Geometrte Pars I]. Cap. V. zj"^ 



xa!;ona(,linca A B (it ^.pahn.IatuJ vnnm fit S.femilTis pciipbe- 

 ri^ crit I U.palm. Hahcpeiiplicriifciniflein multiplicain pcr- 

 pcndicularcm A B. fier area bafis yo.palm. Altitudo eiufdein 

 ngur.r C D fit (J. palm. qua; fimiliter duda in bafin rcpcrtam, 

 exhibct capacitatem prifmatis ordinaci 540 palm. 



fl b»Jis fittnordinatit , eius fisjura prius refoiuenda crit in 

 triangula vcl trapezia reiflangula , & fnigulorum area: inc]ui- 

 rciida:. Summa enim coilcda dabit aream hafis:qux fi in alti- 

 tudincm prifrnaiis multiplicetur ,con(labit c-jpacitas defide- 

 rata, Porro fi bifis prifmMufuirittrnfezium^diio habens Utera 

 piiYxllda, duo illa parallela colligautur in vnam fummam, cu- 

 ius dimidiumducaturin perpcndicularem, intcr Muo illa par- 

 allcladcmiffam , & conftabit arca bafis:qu.T inultiplicata in 

 altitudinem , hoceft oppoliti hedra: diftantiam, cjthibet fo- 

 iiditatcm trapczii .■ vt fi latus A B fit 5 pcd. iatus parallclum 

 E E 5. erit fumma 8 ped. iqnorum femilfis cft^ ; qu.r inulti- 

 plicata in perpendicularcm C D 4 ped. exhibct areambafis 

 1« ped. Altitudofit loped. Vndc foliditas trapezij crit i 60 

 ped. Si trnfez.iabafis non habent pnrallela iMera , duas per- 

 pcndicularcs ducito exangulis oppofitisin diagonalcm, ca- 

 rumque aggregatum in fcmilTcm diaijonalis multiplicato. 

 Sic enim aream fcies, quara duaes in altitudincm, nconftct 

 trapezij folidi contincntia. 



P^. Arettm cyltndri ccgnofcere. 



Gcodi-lia cylindri c prifmate lepetitur. Itaque capacifas 

 c)!uidn cognofcitur vx muhipticatioiie b.ifis in altitudmem. tt 

 cum bafis fit circiriatis, arta ipfius inueftigabitur ex diamctro 

 circuh.diccndo, vt i^ad 1 1. ita diametri quadratuni adaream 

 dcliderarara. Ita V. g.cylindri bafis fit 58-p.exea & altitudine 

 li, crt (oiiditas 4fii. Ita (i bafis cylindri continct;io palmos 

 quadiatos, cxplcbunt lo cubi pahnarcs fupra ilios':o palmos 

 quadratos extrufti, cyiindrumvfqucad primumpalmum alti- 

 tudiais :at 10 ciibi cundtm cxplcbunt vd]ue ad fccundum pal- 

 mum ; h ncrape cylijidius fit reaus.Quod fi cylindrus fic ob- 

 liquus.cxquirenda crit eius a'tituJo pct lintiui pcrpcndicula- 

 rcmex lupcriore baft^dcmiiram ad planum , in quo infcrior 

 bafis cxilHt.-atque in hanc altitudmem area bafis inuenta.mul- 

 tiphcanda. Produc^us enim numetus dabic aieam cylindri 

 propofiti. Hinc capacitas vafis cylindracci arftimabitur. Inane 



-cmm tanquamplcnuin metiendum eft. Sit v. g. interioriscir- 

 cuh^diamctcr iii v.ifc,6 pcdum, pcripheria i8;-. Arcaigitur eft 

 Z8-V. Exqu.T&:altitudine planuselti8i~.Sicigiturirtima- 

 bis, quannim liquoiis vcl contcnti cuiullibrt.pcs cubicus oc- 

 Tupct.:Sol_ent antcm ahena fermc eill- cylindracca. Sit itaque 

 alvcnuin foima cylindr.icca cxtruaum. Diamcter bafis fiue 

 laticudoonficijfit {.peduni.nic igitur vt 14 ad ri.itaauadra- 

 tmn diametri, vtpote i5,3d aliud^^id cft,areamonhcij hue ba- 

 iis , qu« ent 19. Arcam inucntam multiplicain altitudinem 

 ahcai, qua: fi fucrit loped. contincntia ahcni erit 190. Scd 

 compcndiodicamus,quommodofoliditasprifmatis,coni, cy- 

 Jindn.Oii cuiullibct parallelipedi inueftigctur. 



FU»its e bafip- altiiudine eft foliditM hornm corporum.hiq\ic 

 opoitct primoinueniie aream bafcos, & cam multiplicarc in 



. altitudincm pcxpcndicuiarcm. Quarc II bafis lit iriangula, 

 qnadrans^ula Scc. inucftigcturarea huefupcificics. Eadcm cft 

 geodida in thombo, rhomboidc, trapczio, & quolibet mult- 

 anjulo lohdo.Bafis mcticnda e/l , vt priiisitum cx ca & alri- 

 tJdiiie fohditasconlbbit.Vtin rhombobafis llt i^.altitudo^- 

 lohditas crit 96.1n rhomboide bafis (it ii 5,altiEudo u.folidii. 

