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# Title: [Francisci Vietae Opera Mathematica] Francisci Vietæ Opera Mathematica (shelfmark Leibn. Marg. 101)
# Folio 265, page id 845634801:0271
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DB2gt
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peite
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udt
265
PSFY DO- M E SOF A B V M.
ca. CMigitur differentia extremarum ad differentiam mediarum ut) au L. Duare qualium AB eri
proporcionalium erie minor dupla, ansuli sectionum erune majores quidem angulo CBA. sed minores
angulo DBA.
Placeat autem cum proportionales sune in ratione tripla systema adnorare. Ouoniam ratio est ut Z
ad 1. numerus aucem proximus post ternarium est quaternarius, ducantur q in 3 fiunt 12, quibus adda
curunicas. Eritigitur differentia excremarum ad differentiam mediarum uc 13 ad 3. Ouare qualium
ABerit 13 talium subtendet DCMum. Ceanulus L.BA s sea lalton Etpla. Et cumratio con-
enue proporcionalium erit minot cripla sed major duxla, anculi sectionum erunt majores quidem aneu-
l0 DB A, sed minores aneulo EB A.
matur XC. faciendo ut 7 ad 2, vel 13, ad 3. e ea in infinitum methodo, ita 100, 000 ad sinum com-
plemenci anguli qui fic ab inseriosa es diamerro. ut in cabella
7. calium subcendicor BD duarum, eric angulus DB A systema rationis dupla. Et cum racio continui
Ex Canonune numet B trianculorum dabuntur iidem aneult. in parcibus qualum rectus astr
Paqualitario
qui
extu
(33. 333
2, 282
(XIX. XXVIIT.) Cajus
EVI. XXXVI
TXIL. XX.
.
PROPOSTTTO XI.
entu
EXCKII.
2
(EXX. XXXII
XFXT. X
f1. XL
X.
XLLE
L. 13
comple.
est iequ
Si auapalallera aglales Bal Cneuo, ce acla pelotioet
dema perpendiculares majorem abscindant: excessus majoris ex utravis
Parte erit ae qualis.
inscribancur circulo, majoremque
DOaCEX AR, BS per extremamino-
ris AB normaliter secenFInR, S
DicoDR, SO esse equales. Circuli
enim cenerum esto C, per quod ag2-
cur diameter ipsis R A vel SB paralle-
la secans DO, AB in V, Z. Cum igi
TuT IN(CTIPEA DO, ABSCceNEUF C Cen
reo ad angulos rectos, ideo lecabun-
cur bitaciam. Frir iraq; DV ipGVC
aequalis, et AZ SCuRV iph ZB scu
YS. AB aequalibus igituEDV, VO
aequales RV, VS SUb dUCUNEOE. ErgO
DR het equalis SO. Ouod erat
ostendendum.
Ouxparallele inaequales DO, AB
PR OPOSTTTO ZII
Data reca _ UCa PCIO, LeMC CNCuTum cui data in (cribeTUE, d
cum diameter eam abscindet in dato punCtO, CTUHELCGMENTA ILCTIPEX in
CONTINUA PrOPOrtiOnC inter mutua (egmenta diamctri.
Sit data recta AB, ae ineapunctum C. Oporret facere quod propolirum est. PiaE UE
BC ad CA, ita C A ad AD, e coeane in eandem rectam BA, AD. X ad A exciretur ip (I
CD perpendicularis AE, in qua SUIMAEUT CE cori BD aequalis, _ abscindatuE C F ip ( AD
equalis. XC per punCta A, B, F ducatur circulus, quem FC quoque secer in C. Sunc igi
TUK