Opuscula mathematica : nunc primum in lucem edita, cum rerum omnium notatu dignarum indice locupletissimo

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122 ARITHMETICORVIW . G4 ----~ 8% 8% 31111316 erit ei,quod ex 9.in 68. Igitursx 52.1'11 68.13am- LIBER SECVNDVS. 12; P R o P os x T 1o plum die a: {umml' qvnhatomm : quod‘cratdemonihm1. Tun; prorrfims rat'oncs [(‘fiék‘flffrel :311171'0 due; rationcs, dun]. ubd nutem 7;..ad 9.flt {icut 68.nd 5.1 patctmam 7 2. ad 9.efi oc'mplus ex diflinmmltiplic;1tionis,ntquc 68.311 8; fimiliter oé‘tuplus : con {ht cnim 68.<:x duo‘nus, {Cilicct 64: qlmdmro,& cx dimidio furs mdicichilicct 4.6351; 64.o&uplus ad 8.1313111 radican , 8: totuplus etiam quatuor dimi~ dius Linfiicm mdicis fi'd L. @rc totum (v 8.;1d totum 8;. fimiiiterofluplum. Confirm .0 propofimm. quod iicm dc o¢‘ro,ir_:z dc quotcunque propoiitis radicjbus fimilircr oflcndunus. ' 6r: pm" 361' [himn'i [Gaff PROPOSITIO 38. V113 Pfr (11103 X‘- UUWC'TC‘S (1b. & fllfk'l‘fl l‘vfl' ("‘05 null‘k‘lCS C L}. fignificam , 013mm: & .s a~x;?vr(‘cz'v : h c L95, 3':1‘{‘('1!r‘_111 cx iplis duabus (:crmpoi‘m jmrc-uirc . Rec 1% y: 1* 1111iphcanoncm tcnu'norum x'nms '31 rcrminos alarms (EC: Duck C-f---c.1; Hr: a. in and? EM 6. Dummy {min 14,. but g. Hm: ur, 0.11.55 :1. 3 ‘ ~ ‘< _ L l m mucmzm and 1‘. 8. L. ad 0. 11m p. z>‘~ 0.4. -v~--r 3' 3 ratio cadg. 5.. 7-"...1 ‘uniiuru:mucznm madlxi'g cx efl,qu<‘:d1‘azio c. m"_ .mtfonc cad d.Q;w , 1* o. (Emu-Ex 3.111 13.. Hit f. &' runc, c. v as Cdfaglz :pfixs c {mt =‘ ». riqucnixm :s. 111.: d. a muhwhwn-s d. hanging 1'7. 6.3(1 «Lift: c. nifcu: mam 1'1 i171}13;1§'.![>10."'1: ‘! igl s 5: Hit Ftut'a. ndltJmLJf‘i E4 "J. d [3.we qwdmr-o_ szadfit m: TCW‘C'JJN) qriotx'ibez‘rmlémm .1171 wzitate ordim. mm affix . tarifi f7; fm' " hum: , 311.12.15'cey'2‘ aggregqro m: 1.11m Cubomm .3. _, A ;;¢.:1'J!:5)‘r7u50;'ltvz.z.Nanipcl‘dlflihnggrc 1 -‘_'I 2 8 z 3 7 4‘64. 5mm; 1 5 ‘22? natum mdicum ab vnimte ordinamrum, eff triang‘uhlskfiu- b . . . . . mcrus poflrcm; radicum. Scd trmngulus m'ns m {c dnchls, , , . prodnat zuux'chtunx cubcrum ommum mdmum quucad polh‘cmam incluhuc,pcr 5 8" PFCFCCdc'nFis 1:. wimr &' aggrugamm ipfnm mdicum in {cic multiplicamm ifroducit corundem cubomm aggregarum. quad c112: <.i.'.‘-.1L11;tr:.ndfi. {i0 mod (3'. (11:4 (1.an ‘ rigit'izx * Eitus,i< , rcmrur cx ncmmihxs requa- :atu. 3.1.1 {..C'\ 4.. __. (i. /ny~.d emt demonih‘andum. COROLLARIVM. Non aiiicr trcs,3ur pluses rarioncs in vnam colhgcmur. Pianpostrl 0 40". , I' :11.ththpropofimrmzz zzb'reri a!) altrra fixbtralxcrcz. Sumo gins: rarions mad ‘0. 8: C. ad (Loycrtccfix‘ntmhcrc harp" 2% Us. Hot fizz mt nmizzl licationcm n'rminorum [ucarur din mfg fiat ‘C‘. Ducazur C. 1'11 Ord‘nc pcrmu mm ‘ _ . . . m ‘ I {.mrm 17011 mm oluw c. ad I." ch, rmo uch Dice «b 8' EFF. COROLLA Vndc manifcrm Er :‘Pguln program ficurin qnadmtifi, nommium, gin-:1 ‘ 117137;..." b '~ V'"!i<:-r.il\us (and f. & 2111.13 f. ad g. pm mu nnnml‘11i5:qu;1mit.1tcs {ccumium grunt; crcmaz (yum-1 continuum : tunc preporzio {11"1711 fingu. ilrngu ".5 1341035 tripligndi at; 556 fecundfitn EJL" .1 gainf- txonem manqcnda cut , V63.111inm'1mh:umma CJ.:;0.11‘.11;:| radicibus thctorumwtproucniat fuming cuborum props. flmrum qugnnmtum. 'éthncm 211::011i3 and d. L1 rations ipfius mad INCL-0d 11C 0. fluxdimr. 1,): c. in :1. flat g. Cx' tunc,flum c.131ult1plchnmpa. n c 3. ad _ f. 4 <3: quonmé avdb.11 crit ,1:cum. ‘ m fos a b. {mirqfi ‘ S < V. ‘ . _.11c nulltiplicn.ns 1pios c d. 1.1mm: gums 3c.cr1t.1cuf c. ..d g. ad 6. hm 93.3" v. Sud mrso q. ad f. componztur ex muons n. :3. 1d f. ergo ratio :1. ad b. Com‘gcmtlur ex yuf- & mg: C ,ad C. 1311M mm) 2.21: b. ..11:cm (km: (.3 ‘ dam ' . 8: c. ad i. Quarc , ablam cor. gum-tux" cx ruiumbus c. . and f. quod mime C add.:1‘.1ti011ca.ad . {bpcrcrit ratio }. stat dumoni‘tmnmm COROLLARIVM. l Item huc {pccvat quidquid dc pyramidibus in prarcsdsnv ti lib 1'0 conclufum eff. Nam pyramis trianguh 63: conr ics Pnovosxrxo 41". triangn‘xomm : quadrata, quadratorum: pkcnmgyonlfixsnm- gonomm 5 hexagon; hexagonorum, 8: dancmfi ah anrare ordinatemmfindc to tidé Progreflionfi regular. ruplgitllrRa . P o ‘JC J. .‘ . 711).. 5 L.r,'«5 '7 00077.1" A , "J ;»[l1[ htntllki» "LUCK illtuPtC 11 "hlhl » L , . _ .u I77 Jim/F} 7):} 51 data. ""10 h» 5-5»--9-7~27---Sl z~z ~~r4~ S --16