PRiEFATIO Prttitmmm dmUtdtntm vtl frtmmbus Ubrtt ViX4tHgtfi,futt, mfmtfit, cmtmfd^m ttt ^mdt mtdu4rtr r^tttmemf; gtgmemttmm ft^m^rJ fil^ fmmjmmgtmtt,t/ikdtstmf4r4„m, msxtmi /^nUdmLb^, 1^if^tfrttrmmf4,tmtmm ttmdtttm, 4dttm4t4 fi,mr4 dtgeme^ Urttu, .t4U4m tmmtmi mSttfdem r4tt.mem /ejLtJ^Z^, •Bmtmtt^umtmt, tfittm/dtm ^srtflms.cmm ,4m,m r* W/r. • D»: l$p*mmHtft4mgmUdt{immttmmm gtmttMmtis^ dmpUp,rr,m»t^ t4mt/fh4r,m, vtt i^^msffh^rttdtt.mttmtmttnttdtsf^r^btlttmm! 'jr.Vj^r-^^^f^MfrmtMttrttbmtm/fh^^^ ^^r'Mim4jtjr^'^»duvtrt^dmfUts,tmmt4megtg.,J^^^^^ < Cc. /i» tJltffim.frtxtmh4,ttmemh4it4t, fm^m^ fm^tmtrdttmt 4d » 4. •mUtt, 4df^4btlAver»fit tm r^tttme i /tnqmt4Utr4, ^•/•,«.«, y^Z^t^ &mfUmufigmruftrrtmtUt,ttmf^'» m'>''>tetfLi»,e»dem-^^ udem pe't i. I. i tertiapariem itufdem >ixif.Smtiitet iH Cf.n9, ie parabeltce tltui kUtm 41. '^t^^xfperf^ttrtiamtartem di^unsabafi, inparabilaverUp^ l'ArcV g/''»^*'"'''»'' Pif ^duastertusett»fdtmaxiiremmu,f 4htpf4 %tt fquepi ^*f* f"?.' f^^i^ varietatem t»plurimit!$tjsfigurii fapiutmt fitiifm^m mexindifimttlt>^ereirU MgitUsper axemtraHfeHmbusveiuiieempaditTM effiwens.bd^ htu JiSlirumpUnoru •»<,iua ratiene , tU,4 ^ ipfira » /huiiiri^^. ab tpfitgenttirum emerger^ratitn.mtxtfimabam.cttm tampUi (•? cinfidretpU^rum ratimt^amtJttHm. a1,'^f49m^f»ii4or^yj^ tioftemminimictnc/trdarei^igurajtuWmefifltyamuhtk^ quirentem eUum,^ oper^-nperdm, ^c>em»^bn, fai/it mtiii Pdm/alurum eSe,miht inrt ef^yfenaw» '^idebath^^.VtfUmpnttt^ profmiiu, rem contempUtus m h*nctM»iideiffnt pmnttdm nempeairem niHram liness,&pUsa,mv.Uinuieer^eeintiititpi t,4,fed»'>'i're.^<^t'ndrnygttur,f^conum^^^ t.l.^. J^fratttnjmhabereiUacomper.f.^uam. i.vifmkiaM^ o D:f.,.9. oyUndnaimntapUnactni, oreguU comi^iimmCmmpiZ gt4 gls pUni ) di 0f^^lti4m hjfm antlntlh illi s^^iJiTfdBter fmimfit (jB9d4!Hm$d$feltn^m imieUtfinntnf ) ei »(]ndm bdketejh hndrut 4de$nnm. Ofiimsm etgo methdnm ffnfdrmm ftrutidn menfnrd tititcdni prttisUnedrnmpro fldmtt, dr fldnorum pre fpli^ dis rditenes tnidgdre , vi iOsee iffdrnm fgmrdrmm menfmrimthi €9mfdrdrem,res»fmt$, imxtd veidfmcceflti^vipefUgenitpdiebtt» Art fiet$dmtem idls vfms fmm , tfmdfe ddpr$^fitds qmdfltinet dh^ f$lmemd4s Algekrsttci ddhtbtre foltmi; ^mijmt^^m numer$rmm fddtces» (fmdmmts ineffMes.fmrdds. dcigmotds, nthtlominmsfi^ $t$ml d^re^dntes . fmhtrdhemies , mmliipltcdntes , dc dtmtdentes. dmm^§i$pr$f9fiit ^et exfpididm ft(sim$ittinmenmdfdre valeif^ fmdfdits eh^^e mmmerdfiht