadem diametro parrium 7 1)
circumterentiam majorem esse partibus 223. Sed nos crresi longe fines
Archime deos, et (i lua insequuri vestisia: polita diametro particularum 100.
000, deprehendimus certo in Analycicis angularium sectionum; circum.
Fexentiam majorem esse 314, 159 co. Cs; Se d inorem 314, 159  . Traque
duo Theoremata inde elicuimus, d totidem Problemata, ad Mcchanicen
bene adcommoda, qualia hic Lubjicimus.
PROPOSTTTO L.
Si secetur linca rectA per extremam e mediam rationem: Crie proxime
utminus segmentum ad tocam, ita diameter cir culi ad dextanLeM CIrCUM
terentix.
Linex rectae sectae dupor nai pesor nogor, minus lesmentum sF109, 000. FOTA H
Paulo major 261, 803. Consticura aurem diametro 100, 000. Fic circumferentia tot
314, 160. Uncia vero26, 180. Dextans 261, 800. Ouare bene proxima vera est ana losia.
PR OPOSFEFO II.
Si secetur linea recta per extremam et mediam rationem: exie proxime
UEEOT COntinUata minOre sesmento ad toram duplam, ita qua porest qud
drato se squialrerum semidiametri ad latus quadrati circulo ae qualis.
Lincarecta (ecta arpor na) ueror nozor, (IE10O, 000. Minus legmencum Er paulo nta
nuS38, 197. Constirura aurem semidiamerro circuli 100, 000, qux porest quadeaco 
quialrerum lemidiamerri, paulo major est122, 474. & est uc 138, 197 2d 200,000, 1a12
474 2d177, 245. cujus quadcarum est 31, 416, 000, 000 proxime. Panca auremtere
area circuli semidiamerium habentis 100, 000. Ouare bene proxima vera est analoB
P ROPOSFFZO III.
Ouadrant circumterentix daci circuli invenire proxime lincam rectan
requalem.
Sic darus circulus sub A centrO
dc(CripTUS BDCE. OpOTFCE qua
dranci circumterenrix dari circul
BDC F, invenire lineam rectam
Prexime aequalem.
DaruSBD C E circulus seCCt.
quadritariam a duabus diamerrt
BC, DE, Cele perpendicularice
intersecantibus in A, ip (aGWCDA
secetur bifariam in F, _ per puI
aum P inscribatur B C, et in L
cadac perpendicularis CFI. ABSB
aurem auFCTAEUF Z. F ip (I F A a qua
lis, unde Hc BZ latus decagoni, ct
Ponatur in E A CemidiaMCEO
qualis E L: _L AaC UE A L ad AF, 1
AEI ad A R, juncta videlicet II 
VARFORYM DE REBYS NIA ZHE M AFFTCF3
dc aCta F.KL ip Li HIIparallela. DicoreCtam AK esse aqualem CirCUNFerentI DCC
Ouoniam enim LF. polica est aequalis ipl B L, leCD HCaruT A F. per mediam et exit
mamcarionem in I, ec est A Iminus legmentum, LF ma, lS. Lraque ex proposirione t
ma, licur est AL ac  C, Ia e Calte At alaise circum terenrixe, ira Cemidiamc
d
r