Architeilonicaj Cap. XIV. 



2-45 



Itaque 



f quadraiigiilo 

 qiilnquangulo 

 lcxaiij»ulo 

 (eptani;uIo 



Cortina erit ad Alam 



In 



Ala fic inucnt.i, (i faciem vis immutabilitcr eireduarum par» 

 tium.qualium cortina cll trium,variabic collum. 



VII. Longitudolinet defcnjioms fit circitcr Soo. ^f- 

 dum-.nempe pro iclit boinbardi furca fujh/itat^ 



VIII. Dijiantia Hne<c defenfioni^ ab ala variat, 

 S'.int enim artifices.qui volutc,^ cHc tantriduoJecim pedum 



aur circiter.Nounulli ctiam pianc nullam cfle volunt.At inuc- 

 nias cimpla viua arcium cxartinlnic niuniiaui, in quibus di- 

 ftanria illafit plus qua ioo.pcdii,& pcrpcram a medio cortinx 

 diftct.V.ide (upta in fchcmatc propugnaculi linca G C Sc F P. 

 I X. In proportionibtu lateristn alicnnts arcis vna efl 

 eUgibilioraltera, 

 E. g. Quando facics & cortina funtaEquaics , vr fupra in 

 fcliematcpiopugnaculi , cortina maxiiiit: tacrt ad dcfcniioncm 

 facici. Verii cnim veto liic rationc aliquid deccdit robori pun- 

 ^ftoiupropugnaculi Hacde rcGcrmani .irchitedi ficdilicrunr. 

 C23aim &ic cortin J;ii rocit ;u niiF liiv/f'in )h' 6<.'»' facrcn wh'« 

 ng £>ct^ffrtiib tbuii / viiD inaii faft iiidit fotticlbtc flfaiuf 

 iviiiti} biU- aiifi Fabcii. ;i?ci'i^wciU'ii ift aiuu^fclic» bic facicn 

 fl(cicf) Ccr cortinen ju niacf cn / bumit man bifcii nuuuicl cv* 

 fc(3Cn/lMlb &iC defenfion , fo ;SU WClt an tCV coitinen 6af)in>: 

 ten (aj?/ iMib aufi ^cii (ic|Tcf)(crn xxniv/ ins gcficfit bcfcnic. 

 2I?c(c^cs3vo|7cdefcnfion ancincrfortcza <^i|it, 2(lfcin ()at 

 cs fcifcnmanctcf : ^n bcm man civoiTc |ravct'c fiicf)t / (nicfjC 

 man icn tolfrrcv cf fpnuctcn an jfirer macljt ab i bafi fic vor 

 t»crartc(crcp iitc(nTOo( baurcii feinncu. ^n fof^ciibcr pro- 

 pottion jicfcfricht cs iiic^t A\\o fc()v. .©auu Cic fcodwcvcf mt 

 ItavcFcvTOcrDcn. 



F\^--^ E C 



ma 

 M 



centro N cadat pcrpcndiculum NO in lincam AB Itaque dimi- 

 diusangulus ANBcll 45.g1aduum.Vt iiiucnias polygona, dir, 

 Vt finus totus fiue tadius Ad tangentcm 4 y. gtad. 

 ON OB 



lOCOCOOO 



Ita 

 ON 



joopedum. 



lOOOOOOO 



AD 

 OB 



yoopedum. 



Hic A B eft cortina : C D & E F facies. 



X. In operibm regnlanbHi angnlm centri seper efi notw. 

 Nam citculo diuifo per numerum latcrum,quotus manife- 



(^atangulumccntii Vidc fupta legulam i.Sicv.g.in uceregu- 

 lariquinquanguladmide jto.pcr j.quotus offcndit angulum 

 ccntri.videl. 7'i.gradus. tifitatx tcxangula.diuidc 560. pcr 6. 

 quorus ol^cndit "angulu centri.puta 6o.gradus.Sumamus fchc- 

 ma propugnaculi fupra propoliti. Arx c(t quadrilatcra. Dmifis 

 itaque j^o.per ^.orodeiit jo.gradus pro angulo ANB.Subtra- 

 ftahacfunimaa 180. rcllant yo. quibus diuifis pcr i. prodedc 

 4j.pro anguloN A B & A BN. quorumangulotum vnufquif- 

 queert diraidium anguli circumfcrentis C B R& F AS.Itaque 

 angulus circurofcrentii e(t ^o.grad. 



X I. Fojfa non tamhnprofcopo arcis,fed etiampro ra- 

 tione terr£,cjuji. advallum congerendurn requmtur,& 

 pro ratione fiibie^ifoli vel arenof,vel fcatnriginofi, 

 velpetricofi, & fecnndum latitudinem atque profun- 

 ditatem, variat. 



X I I. -^ vallo vfqiie ad fojfam fpatium horiz.ontale va- 

 cmmhtriginta aut cfirciterpedes latum relinqiu, & 



pecuUari lorica munirifolet, 

 Itaquc ambitus folTE interior non eft vallo contigaus,nec in 

 ca.idem cum illo lincam incidit. 



XIII. Imtentio & dimenfio laterumefi mechanica vel 

 mathematica,& h&cnirfus efi operationis arithme- 

 tica communis ,velfingularts per tahulas finuum. 