ferfmdiemt. U$n dltier iffe efg$ indt^ ms/titUmm fime Itmedr^m.fime fUmormm ecmgerte (^fdem z $ in Itk %. exfUcdimr dfmmftii)ltcet (jmodd eormmdem mmmermm tcnomi- mdhU.fmfdd,dC tgnttd.ifm^di magntimdtnem idmem confpcuis U • mtttkmt cldtift. dlc9 ^ttnmormm tnnefitgMnddm moinfmrdm vfm fmm, VI iegemit tm frecefm $fertt dffdrfhtt. Frofofiimm mthi eB dmtem iGevmetrd inhit feftemUbrtt (jndmflnrtetm tnm pUnd^ rmm p/fndm rmm mIkjmm eii4m jf> dtfj » 4t frsttpii} Emdide, & Art htmtedt fertrsciMi/ifsermnl, rtli^jm* ver» memimi,fm»d /ii^m tmem/f,4(' temidW, vmt tmmtn exctft» Kefler» , fmHesfi»me Dtlj Amfirim- tiftrvirgtm me-ifi rimm dimttlttmdi ,fi(lijm4mtm fm*f Slire»- ^J^^^f^t metrtmArthnndt» fm mm srt} ipfms Arehtmedii tdtnmtnufiit «.rttol » tfftrinmt rectnfott , ntmu tlHfmdtidt, jmtlefemm^ifint . tdttQtt fditmitmi.ttniiemtmmftriemfuftrdddtdit.^mdmSieretmtiri^ Archtmedetfmfflemenlmm nmncmfdmtl. tn f«4 mmlitflictm St" {itonmmttmttmrmm.Ctiemli mtmp}, PdrthU, Hjftrheli.& tBi. ffti, mte mtn iarm itm ptrlttnmm (ire* dtmerfii *xts t tttotuiitiitm (ontemfUtmi .ftdim mmmeritciadgtmij fefttm ,fr*tcr qmintjmt drekmudtd, Sfhtrmm f(,li(tl,(.inttdtiptrshtltiii.i init(iti hj' ferMiemm . Sfhtriidti ibltngm,& prottimmGttmtiui firqmdm tttztmprtctmtfrimmtetim. CmmtrgeUmtxft/iiMm mettem* dsr^^n ft^Hfiftim mti4m,di,f$ dicerifds /!t,vaUe compendicfem fntthoh^m 4 iinutmfsem , ftUetter mecum diium efse extBims^ cti, vthMc fj'$d4 ^fr^ttrilld Archimedcd, mtht fupftditArentur^ ctrcd (jttd tfhus vim 4C ettergi^m, experirt tictret. Ne cfuis tdmert putet mt ommum diilofum foUdorum dirr,enfionem futfstconfe^ cfuutum, (icuti ne vt pr^dtil^m Stereometridm , 4c Jsfpplementitm perle^enti conHsre petertt : fttis mtht futt eorum 4\tqu4 certicri t4m?, m f^llor ratione^tnuefligdre^cjUd ctrctter nurr;tro plufcjuam vigtnti ennurncrart poterunt , pr^ctpue fi Archimede4 tn numtrt ti^mputtntH^, (jmncfifciiictt pro fingults cfUdtuor Cor>t feSftomhus^ tfr 4mplius 4ltaUi dr fic fiunt foltda Archtmedea^ ^ Cttf. 14» circulo ntmp} Sph^ra , tx p^rahoU Conotdes parahoUcurr , ex /corf 1 ». hypnboU hyperboltctim^t^ ex tiltpfi fph^rotdes ohlcngum,ftu pro j 1. 