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# Title: [Francisci Vietae Opera Mathematica] Francisci Vietæ Opera Mathematica (shelfmark Leibn. Marg. 101)
# Folio 294, page id 845634801:0300
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294
TH E OR F M L
cix quoque diameter cum subrentarum maxima. Eodem modo ostenderur esse quoque
DC ad difterenriam HC, C.B, ur semidiamerer ad eductarum maximam.
T H E O R E M A VI.
Si atermino diametri Lumaneur in circUIO CiTCUFCFENLX quoECun que
aequales, e ab altera extremitare educantur linex rectae ad sumiptarum cs
cumferentiarum aequalium terminos, eductx siune bales criansulorum;
quorum communis hyporenula est diameter, ac balis quidem diametie
proximior intelligitur balis anguli simpli, succedens dupli, X co continuo
Ordine: Constituatur aurem series rectarum lincarum continue proportio-
nalium, quarum prima lic xe qualis semidiam etro, secunda, bali angulisim-
Pli, is reliquarum balium oxdine succedentium exir prosxesus.
Terria concinue proporcionalium, minus primabis, critaqualis balt a
suli dupli.
Ouarta, minus sccundater, bali anguli eriplI.
Ouinta minus certia quater, plusprima bis, bali anguli quadcupli.
Sexta, minus quarta quinquies, plus sccunda quinquies, bali ansuta
quincupli.
Seprima, minus guinta sexies, plus tertia novies, minus prima bis, bal
anguli sexcupli.
Octara, minus sexta sepries, plus quarta quater decies, minus secundu
septies, bali anguli septupli.
Nona, minus seprima octies, plus quinta ricies, minus tertia sedecies
plus prima bis, bali anguli octupli.
Décimaminus octara novies, plus sexta ricies X sepries, minus quatta
cricies, plus secundanories, bali angulinoncupli.
Ecita in infinitum, uc per loca proportionalium imparia nora affecti
succedat, aHIrmaEX negata, negatx adtrmata: e proportionalesilla lu
semper alcernae, ee mulciplices quidem in prima adfectione perunicatisct
mencum, in secunda per numeros eriansulos, In CETLIa PCENMEOSpYC
midales, in quarcaper numeroscriansulo. criansulos, in quinta pernunta
eos triansulo. pyramidales; non quidem ab unitate, ut in porectatum 3
neli, se d a binario luum AuCenteS inCFCmentu.
Sie lemicirculicujulvis peripheria se eta in partes quoreunque xquales, cujus quidet
semidiameter esto Z. et ab extremo diamerri educantur rectae ad qualibet sectioni
puncta, quarum rectarum prima sic B. Frir iraque ex praecedeni Theoremate, W1 L. ad
ira B ad compolicam ex diamerro ec ex ea quae iplam B proxime subsequitur: est aucente
30
quae mulcara diamerco vel semidiamerro bis, celinquie B4- Z 4.
deinde urZ ad B, ita
ad compolitam ex secunda de quarta, à qua ablaca le
BC. = Z. 9. in B3: aequalis quartae. atque ica (1 quo d Sc sub Lecun
L.4.
da e ulcima, iplius Z. epanaphorae seu gradui qui elariori porestariproxime succe dic d
plicerur, muliecur que proxime anrecedenre, prorenientreliquae proporrionaleseo qu
diccum est modo affectae, in intinicum. Sic
B99. =Z. 9. in B9. 4. lic + Z. 99. 2
Z. cub.
B
de
Deec
que