Geometri^ Pars 11. Cap IIL 557 



qbJsntur an locus C loco A fit iepreflior rcl altior ? Aqua 

 cnim naturaliter fluir in locum dccliuioicm, vcl faltcm xqui- 

 diftanccni a centto tetrx. Surngatut afl-r fupcr fcatuiigincm 

 A,&in tcrminoCfigJtut baculus CB, Tumfiat coliinutio e 

 pun£lo (t ad baculi vcrticcra B, duifka linea radij viliui nc. 

 Adiicrtitur ieitur, (i angulus a linca vifus & linca pcrpcndi- 

 culi ab comprchenfus , vidcliccti^/if, refltus efl: , linca A C 

 eric horizontalis -. & qiiiikm (i ca mille pcdibus minor Iit7 

 potctiL aqua de A in C naturalltcr deriuari. Si vero angulus 

 6/if ell obtufus , locus C ioco A multo cft altior , & aquam 

 perfe ifihucfluere cft impoflibile. Re<iuiricur itaquc impul- 

 lus violentus per macliinas artificiofas. Si dcnique angulus 

 bnc eftacutus , vc iu ipfofchcmatc , tcriKinus Ctermino A 

 «it depreirior. Vt au;e?n inucniannis quanto dcpteflior (it, 

 antc omiiiaiTienfuraii oportct diftantiam inclinatam A C,feu 

 icjualcm A B. Imaglncmar igitur diftantiam horizontalcm 

 A D, &a!titudinemlcu dcpreinoncm pcrpcndicularera CD, 

 qua paniftum C dcprcirms eft punifto A fcu D , \c cxiftat 

 ttiangulum A C D. Q^uot veto mcnfurarum e!t A C, totidcm 

 particulas conftituemus a pundo aiigulari x vfque ad c. Po- 

 ftcttc punAo c in lincam peipcndiculi dimircacur norm»!is c ■ 

 b : eritquc c b dlftantia honzontalis A D,Si n b erit dcpreflio 

 quslita C D. 



Ad extremunt funco duo loca A & B per libtationcm ad in* 

 uicem comparanda , qua: pcr ambas^cs ciicuiie liccac, Ereo 

 notamusmodicis interuallis , videlicet ad paflus looo , vcl 

 pauciorcs , quoufque ncmpc fcfe acics oculcfrum in coUima- 

 tionc accuratiflimc facienda extendit. C. D, E. Primo itaquc 

 inquirimus , quanto altior depteflioiue lit locus A quini G : 

 dcindc C quam D ; ciun D quam E : dcnique E quam B. Ita 

 cnim fciemus , quanto altior dcprcfli6ru.e tjt locus B quan» 

 A, velyiciHim. Eftque hic raodus librandt fatis cxquifitus, 

 quia propter ftaciones iucercedcntcs linca librata flcium tcr- 

 rx ambitum qaim proximc xinulatur. Ergo capimus afle. 

 rcm , inquc co trahimus lineam parallclam ^t , ad quam li- 

 ncam ducimus normalcm a fr, Linea: <»f accommodamns ap. 

 paratum colliniationis , lincx a b pecpcndiculum. In loco G 

 pcrpcndicuiaritcr infixus (it baculns niger benc longus ,' in 

 quo annuhis p.ipyraccus albus ( vt accutatius notctur) furfura 

 ac dcorllim trudi poflit, ,McnIbr pcr lincarrr/rc coljimct ad 

 baculum C, vbi ftct quifpiam, qui, prout nionitus fuciit, an- 

 nulum trudat lurfum vel deorfum, quoad in ineuforjs radiuni 

 coUunantcm venerit ; (itquc annulus X,& radius collimanj 

 horizontalis fcu Ubratus a X, Ergo quando altitudini A « in 

 pertica iqualera dimcnii fucrimus C (3,diffcrcn;ia /3 X mon- 

 ftrabit, quanto locorum A.C. vnus altcto humiliot fit vei al- 

 tipt. Poltca in loco C fimilitcr fiftimus a(rercra , notando 

 pundi cius <» fupra locum C elcuatipncm , rcfpeiTlu punfti 

 librati X-: ncc aliter definimus punAum horizontalc in pet» 

 tica in loco D pcrpcndiculaiitcr depaiia. Atque ita confc-. 

 qu.nter proccdinius per l'equcntesftationcs,quoadadmeum 

 B dcuenerimus. Tandem faifla comparationc altitudinum Vi 

 dcprcflionum interracdiarum (cicmus, quanto ipfoium extre- 

 morum terrainorum A & B vnus altcro fit altjor, vel dcprtff» , 

 fior.vt patcbic intucnti hocichcraa ; 



Pluractiam prxftari poflunt bcneficio liuius abaci : v.gr. 

