: fiot 



Geometri^^ Pars I. Cap X I 



ap. 



340 



^uintam. Itarjue c/Tent quatuor rcfti & tres quinti. E plu- 

 iibusi'Titur multo miuus eft poffibile. Demonllratio \\xc ac- 

 cu.at(; far.t & maiiifertecolligitj^iiamuvb planaoidinataiiinu- 

 meiabiliacflc polTint j attamcn c gcneribusangulorumqa;n- 

 quc rantiim corporaordinara infhtui pofle, vnjc tcttacdium, 

 odacdrura, & icofacdtum, bali tiiangul a, cubus quadiata.do- 

 djcaediuna quinquanguia coraponitur. loiro cx toto pyra- 

 midum gencre vnica duntaxatfpccics cftordinata, vi^cl. tj- 

 traidrum : ex omnibus piifmatibus folus cnhm e!l ordiiiatus: 

 ex corporibuspolyedri? raiflis funt i-ria folum ordiiiacj,vidcI. 

 tcsaedrum, icofaedrur», & dcdecaedtum. Et h;EC funr quinque 

 corpora principalillime^ac propriiffiinc ordinata. Quando au- 

 :em fphira dicitur otdinata intercorpora gibba , hic cJl fcn- 

 fus , nuod fit corpus £jibbuni (impliciirimiim & minime va- 

 tium.libiiquc limillimam : quo paflo circulus dicitur fupcrfi- 

 eics curuilinea ordinata. lu ergo ambigue dicitin corpus ot- 

 dinatum. Ca;teium non omnispyramis tctracdia ell ordina- 

 ta. Sicut enim in planisreftiiincis in vnoquoqucgenercvni- 

 ca folum ell fpecLes ordinata.c triangulis.T;quiiatcrum,c qua- 

 dranguhs quadratum.e multangulis vnum aliquod in fuo gc- 

 nere:licmodoepyrara!dum gcncre vnica fpecics ordinataeft, 

 ncmpe tetiaedra : neque tamen omnis , ted quJE comprelien- 

 ditur a ttiangulis noii folum ordinatis ouidcm ligillatim , fed 

 i'qualibt:s intet fe fimiliburque. Pollunt enira corporacom- 

 prchcndi ab ordinatis hedris , quat tamen non funt ogtlinata: 

 quia hedr.-E ill.T: polTunt ordinatx feparatira clfe, fcd nequc x- 

 ^ualcs intcr fe , neque fimiles , neque idco o-tilinatam corpus 

 comprehendent : qualia lunt Ardiimcdis ttcdcciin corpora 

 apud Pappum 5. lib. 



y J I, Ouatuar corpora ereHnaU /hnt rcdprocafvt cu- 

 bus,o^lacdrHm,dodeca'idrHm,& icofaedrHm. 



Quatuorex cotpotibus ordinatis, fiue rcgularibus, funt re- 

 ciproca, quod ab bafcs auinct & angulos folido.s, id cll, ilios 

 angulos, qui comprehenduntur a duabus fupcrficiebus , vt in 

 a::gulo vidcreeft, qui coinprehcnditura daobus parictibus.. 

 Namquot bafcs in vno contincntur , tot angulilolidi in al- 

 :tro tcpcriuntur , &contra. h.icub:is S<. ociaedron funt reci- 

 procl : quia vt cubus habet fcx balcs , & odo angolos foli- 

 dos : (ic contra oiftaedron habet otto bafes & fcx angulos fo- 

 lidos. Dodecaedron quoque & iccfttedrort funr reciproca. Nam 

 vt dodccaedton habct duodecim bafcs, & viginti angulosfo- 

 lidos : ita coBtra icofaedron liabct viginti bafcs &duodccim 

 angulosfolidos. VidefcJacir.atainpra:ccptis pofita. Solum te- 

 traedrencam nullo reciptocatur, nifi cura fcipfo. Habet cnitti 

 quituor bafcs , totidemqueangulos. 



VIII. Pyramii ajigtirk bajis denemina' 

 tionernjumit. 



Sic pyramis triangula dicitcr . qua: triaiigulam habet ba- 

 fin : vt A B C : quadrangula, <\\xx qiudrangulam habct bailn: 

 pcntagona.quandobalis cftquinque laterum & angulorura:& 

 licdcinceps.Sicpyramis D E F habet baCn non triangulara. 



ntmidi? 



ijraquoi? 



Hmsii) 

 itqiioiy 



IX. QHilihet pyramis tet ajfttrgentia & ncjualiterfa- 

 fiiglatahahet latera,cjuot angulostjiue latera, 

 bajis ipfa centinet. 



