ZAZ Encyclopedi^ Lib. XXXV. 



Quanti. 

 tas lateii 

 arcisin- 

 definita. 



feptcmangalorumTotusc.rculnsd.u,daturperfeptcm^qno. 

 tus eritarcasBC. mcr,fura atiguh B A G : quo dctraao dc 

 duobus rcais.in triangulo plano quouis, atque adco ct.am in 

 tr.aneulo A B C,exiftcut.bus:rcli.iquctut fumma angulorum 

 A B C & A C B : quorum angulorum vnufquique clt dimidiu 

 angulicircumfetcntixpcr (huauram. Ergo fimul fumtiex- 

 hibcnt ipfum angulum circumfcrent.s. Ita crgo ci it. 



B A C VI grad. ij.min. 



A B D 64 giad. i7..nin. Similiter A C B totidem. 



B ADz5 grad.4imin. 



I V. ^amitas fiue proportio laterwn fingnlonim 

 vnnifcHtuque arcii reguUris efi indejimia. 



Etfi enim Specklim vult effe looo pedum,& Itali 800. pc- 

 dum:tamcnBclga;vaiiant. 



luxu Specklium talis erit propottio fingulotulateru.v.gr. 

 inarcc feptem l3tcvu.& pofiro vno vno latcrc iooo.pcdu,etit 



Scmidiaraeter 1 151 pcd. 



Cortina— — ■ po ped. 



Facics ■ 400 ped. 



luxra Italoi -ft eiufmodi proportio. 



Polygo.ia 800 ped. 



Cortin- 



Facicn.- 



Gola* 



Spalla- -r . ,,.- , 



Cafamatta z fpa l^: jipcd. 



Orechion f fp^j'* ^^TPed- 



■j polygonjE 480 pcd. 

 • \ cort.nx — 140 ped, 

 .1 polygonx i<Sopcd. 

 "i polygonz 1 18 ped. 



Aperturacafamatta 1 cafaraarta;^»' pcd. 



Alij a facie propugnaculi incipientes.eam volunt cHc .n arce 

 maxima 40o..n mcdiocri jso.in minima joo.pedum.Deindc 

 facic pro lubitu allumpta.cortinam voluntcot.ncrc qu.nquc 

 <]uartas, & alam duas quintas facici. Quae proporno cum 

 ipeckcliana prope conucnit. Nam fi fac.cm 400. pedum d.- 

 uidas in quatuor partes.h.c.in quatct cctu.n pedcs.cort.na.C 

 {\t ^oo. pedum , exadte contincbt quinque talium partium. 

 Sincandemfacicm^oo.d.uidasin quinquepartcs.dus qum- 

 tzcfficient 160.pedes.Qu3eparumabfunti1jo.pcd.bus. 



Alij diuifo htercarcis in quinquc partes, cortinx tr.buunt 

 huiufmod.partcs trcs,facici duas,aljE ^, h. e.\ cort.ni. Qua 

 xatione coUo propugnacui. vtrinque rclinquitur pars vna. 



.<4/»hanc proportioncm obfetuant. 



Facies & cortina funt squalcs.nempe 1 polygonx. 



Golaeft ^polygons. 



Spalla in arcc quadrangula cft \ cortinac:in quinquangula 

 Telfciangula^cortinz:quanquarainfcxangulisctiampoten: 

 cffe j:in fcptangula.oaangula 8< arce fpalla eft ; coriinx. 

 Jlij hanc fcquuntur proportioncm. 

 Gsla • — ] "1 



Cort.na- 

 Linea princeps- 



\ >polygon2 



Angulas 

 ptopu- 

 gnacili 

 vaiius. 



Facics & ala var.am forriunrur proportionera pro magni. 

 tudine anguli propugiiaculi. 



V- A>ig'.dmpropiignaculipotefi efe varitu. 



