S04 



Encyclopsdis Lib. XV. 



lear pio- 

 porfiona- 

 Jes quH efc 

 ficiini i 



XXVL Si tjuatuor re^sjtnt profortiotiales, rcBangu- 

 lum mediarum i^HatHr reclaiigulo extremarum. 



Proportionales autem funt, fi fe Iiahcant, vt prima ad fc- 

 cuDdaitijita ccrtia ad quaicam. e.g. 



A,- 

 E.- 

 C. - 

 D.- 



-i pcd. 

 3 pcd. 



-(, pcd. 



-9 pcd. 



Sitisttibus 

 icftis pio- 

 portionali- 

 bus,d.itur. 



Ties rcaac 

 pioporiio- 

 nalcs <]iiid 

 efiiciani > 



■R.eaangulum faaum cx mcdiis B & C, .Tquarur reftan- 

 qulo fafto ex A & D. Nam vt bis nouem Uint 18, ita tcr ItJC 

 lunt iS. 



XXVI L Si ^uattior reHd. ftnt -proportionales , datis 

 tribtu, datiir quarta. 



Eft corollariam praicedentis propofitionis. Nam rcv.T:an- 

 gulum mediarum diuifum pcr cxtrcraarum altcram, relinquit 

 altcram. Vt in propohtio excmplo 

 Sicut i ad ;,ita 6 ad 9. 



Reaangulum failum eft t, & 6 , nempe 18 diuifum pcr 

 primam.i, relinquit extremam,^. Atque ha;c ti\ ratio,cur in 

 regula Dctri duo polleriores tcrmiiii inter fe multiplicen- 

 tur , &: produftum diuidatur pcr primum : quia vidclicet pro- 

 duftum multiplicationis fccundi & tcitij terniini clt etiam 

 produiSum multiplicationis piimi &; quarti , diiiilum itaque 

 petprimum,relinquitquar[um , nam diuilio Sc multiplicatio 

 muruo fe produnt.Nihil aut<;m intetcfl ad praxin.vtrum ter- 

 minorum mediorum fccundoVel tertio loco ponas : ctG in- 



retim mutacur proportio, e.g„ - -: ' 



Vt z ad ? . ita 6 ad 9. Siue, 

 Vt lad 6 : ita 5 ad 9. 



XXFin. Si tres recfa/i/it proportionah! , e/fiadratum 

 medite. mqttiitHr ohlongo e.xtrernarum. 



Quiacnimmcdia bis ponitur, perindc eS: acfi quatiior ef- 

 fentproportionales. Ideo quidquid de quatuor proportiona- 

 libus diftum fnit, de tribus quoquc proportionalibus eft iu- 

 telligendum. e. g. 



A- 

 B- 

 C- 



- — t ped. 



-4ped. 



• — S pcd. 



Komencla- 



tura Gei- 



manic.i 



quorudam 



tcrininoru 



geometri- 



coium. 



Confcr hanc & prxced. regulain paulo pofl; cumcap. 8. 

 leg. 8.&<). 



XXIX Oper£pretiim eft in conff^eHu habere terminos 

 Geometricos artificum Germanorim. 



Ex iis pr.-rcipui fic fe habent. 



Punaum ift £ies inc(Ten6 aiifaiig/biis fcine otroffc ^nf. 



Linea i|f ein Iati(jcr ri|"; oter ffricl) voti ctiiem punct Jnm 

 flntern/fo leinc breite viiD 6iclc hat. 



Linea reda tft cin «criiDcr flricl)/ivc(cf;er fcfjnurzec^ ittji* 

 fc^ett ^n>et;>cn puuctcit fijict. 



Linea curua iff eiit i^riitnmcr fTricf) / bcr (Tcf) ttoii fcineni 

 jn?eocn ei;||crffc!i vnnctcn erftebet lonS nibcrfcgt. 



Linea mixta ijf cin i'crinifcf)ter ffnc^ anf; «jeraben tonb 

 frttmmcn fnttcn v>nifefcF)r gcntacfit. 



Liuea perpendicularis iff cine TOincFctrec^te / attfrccf)tc/ 

 6(et)rcchtc/ obcr n^^narccfjte (ini. 



