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# Title: [Francisci Vietae Opera Mathematica] Francisci Vietæ Opera Mathematica (shelfmark Leibn. Marg. 101)
# Folio 395, page id 845634801:0401
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=845634801&page=401
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# Lines: 73 recognised, mean confidence 0.84
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ceri le
verto
JUMre
iaAB
equale
exrect
jaMCHI
pprin.
pium B,
Ila
12BE, C1
CHO
B, in
l
l
rcirelt
a
RR E SBONSORVM. LFBLR YSII.
P R OPOSFFFO 1I.
Si describatur helIX CUIjUS PTINCIPIUML LEI MMa CKILCMitate diametri ali-
cujus circuli, quadrans vero principii convertionis st ipla diaeter, In CI-
dant autem in helicem duxe rectae qua Faciant angulos cum diametro x-
quales, ex ab extremicare diametri ad punctum incidentia cduCantur dux
alia linex rectae, a quibus qui fit angulus secetur bitariam a certia quapiam
recta. Tercia illa in ca anguli bipartitione helicem Fere continget, tanto.
que propius cum contingenre concurret, quo incidencium anguli cum dia.
MCEFOFactI CTUHE ACUTIOTES.
Sic circulus AB CD, cajus diame-
ter BD, _ describarur helix BGIIZ.
cujus principium convertonis intel.
ligatur recta contingens circulum ad
B, quadcupla ad iptam B D diame-
erum. Teague HE B D quadrans prin-
cipii convertonis. Sumaneur aurem
DE, DE circumferentiae equales, et
ASaNEUE BK, B F incidences in heli-
cen ad puncta 6, FI, d connectan-
cur DG, E) D secances circumferen-
ciam in l. K Iplaque circum ferentia
IR Sececur bitariam in L, _E jungaEur
DL. In helicen ioirur in identes
DO, DE, Faciune cum diamerro BD
angulos aequales. Angulum aurem
ab eductis D, ID secac bitariam
recta D L. Dicorectam DLhelicen
Fere contingere in iploD puncto.
Helicen enim vere contingat re-
eta D M, intercipiens in MI eam qua
circulum ad B concingit. FA igitur
B Ml semiperimerro circuli ABC ~-
qualis. Oualium itaque DB CA200,
000, talium BM cA 3T4, 159 PFOXI
me. Angulus iBitur BD ML AC P2E-
EIUM LVIT. XXXI. ri. Ipla aurem
DMI circuli A BD circumterenciam
incercipiat in DI. Erie circumferen-
eia BN parrium cxv. 11. XII. Sed e
helix continoencem BMI incercipiae
Primum in 6. Ieaque BO sic Cemis
principii convertionis, _ jungaLIE
DO secans circumterenciam in P.
Duoniam BO dupla est BD, HEaH-
Sulus BDO parrium LXIII. XXY.
LFFTI. Jeaque circumferencia PB
PAREIAM CI CXZVF. LI. XEVTI. RC-
Sidua vero e cota perimetro BND P
AE PATTIUM CCXXXEF. VITI. XII. LC
E relidua illa secerur bitariam in R, AC BR CCU R P ParriUI CXVY. XRXIIII. vI. excedens
BN AAnTATAEDET PAETEI L. ZXX F. LFLII. eriam s angulus ex incidente BO ee diametro
sic rectus. Ieaque sic BO maxima incidentium in hypochesi duarum qua cum diametro
laciant angulos aequales. Dux aurem illa incidentes quae in expolica constructione sum-
cC
PE3