Itali pleriq; eum faciunt obtufum.quod is aliis fit firmiof 

 S/>ecW«a* vult eum fcmpcr clTe redum. Erhardtt-s lie Bar le 

 diic itidcm. Atqui in atcc quadrangula vcl quinquangula id 

 Jocum habcre nullo modo poteft:vt ipfimet fatentur:im6 in 

 arcectiani (exangula velfeptanguladifficulicr. Idco prxce- 

 ptumilluddearccoilo vd plurium angulorf. inprimis cfl in- 

 telligcndum. lnbe'gio(\ini artifices nobiliffirai, qui angulum 

 propugnaculi prorafoncangul. circumfcrcntia^atcis varian- 

 dum cllc ccntent : fic nimirum. vt quanto magis apcritur an- 

 gulus circuBifcrenti.e , tantb inagi'i etiam apcriatur angulus 

 propugnaculi. Abfurdumenim cftcputantjVtangulocircum- 

 fcrcntijc ctcfcente , angulus propugnacul. non fimul crcfcat. 

 Inarccigiturquadrangula.quippeomnium minima;quiaan, 

 guius circumfcrentiae eft mmiinus , ncinpc tantum 90. gra- 



duum,etiam angulum propugnaculi minimumenevolunf. 

 Minor autem nunquam cde dcbcr , quam 60 vel j^V gra- 

 duum.H.nc Gcrmani architcdli dicunt iJcv angulus VCln MU 

 iwcrctfaQct »nbcr6o. giadiiicljt. 5)H'tticil&er angulusv^oii 

 40. oticr jo. aljufpii; tomt Da)] i'r Dic nic|clii fes gefrdiif^cs 

 nitWcrtragen tait. Augulus ergopropugnaculi,fiue angulus 

 defenfus,arcis regularis quad.ilatcii cvit 60 graduum.Quo 

 pofiio,angalus defendcns necclTario erit i jo.graduum.In cas- 

 terisarcibus,quxangulum circumfereticcrccto maiorcmha- 

 bent,anguluro dcfenfum & dcfcndentcm fic inquitimus.Sub- 

 trahatur angulus circumfeventisminimus , h c. 90. grad.ab 

 angulo circumfcretia: propofitac arcis:rclirti dimidiu m adda- 

 tur ad minimum angulum dcfcnfum,h e.ad 6o.gradus:idem- 

 que dimidiii auferatur a maximo angulo dcfci.dentc.ncmpe a 

 ijo.grad.Sc prodibirifta quidc.Tiopcrationeangulus dcfelus, 

 hac vero anguiusdefcndcns propolits: aras.c.g. in arce qilin- 

 quangulaanguluscircumfercnti3e (it iq8 gr Detenfus angn- 

 luserit69. dcfcndens 141 In arce fexangula anguluscircum- 

 ferentiaE fit iio.gr.Angulus dcfcnfus erit yj.defcndcns 155 In 

 arce (eptangula angulus citcufcrentix lit j 4 gr. defenlus cric 

 79.gr.dcfendens 150 Hac rationeangulus dctcnlus non priiis 

 fit tcClus, quam vcntum fit ad arccm 11. angulorum. Sed fic 

 tamen icdlo proximus : quod fatis cft : & angulus dcfendens 

 non fit nimis obtufus.quod plane vitiofum eflet.Nam vtan- 

 gulus defenfus,qu6 redlior,e6 meiior,ita angulus dcfcndcns, 

 quo acutior,e6 melior. Sic igitur anguli dcfenfi pcifcftiocu- 

 randacft, vt anguli etiam defendeniis perfcdioni , quantum 

 fieii potcft.ftudeaiur. Cscterum angulus circumferentix Ita- 

 lis dicitur angidnsgoU. Qu6 pcrtinct vfitata regula,' qux in 

 operibus tcgulavibus iuxta & iiregularibus eft obfcruanda: 

 vt nempe angulus propugnaculi duabus tcvtiis fit minor an- 

 gulo.golx, id eftjCiicumfercntix.v.gr. 

 •o C Circumfc- Quadiang. Quinq. Scxag. Scptag. Oftag. 

 -g J rentis 90. 108. Iio. 1x9. 1 ; f, 



^'"-) Propugna-Vna tcrtia jo. 36. 40. 45. 4y. 

 <C culi Duij tertix 60. 71. 8o. 86. 1,0.. 

 Potcft ctiam taliscireproportio 2ngu'orum propugnaculi. 

 Grad. M.n. Giad. 



Quadrang. 59. 4(5.~\ ^64. 



Quinquang. 67. 6. | | 75. 