1 4« Utnm. Vt\ rettoltttio ^t circ4p4r4ilLeUm 4xf, extrs fgs^ram^ ftd \oXs' ' ^ noinim} eandem tdngftem conlfttut4m,(jr fic ex ctrcttlc fit ^ ^nct* iCor. 14* lufUsurcircttUriSftx p4r4boU* ftmi^nuttts l4tus par^boUctts, ■ Cor I j. hyperboU ^ hyperboticus (hos Keplerus tamtjuam montts t^/. j4. l tt4 cAUitatifimitts Crati rts voc4t) ex Elitpfi ' Atulus l^tus tl* \ M 4 ' lipticust gjucm idtm Keplerus , velut ferto f uHtcarum ; ucliarttm y Cor. 15. jtmittm^Anulum 4rduum ^pptBat. V tt reuflutto fit ctrcd p4r4lie^ Vcot /^m 4Xi , 4C figur4m tan^entem , tunc ix cm uh fit Anu^us 34 l^. m^riilus circuUrif^txp^rabo a^ femt4Kulus firtcfus pafdholicus^ a Cor hyperh^d y hjperbtlicMs , ^ tdndem ex elitpfi, cjut pnrtttr Anu- bco^ ao. ittsHrtciUi^elUpttcHs nuncupatur» Demfutrfuoiuttone fs^s * *i J 4« Circ4p4r4ltel4m ax$ ,ftC4ntemq\ figuram tn duas portiones W4» 4 cor, %u tfnaltSfCX ctrculiporttontmatcri ftt Malumrofeum ^et mtncri icori M^l^^rscitrtum. In etttpfi vtro ex m4tort Malum ^ cotontu^ d^tX 3 1. 1.4. * minori fit^0liU4 Bxp4rahot4porttone m^tortfis ' Aceruus m^tor • ParaboJi- p frabottcus,ex rntnort^ Aceruus minor:tx hyptrLc ^pcrttOKe ma^ iisconfor- \ ^ ^ */ / ; 4- Kittr. ^''t pt Actruus mator hyptrbottctts , cx mtnort /iceru.vs ■ mtr^or. tiMonfoi^ ^^^^^^^^ /l^rrwi mtnrrts fdraboUcos,^^^ h^lithttios ^tdcm inifi. Ktpit* i ifltfMt cttnthui reilis fimilti ext^tmdf, ^utrttm gUd /%nl dctt- 9d,^4ti4i$i>tnfd,vi wpeoiitbfis. fjMMndopftmitm, tnfjyit^etfnt" ius coHtfcttnt. Hdt vtro fttnt fohdd numtft vtgtntttCjuthtti tttdm Jinttlas artcli$s%tUtpt9cns4ltefd pdftt Idtitf ,& Anultiildtms * tUtpttctts 4ittr4 p4fti k ifft^t$f,dddtp§fittnt,(jtteKtpUfHi Ttd^ b Cor. ip. fd,feH'M)$J9irctctftmtkmpHtdt.ntcntmtdfiltd4. f$Ud4 i n$hts htc confdef4t4 twritef profeejue^ mur. in pnmi tgttmr.f^ fecido LtlfO, vtplurtmtim Umm4t4pf$^ ponuntur,eju4 4i fefuentium Uhorum dcOrinum cMptend^m ue^ ie/f4ri4 viJentuf , Ucet in eifiem p\urim4 eju$ejue fmt fmgr^ttm fimpUcttef demonfir4t4 : /n i ^ & 5« Lth. f$Ud4ex^mtn4ntuf. ifu4 ex c$nicts fecltonihus fu^mgeneftm Mg^ofi it. in t.4giiufde fp4ti]s heUets, 4c foUdts dh etfdem genitts .frohUrf.utsej', cifC4prd demonflf4t4ConHfuuntuf. in fepttmodent^', Lth, f.c/ir^mtr.pnt' t4tis tndtutfittUum Octdnum emenf^m rutcm, dUa ir.pitntM mt^ i 2 thodo. yhd$ , m fsrt^m deducimus , vi in illini infihiidiis fiepulisffrh cliidftM omm idndem ioUdtur dmbtgmttds. Sao tamcm hdt fnmd froBti Uuitirferfendentibtts , qmpfe (jud ftf iamdiit trtiam Geom metridfemitdm haud fidennt ttxftttfitn , wtf^tts effe fnhAndd > d$ qui ndnfeantisflomdct tumentesfititns imtto fpfpftmentes sd ex^^ tremdm Itntns dtHrindmetdm pefnefitfe hdud dedtgndhnntur^ f^rsi fnfer hdc mtnim} amfltus naufeahttnt : Ne tjuts