 Tom. n. 



tas ent U 75 . Ita m prifmatc longitudo fit 4 ped. latitudo * 

 altitudo 1 1. Hic planus «i bafi cft 14 . & altitudinc 1 1 eft 1 64 

 pro lohditate. Atque eadem gcodxfia crit in dimcticndis p a 

 nctibus rcclanguhs vcl patictis aliqua feneftra , aut caniiaic. 

 v.icu;s,fi vacuaipladctrahantur. Vt fic fpirtiiudopatictis ;pc- 

 dum, latitudo 1 1, altitudo n. Tota icaquc folidicascft 596 

 Scdin hocparictceft porta fpilfituduiis ? pcd. Latlcudinis j.. 

 altitudinis 6. Soliditas porcient 71 pcduni: quibusfubdii<fl;s 

 a toto parietcteftant 514 pro rcliquo parictiscorporc.Rurfjs 

 /itpaiies!ong.ped.i?.lat.8.alt.7.foliditascrit5(;opcd.SedtA. 

 teneftrainhocparictc,longitudinis^,latitud.4.aIt.7,facit i6Si 

 qmbus tubduau dc 5 <;c,rcliqui fumma cft j 9i.Sic amplillimi 

 idihcij parallehpcdos paricces muiofquc omnes mctui liceat. 

 Acquc hinc vafoiumqualibet plana foliditatc figuratotum ca-' 

 racitas xftimari potcft. Sit cnim planus 105 c^bafi fcxan^u- 

 U vafis , vidcl.41. & altitudinc 5. Itaque fi pes cubicuj coii- 

 tinct quatuot pattes.vas contincbit quartas 810. 



ri. Aream pyr^midi, & ccni cogncfcere. ^'iJ:Z 



ni Tt inda- 

 ryrHmid^ ^ coni areafiue capacitoo. co^nofciturex mnhipli. E""' ' 

 catione baf.s ,n tertiampartcm aUitudm„rvdex muUtplicmwn, 

 tertu bajts pariis in altitudinem. Pyramis enim cft teftia pars 

 prifmati.s,& conus ccrcia pars cylindri.eandcra cum pyramidc 

 & cono nabentisalticudincm. Ex quo fit , fi balis ducatur ia 

 totam aititudinem, tertiam partem numeri produdi efle 

 quoquearcampyramidis vel coni. Bafis porro pyramid'is fi 

 triangularis cft.cognolcctur ex cap. ameced. a niultilatera' fi 

 militer ex eod.cap. bahs coni itidcm. At vcro altitudo tam py- 

 ramidis , qu.im coni.obtincbitur , Ci in vertice ftatuatur pla- 

 nuin bah .vquidiftans, ab e6qucad planum , in quo balis de- 

 mittatur pcrpendicularis , caque cxquihcc menfurccur.' Sit 

 v. g. pyramis bahs quadtan;.;ula,- , vtpote rhomboidcs. Arca 

 iphushc 56 palin.Hi-cmultiplicaca in rettiain aitirudinispar- 

 tem.qu.efic ic(cota cnim altltujo fit 30 pa!m. )contincbit 

 lolidicas pyramidis 560. Rurlus fit columna cx iiutmorc py- 

 ramidalis A B C. quxritur quot libras contineat. Adhilsc 

 cubelluin cx marmorc conteaum vnius llbii- , & pcr ea«f- 

 ttcC> inquire arcam bafcos A C. quam multiplica cum ter- 

 tia partc altitudinis pcrpendicularis , & habebis arcam Vt 

 bahsA C cft II parrium, alcitudo perpendiculatis 9 

 Tertia itaque parsaltitudinis cft ;. ex qua & bafi planus crit 

 10 , area. Altitudo autem rcai pyramldis habctur intcr 

 aha, fi quadratum c radio bafeos tollacur e quadrato latcris< 

 Latus cnim reliqui crit altitudo. Vt in cxcmplo quadratum 

 lateris A C eft 144. lam vero latus poteft tripluni radij. 

 Quare radius bafis erit. Itaquc quadratum radij erit fubtii- 

 plum, ncmpe 4S. Rcliquum 9-? crit altitudinis quadratuin, 

 quadtatique latusjfiuc radix 9, critalcicudo pyramidis. Pa- 

 cihus camcn lineain pcrpendicularcm inucnics, quando avcr- 

 ticcadbahn, vc diximus , lincam extruxens , qui bafinad 

 angulos reclos fccec. Hanc enim mcnfura minoris cubi potci 

 raeniurare. ^ 



Ladem cft coni , qu.v pyramidis geod.rfia. Itaque f, bafis cotit 

 atcaducaturintcrtiamalticudinispartem.foliditasipfiusprtf- 

 ducctur.Bahs autemconicx diamctrocognoftitur. Sicut iei. 

 turi4 ad 1 1. itaquadratumdiametriadarcam. V. g. diameter 

 bahsconi (it 4ped. quadratum cric 11. Dicos igiiur vi i^aj 

 ii.icaii ad 9. qux-arca multiplicata in tertiam partem alti- 

 tudiimconi i qu.r l,c 5 pcd. ica vt tota altitudo ht 1 5 pcd,) 

 cxhibct (oliditatcm coni^, pcd. fcl canth..iorum..Sic itaque 

 pUntuefua hnfi crtritnte altiti,dini4 eftjolidita^ p,ra,>.-dua- 

 com. Porro quia cylindrus eft triplus coni b.ih Si altitudinc 

 i-qualis, idcoplanusecylindribafi & tncnte altitiidinij cft 

 lohditas coni bali & altitudine a.-qualis- 



f7/. Tyramidis curu, eonicurti , & Cyii»~ 

 dri cmi CAfacitatem fcire. 



PyrMnidis decurtat^ , Coni decurtati, ey CylinJri decHrtati 

 (alii vocant huflra piramidis coni & cylindri) capadtatem 

 cognofcemus ,fi l.mra ipforumcontinucmu^ , ^ -jnuurfx pyra- 

 m,/„,coni , & c)i,ndri fol,du(Uem inquimtns^, ^f tum mno- 

 remn maion [tibtrahamtis. 



rytainidij 

 curi.% &c. 

 aic.i VI in- 

 daj;ciu[ i 



li 



yuL tm- 



