570 Encyclop^di^ Lib. XV. 



, A, Cuiu.Uet circullperifheriA Vrifla cfi d:.%tmtri . & "'^^'"^ 



J, feptLa parte iLmetrt. n>w.r ^cr^odccem feptu.^gefimi^ prt- 

 mJ. Itaque fi diamet^T- 5^ rault.plicctui g.gnttur nu- 

 xnerusmaiot, quin cUCumferentLa : f. vcro .m,lt>phcetur per 

 T^? pTocreabrtrminor numerus , quim ar^imterentu. E 

 ComtariofT Wrcumferentiadiuidamr per j-r. producetur m.- 

 ^ornurpcfar.qtrim di:n««er : h vero dtmdatur p« jtt. 

 prbfilbu numeris maior . quim d,ameter 5- CucuUu qujl,- 

 J,tt»d c,H^dr<^tum diimctriproportwncmhabet,quitm II ad 14 



trox^Je. Igitur fi latus quadrati fit 7 pcd- quadratum cnt t8 

 &fitriangulum fiac dato circulo a:quale , tiiangulum ,llud 

 '\m quatta pats qHJarjtu Ergo circulus ad quadratum lux 

 alametricftferme vt .. ad iS.hoc eft,vt ii ^d M-Vide figu- 

 ram ptoximl:- f£,quentem : vb> citculus pft A B C D. Qua- 

 dratumEG H J. triananilum circulo aiquale B E !■. Uibus 

 •his propofUiQt^i,bws refte adduntur tres alix ex Pappo Ale- 

 xandtino. i.fcirciilorum diainetri funt uucr fc, vt circurate- 

 j;enti« 1. Proportio quadrati ex diamctro cuiuflibct circu- 

 li dcfciiptladcirculi ate^m maior eli, quam i4.ad ii.minot 

 autem.quamrS^a'!."^- j. Proportio quadrati a circumtc- 

 rentia circuli cuiufuis defcripti ad circuli aream maioi clt, 

 nuam 8 91 ad fKminor autem quain %Z ad 7. _t;_ 

 "* jn — r— -,— -T. ■ ,3 L_... -,£i. 



.-,• . ■ '■' '•"' '^' 



•: His propofitionibus Archimedeis ita prarmllTis , fequentia 



ftbiiciruusftobleraatas&problematis theoremata. 



',' ;. ^reatndrcufi trihuitv'(u cogiiofcere. ■ , . 



^readrculipriducitur e.v midtfpUc^iione/emdia- 

 instrt infetmferifheriam:vel ex Mintotimpcnpheri£ 

 infemijfem femidiar/tttri , hoc eft , tn qnartam panem 

 dtAmetri .■ t>el dertit^ue ex du^ totitu diametri in 

 t^rtani plirlkm periphent^'^-, .^J^^^'^ ;;> 



Eiima tamen via eft vfitatifliraa.S: breuitei- ita habet .• Jre* 

 cuiufms dati cirt:ftli froditcitur ex multtplicattonc radi^ tnfe- 

 milfemperipheriA: £xi€tk autem hic opera: f r^tium bafin tii- 

 anguli ftacucre lafcuV., quod peripheriar fit a;qualc. Sit diaitie- 

 ter 14, petipheiia/vdped. Muhiplica diantettum in periphe- 

 iiam,& prc^u{Uiiirtittty«pct 4,hoc i»o*lo. .^ 



'^'^ ■ • ft- 1 

 . ,,, '.,..r<.r.3i ni ■soJ.-.wu.-.i 4 « r^oKni uvt t. 



O bal ri.r -.^i.ii- ■ 



..■.lli.*' jicA Vv« «««^■"•^:. -117-^ • 



,:SiS ?ltm?iljl i3:i '^4'.^" ■ ' 



Fiatvt ii^ ad 71.it 4 data circumferefitia ad aliutL 

 ProduUHi^ enitn nnmerm dahit diaiytetrum lierk 

 rnaioretn. 



Vt fi citcumfcrentia fit 88 pedum , diameter vera maior 

 erit i8-nv-. 



5. Zx data circuli circumferentla diametrui» inuefiigare 

 vtrd minorem. 



Fiat vt tt^ad 7. ita circumferemia data ad aliud. 

 J^umerns^ enim procreatnf ojferet diametrum ver^ 

 minorem, 



Vt fi fcitcumferentia fit 88 ped. diaraeter etit 18. Data igi- 

 tur circulicircumfcicmia, inucftigabitut diametcr prope ve- 

 ra,(i hjEcviateneatur.-SrfH^ ii ad y:'tadatapenpheria addia- 

 metriim.- In maioribus tamcn clrculis , dacam periphcriatu 

 multiplicabis per W\--yel fiat vt 11} ad j 55 = itapeiiphcria 

 .data aJ diamctruro. c. gt. cx Aftronomotumoblcruationibiis 

 coHigitur , pcriphciiam globi tertcni continerc 5400 millia- 

 naGermanica. Quaifitur diameter. Mulciplica 5400 pcr ;^ 

 producctur diametcr i^iSrForo- vel per proportionis tegu- 

 lam eadcm diamcter fit concluditur: 5 5 5 dant 1 1 j.Ergo 5 400 

 milliariadant i^iSrs';^,. 

 i 6. Ex diametro areamcirculiveramaioretntnitefiigare. 