tgttur h. nc rogo methidnm fftns damnare veitt , quam hac othma puro et> iii ocnlopfinceref; tUtus affeeiu fnertt perlufiratus , hu t Ji fdtione demonftratacnm alttvnm tnuintts advngucm ( vmcr^^cre ongiter dnimadnertei. Nemo autem hac aggredtatur,qui fx fal* $$mffiores Ubfos,^ vndeoimS tlementoriinoncaUnertt,(jUodfi •f ApollGn^^dr Arcbtmedts Cptnhns Lr^cr partter verfatusjfue^ fii»faetttus hdc dpfrdhendetfftn mit^us.qudclam pauca,qna ab ,fm y Kepleif (ts defumftdfnere,fotefitfnffone9C. ^tveio vtderttVCcm. dc t^^arTif. ^^^* ^rf^/i/ frafatt KepUft per has noftfas fftiulattones flani onteUtgei t ijuam factli tndimenfione flanteUtffis fotnerti tfft baUuctndritdnm omninm difianttarnm Planeta a Sole.fer elltpti^ cam Itneam circumntlnsi, menfuram putat aqtsipvUi re plam eUi* ffis mefHfa(quod efi quodddm fimtle errcri,in F tma Ccometrictfercipeiuralibn, Jii (jkOfift d'i]u/ fo t difcfs f patia alma metiri, Jngenijmitos arrt i fquimocos. rolftnapUkditouansitaiiioque luperbatriumphoy ^audia non vrtju>;m diptriiura citf. Co. Fran. Carolus Caprara Coll.Nob. Alnm. Dc OcLibPoGcofttctrir. EXprimit egregim n$bts '^^L^RirS, wum Ingenioqui refert abdtta (enf^ noao. Huic veterum penitus cedunt umnumeutu VMrum^ ytlongi merttn infcriofafuis. Co. Marcus Aittonius Hcrculanus CoU. Nob. Alum. Dc Libro Gcometria:. Pten^ Geometrich funt htc motumenta figuris$ Qm^ B0N4rENTrl{y4E condiditalma mwuf. Ingenij vites . & fi4fpice mentts acumenp Qkod merttd £ternum conceltl?rafe Itcet^ Sola latere neqmt yi^TyS: h^c ftdera tranat^ Imaqui d.fpiciens limina^tfumma pettt.] Marcus k Cartis Coll. Nob. Alum. Ad Auaorcm LibriGcomctria^ I^m noutluxfplendet, iamfpUndor praitet omnit$ ^rte Geomctricay dum noua tttra refcrs. Luxfuit ^rchttds, lux ^rchimtdts opufqui^ Luxeafedtenebris confociAta fuit\ luxtua peltticet nuUa catigine preffa^ Inslar ^pollmet ftdms tnflar adefl. Pctrus Fran. Coruinus Coll. Nob. Alum. ttM Fdcnltds J?. P. ric. GcfserdUu NOsF?atcrbcobus Schobrius Vcnctas>Congrcgntionisrcriiato- rum Vicarius Gcncralis ApoUolicus, Opus, cui titiilus cU, 6V#. mcif d^ a noftro in Cl.rilio tilio h. lionaucntura Caualcrio, Machc- nvuicarum in Akiio Bononifli Gymnalio pubhco Protchoic,ac Con- grcgationis aoftr.r Saccrdotc, claboratum , vt typis cxcudi poflit, lcr- uatis fcruandis , facultaicm pcr prxfcnics conccdmuis. Da t. lcrraria:, in Conucntu S. Hicrony mi Oic prmu Noucmbns 1632. F'' Go F. Conft fuinus Bucius Ordinis Icfuatorum