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# Title: [Francisci Vietae Opera Mathematica] Francisci Vietæ Opera Mathematica (shelfmark Leibn. Marg. 101)
# Folio 390, page id 845634801:0396
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=845634801&page=396
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390
Y AR TORNM DE R EBV S MIA L H E N A TTCTS
ACLD AO, OO ad id quod Ertub AO, CL, licutOB id est CR ad CL. Ouare est KC
ad AM, SICHE CR ad CL. Sed CR ad CL est, sCUE C K ad C A. Ouare cAt KO ad AM,
SICUE CK ad CA. Er converrendo cst AM ad KO, sicur C A ad CR, ec subducendo ell
Ca minus AML ad CK minus RO velOC; tell alirer eAt MNV ad OC, sICUE AC ad C H
id eA sicur DC ad DS. Er constat propolicum.
PROPOSTFIO LV
Invenire lincam rellals e cumterentixe daci circuli aeslate.
Sic datus etrCuHs CHs A Cen
erum, diameter BAC. OporcertA
cere quod proposicum est. Delcriba
rur helix cujus principium A, prin
cipium vero convertionis AC. C a
dacaurem in A C pervendiculart
tex recta D A, quam alia recta ran
gens helicem adC intercipiar in D
Dico D A cori circumferenria da-
ei circuli B C esse egualem.
Si enim non (F aqualiS, erit isi
tur major aurminor. Primum (HC
i poltic esto DA major circumte
rencia dari circuli BC. Itaque et
propositione prima Cumatur recto
minor quidem ip la DA; sed major
ip(a circumferenria circuli BC; d
SE illa ZA. HTelicen aurem tangens
recta CD, incercipiar circumferen-
tiam in F. EFEcenErOACtA AF leceL
inscripeam E. C bitariam in F. F.L
IBITUE SICHE C A ad AD, it C P aC.
FA. Sed SICUFC A ad X A, ita criu
C Fadminorem quam A F, UEPOEC
FZ. Iraque ex propolcione lecun
da CONFIHLCTE F C, _ CduCAEUI
AII G ita secans circumterentian
quidem in FI; CONFINUATaM VetO
E C in G; urHIG ad CFI, Se habeat
AICUE C F ad FZ, hOC eA GICUEAC aC
AX. Converum igituE d permu
carim exit AC Ceu AH ad FIG, GCUE
AX ad rectam C FI. Hlocaurem ell
ablurdum. Ep(a enim AO incerct
Piac helicen in l. FX proprierat
igirurhelicis, est A FTadFIL, sicuD
circumferentia tora circuli ad cir
cumferentiam CHI; _ con (equen
cet cum tora circumterencia cedat
propoliione Pa LetalL LCCLa LIC GCTECMT CHCHIMLCTCHCA CMCMI F. BC; se d mase
ipla AD, _ I HS. LHEIBIUE AC Ld R 3. HCuLC L Ae tmajorem quam F A, ue pore l
leaque rangat quaepiam recta circulum ad C. et ex propolirione rerria e duenrur Al
reCt A Z, CTIT AFL Ad HI L, SICUF A Z ad majoLCM CM CUFerentIa C FI; e cum H1C p
Aecipli E (rangir enim helicen recta L C Non ellam secac) mulco magis erie AL
HYG Sicuc A L ad majorem longitudinem circumtereneta C. I1, nedum recta C. H. 9a
minor elL GNam CurrA C FI. Non CIBHa DHMMOL circumFerentia circuli.
Sed h heri possic, csto D A minor circum terenria dati circuliEBC. Ieaque ex eadet
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