 <5uoniodo ad pr.-E(U'uciiiT\ locumfit rcuerrendum ,quando in 

 Tia-ji'*jtionc k rccliVitiiicrc,noc!s intecuallis &angulis dcflc- 

 rtitur ,quomodo (iibterianeicimiculi (i»b prxlritucum locum 

 fint a^ciidi , & quideni (ine a^.:ninicu!o magnccls ; quomoiio 

 omnis gcneris area: pollint dc-ioimaii.&c. dequLbus confule 

 Xub.crum , pra;ccpcoi-cm ollm noltrum Ealilea: ; Scliwcnte- 

 rnm.profeflbrcm Altoilinum ingcaiofillimam ; & lohannem 

 Molthcrum.infigncm li.iius Trigonomctri.c lineari.f illultM- 

 torcni. Hoc fuperponj j loco monemus , abaci huiut & qua. 

 drati gcomjtrici collationi.m reiTte inftitiitam piutimum lu- 

 cis adfcrre Uulc pLa2raaci.-e, ' 



U . 'j 



//. Rttisf Geamctrici fAbrkam & v/um/cfte. 



P--trtis Ramus , non infima: claflis philofophus , r.tdittm 

 fqucm alij vocant mctricum , gcomccricum, 8c altconorai- 

 cum, vulgu, barrilnm lacobi , tanquam .-i fanifto illo pattiar- 

 cha.iainolim inucntus fit, appcllat)accurate dcfcripfit. Fic il- 

 le duabus cx.rc!',ulis ; quarum illa, qua; eft loag^ijpr , dicitur 

 Inclex ; qua: brcuior , Tranfvcrfaiium. In hisrcgulis diopttx 

 infiguniur , pro icctainmctam data: magnicudinis collinca- 

 uoiie , vc nimirum linca optica fcu fiducia- ( qux Gcrmanis 

 dicitur Oie aiiaefditi 3 per illas cxcurrat. Hx porto rcgulx 

 fifte cruta radi; fiftulis fic coaptanda veniunt , vc tranfucrfa-v 

 rium hinc indc pcr indiccm, in qu'amuis parrem volui polTit. 

 Iiivlirradij ficconltrnftl, rcquiritur aptitudo menforisialtcr 

 videlicct oculus obdurtus : infta in mctam dift.incia : radius 

 ad o? gcrt» appllcatus (oculu? quippc hiccft ^anquam ccn- 

 tnimcirculi, cui infcviptum fit tranfverfarium j mainis quie- 

 t* : (tarioXi fieri poflic.crcfta : indcx dcnique reiftus fcu pcr- 

 pendicularisad terrainum rciS.i: lincr mcticnd.T:(quod bcnc- 

 ncio bolid s cxplorari poreft j tcanfvcrfariuni autcra pajallc- 

 lum.Eft au«cm triplex Gcodxfia rcftarum lincarum in radio,^ 

 vt&in retiquisinftrnmcntis : vidclicct Gcodxfia longicudi- 

 Bis,altitudinis,& iatirudinis, fiue pociiis linca; hanfucdx fca 

 iiicetualli. 



Geod&Jia longitndinis duplex eft : c diftantia: vidlclicet , fcB 

 . ftatione,vnifa, vcl ^iuplsx. 



E fiaticine vnicA fic fit : Si vifus fic ab inirio indicis re«.t?'in 

 metam longicudinis , vc tunc crit fegmentum indiciS ad" 

 fcgmcntum traosVerfarij : fic menfoii* altitudp ad<jusfitam 

 longitudine^jn. 



mfi^jits I 



Hic vt «£ fc habct ad f f :fic«« ad 4it^P.cs facili ncgotioex- 

 pcJictur, fi ptoportiona cs ternjiiii al{crnatim colloccntur, & 

 opciatio pcr auieam rcg alara jdftituJ^tur : vt c» fit iSpart. tn 

 ^ patt. altitudo mcnfot iu»{aflx pjxcognita fit ) 4 pejum. 

 Longitudo itaque incufi tanda, etit li pcd. Vbique cnim clt 

 ratio (ubttipla. ■' | 



E fi.itione diiplici Jic ftt/Geodifia ImtgitHdinit : Si vifus fit 

 ab Initio transvcrlatii p; tallcli , in mttam longitudinis , per ^ 

 tctminum indicis rtcti aH aiB t iuw-tw^Jlto politam .- vt crit ia 

 indicc ditFctcntia miiork fcgmenii ad miiius , fic dilrcrcn- 

 cia inter ptLjTum &..fcpuada'I& ftatioocju ftd iQogitadincm 

 ciua:ficauu ■■■,■■ : 



.■■ liirrlvhlritil tn 



j . I fiiloitj m oLr: ai 

 Tjip i-mi) tii.up>x 01'; •' -j. 



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