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Show 7A8 ARITHMETICORVM" PROPOSITIO 14‘. Hexagon!" (quiangulus tum pmredmti cubo iumflm, confi. pit (141mm fibi (cliatcral(nz_~. Hoc tfl,aggrcg2tvm ex iffis d c f. qucd , per preccdcnnm , (fl hexagonus zquinngulus, coniunflus cfi gfuko (611:2: irfi‘m l.cnbfi:quod oflmfiun LIBRI PRIMI, PARS II. 79 quoniam dxifcrentin ipforum k 1.11:): efl: E fupcrat difi‘crécii ipl‘urfi} 11, 11.): £1,911 11 d in ‘qurs‘pto ipforum 1) aquod PCL‘ (0‘ prx=ui111r111n,cfkid,quo f. fi1psr1tipfixm d: idcirco‘ aggrcgntum ipforum g1.maius cft .ngrsgnro ipforum 11 k. in aggregate ipforum b c. Q19d Eli: dcmouf‘tmndum. fuit in 5 zaprimi bowm Aritl'z-mcrjc01um.0fi( dctur & 111C, hocmcdc.Pcr 105 pla‘cedmumfipi‘l (1 c1. numnifunr trcs diflErcntiq iffm E g 11 k1. fit ergo, vt forum (1 c f. coniunflfi -cfi ipfo g.cuko ccnfciat ipfum Luxbiitqd {mt dumcnflxédfi cc f bc 1----g. PROPOSITIO 15‘. Tue (Mbi fartfkm (um tripli: medicrum proportionalium ccnfunfli (onfitéurzt (141mm totim. Hoc L11, ipfol um b c. fiuc vniratefiuequocunq; numero dificrentifi cubi,qui {um ipfi g1.cfi triplis ipibu‘l‘gkmcdiorfi Proportionalifi coniunéh', pcxficifit cubfi totius b c. quod in 1. 1"1€wndi horfi arithmcticcrfi {uitoflcnfunuhic tfi facilius of'tédcu1r,fic:Pcrgn- c .-----h. [5 prxmiflérfij pfc (1.111 fingmos b c. facit fingulos g 11.1mm k.-~luh. (-kk. 1-1:. ( -----1. Igixur. ("g d ccf hhh kkk duplum )pfius c. in fingu1os b c. Facit h 11.:uquc 1<1<. hoc cfl, duplum ipfomm h k. Adhuc f. in fingulos bc. £1ch ipfos k l. fingulos Igitur,pcr Primé prmmiflhrum , ipfc'b c. duéhls in aggcgatfi ex (1 f. duploq; ipfius «((13 pct Izfipm- milfarfififlquadratfi ipfius b c.) Hoc 611 b c. radix dué‘ta in {ufi quadraFfimroducct. aggregatfi exipflsg1.t1‘ip10c'1;ipfius h. écfltrlylo xpfius kmdlx nu: m qug-dmtum Iprpducnt {uum cubulirgo mlc nggregamm ex g1.rr1ploéump101um h kxfi L1 cubus ipfius b c. numeri. (@0451 fuit dcnxonflmndum. PROPOSITIO 16‘. Duplum ipfius mum 'L'nimte, céficit aggregatfi 1']:fbrum df hoc eff,duplum numeri part6 altem I'ongioris,mm (whats can, flat aggregatum collaterali: (3' precedrntés qmdi‘utcnmu. Patenquoniam fi difl-crentizt ipforum d e. & ip1b1‘um c f. cffcntcequalcs , tunc dup1us ipfius 6.611%: requaiis aggregate ipfomm df. Sc_d (Elm diflérentia ipforum d f. lEEk/vm'mtc q maio‘r,quém diflcuntia ipforum d 6.11121, {ciliCCtC.&1m‘C b. 31 per 5"huius,idc1rco fit vtaggrcgatum ipforum d f. vnimtc {upcrct duplum ipfius c.11cutpr0ponitur. PROPOSITIU x7". Aggregafum ipfomm [2 6. eff exceffu:,quo aggregatum 117]?» 'f‘"? g]. mam: (fl ngH'gato ipfiJmm b lgPatet‘ficSi different1a1p1orum g 11- t‘flEIEqLIalis diflbrcntimipforum k 1. Tune aggregatum ipforfi g 1.6116t :equalc agorcgato ipforfi 11 k.Scd quoniam ' PROPOSITIO 18". Ex aggregato ipfbmm {2 air; ipfim aproducimr 4g @ngth ipfbriib 1" P.1tctzn1m perSiprgini1111‘mn,b.in cficit 111:6éluc b. inf. F.1d: 1:. Std p2r7" ficut 1). ad c. fic c. ad F. Igitur PC! 45‘ ipfi: c. in a. {mist k. Lnrcper primam,totum b C. in c. facit totum 11 k. de eft propofitum. Pnovosx'r1o 19'. Ex dggregato ipfomm [7 c.2n aggregamm ipfomm a e. produ citur aggregamm ipforum g l. Nam cfim,pcr prfeccdcntcmfix aggregato ipforum b C.inip1hm c. fiat aggregatum ipforum hk. 1am ex 13 c. in a c. (qui ipfilm c. vnimtc cxccdit)producctur aggregatum ex 11 k. 8c b c. Sed tale nggrcgamm , per ante przcmilfim, cfl mqunle aggregato ipforum g1.1gifur 86 ex b c. in a c. producctur tomm g1. Chgd cfipropollrllln. PROPOSITIO 20". Ex aggrchto ipfin'um [1 c. in aggregatum ipforfijpfiwum df producitur aggregatum ipfomm glakl. Nam cum pct ante prxmiflhm ex 1) c. in c. fiat h k. 8: Pct prmccdcntcm, ex 1) c. in a c. fi:1tg1.iam,pcr primam prazmilfirum,cx b c.in aggrt gatum ex duplo ipfius e. 85 ex :1. producctur tomm g h k 1. Scd per 16.dup1um ipfius e. cum .1. vnir;1te,conHataggrcga- tum ipforum (lfligitur ex b c. in d f. Producctur totum g 11 k 1. @011fuitoflcndcndum. PROPOSITIO 21‘. ' Ex aggrrg‘ato radimm tummtc difz'antifi, in aggregétum qua. dratommipflwum radium, producétur difi‘vrentézz fecundorum qmzdrarorm‘rz . Hztc cfi,89' primi horum arithmeticorum: tamcn 111C breuius dcmonflzmtur.Nam cfim b c. {int radian vnimrc difitmtes; qux fempcr faciuntimplré Collaremkm ipfius F. qundmti , quzm proximcdprxcedzfi d. quadmms conftatq; 111C id ipfilm prop nitur cmonfhlidfigp in difln 89". Iraq; cf: pct 101 Prrmiifirfi‘aggrcgntfi ipforum g h k I. {it difll‘rcntia ipforum m q_ qui fimt chundiqu.1dm:i diéhrum radicum, hoc (:11 , quadmn ipforum d f. qtudcatov rum: atquc per prxccdcntcm 6:: (0:0 b c.in totum d f. pro-- ‘ ducamr |