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Show I4 ARITHMETICORVM [JEER P'RlMVS.‘ I} gu‘rorum. Scd pcr diffi.vniras,&quamor {equcn res A" Facifrt a b d c par :rir. Eflo igimr ipfe dimidius a d. qui iam exceditipfund .----------- a b. numcrum ipfo b d. ducatur numerus a b. in ipfum b c. 9 S 17 (Sc fiat c. igirur quadrarus humerus crit c. per primam noni pyramidcm A" quinmm :& quaruorprgccdm tcs A 1‘ facizmt A" pvramidem qmrmm. Ergo qztinm pvmmis pentagon: c clemémru m. Quandoquidcm cx (luau quadratorum {cu fi- conftructur cx aggrcgationc pymmiriis A" quinr 1', duple- 11. 5 f 64. milium plnnorum fit. Sit deindc [1m ipfius b d. ipfle f. numc rus.Ac deniqnc ipfius a d. vcl d aquadratus ipfc gnumcrus. Sic cnim , per qulnmm fucundi elementorum ad numeros (inc 4* . Puoposxrro tum eff xqualc ipli g. quadratoCéI‘tat ergo rurfirs Propolitfi. 3-89 PROPOSITXO 54.". a, Omnix pyramlk triangula cum praca'em) pyrlmzide triangu- la coniunfia,conflruit pyramia'cm quadmmm filzi (allatem/emJ. 361. 0mm?! pyramz'a pentagonz conflrztur ex pyrazrzirle qmdmm redaé‘ca‘mfionfinblr qubd1pforum,e F. quadrarorum agrcga- .------- wd cfi propolitum. Similis eft cwmrorum 10- corum dcmoulfrario. collateral"? ex pyramids A 1" prcccedcnti. Nam, cum cxempli gratin,pymmis pentagon: 5" per prqcedcnrcm,:equiualct ag- grcguto ex quin {.1 A" pyramidc , 6: ex duplo pyramidls A" quarro::& psr ante prmmiflum, pyramidis A" quinzcc, & py- Nam Emcilimris gratin, capiatur pyramis quinm conflans per ramidis trianguld: quarrx cumulus conlh‘uat pyramidcm 1-- 3 .. difiex quinquc triangulis.1.5.6.10.15.& pyramis qunrm c6(lnns ex 4"" triangulis. I. 5 . 6.10.Aio,qu6d horfi aggrcgntum ;~---6 .. ficir pyramidcm [1‘5 qulnm. Nam per I 15 huius) iccundus quadramm 5-" ,1cquitur vr cégerics pvramiu‘is qumh‘nrgquin ‘ I; cum pyrfsmidg triangule. quarm con ficiac pyramidcm pen mgonam 5" .8611mi1iurgumenro omnis pyramis pcntagom fie: ux pyramids D" collaterali, & ex pyrumxdc quadranguln preced:ntis,t1cur proponitur. I .. I 10-15.. 16 10-15.. 25 20. 35. triangulus ab vnirntcicilicct 3.01m vniratc facir 2L1 quadra~ tum {gilic'cr 4.1mm 2.9 8: 59 trianguli ,‘fcilicet 3. & 6. faciunr 5" Cf" {Clllccr 9.1mm 5' & 4.9a" rcihcct 6.&lo.fl1ciunr4 " 55 [3"1 i‘cilicer 16.AdhuC4.' & 5' triégulifixofcilicct &15.Facifit noposr'rxo. 5. pym. J trieig. (xi-an g. 37‘. Omnis pyrami: bamgozm lelmgonica conflituitur ex pyrami- quintum quadratum 25. igirur vnlras, &aggregam ralium de pentagona col/attra'i, (3* ex pyramide triangula pmcedmti. quadrarorum confumant quinqu‘c per ordincm ab vnirate quadrntos : &idco,perdiffinxonflruuntipfam D" quintam Excmpli gratin , ofiendam q; pyramidis hcxagom quinta. :cgualct aggrcggtodmrum pyramidum, [‘cihcct pcntagonx pyramidemtidcmquc fimilitcr,in omni example, cuiuslibet Collatcz'alis, 8; triangulx quarter: fic Fer dimmpymmidis hC< PyramidisA" & prxcedcnridemonfimbo, per 11"1 huius 3r. guendo toties,quotics combinfitur A".erc pyramis quinm A" {cilicct 5 5. cum prmcedenti pyramids A" {cilicct 1.0. confirufit 55 . pyramidcm [1" quinri. ({uod cfl propofitum. Paoposleo 55‘. Omm'; pyrami: pentagom romfimitur ex pymmia'c tyirmgil- XIgona quinm coalcil‘it ex vnitarc & ex quatuor hexagonis {upcrficinlzbus ibqur‘ntibus : tales autcm llcxngoni , per diff. finguli LX quutuor pcnmgonis collateralil‘us , 36 cx totidcm prxccdcntibus rxirlngu'is. Cumque vniras 6: quatuorpen- pcnragonam : quaruorc'lne rrinnguli Prmcedcnres conficmnt 10.:5w--~45 la coll:zteralz',é~ ex dupio pr‘ecedmtzk. Cum p‘cr diff Pentago- quarmm pymmldcm niangu'um : lam , Pyramis hexagon: 20.75. na Pyramis conlh'uatur cx prnragonis ab vnimte per ordiné _ I-‘I nggrcgatjs: 1'5, exépli gin, guinta pyramis pcnmgom confin31.1.3 3 6:1 i bu ex vnimre, &' quntuor Icqucntibus pénmgonis {uperficia- 6 . 6 . 10- z 2 guns. (lugruornut mPcs penragom,pcrd1flm.fiur (x comum quinm. {cilicct o5 .conflx'm'tur cx Pyramid: pcnragona quin- 10nc quatuor collateralzum quadratorum,& quntuor pm;:2: 2‘3: 2;:éi Cffc‘nriun?i A1011: fingtfli‘fingulon‘lm. Quuirati quoquc tales __ 4 per 1 1 luuus coniht cx comunc‘nonc quntuor collarcra lium A 1"" &r0tidc1n przrccdcntium Al"'*'.igiturquinta pyri- tagoni {squentcs , per difE'n‘n. filcimr quinram pyramiucm ra. {Ci icct 75. 8: ex pyx‘11nidc n‘ungula quarm , {ciliccr 10'. & flmflircr pct alns locis accommodabitur dcmonfiratio propofiti. P‘ROPOSITXO 383. 07717213.! gyramk bemgom tetraganicz confiat ex Pdeitl? triangula pryceicnn, (y infiwer ex ij: , ex quibws pentagon} pyramz: collxte'uEycbffwzrc oflmfiz efl. CG cnim, per prmcedc- mis pentagom conflabir cx aggregation: vm'rarjs quaruor {c- tem,pyramid15 hexagonamxcmpli gx‘atia,quinti lon- célkcr ex qucnrium triangulorum,d11phci toridcm prgccdcnrifi trian- A" Pymmidc +3 85 ex pyramid: Pmmgona qnmfic péragona pyramldcs ' gulorum. "W .) |