S. H icronymi luffu ^ Kcucrcndifs.Patris Vic. Gcncralu pcrlcgi Opus dc Gt0fijftf$s Ad. R. P. Bonaucnturar Caualcrij ciufdcm Urdinis,in quo mhil CbatoUcx fidci, aut bonis mortbus aducrlatur. DOn OilauianuJ Finatius Clcr. Rcgul. S. Pauli , &: Sacrse Bonon. Pocnit.Rcdcrr pro Emmcniifb.ac Rcucrcndifs.D.D.Card.Arch. Imprimatur^ FR. HicTonymus Onuphrius Dodtor CoUcgiatus , Lc^lor publicus, ScSanclifs. Inqmhtioais Confultgr, pco Rcucrcadifs. P.M.Paulo dcGarrcxtoInquifu. Bon^n. fBfUm I 1« f 14 10 f 13 10 16 14 xo 15 %• 17 »? it »3 14 16 |i jo 40 19 D ScAio q«ib«(HiBi fiDt diu<^cnttt igitut COfMOI corum rcfpcOaerpcAa f fopoC IV. bafii AP. cifdcm D. IV. quibvfdJcn fAMlIc- lii finl diuiJentia inquaai ca.un cafuaa icfpf^lo Fropof V. circuKM A2 figuiam,AT,pfO plawui» , AT, pfO 3t figuits, AT» rM, produ^ai 41 20 cft fciti» 41 14 t^c VCIlKCai 41 7 «^og'» 4i 8 fcftcx 4f 4« ji q«« Si 16 quiia 5i 5J I j quo «11 II ciuldcia 18 76 19 Cniilc» 7* 79 if fertif 84 I IkirorcrBlta %%\ It CIIICM fig^fwu, AT, FH« I rodunaru (^iaca cH vnicui reitcx ctfc vBiii TCritiCA tanfrif, fcl ircai vntcutfrrtci ^uo f6 (•lyidim Annot Ifop §• ivilia Annot. prop,j, kttntt 1 bcorcM fXIKtta Tm ♦ I y 14 9 II li» 10 »^ 10 litl Ifif idc&tet hanc faci^^CAte dcfctipm dcfcriptx ^uaruoi qvorum altert •ttrraia eorani earuai coru!« earum eorara eariini p^r tenti rucnaiMf perurfieriiQiii niysi SY.8C • habcQtea 7y xiivac hi^ntia Vidt dtcls Lib, y. {Annet.prop. ^ ) tn fg» due lihtMm^ ir-FS. !n Ttrti0 tihro, ^9 ftqaadratnnaiif rtquad.diinidiiax* yide di^a Dh >• ^7 aa 44 AnneU prop,i.i% Vidt ibtdem diifa M CKB '^•qiadraU ciim -^•qtiadiati ToUibis 17 I» 54 »i BDC. >8 ZC, 69 RF, i^ene dntteedeniis Fr§p, fiiuramt ▼oltti tn S^artfi Lihe, OR, BOE, PF, ;w 'S^into Lihfi, 6 I ▼rque ad caruim vfq^ad latera paraU hyperbolira, cui lcIogtami,qMibiit 7 tx,MX.&.ON,Si cv. NX.&.OM.4e 15 17 ioteccd. propr foneinfii.il e XF. Delt hMcvertfA^i^m «•ipfa.OKJ pfop./i. # f lO It ■I 7 tz lO II »7 If f |o U 54 » J4 3 3S 4 3f 1» i7 lo 4t « rupctahtAl fcaor •|. OR, paraholt I I V i LVB, portioocf f dicartf '1 • FKM. '/ ^ altitudinet *l '4 Bl^KTAf ^9 »6 cylindticat * runtbafes de vfq\4d Mfyfftpt0m toe » pontnde ir^ 9mrJi$Utf0est^Sj^ UHtoLitf0^ I>EC. rtferahtar 6A«re B;. parabolc CB, portioae ittfilierMdeif,Mli^ /» Septimo Li6roi dicaottc FOH» thittdiaif BZ. c/I)tdricoi fiac r«Rr irt hafci ?y h«cC»iIitirfeaa h«fiailjtcffoto «X. diaifn -»7*1 iMccra *4 diQam ^9 ^o