Geometri^ Pars 



D 



Qujlis etgo pars tiuadrantre c/l vna illarum,in quas qus- 

 draas diuifus eft ', talis erit arcus DH totius periplictia:. 

 Idem fic expcditur : Peripheria circ»lr, hor eft.gradu! j 60. di- 

 wdantKr fer tiumernm Imertim atfgnloriimve mtdtangidt dc- 

 fcrtbendi , ©• prodnHi nttmeri nrcu^ in circuli dati peripheria 

 acapiattir. Reiia iftnmarcum fubt.mdens , erit latM multangu- 

 li defcrtbendi. Sic v. gr. heptagonum c(efcribcndum; diuifis 

 ^60 per 7, fiunt 51 g;ra^us : quotum fvbtendens cric latus 

 heptagoni. Ita in oaahgulo infcribcndo ^& 5 60 per 8 dlui- 

 lis.fiunt gradus 45,Rciad fabtcndcni arciiTi 45 , erit latus 

 oflangulicirculoihfcribendi'. I \ 



^^y^I I /. Oflo^ofium ordifiatum ad/j,-itam altltudl- 

 nem confHtHttur , ft ad datam altiatdinem conflrua- 

 tnr cjtiadratum , & illud diiiHs /tametris fecetur in 

 angtilis. Tum enim ex ejuatnor anguUs reSIa lineie 

 duS}£ &cotinex£, dabunt otlogimHm ordinatnm ,'ad 

 altiiudinem datam. 



Vt hic ad altitudinem datam A B cpnrtruatur quadratum 

 A B C D,& proccdatur eo.quo didtum qlhjnodo. 



XXIX. Si in circulo tjuodcun/^ue ordinatum multan- 

 angulttm infcriptHm fuerlt per 17. prop.huius cap. 

 G~ ad extremitates radiorum ex centro ad angulos 

 ditEiorum linea pcrpendicularts excitentur,perpendi- 

 culares confiitucm multangulum ordinatum tottdem 

 laterum & angulorum dcjualtum circnlo circum- 

 fcriptum. 



Vt ex centro pentigoni A egrediantut rajij A B. A C.A D. 

 A E. A F. ad horum extremitates ducantnr petpcndicuiates 

 G H. G L. L K. K I. & I H. Ha: conncxx d(.fcnbuuc pcnta- 

 gonum citca datum circulum. 



I. Cap.Vril. 527 



vclut per fcamna diuifus : ftrigatut , qui i fcptcntrione ift 

 meridicm cxtenditur, vclut pcr fttigas diuifus. Vtcrquc hi-^ 

 bct limites duos maximos , cauiiiiem & decutnanum. Cardiii, 

 a fcpientrione dirigitur : decumanus , ab orientein occidcrt-'- 

 tcni. IUc (ic dicitur , quia coeluni nobis vcrtipur circa polum 

 fcptcntwonalcm : hic , quia facit toimam litcia; vcl potius 

 nunieri X, hoc modo. - . , 



yiger ftimmatur. 



Sept. 



b b b b h - b 



Or. 



7 



Mcrirf. •' 



limites decumani Iongior«/ 

 Jiuiit?s cardinis brcuiorcs ' 

 ^S^r ftrigatus. 



"Sepc. - ■ 



. a a a ' , , 



ii..Irj.ll3 iv'. 





.•.3. .frnibfrf)ioTr3-p\«ij 



in rt{ 



m 



'f.tj; i3no,. 



Merid. 

 a cardiftis limites longiorei. 

 b decumani limites brciiiorcs. 



XXX I. Quo coTnprejfior rhombusfue.rit. , tan0.magk 

 dtto acmi erunt angkli.i^ <^uo obf^M^ , . • . -, 



Id facilc cft cuiuis experiii. SimHKer^riMmth Vqititnfi 



^^i^r co.traatio faerit ^tanthmaiotinitmiiias crit (ingHiorum 



octttortim ^ obtuforurry. ,. . .„j ,_,..> ,^>,^, 



\' w 1 r o-_ • •' ■•-■.- ''■'''.'.• r, 11! :i,jrjii;^,'rtl 

 .KAJii i. t>t ^utn^uangulum a^tttlaterttm tribus angif- 



Its £quatHr, efl £quiangulum. 



Et hoc facile e<icxperiri4 



X X X II F. Triafexangula ordinata tpmplem locum. 



Ratio eft : quia fcx triangula funt a:quilatcra,tefoIutis iex- 

 angulis in fcx triangula : vel quiaquilil.et anguius ordinati 

 lcxanguli valct tcotum & -f reai. It.ioue triplc* angulus fcx- 

 anguh valct if rcrti , id eft , quatuDr redas; Priterea vero 

 nulla e planis complcr Ipcum. Q.ulnquangUlum non coni- 

 plct : tripl-?x enim eius an^ulus fnccret taniiim rcaos «4-. 

 quadruplcx faceict 4-I ; q;,oJ amplius & maius cft.Scptan- 

 guli angulus duplcTf faccret r^nnim reaos if : triplex j-^-.id 

 eft 4-f,quod phitefti &.(Jc dcinccps ihducefiti conflat tri- 

 bius tantum planis ordinatis ccmplcri lociun. Vide paslo 

 antc figuiam tcg. r o. C.vtcrum quod dixiipmi , truer<tt ri.ero 

 uuUaephinis complct locttm.id icclykndim^ cl^ dcmultangu- 

 Iis:-Nam alias io planis niangulum,quadr.itimi, & oblonguni 

 ctiam complcnt iocum. Itaquc- quatUoi £ plai^is eoaiplihc. 

 locum. . . ; . 



Rhombf 



Qiiinquan- 



gulipio- 



ptietas. 



Triifexan- 

 g.j! : Pidi- . 

 DJia tom- 

 pic.nt loci. 



'•" i •' •-",ir> 



XXX. Ohltngum ageods.tisappellitHrai^erfcam- 

 natus , veL flrigatus. 



^ger fcamnatiis eft , qui ab occidcntc in oricntcm crcfcit, 

 Tom. II. 



c A p V- f';.' :t^. 



P R. i€ C E I' T A'. 



_ ■Veufcire fuit fuperficics plana reAiliiVer. j fe- 

 C^ quitur plaua curuilinca, qui: comprchcnjituc 

 i curua. ■ .. <■ 



Ellquc /ImpIeT.vcl mx^z.Illaefl fingularis&vni- 

 ca,pttta circulus : h<tczaria,<^iiippe ejud. insjuaiiter di- 

 flat a medio comprehenfi fputtj : vtfttnt figurtt otiales, 

 lemicularcs,& fimiles,e tjuibtfs ali£ dickniur ellipfes,vt 

 figura oualis •<Q- : alis, pataboU, _,,— 4^ -'y-— x • P»c 

 <juo rirculo fwitftwlioresycopcrfeiliores, Hedt^u-a cir- 

 ciilfts in Geometrik cttrudintorwn,fenohli(juiliniorum^ 

 priwipem obtinet locum, illius natiiram diligeifiiisri' 

 mahimHr. Gcnclin «luntaxat figura: ©«alis proponc- 



L c i mus: 