Mechan!cei(i[\\he([3\- fcala gtaduu.^CV f crjlUUltC maf;(la6/ 

 ciufqucheneficioquantitas omniia Iincarum inucnitur:vcl vna 

 aliqua linea,v.gr.polygona,a(rumitur,8: in aliquot partes diui- 

 ditur:pofl:ca ope circini reiiqui lincx ad illam cxiguntur.O/>e- 

 mtio aritbmettca commufiM nlamh ccrtaaliquam proportione 

 cx rcgula j.indequc totum ncgotiam conficit:vt iuxta Italotii 

 ptoportioncm polygona cft 8oo.pcdum.Cortina cft ^So.pcdu: 

 quiacontincnt ttcsquintas poIygonx.GoIaefli6o peduin:quia 

 continet vnain quintam polygonx. Operatio arithmetica fm- 

 gnlarkper tahulnsfinuum eo fit modo.vt in gcomctricisoftedi- 

 mus.e.gr.in primo (chemate propugnacuH fupra propofiti an- 

 gulus ANB e(f 90 gtaduu.NAB 4i.giad. ABN totidcm. lara es 

 Tcm. I y. 



Dupla fummamxjoo pcdum , &exibit polygonafiuc latus 

 A B looo.pedum. 



Si vclis fcivc quantitatem lincx N B.dic, 



Vt Ad Ita Ad 



ON NBfccantcm NO NB 



loooooco 1414115? joo 706. 



Si vclis collii CD,quia in hoc exemplo e(1 1 polygonae,diuide 

 polygonara per 4 proucnient i y o.pro collo liue gola. 



Si vcliscortinam C F, fubtrahe vtrumquecollum apolygo- 

 na i prodibunt yo^.pro cortuia. 



Si vclis lincam principem B E, quoniam illa efl } polygonse» 

 diuidc illam per triaiptoucniunt pco linci B E 5 5 j |. 



Si vclis faciem D E, illa in hoc exemplo cll I polygonac,hoc 

 eft, 500. pcdum. 



Si vclis alam C D vcl F M , illa eft f faciei , in hoc quidem 

 cxcmplo, hoc eft ico. pcdum. 



Potesctiamfinculas lineasinuenirc per tabulas finuum , (I 

 parua triangula foluas vc moris &artiscft. Ita enim in quolir 

 bet triangulo habebis angulos & latera proportionalia. 



Sumamus pro cxemplo arccm fcptangulam regulae i.videli- 

 cet fchmaEB D. 



Ex hypothefi Speckclij latus B C fit l ooo.pcdum : eiufq; di- 

 midium B D 500.pedum.Hoc dato,Iatera AB & AD in rriangu- 

 lo ABC ficinucnientur. Anguliomnes funtdati perrcguiam i. 

 Pofito igitut latere dato Bl3 pro radio.Iatus AH crit fccans.A D 

 tangcnsanguIiD B A. Qijiangulus in propofitoexemploarcis 

 feptcm angulorum eft 64. grad. Sccans ciufdem angulr cfl 

 xjo4763i.tangciisio76ji9J- Dico igitur. 

 Pro inucntione latcris A B 



Vt B D radius looooooo. 



ad A Bfccantem 15047(^31. 



ita B D pedum — f co. 



ad A R pcdum— — — 11 f 1. 

 Pto inucntioiie latcris A D. 



VtBD radius. 10000000. 



ad A D tangeni ir— — 1076519J. 



itaBDpedum 500. 



ad A D pcdum tojS. 



Q^uod multiplicaciuT) per B D— — joo. 

 cxhibetaream trianguh AB C 5 19 115. 



Ciux arcamultiplicata per —7- 



cxhibct atcam totius arcis J*3 5 9C9. 



Vide etiam tegul.feq. 

 X I V. Cafirum plenmqtte ad quadrangttlarem arcts Struauta 

 fortnam acco>nmodarifolet, 



Sit ergo extruendum caftrum quadrangulare.quod in ambi- 

 tu habeat ducenras duodccempcdas, hoc eft, pcdes 1400. Sc fic 

 fcruanda pioportio intcr cortinam , facies, & alas ; vt qualiutn 

 partium cortina crit ij.talium facies fit 10. ala 4.angulus veto 

 propugnaculi pcr tcg.i.fit (io.grad.& lineadctcnfionis ex con- 

 curfu als & cottinae ptoccdat, hoc modo. 



K 



O 



H 



M^L ••, 



Ambitus totius caftri debet elTe ico.duodccempedarum. Hunc 



ambitudiuidepct^.Quotus^hoccftquataparsambitus.eritjo. 



lam collige in vnam fummara numeros quartx pattis to- 



tius ambitus per datam propottioncm dato.s,nerapc 



10 faciesvna 



4 ala vna 

 I j cortina 



4 ala altcra 

 10 facics aliera 



KI Deindc dic 



I B fcoftina ij 



B C 4} dant pro^ ."acie 10 



CG lala ^ 4 



GH. ^cortinaiyif. 



Sumina 43. Ergo jo. dant<[ facie i lij. 

 pro lala 411. 



X i CoUcaio 