comflirt AC.PS. RC »6 foHdaai cfrrccrint (4 i 5 7 «Cor.pm 7o 18 H^/ ♦ Tt qtadratlKii FX. latero didt« conftart HC.Tf.RS. roliduaa tffectrii ^il' ^rr*J,tcl,HC, HC. Coi, priatoi j HM, ^ Vel^ntdcacra f 1 1' f ¥^ f iS"f V f 'f f ¥ f I f ^f GEOMETRIiE C A VA L E R I l [...] I-IBER SECVNDVS. In quo de Triangulo prxcipu^^, c\ P..raIIeIo. gra mmo, ic Solidis ab cildem gcnitis plura dw-monltrantur, necnonalijequsdam Pio, pofltioncs lemmaticx pro llqacntibus Li- bris oltcndmitur. ^BFINITIONES. ' I pcroppontasranGcntcscu: iulctmqi darce planje figur.r ducarurduo pJani inurccm paralltb,rcdi fiueinclma- u ta ad plaoum d.ir.r fignra-, hinc indc indcfinirc produ- ^ Ct2 ; qnorum alrciu mouca- - tur vtrfus rdiquum eidi.m_. lemper «quidiflans doncc iili conjrrucrit : fipc,u. rcdx llnc^,qux in loto motu fiunt communcs l'.^;tio- 7 GEOMETRIiC fedicnes plani moti, & dara? figura? ^ Gmul colfe- prfin. (^ta? vocentur : Omnes linea? ralis figura^, fumptar regula vna earundcm ; & hoc cum pfana funt rc- ^ ad datam figuramiCum vero ad ilfam func in- clinata vocentur- Omneslineas^eiufdemobhqut tranhtusdata^figurar, regula pariter earundem-* vna 3 Iibeat tamenjcu expediet y etiam pr^didas vocarcj^rci^ii tranfitus,ficuti has,obliqui tranfi* tus, eius nempe>qui fir m tali sequidiftatium pla* norum ad datam figuram mclinatione,. C O R O L L A R I V M . roro.Pri T T / pafet^ cfUQniavt oppofiu tavgentefrcguU cfuacvncji im JL X darjfiguradt$ct poiiynr,enamomr)ffifneaiaataf^ur(g, reguU quacunf^ reiTa Uneatrrtpofita habtrt po fse^ tHfn nchjun^ tuam eiufJcm oHtj^ut tranjituu if. fita phma tangentia regnla quacurq,- Av>(k^ fuerinr,hinc rndc indefiniieproc)u^a,quo- Fofe scr. nirn afterum verfus rcliquum moyeaiur fcmper eidem a!qurdiftans,donec illi congruerir j fingu- laplanajqujeintotomoruconcipiuntur in pro- pofiro foJido, fimul collcda , vocentur : Omnia.. ji^Defi,,; ptana' propofiti folidi , furopta , regula eorun- L I B E R n. C O R O L L A R I V M, Hlnc tli4m Jifcimus, vtlntifrepofiti fUtii tpff.fiig ungm. Co,o. tu pUn4 q„4(Mr,q; re^uU ducipcfiuni, it4 ttMfdtm om^^ '' *>I4 fUnx rtgitU qutcMnf, pUne hdtrt fopt» III. SI oppofitistangcntibus pUois occurrant in- terius d\ix rcclic lincx, vna perpendiculari- ter, rcliqua oblique j punaa, quaj funt com- jnunes fedioncs propofitar lineiE perpendiculari- ter incidenti^, & (ingulorum planorum, qua:col- Jeda d!cuntur,omnia plana (ita tamcn produaa, vteafdcm fccare pofljnt^fiuc