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Show "6 ARITHMETICORVM PROPOSLTLO 28". ma'imm ab vlzftatc per ordinem déjlpofimrumm/tfma inf". cedcm‘em muitiplimm , prod‘ucit mnnerum , (1mg: dimidéum Lfi aggregatmnipfizrmn nadir- m omnémm. Nun per {cptimamr prtcccdentis 11in talc pro duc'tnm cf'éduplum trinnguli col; latcmlis vltimg radicis : trinngnlus autem CR, pcrditfinng. 313R] PR1MI, PARS II. 117 Wxiszvt"; ma ii'li‘l'HOl a 1') C0? q:1*',i,:9111ccc&etincndé‘pfortionu 1:913. ngrzrr. Dana: n k c Eda tux-Kin: V113 P'V'..L‘- qufititm tcs.1.quinq; if 11le .lm L6p31‘1r1',n Ch ifiku'l f‘§;,fitwqua- lis iffi {LEE (1'11; rcmi : {NI/:5.- E} h. aqulis Ipli [3.8; din 'Tv‘tfaRz. g. k. :L'quaiis 1172. c.64 ditl'bfcntia iyilr‘; u I", l. aquah's i111] d. Tunc 30,97 (QIFCR m1]: 11‘131'1'111 flwl‘itr-zqul‘d grcgntum omnium tadicum quue ad Vltimnm inclufiuc. Cum ergo dimidium mlis produéfi {it gqulc rri;1ngulo,crit & azqualc aggregato radicum: (god eff propofitum. PROPOSIT x o 29". Numeru: multitudims imparium ab qmitate "dflofirorum in ft dufius, producit @grqytum ipfommeémparium omnium. Excmpli gratin , fint quinq‘us impares a b C d e. :11) vnimtc difpofiri: dico, quéd quoniam quinquc fimt , quimrius in. {eduétus produciraggrcgamm ipibrum qmnq; imparium. Nam, pct quintamciccmmm prieccdc‘ntis libri,quinq, diffiimpares aggregati conficiunt quinmm numcrum quadratum, qui ex quinario in fc‘dufla producuur..Verum cfkcrgo propofimm in 0mm cam. PROPOS [ 1": 0 _ Unmip- {an} a b c d. 17‘ntcrp1‘oy01'izfi: (:xfi diflhmnria 1339,19 {L cxtrc- marfi conficimr cxdifih‘rntijs qmmorwm'ijs: q 2:: yrr hy- potvflm (um xqunLS ipfis quntuur a '1‘ c d. quantitatiltus. Scd {uppoliris )mgnitudinib" primi ordinis; ZFC inuenier magnimdincs fecundi ordinisflinflh w. a l .zlificrcntm m.&' 1 1‘_ 18C d ficut 6ft mad ipfam mfic fit and E6; {iatutcik a. 2d ulic fit F. l, N_____ .__ _u c I ad I. Vmic ficut ilufis a c. imcrfimt rrcs twdia' 1~1':)}‘(~1'ti0na- _ -------_ -____‘ L‘s: im& ipfis Fl. rotidcm medis: Pl‘OPUl'IiOX‘AL'S 1n c.1dun"+%i proportionc intercrunt. qux [Ent g h k. Er, qmmiam pp fi- mjlsm proportioncmficnr LP: :1. ad f. ficdi (inflbrentia ipfh- 81 rum 9. bfcilicct m. ad difl‘cr‘cmiam ipfiu‘fi Fg. fuitt'l; & m. ad afcut. .ad F. idco m. candcm Inhabit rationcm ad a. 85 ad dil'fl-rcmiam ipfarum fgxrqunlis ergo c1}: a.dif'tErcntizt ipthm go‘. {9. Std cum d'ifi'Ercntise {cruent con tinuatnm magnitudinfi Numeru: multit'udini: parium d bin zrio [itccefliuc a'ijqu'ito-v rum, multiplicarm in mmemm vnimtc maiorem , producir ag-l gregatum ipfbmm parium amnmm. Exempli gratin, (unto quinq; pares a b c die. ‘a binario per ordinem difluofitifiauv tcm {it quinarius numeras ipforumg autcm numerus vni-- rate maior, fcilicct fmarius, & ex Ein‘gfiar h. Aio , qubd h.. ct} aggregarum ipforum a b‘c d c. parium. (mod fic patch. Palam‘eflgquc‘nd in mli cxempIo'f; cfl: quinm radix, (S: 3. {an radix:Igiru1-,per feptimam prmccdmtis libri‘hxalium radi. cum produflum cfl: numcrus Parts altem longior fexms :quizperoélogefimam quintam diéti libri,et}‘aggrcgamm ip- fins c.p1ris {exti loci,&_omnium precedentium : quod era: demonflzridum. Er fimilircr in of caf'u. confhbir pro pofitfi. Pkryoportioné,proprefn tam b.c:'ii'a: ipfhrfi 011.}: aidiffijrfintire ipihrum 11 kfi: d.u§iff:rcntiw: {plan} kl.gqu;1ihs cntJ-Imc ori tur rcgula progr; moms m ziflmtudinfi cfmtmne proportio~ mlium. Nam ex 111.8; (Liam notis, notclcir f. dcinde ex :1. e. &' Knots. vcni L' LCuius it ipfius E cxceflhs cfl: aggregatum ip{Mum a b c d. {icur ofl-enfilm cfl. PROPOSITIO 3;". Sifeczmdli duos tcrmirox fitmmmzmr qgoflz‘ffit quitimfcls r5;tinmr pro! ortz'ondcsfiqwrfi c‘flrtmz ‘multyzflzz‘et 5:1,? rcr'rrfmz: ruc prodflrfr'orfi Jiffhrvxri: diuéji: :mcr minor}; dficrm 1,161,110.?! 4g: , tcs‘fit mcdius proportionalis lO.CL11HS duo "It'd" propomo nales 2.0.6: 50. {ecundis quadratis rrcs ntcdu propcmogales 4O.YCO.2;Q.C1L1HAX'::,;UH producunrpr cx duQu [ammo 31". portionales , 6‘ infecundo ordine quantitate: "um: plure: in exdam ‘ratione continue proportionales ', it; w earum‘ difl'crentiz' {int qmntitatibus primi ordinisfingulaz finguli: .equales: mm: differentia prim}; (y'- pofirema fissun i2 ordinfrr MIME: crit' aggregzto quznrimtum primi ardénis . Ponmmr in pri- mlo'ordinc quantitatcs continue Proportionalcs quot-w uis, I '2 4 - S 10 . If 12; p1i,numcri 2. (Y (. quorum quadrnti 4.8; 25.6ub1autcn 16- 40- 100. 7.50. 61!8.& 125.1}:cundi quadrnri 16. 8x" 62;.q11mh‘3tis :ultcmip- gregari/Lipfizrmf; q/Hntimtzmp. Sumo duo tcrmlmgmtm cxc Siin 'vno ordine fuerint quotlz'bet quantitates continue pro. Pnovoslrlo 8 H. rum in f}, 8:;1d imliccm , & finds in hngulos {ccundl , & n‘rti] ordinis mzmcvos , Vt afllrlcr multiplimtozum. In 110s propor- rum Icrzio ordinc {umquatuornumcri continu nonnlcs iliiicct 9.. 20. 5o. :15. in quorum extrrmos 8. b: 125.1nultiplimti termini. 2. at 5. producunt 16. & 615. cuorum Dd 5 8- 2,0 . so. |
