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Show ARITHMETICORVM 4 ‘ LIFER PRIMVS. 5 locis , paribus radicum inucniantur alternatim, licutpro~ pomrur . PROPOSITIO PRIMA. ' Omnid radix cum radius pmccdenri,j%cét fibz' collutemlem Vo'r vnftdtes Imbct mmzcrm quilz'bct, forum in err/inc radimm 10mmfbi'titur. Eté {oxtrarfn‘ mom/m in mdicé. 11M locum obtinet quéztzk numcrm, for (1140415: (Oillplfcflzltlfl‘ wzi. rates. Nam radices ab vnimtc cxordium cxpicnrcs per linguloslocos fingulas acquiruiir vnimtcs, Q}: ‘Z‘UPFCY millc. narius numcrus , quoniam cx millc (Curr: mernus, millclimus ell in ordinc radicum: Er viciliim numerus, qui millcfimum in radici'nus locum lorximr, millecomprc. hcndcr vnirarcs,hoc ell millcnarins iglc numcrus cm. hr l10C 1.‘ cliquod proponitur den-ionllrandum. 0mm} dam: numcrm inucnitm" in or'dinc mdiwm . Elle dams numerus mquicunquc lir,1io quod mnumcrus inucni« Imparemwum fequemi 'vcro‘ fequentcm . Nam binarius Cum vnimrc ficir rcrmrium : cum termrio autcm iunc‘his, lhcit binario maioremzék idco imparcm {equenrcm lEilicct 5.196: quarram pro:millEim.Rurlils,Ci‘im tcmarius coniun ch13 cum binario, EICiCLt quinarium, imparcm fibi collareralcm : Iam idem cum quatcrnario radicc fequcnti £1Cl€t bimrio maioreimliocclhimparem ll-qusnrem, perquarram prmccdétcm, qui leprenarius cl‘t . Eodcmciue modo in inflnitum , licur propolitio concludir . 0mm}: radix maltiplz'cam in radiccm fisqltentcm, prod/Mir du- 7 plmn triimgztli fibi collateralI/k. Excmpli graria, ducatur qmtcrmrius in fequcntem radicem , {cilicerquinarium : 8: I- ------ ~4 Producuntur 2.0. Aio,quocl zoduplus clltad triangulum ipli z--~ --~~-5 turin ordine radicum omnino . Habcat cnim a. quoruis vnimrcs, vtpummille. iam cnim per prmccdcnttm mnu- quatc‘l'nario collateralcm . Silnmntur cnim :lb vnitatc ad 3~-‘~‘ -~ 7. qmtcrmrium radicrs:quibus appliccnmr totidem & ordinc 4------- -; mcrus millclimum obtinebit in radicibus locum. (Lupd ell Propofitum. . ngices fingulw dub/2mm conflztmmt pare: fingulos Per prmpollcro ab vniratc radiccs,lingulm lingulis : fic cnim list Vt crclcenrcs cum dccrclbentibus finguli lingulis coniiinfli am tall; dupla mcnluranrur 5. binario: ordinch. quandoquidcm per lvinarium multiplicantur: & idc-o per dilfinitioncm flint ipli pares numerigquorum primus {cm cl, fecrmdus bis , tertius rcr; & lic dcinceps ébinario menlw rantur . 7mpares ab 'L'm‘tate per binarij appofitionem [itccejfiue fimb . Nam vnitas bimrio appofim, pcr‘dilfcrcn. faa‘t numcri faciunt quatuor lummns requnlcs : hoc ell: quntuor rquinariosqlmrc earum aggregarum erirplmus numcrus,qui fit ex duc‘hi quaternanj in quimrium :6: idcirco zo. erir mlis plnnus . Duplus au'tcm ell planus ipfcad triangulum quatcrnnrij : quandoquidcm, per difiimlis triangulus cl} aggregarum vnius dic‘torum ordinum : quod clt dimidium ‘plani: Igltur zo.duplus erir ad triangulum quarernari}. Er limilircr in 0mm cal'u id quod Proponlrur demon‘ lh‘alnmus . imparcm , {cilicet tcrnarium: Scd pcr prxmillam Parts numeri propagamur 2i binario per binnrij crcmcntum : 86 pct diEcrcn. imparts addunt pariluus lingull lingo- lis vnimrcm ‘. Igi‘rur impares propagal‘umur 51 ternar10 peridcm binarij crcmcntum (Vt linguli lingulos imparcl vnitatc {cmper cxccdanr.) (bled ell Propolitum . . . 7n ordine radimmimpare; (rpares alternatim é" mmtcm fltcctdmt; . Nam, Per przmillam , 1m pares ab vnirate pen binarium crelcunt; quo fit vr in radicibus , vnitas , 81 WP femper intermillb numero, {equétes lint imparcszpcr antcp< milfim vcrfnparcs 51 binario per binarium crclcunt;qual‘€ m radicibus bmariusfic vno lEinpcr'in[crmillofcquenrcs (up! pares. Sic erg-3 fir,vr imparcsfin imparibus,Parcs leilnpfir m ocxs 079271215 triangular dllpliC.ItM/5, cfficitmmzemm partc altcm 8 longiorcm fcqucntem . Exempli gratin, triangulus quarti loci,cltdm;1rius. Aio,quod Io.duplicatus cchit parts altcm longiorcm quimi loci. Nam per diff. ralis parrc alrcm longior producirur cx radicc collarerali in prmcedcnrcm : lcilicct ex 5.in 4. Scd pcr pi‘ct‘milliim 6X diiflil4.in 5. lit duplum rrianguli qmrri: Ergo mlc (luplum mqualc all, part: nlrcra longiori quinri loci. quod cll: prooolirrlm . 0mm: quidm'm: mm mdit‘cfiuz (Onlifllffllal,50)ifillrfi‘qHCN' 9 tom pane m'rcm longiorcm. Excmpli gratin , quadratus quzim loci cfi 16.61'L1lfiucmdix 4,. Aio,quod {Exdccim cum quatuor conficit parts alrcra longiorcm quinti loci. ‘ V 5 4--- I6 4 Nam‘ V mg?__, , ran-v4* 9.7.6:.» 4 W ‘ L/WJ 5-10 |