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# Title: [Francisci Vietae Opera Mathematica] Francisci Vietæ Opera Mathematica (shelfmark Leibn. Marg. 101)
# Folio 298, page id 845634801:0304
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# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 83 lines, status machine
# Lines: 83 recognised, mean confidence 0.84
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E E O R F M A L A
ad differentiam FB, EIB; de PA ad difterenriam GB, F. B; dc E A ad difterentiam FB, DB.
EE(IPTOTTAHANTELICK, LEIP, EIBP, CrUNEFIANBIIa HCB, TIKP Cimilia: Sunc enim an
suli HCB, EIKP, ille in cenero, hiC in CIrCUFCFENEIA, a quales, _ angulus CHBCOn
munis urrique, ergo ecreliquus reliquo aequalis erir. Ca GITuTUEC FIadHIB, ita II K d
HIP, Csaurem HIP dupla ip lius FIB, angulusenim LBP aequalis est anguloLIII, de anst
lusBPTangulo BHIC, ilolcelesigirur estcriangulum BIP, X crura BP, BF, id est BP, Bt
equalia. Non cransear jam diamerer per sectiones aequales, Ce d inrer lectiones circunt
Ferencium secer in B puncto: ductis ur lupra rectis , AL, VBI.
298
Guoniam circumferentia G AR,
ACHI Cunc aequales, (aequalibus po
Eris sexmenris AH, OFL) crunE d
Tubcensae AII, K C aequales: est que
uc prius, angulus ABC aquali c
quem Facie subrensa cuivis periph
rix aquali cum diaeerO, d GR
aequalis angulo in centro. Iolcele
igicur eric criangulum GK P, simile
ei quod hc a duabus semidiametris, c
recta uni cequalium SeBMENEOTUI
Tubrensa: uE igirur CemidIAMeTCFA
Subrentam dictam, ira HG id est AL
ad C P. Es aurem BP aequalis iplo
BI, nam in quadeilatero inlcripec
KCBL, erune anguli exteriores PBI.
BIP equales incerioribus OHI, ROB
estigitur eriangulum BIP ilo(celes, l
milerriansulo OHP, laceraque BI, B
aequalia. AE uc semidiamerer ad subrentam parri aequali, ica ex hic quoque BF) ad dita
renciam AC, AI: es enimangulus BEIK, aequalis eiqui st a diamerro et subcenla cult
legmento aequali, ec angulus HBF, aequalis angulo in cencro sectionum aequalium 
insistenti. unde rriangulum BMFLilosceles erie, eique simile criangulum FKM, iia que l
radius ad subrenlam cuiris segmentorum aequalium, ita BLL ad FMI differenciam seda
rUI HIK, KP; est aurem HK aequalisips AL, (sune enim (CBIMENEA AK, II I aequalia) qu
bus addiro communi HL, hune K III. AK I aqualia, ec H P a qualisipli AC, nam les viett
AIE, FC, ponuntur aequalia, quibusaddico communi AF, BUNER AF, AFC. aequalia. L
demque modo ira AG velHF ad FM distetEntIAM RECTAtUM BF, BM vel BFI. Quodet
demonstrandum.
P N E O R E M A 1X.
Situerine criansula rectangula aequalis hyporenula, quorum primi all
sulusacurus sic in submulciplaratione ad ansulosacuros tuccedentium 
dine criangulorum, ad acutum videlicet se cundi subduplus, certii sube
plus, quarri lubquadruplus, e co continuo ordinc: construatnr auremte
ries rectarum concinue proxortionalium, quarum prima sicx qualis len
lixporenulae, secunda perpendiculo ansuliprimi, inter succedentes conta
nue proportionales e succedentium rriangulorum bales ac perpendicula
HXC CTIEXqUALITAS.
erima bis, minus tertia continue proporcionalium, erit xqualis bau
trianguli secundi.
Secunda ter, minus quarta, perpendiculo trianguli certii.
Primabis, minus tertia quater, plus quinta, bali trian suli quart.
Secundaquinquies, minus quarca quinquies, plus sexta, perpendicuta
criansuli quinci.
Prima
Prima
Buli
decun
lara,
Prima
adnon
Decun
parane
T ICd
LCIC.
dle se
dle
Ecrian
elio
Ldleo
ipsi
X
2e. in
 1
2e
epri
Scrian
epend
149
leoin
M
Iporen
pperime