Vide figuras in ptaiccptis & prop. antcced. Bafis aucem py- 

 raniidis alitet dicirur planum ipfius. Tot autcm triangtrtis 

 quxlibet pyramis comprchcndiiut , quot angulos, fcu latcra, 

 didutnplanum continct. 



X Pyramidis hedrt funt vna ptnra angulis in bafi. 



Hcdridicuntur latera , qii.r funt circacorpus. Scnfus au- 

 tem huiusconfeclarij cft, quod hedra; (iuc latcra pyramidis 

 fcmpcr fintvnitatcplura,|quamfunt anguliin ba(i : vt fi balis 

 pyramidis (it triangula,hcdr,T pyramidis funt quatuor ; (i qua- 

 drangula, quinquc ; (i quinqiyangula,fex , & fic deinceps ; id. 

 efl:, pjramis elt ttilatcta,qtiacki]atcra&c. 



XI. Hedr/tprifmatis Jim hinario plurts angtUid in bafi. 



Hoc eft , (i anguli balis funt ties , prifmarliabebitliedtas 

 Tom. II. 



quinque totura prifma compr^icndentqf : (langali bafisfunc 

 quaruor, hedrr cruncfey , k fic dcinc«(>s. It vt pyramidis a 

 quaternario , ira piilinatis /( qur<u.riQ ad inRnitum vfque fit 

 accrttio. Spccialitcr autem priftnata a raultiiudinchedraciim 

 dcnominationcm ibrtmntui. Nam a-b.i(i tri:<^.;u!<i, quidian- 

 guU, pcntacdra , kcxaedra ,>. & hepii^dra pfifmata dicuntut: 



EUO.C 



qu.tcamcn a^tria ftilcnt rcuoca/i , ntoi/um ad pcntacdra 

 hexaedra &c'polycdra. Ca;tcroftui dcmOfaflraiio thcoretna- 

 tis h.rc cft:. Pyramidis' vnica fuh bafis /ptifmatis dua; func 

 bafcs oppollrx , qux Iibiinui^cm fijnt fc a;qualcs , & fimiles, 

 & parallela;, (lue (iiit triaiitul.-rptfuemtltangaJa' ; tciiqua vc- 

 ro ptifmatis laterafunt paraliclogramma. Et quot in vnaqua- 

 libet oppolitarum balium anguii fiue latera reperiuntur , toc 

 quoquc parallclogiamma p>:a;tcr ipfas bafe's prifma contjue- 

 bit. Hicob^tcrobfciiia, quomodo ptifniatis vocabulo vtatur 

 Luclides. Interdum (pecialiicc vliirpac de pentacdio : vt >•«- 

 tMn^«/H»>;in planis pio oblongo &c pyramts in folidis pro 



tetraedro ordinato ponitux. *" ; 



1 



Xll. Parallelipedum eft fgHrafolidafe.v fignris qua- PaiaUcIip* 

 drilateri^ , cjmrurn ^iia e^ aduerjf), paralUU '*'"" ^''''* * 



funi , conttma, i 

 \ ■ ■. 



HuiuCmodi figuram folfdam cxprimit columna aliqua 

 quadrilatera vniformis crairitlei. Vt figura A B CDEFG H: 

 in qu.i tain duo plana oppofita A B C D. E F G H, quam duo 

 A D E H. B C F G. & duo A B G H. D C F £ parallelo- 

 gramma , funt inter fc parallela ^ squalia, dicitut parallcli- 

 pcduiii , quafi parallelis planis ccfmprchciifura : cux quideia 

 parallelaplana oppoCta,funt xquilia &.' fimilia.E.i^.ft.i. 



Itaqiie paralletipcdum in folidis rcrpondet parallelooram- 

 mo in planis. Hic cnim hed^x- oppo(itx, funt & paraUd» Sc 

 .rquales : illic oppofita latera lunt parallcla & xqualia. Hinc 

 quot funt gcnera patallelogra^imorum, tot quoque funt pa- 

 rallelipedorura. Si enira fex pijrallelogramma rcdan"-ula& 

 .rquilatcra,hoc cfl: fcx quadratafoiidis angulis componancuf, 

 fietC«i«j,&refpondcbitqaadratoin planis. Eftque folusor- 

 dinatus inter prifmata , qucmadmodura quadxatum intcs 

 quadraugula. Vidc A B, 



B 



A 



Porrofi fex parallclogramma, re<ftangulaquidem, fedn»n 

 a:nuilatcra intcr fc (quamuis duo fueriiitiequalia^componan.- 

 tur, iaec parallelipedum oblottgum : vt C D. 



cz 



Qu()d fi fex paraHelogramma copulentut *<iuiUcera, fcd 



non icftangula,vocabicur Rliombm ; vt E F. 



Gg 



Dcnique 