Linca flexuofa vcl fcrpcntina citigcitiitnbcnc obcr ^(i)\Ckni 

 5cn(ini/ivirb gemac!)t aufj lauter ^affccn vmWreijTen bes 

 Jircfcfs. 



Liaea inuoluta fimplex ifT ctnc mnfc^cffini. 



Lineaoualis \\\ ein eolmi/obcr ct)er:in!bnn.ct. 



Linca inuoluta multiplcx.fiue fpiralis aut conchalisjiff eill 

 fc()iiccFcnltnt. 



Ellipfis/^^ Iine3clliptica,iftcin a&fancjc runbnna/obcr 

 ctia(!ini/bic tcinc genicmfchaft ntitbcm ^ircfcf f)at. 



Paiabole ,/(•« linca parabolica , i^f cin dtlaitijc (ini / bcin 

 tri.in?;ulo vcrtran&t.Appcllatur bic brcnnfini. 



Hyperbole ,/«< linca liypcxbolica, iff bcr parahole tocri^ 

 Waiibt. 



Vc mclius capias quid fit ellipfis, parabole , & hypcrbolc, 

 mcminens triplicem cffc fciflioncm coni.Prima fitpcr trans- 

 ucrfum,itavt vcrticcm &bafimconi non contingat : & \\xc 

 dicirut ellipfis.Sccunda fit a vcrtice coni vfquc ad bafim : & 

 lia-c dicituf pai.ibolc. Tcrtia fit in vttoque latcrc coni a ver- 

 ticc ad balin : & h.rc dicitur hypcrbolc. 



Lincahclica, ift ctii fciiraulcn (lui/ gfcicl^ tric fTc^ fiit 

 fcf^lang »mb eiii b.iunt nMitcU. 



Linci parallcla: finb afcicfweitigc ofccr rauffenbchnien. 

 Linca flcxilis,ci!i Itiii i^te ficfi cicrit f^cuAcn U\{(t. 



LineaccEca c;« blin^c ftni/efl puniflualis,i'f ,it\ 



occulta,tt>elchc gcrtffcn unrb garfubtif of;nc binten. 

 Linca circumflcxa cilt tcttcn Juj^. 

 Supcrticies iff ctn fir.clic/njclcieOat cine (enge t>nb fircife 

 cl)nc biiFe. 



rlanum obcj fupcrficics plana , iff cin cDcnc ^a<i)C I tt)ie 

 Jitan |'ii)et amnMiTer tnciucm hccCcn. 



Superficies gibba ijt cin buffficiite »nb frummc ffdc^e / 

 nnc niaii an ciner fiuicfflfiCt. Ellquc conucxa , vcl concaua. 

 IIU i)f ruiib von aiilTcn/afK n^ann tix ctuc tui]e( an(t()ef( .• 

 H.1.-C ift riinb t>c!i tiincii viib fio(/a(s »»aim bu cinci» 

 fchnjiebo cn t>on iMjtcn auf anfl^ctt. 



Angulus planus t|t cin f(acl)cr iMib e&ciiern)inctc(.Eftque 

 reftihneus,curuilincus,vel mixtilineus. 

 Angulus reilus i|t ctn reci)tcr njinc('c(. 

 Angulus obtufus iff ctnnHitcr obcr Ifumpfcr tBtncfcI/ ifl 

 gr6)]cr afs ein rccfjtcr winctcl. 



Angulus acutui i|J: cin fcf)arpfcr obcr fjJitsigcr ttJinrtcl/ 

 iff tleiner a(s cin rccf)ter. 



Figura ttjirb t>on etnem ober mc^r enbcn (>cfcf)(offcn. 

 CircuUis tft einc f!acl)C }igur/i>oii ciiier f rummcn Imi \n: 

 grtffen. 



Ccntrum clrculi if? ein mitte(pnnct bcs Jircfcts. 



Segmentum circuli iff ein ftacf bcs Jircrcts / en(»»ebcir 

 ftciner obcr groiTcr als bcr fjalte Jircrcl.Hinc eft fegmrti- 

 tum maius& minus. 



Scftor circuli ift bcr Jcrfd^ncibcr bes Jircfels. 