punaa, quac funt comuncs f.dioncs ciufdcm, & moti plani,fiuntqi intotomotu, fimul collcilh voccntur ; Omnia., pun^a rtdi tranfitus propofitar Iinea pcrpcndi- cularitcr incidentis j quje in oblxjuc incidcnic^ voccntur^ciufdcm obliqui tranfuus . ' ( ) I. T. A 1' I \- M. EX hoc hjhtturfi'.,' ul^ f.uuUj raii irinfnms, i tlchfi^mi, in^ , cidtntti ltntt,n(du»n tfse cemmunti ftiJrtnts tllimi ,(fr ftngi4lorMm,>jut cUuad dtcuntur , mnt* fUn4 frofofiti fslidi, fcd ttum.fiper taltm tnctUtnitnnxttndttur pUr,mm,ifstiftA dtenntHr etstfitm m,,es aO/ct/s.t,/we niitjiye ctnfacrH I : B K K II. .y tytTiMcent tvttr rtUqHum txtnwiMm etu[iem purulum , c> r« • tl,m,!Uf ,ma4, tnur qut, 6^ t^trcn,Hm pmo dMum , t^ttrtA^ ttutimnesthftfs*. VI. SI proqualibctcarum, qu.t dicuntur omncs abfciir* propola.T rcdy iincic, .pfa propofT- u linea, (lue eidcm a?qualis, fcmeJ atfumpta inteliig3tur,i(ta?limulcoljtc1idiccntur: Maxi- mx omnium abfcilfarum propofit» lineg,vcl fub- intelligentur fcmpcr elfe omnium , ctiam fi dicc- rcntur folummoJo : Maximacabfcilfarum. o L l .. M. ErfV/.^vM/r.- ■srr;::us,^a.,.e -v^Vommum .c'.nt,df,f,.r.4m e»tlthtt tbf^x TtfnnAtt vrtd m^t.x ima* S.tJ/t mtxtmter^ritim '""^ rr ^ltntdlttetuxt ,,iwitiijmrefiti0i4(mnium ^^^^''^^''^''^"/fus-tdt/t prt iK4mm4xt' -'i^tfemptr \S 4^ UWftlS. VIL SI cailibet omnium abfciflirum propofir^ re- ^la: linc^adiuncla inrclljgatijr alia rc(f>a li- r>ca cuidam arqiialis, comporua? cxomnibus abrci(Tis,& adiun(f>isjimulcoilcd:a:diccrur:Om- iies abfcilTae propofitas linca? admnda tali,ncmp^ adiuncfli illa,cui,quae admngijrur^funr a^qualcs: £ vcro ficrcc hsec adiun(iJio rcfiduis > vcl maximi» C E O M E T R I ^ «mnium abfcinaru, parifer cficerenrur; f?efido«, Maximxomnjumabfci/raru adiuriaa eademj xedli femper, vel eiufdem obliqui tran/itus. A. VIM. PRopnilta ^uacunqj plana figura , & in ra^ duda vrcunq; rc^aa linea vfqjadambitum hincindc terminata , fi ipfa rcda Jinca de- fcriberequamcuq,-figuramplanam intclligatur, iion txiftciitem in plano propofirip figur^, ac de- indereliqux earumjquc^e dicuntur omncs Jinc« propofit^ figurjE, fumpt^ rcguJa iam duda jfnea (& nai trai.firus fi defcripra figura fit ercda pla- no propofita, vci eiufdem obliqui tranfirus, fi illi fitinclinata ,eiu.snenipctranfitus,quifit in tali incJinatione)defcribcreintdIigarriffiguraspIa- nas fimiles , ac fimiliter pcfitas , ^^•quidifiantes primodefcnpt^, ita vt omncs dcfcribentes fint defcriptar um