Sexang. 74- 4«. ^vcX bo. 



Septang. 75. 40. j | %i.. 



Odang. —7«. 34 J L8g. 



Huiu.«locicftilIarcgula:;jincf)rfeitc«»llt> angulos ^as 

 (ioIliocrctf)at/(c rfarcfcrtmrb Derangulus vomtoilwcrcf/ 

 bo)^ cr Jtt loo.grad. tnib mcf)r offcit |tcl)cii tan. Noa tamcn 

 vltra 90. gradum folent afcenderc. Vndc Gcrmani elegantcr 

 dicunf.Kcincs boUtPcrcts angulus wirb Jum ^of)cfleii n^cr 

 90.gradus gcoffnct/^icxxicilfccriTinctelfjacrcn am fiarcFfrcu 

 tft/Vttb.'aucI) nu!cf)ti3 cicnuct tcr artclcrcn fu xt}it>ei)fc(icit/ 

 aucf) bie anguli ^o ttbcr 90 grad f,!l!cn/ i}ro|Tcn naci;it!)C'.( nt 

 cincrfortcza brincicn.Hisadde & ifta.;2>ifc brcprccicdi f,U> 

 feii inctiifmbotfmerif jumcrticn i.Hn-,..;D>if;invoncii;aiu 

 bcrfegttg ter bodtvcrct Lms ma)} bcv imi)";tiiietcn hfj^cl liiclit 

 Jtbcrjjriffen wcr&c/ Das t|t/£ii)); man bie bodtticrct' ubcr 800 

 obcr 90ofcliuf)itim^6cf)|tcnuit ^■'pcinaiibcrfegc.llcrifclic 

 bt);vion Ingcnieurs fcf)ul)cn. 1. ;t])a); maii bcm angulo bcs ' 

 fcoflroercts fciiic acl)iirlicl)e )tdrcfc ^ct>c.^clclics gcl"cl)ici,it 

 toann ber angulusbes boltwcrtfsf f)at bes anguli vor bcr 

 gofcii..f3ierinitfaltcii bic bollTOcrctfpucf tcn iiulrt Ju tpitvq 

 »nb engc/ foiibern tcfommcn ibreii cicburfiOH-n rauni i\\\n 

 gefcf)ui^ »nb vcfct .CO?aii nuiij fie aiicf) iii folclcn cicr aumcn 

 tDcrcten juctlicfimafcn abfcf)iicibcn/ nu'ici)cs in cnctcn faf;t 

 fcl)wcrltcl)fu rf)uii ifr.5 . *Sof bic fTaiicf iruiui fo ffarct als 

 immcr mdjjlic^» 111 bcrcortmcn ctcfucfjt wcrbcn / icbocl) \3,\ii 

 bem angulo vombollnicrcf aii fcincr |tarctc mib bicfc ni« 

 <t)ts iH-nommeii tuerbe:onb t)f iH')fcr nuin pcccire an bifcm 

 le(,ucii/afs an bcu anbcrnjtc})cn/uigiiu af(c brcp jfftcf nict); 

 f6nnenbct)famenfct}u. 



V I. DiEiaporportioUnearumdrangulorumfifnulcon- 

 fifterepotefi , qmmdiuprincipimn linex defenfionis 

 incertum relinqmtur , nec ad concurfum cortuiA cr 

 alA iilligatur.At fi lineam defenfionis ex ipfo cocur- 

 fu als, & cortina perpetuo dutlam velis,certa linea,- 

 rufimul & angidorii porportio ohferuari r:on potefi. 



Igitur in tali cafu , quando nimirum linca dcfcnfionis cx 

 concurfualx & cortinae ducenda cft,vel linea: angulis.vclan- 

 guli lineiscedat oportct.Quod (j ergoangulos retincrc cupis 

 inconcufros,al.-Equantiiatem pro fingulis iiiuitangulis varia- 

 re oportct, hoc inodo. 



Angu!usacortina& lineadcfenfionis 

 comprchenfus eft 

 ( quadrangulo 1 5 grad 



quinquangulo 19 grad.50.min. 



fexangulo 11 grad.jo.min. 



fcptangulo 14 giad j^.inin. 



Iiaque 



Ini 