Arcus tft ein bogc n bes jtrcFels. 



Lunulaift cin ^gur/ g(cic^ bcin tnon/ t»ann cr m a& 

 cber^uuemcn tff. 



Latus eiw feittc/ ^ckQ if^ ein «c^tc lini/ auf tt)e(c^cr bic 

 figur nicl)t ffcf)ct. 

 . Ctus em fcitte barauf bic figur f^c^et. 



Cathctus obcr pcrpendicularis tft Dic aMfrccl^tc/ tnagrcc^- 

 te/ober unncfc(rccl)tefeitte / «)elcl)e burcl^ bas blci^iaewjic^t 

 gcjogcn nnrb. 



Bafis ober linea horizontalis ift bic grunb lini / tvelc^C 

 mit bcr perpendiculari tft nviffcrglcicf). 



Linca inclinata, fubtcnfa , cber hypotcnufa ifl bic fc^ro^e 



Planum perpcndiculare i|f ctu foIcl)c (Tdcf)e bic a(kurf)af< 

 Dcn nad> bem blep aufrccf)t ftcf;ct / afs cm fcfcprccfjte 

 niauer. 



Planum horizontale if? ciu licgcnbc fJac^*/ ir>c(c^e tit 

 lineam petpcndicularem ad angulos tedos fc^ncibct / afs 

 cinc fldche bes tt?a|Ters. 



Planum inclinatum , feu latitudo obliqua & inclinata, tfi 

 cinc fIdct)C/iDc(cl)e bic perpendicularcm ad angulos obliquos 

 biirchfcl)neibct. 



Vmbra refta ifl eln ^c^MiiW ^am ciner pcrpendicular 

 aufgcricl)tcn fint : afs "oow einem t()urn. 



Vmbra verfaift ciufct;attcii i>on eiiter hypotenufa : ala 

 toon cincm naacl in eincr teanbt. 



Sirus hotizontalis iff/toann cin inrtriimcnt aufrcc^t 

 ftcl)t ad angulos reftos horizontis. 



C^uadratum i)r ciuc VMcruiut. 



Figura altera parte longior,l)"t Ciltc a61ansc feicrung. 



Rhorabus 1)1 cinc rautcir/cDcr rantcn Dterung. 



Rhomboides i|t cinc CbdlliCIC rautcu. 



Trapeziuin n)irb aticf) menfa gcitant. 



Gnomo i)> ciii wiucFcfmafj. 



Pentagonum iff eiu fiinfccF / hexagonura ctn fcc^SCCf/ 

 hcptagonum cin {\bt\\t.ii :c. S^\\i figurcn ttjcrbcn auc^ 

 gcnantnac()bcn fantcn. 



Cubus i|>cin corpus g(cicf) cinem n^^ftrffcL 



Conus em fcgcl. 



Pyramis (ffctn corpus gfeicl) cinem fpif?igen triangel. 



Globus cbci^fphira it> ctii tugct obcrtfof!. 



Cylindrus i)t ctn faugc rftnbc. 



Parallelipedumifrci» laiigfierecfigt corpus, als ciiilail* 

 gcr guabcr|rein. 



Pcrpcndiculumcin fcncfc( otcr fclcpgcMJic^t. 



Norma cin winct"c(f)acten. 



Amuflis em liniaf. 



Hcdra einc taittc. 



Libclla cin waffcrnjag. 



Trigonometria linearis ift CiU ffitcf ber geomctri , barin 

 <}elcf)rt wirb/ itMc man bic friangcl btircf) basltnialmit» 

 jircFcf mclTcn folf. 



Trigonomctria numeralis tt)ic mart bic friangcl burc^ 

 bic tabulas finuum mcffcii folf. 



Euthymctria , Longimetiia , Alcimctriaifiatfcs iVXtiXa^r 

 ttJic man ncmftO) btc tinicu iiie)Tcn folf. 



Planta i)f bas >)fan barauf man ban>cn foff. 'Eius dcfcri- 

 ptio dicitur ichnographia. CJuanquam etiam late fic appclla- 

 tur defcriptio, qu.i rcrum plana forma fitufue delineatuc pro- 

 portionatis triangulis. 



Linc4 



