Geometris Pars II. Cap.IJI. 



II. ExareacircitlidatA. eiufdemferipheriMnproximectin. 

 clndere. 



Fiat vt 7\ ad S9i:tta datx area ad aliud: l^umerus 

 fuElM erit tjuadrMHmjieripheriAvero tnit%w. 



Proindc rad.% iftiu, qusdrati „ir pcripheriaminor quin, 

 'cra, terun, 1, fiar vr 7 ad 8 8 .■ ira atca dara ad aliud: produ- 

 ftus numctusdabit quaJratu»^p«iphcri.,;vcro maius. & ra- 

 du emldcm indicat pcriphcnam vcri maiorcm. Atnue har 



^'^'l'^"^^"!.""'"'"'''"''"'"^"'^-?""'"' « proporaonc 

 circuli ad dumetrum . quam Arch.mcdcs inuenit. Brcuiter 

 auccm areac.rcul. ita concluditur, vt fub in.t.ura huius thco- 

 ni di.vimus. i,emiifii cogn.et ftriphent im»tur in Cemiffem 

 d,a.metn , ^ conHahit ^rea ctrcuii : vt fi diametr. fcmdis f.t 

 I i.ped.lcmi(rjs pcr.pher.^erit je ped. Vnde cx mutua mul- 

 tipiicacione .(torum numcrorum producitur area Ita fi fe 

 miWcm dumetri tcrra: mulcipl.ccs pet dimidium pcnphcrir^ 

 produccrur arca globi ccrrcni .5,0478,^!, c]ua.multiplicat; 

 f er 4 Lxhibct fuperficicm glob. tcrrcni 91 8 . 9 , ,-!-• miHia 

 r.um. Quod ,pfum-proucnier..i mulcipl.cctur diamc;»?,! p': 

 nphcriam. In maionbuwamen Albonomorum & Gco4- 

 p hotum crculis aflumi potclt hx proport.o . quam inu?nit 



li. D»to arctt circnU.diametrum iffiu^ inuenire 



farfl r "/"' ^ ^ ^" ^''^''' ^^''"^^ ^ C , fcclaque bi- 

 c12Tt' ^""'"^■P"/P"P^'ldi':ular.s f Bpcr ccntru.n 

 r'y}- .r^"'^ q^adratum ex A F & C F rquale erit 

 rcaa..gulo lubB F . & telioua potc.onc diamctruSi itjitur 

 ^ i- . 1- B . pcr aUquam mcnruram ..oti fianc, & quadratus 

 numerus re.-ta. A F d.mdatur per F B . prodibit tehqua por- 

 fodiamcin F D ;qux- addita pcrpcndiculari F B . conficict 

 totam dumccrum B D , nocam in eidcm mcnfura. in qua 

 Ai.i- Bcognjca- func.Solcnchoc loco tiaderc duo ifta pto- 

 blcmata. •!-'" 



371 



IX. Segmenterum circulUream indagare 

 Sit frimum ptopofitos fcftor circuli A R r n u • 

 explorabitut, /i femidiameret A B 7 pal„ K,"'"'"" 

 fcmiflematcus B CD qm cftpaImo'ru'm ^Ta vt fj" -f;-" 

 c.usficV. Produdus numetus':.! cft area fcclot , A B c' 

 D Arca .taquc feaot.s ptoducitut ex fcmid.amctto Vc^ 

 miflcm arcus fcdoris. ^^' 



Areafeg- 

 menromm. 

 circuli VI 

 iiiucAi|(e- 

 tuti> 



tri«um II n """",^ "" "": '"P" '»^"' c''°^*i «citetur 

 ] 'aii uium A B Dcuius latcra fint coenitlvt & arcu.; B r n 



oc^tu" rm'""- ■'T 'r ^«'"""^ ^- '^S^ -di 

 rd nr 'arram r.""" ••'^ * D- H,cr«,mdetta*ta cx ilU, 

 rc.inquct aream fcgmcnti propofiti B C D. 



Tertih fit Sgura lenticularis . duobus arcubus G H I G KI 

 GHTcKr''' "''^ V '■"<^'""-'- vrriufqt feg^ent 



Q^od fi fegmenta G H I. G K I, fint /qual.a . fatis et.t vniu, 

 %uT. a^tc^m.^"^- "^^ "^""^""^ '^«P'"" ^*b" P~P0fi"« 



J'ZT f t ', '^'^'^^■^'"lorum. ^elcircumferetit-t,. 