figurarum line^ , vel latera homo- Joga j omncs defcript^ figura? fimul fumpt^ dice- tur; Omncsfigurieplanarfimilcs ralis propofit^ figura», fumpt^ rcguJa earu vna, vel regula etiam ipfa Iinea,veJIateredefcnbentei vtfidcfcnW hgur^ efrentquadrata,hje dicerentur. Omnia quadrata talis propofite figur^, t^el fi elfent trian- gula^quilateradicerentur. Omnia triangula. ^quilateraeiu/dcm^. ^ L r B R R II, B. Sol,dum,cuiusonincsJcrcripr.Tfic,„ra,nmiles.- funtomnu phna^dicerur : Sol.dum fimil.uc ^r]s propodris.vt fic -c- nerantur, dicentur abfq; alio addito: Solida fimi- larta gcn.ca ex propofitis figuns iuxra regulas omnium fimilium figurarum,qu:cipforueu3danc omnjaplana,propofi(afautcmfigur^,corundcni gennricts figurg vocabuncur. C. Oim ver6 duarum genitricium vrcirnq; f{rn. Tarumomncsdclcripjfig.jrj nedum fimiicscn.r, quxrepcrrenturin earu.n vnaquaque,fi.-d ctiam quae lanr vnius, inuen.ecur fimilcs omnibus fi<»u- tis hm.Iibus alterius propofir^ fi^urc , Fuerint au- rcm in vtroque folido figurx cque elcuarg fupcr pranagenirriciumfigura.um^tuncfolida gcnita cx propofitis figuris luxra rcgulas C3s,quc funt re- gul? omnium fim.l.um fi^^urarum carundem pro- polirarum genirricium figurarum,d(centur folid» »ntcr fe, vel ad inuicem fimilaria, gcnira ex d-rtis figuris juxca dia^s regulas,vcl intcirigentur fcm- per efle inter fe,ftu ad inuiccm fimilaria,ricet hoc non cxprimatur,quotiefcunqicontrarium ahquii Don ad.jciatur, D. Cumauccmduasfiguras ineodcm pFarro ha- m Caro.Pu* » GEOMETRI^ buerimiis in eadem aUimdine exiftentes, re^aan- gulafub fingulis earum , qu? dicuntofomnes li- iiea? voius propofitarum figurarum , & jlJis in di- redum refpondetibus inaliafigura fimulfiimpta ficvocabimus, nemp^ Kedangula fijbeifdemfi- guris,regula eadem^qu^ eftomnium fumptarum liiiearum regula^, E. Cum vero propofitarumfigurarum altera fue- rit parallclogrammum,cuius bafis^iuxta quam al- titudofumitur,fitrumptaproregula,di -BCfumpt^ reguU earu n^r.a, ^t, BC. re6ii tr^yil jttus cumpUna paralieU neie fecunt figur.m ,^BC, i^iufd,m obuqm mnfim. > cum iHam obU^ti^cfk^nt , €tUS ^ I B E R U iias/ctlUtt trdfj/i' g tus, qui tn tdlt tn- €lm4ttone fit, Intellt^smtts nSc •ABC .«Jftfoltdii, «mus dH6 oppnJtt4 pl4»a ttngenttAj ftnt, quA tr*nfeunt per, EO, BC, mouegtur atitemad. httcpUnum^per, EO, extenfum,fetft$spUnu ptr, BC, femper tUt AqutdiflTu, igitur hums pUnt moti,fiuefluen' tt r conceot^ in Joltdo , ABC, figurx , ^«ui.