Fiat vt 1 4 <t^ 1 1 . iti (juadratHm dats, diametri ad 

 (tliud. Produfim enim numerm dabn aream circHli 

 verk maiorem. 



Efto diametcr 14 pcd. Multiplica 14 in fe : fa^um multl- 

 plicaper n ;&: huncfaitum diuidepeti^. Qjjotus. eftaiici 

 circuli hoc modo, 



' 4 

 i 4 



^ V ' 56 



r; 



.?e? 



6 l 6 

 4 



t ?. .Of: 

 ■- '.•><i,>j.'.'. ... 



('5.4-V^Si 



ef ita ; Planut c tJidio^Sirpenpfietii dimldio eft area qirculi. 



1 9 6 



I l 



196 



19« 



115« 



14 



( 



I y 4 area. 



' f 



^j.j.g,^ Vciij cxetnplo 4iamcter eft: 



14, peiiphcjia 4;4- Duc icaquc 7 

 radmwintli , «4eTit->arEa-Srtr^^ame. ftftqife;^ {*linus e radio & 

 cjuadrante perlphatise-feft area^femicitculi. A^tin exemplo la- 

 diiis 7 duftusi9ii,auadrantefl\pcriphctix,e}thibct 77,aream 

 fc.micirculi.''jFacilius lii^cnti.c.illa dimcnfio fumpw Jimidio 

 di.menfi iaqi^ciiculi. • m. ■. .. ..1.,. 



.1. E* d(i(A ditmetro circuli drcumferentiam verei maiorem 



'-' Fiai'^jMixi.:it^data ditmeter ad aliud, 



Verbi gtattatUameter.fii: xS. ped.^Ciicumfcrcntia igitur 

 etit 8 8. ped.^^maiot fciliccc quam veia. 



3. £* data diametro circuli circumferentiam^era minorem 

 elicere. *-'^''"*-»., 



Fiat vtji. itd ti^. ita data di^eter ifd <j/»««^ 



Site. gr. diametciiS. & pioJvuictfll citcum|cientia i(^~ 

 minor quam vera. Itaque ex dahi qrculi diargtsro circutijfer. 

 vet^tiam prope -ueyum inueniemm , filter rcgulA>i proportilnis 

 ^Ha concludamM : Vt 7 ad 11. ita da« diamctcr aj petiphe- 

 jriam quarfitam : vt fi diameter fit ii peiciicumfeicjKiacric 



i.4/jed- _ ^ " '-. -'"^ 



^Vfetf •d»t«r.i^iculi circttmfereniia, i'tametrutn}vera maiorem 

 indagare, * "'"•«-, „^, __^ 



■y.Tx diametrf ttreamcirculi vera minorem intiefiigttre. 



Fiatut 184.«^ 2i3 :ita qitadratHm datx diametri 

 ad aliud.-Nurnerta enim pracreatf» aream circulive- 

 ra matorern offeret. ■ 



Aream icaque circulipilori vilfic coucludes ; Vt i^adiu 



ita diametcrin femultipltcataadareamcirculi. ,: ■ 



8. 'Ex circumferentia aream circuli vera maiortm conclu- 



dere: 1 • r 



Fiat vt %^i ad-]\ : ita cjttAdratHm datct circumfe' 



reritix. ad alitid. Trocreatfis namque numerm aream 



circuli vera maiorern indicabit. 



9. E.t circumfcrmtia circuli areamvera tninorem coUigere. 

 Fiat vtZ% ad 7 ; ita ijueidraturn dat£ cfrcm/iferen- 



titcadaliud. Nurnertu namcjue quigignttur, trit arect 

 circttli fninorquarn vera. 



Sic v.gr.peripheiia circuli 44 pedum. Multiplica hqnc ns- 

 mcrura in fc , &c fa(flum diuide per 7 , & hunc faaufli diuidc 

 per 88. Qjuotus cft aiea circuli,hoc niodo : 

 44 

 44 



176 

 7 



10, DitM. tirculi are» ,, diametrtim etM prope verntn cogno^ 

 fcere. 



Fta vt 1 1. adi^. ita data area ad alitid. IJumerHs 

 c^HippeprodHtlus,ef qtiadratum diametri vero minfts. 



Quod fi fiat vt 11 ? ad 184 : ita arca circuli dati ad atiud : 

 producetur quadratum diametri vcio maius : vndc & ladix 

 eiufdcraerit diametci veri maior. 



1 1 . £.'tf 



w^^mt^ ^ r m . ' . " ^TM 