 ^u duobu. latertbu. bomolog^ duorumfi^urarum fimtLm 1 



imir jc HAbcaiit . cognofrere. ^ " Pguit, 



l^.lS^^TT ^"''''' • ^ ''S"^* '■'^i'" fimilitc'rquc podtx 

 rcrcnc aium , 5. larctum Iwmologoium : (i maior diameter 

 vcl c.rcum:crcnciapcrmiaorcm\ &.naius Cs 1 omTo 



^ Srf =-;Ecm^:,:r 



'2r '''-''"'^^"' •■ "r f'''"^'« /.?-" fimiiih..fimiSue 

 ^S^iZT"' '"'' ''"-l^S-H nota hnuentrediamZlm. 

 IZaT^rT' ■ '"■■'^■""•^'^ omn,bu.c.rc,.lt.frofof2 



{;rvcr "^'r"'^'"^"^''-^'"^^"-' '^"'^'^'-'■■^^urdTam - 

 tr. vcl ci,cumfc.cnci,r. aut latcra homologa in fe , & numeri 



fai fu;7:"r '"™"r ""■^''"'''^- R»d'-"-quad a 

 quxZm rT"// " ^'•"^-«^. 'i«"nf«c„tiducaut latus 

 citcioTm ? I " '^"•""°'' '^'="""''- 'ifcunfctcnti=euc 



lu«t pollcar m T; T"""°^' '""r '^^?'"-"-' '-*- 

 g.ic,uurnumc To, . o'",. '^"' '" ^-'^"'^'P!i"'^tur.gi. 



cr-6 nuadralrK ' ;■'" ' "^•♦•^^''tum fumma 7iM-R.->d.x 



ti^uccircu , au^ir ."'"'"■; '' "'^ diamctcr . citcumfeten- 

 t uuec.rcul, autlatub homologum quodqu.Trirur • itavt cir 



P rX;,^"T""' "-' -^-^'-■-niacft S,.a i figu7a i^" 



H.1 q ul^ctEauTfi"'^"^''"'''^; '^^^"^'^ ^^^'='-^'- 

 crculi candcm h?K ^'"^" P^°P°^'"S. Ratio cft : quia 



mcr ;\,r. Tpromd"J P^^P''"'"''^ ' ^-^- ^-^"" dia- 

 quod cirCmfc/cnt ".'=.'" ''" "" ^"^"'"^'•''^''"•atum; 

 Lu,a.fin ufr ' , '"^"'^ '"it proportionalcs : itcm 



Eodem denique modo mcticmur figuras cx variis circnl». 

 iumfcgmcnt.s coagmentatas . fiue Smnes circumtctend^ 

 cx orfum vcrgant auc .ncrorfom . fiuc partim intrS 2 • 

 part.inemorfum:vtinligurisA.B.Cviderccft ' 





In quarum figurarum prima A oportec mctiri auadril^r. 

 rumvnicumfcg,aent,scircul, ..n fccuudar& tc?^aC lcn" 

 tagoflum vna cum kgmcntis ctculi. ^'^ft.aC pcn- 



X -^ream fuperficicrHm gtbbarHm tnuenire. 



l- Fl^ntulmaximaperibheriA I r.,u .,,*-/•• , . « 



maxtn. circulo)^ e.u, LL^^^jtl^l:!::;'^"' '"'-" ' 

 Vt dianictct hc 14 . pcriphcria . . Pv\« ,1 ■ '■• . 



rum nun.crorum ex.lHr^are^';\T I^^m!;^::^} iS:rCa: 

 urquacuor n,ax„n^ c.rculi, . vcdcmonftr.K Euci.dcs ha"^ 

 vt ancca c.rculi aica eft d,n.cnf. pci te^an^ulun .' ^f.Tj 

 tum dumccii cum pctiphetic • n,ul,.^- d.raidio 

 _ I „- ' " ■ 'f.*'"cpcrtO[ji,i ij,anicpriTm «r 



pcriphcr.am cft.c,rur reC>anguft,™ prioris q:i.lT n ' ^ 



tra mult,pl,ca.pet di„ViJlu.r, . d.uid.s pcrdupluritaaucUlTc 

 ctcuius hmplcxcfficicur. I.ic q^iadruplu.. Acquc cx hkct m 



analpg.aconcluditurarca lKmrfph:e'rici,&f:!rtio„Ttum T 

 noris.tum ma,ans. Sic in cx.mploplanus c .nax.n?5 o,T-k 

 na 44A- radic.. 7,cft area hcm,fjh xirici.nan;"';;^ ^ "^^^ ' 



.y? Viir '"'"" ^ "■'""" '"-^^ • '"^'^'- M'^' -«'*? 



Vt cfto conicun,, cuiuslatus fic ,,. fe,»ipcripl..eria r<i- 

 v.^c pla..us rr4-^ cftlupcrficcsconica;: cu. LdSc ris luk^ 



j . Planu^ ifud btifi cr altit»4,ne eft cyUa^ccum. 



' Vteftc. 



' QuoinoJo 

 iiiuf rtige- 

 tur area 

 fpharici , 

 c»nici, Jt 

 cylindiaccil' 



