^66 ' EncycIopa:*di^ Lib. XV. 



Qu^adiilt- 

 leioium 

 obli^uan- 

 gulorum 

 aiea vt co- 

 cnofcatut } 



aulo A B D Bon leftangulo nota Cint duo latcra.vna cuf» a^-. 

 lalo ab ipfis comprchcnlo , ex duobi.s UtciiUs &: angulo 

 ifto inuenietur tertium latus : ac ptoinde.vt paus,cx omnibus 

 xr>bus latct,bus area ttianguli efficietui cognua. H.' '"^"» ^ 

 nens. mechanicam iimenfionem latcujm pev •"« )■" ' ""^ 

 pattiJm.vel f.alam pert.catum. ^ angulotuu; Pf ^ ^'^?"';.^^^- 

 Iu'1, vel quadranteti (de quibusfupra pa>t.i,. lu. cllc fernc- 

 ccffanam. .:.':r'^i; 



r, SHadril^tcrorumfeH .pmdrar,gHlorPint obUqmngn- 

 lcntmarfAcognofcifHr vtugcntrji,-vel ifcadi, 



V.a eeneralis contuietur hoc thcoienwc : VMHm quar.m- 



&""!■/«- bin.mansukrum »re4*mm .u.a. con-Paunt 

 t?Z pfit. ohUn tiu.drans.1. : v.sr,lu .nenlurandus campu 

 XbCD D.»£^onal,>AC ht i.l pcruc.rum ; cjua- rclolua 

 ^aramfiguram in duo triangula ; quorum ^.r^M^^^^ 

 J.t«funto.DF a: EB. qufrum aggresatum .u d.m.d. m 

 iT^-onalem A C du£lum , «hibct aream toc.us l,sur.x. Idcm 

 .lettf. totadiagonalis in dunidium agstcsatarun, Fr^efldi- 

 ^ulariura ducatut ,1 oj^ii. 



«, ■: iil 



^V 



Ff. Fimrarum mvMlaterarpmJmt nuiltaKguUrum\ J\^^r^^ 

 , trregnlariam , arca cognofctiitr , Jt r(JolHuntttr »«..„„„„, 

 trianauU , & fin^uioritm trimgHlorurfKtre&inHe'^ guhaui. 



tS .^ o I fc,' 31C4 Vt ( 



figentHr. ' " " "* gnofciiu 



. Nam omnes h« area: in vnam Cummam coUeAae » xqualcs 

 funt arcxtotiusti^urx propolit.c.Vt ii figura (eptem laterum 

 , A B C I) E !■ G, rcfoluatur in tuunquc tnangula, .ta , .ta vc 

 coium latcra fc mutuo nou i.Kerftcent , inquireridx tunt_ 

 arcx t.nguloruin hoc niodo. Dcfcrib.^tijr in cnaria hguta. 

 qux agriim propofitum icpia-lcnaf, & linguloium atea: m~. 

 uel1i£;?ntur pcr peri'cndicu!accs ex a.igulis ad la;cra oppolwar 

 demiais , vt pauloantc docuimus. Ita liic linca AH elt pej;.-:_ 

 pcndicularis in tviangulo AB G. In rclKiu.s codcm iflodo de- 

 micratur, 





;."v->Q 



Deniquc omncs areae in vnaro redigantur fummam , vt 

 area,totiusfigut.cl.abeatur. Hic vteris i(1o compendio. Pe» 

 ipl'a.n agri medictatcm.vcl pocius Ciica iatus campi.quodma- 

 gis cft irrei;ulare,diicicur linea.quam dicunt fundamentalem, 

 i;x hac cnim liducamur linca: perpendKulares in fmgulos 

 angulos campi, tota figura refoluitui in triangula { fxpe re. 

 aani;ula J oWonga,&: tiapczia. quoium finguloriim area: per 

 fupcriora thcorcmata & problemata inueftigantur. Vt in agro 

 A BCD linca fundamentalis eft AB. ■ . » 



Via fpccialis habet hasc theorcmata. i.rri» funt genera 

 atntdrilaterartii/i figurarum , qiu vel nitihim mgulum reciicm 

 Uitbetitj-vel certe non omnesrcctos ifuta.rhomjfus, fhi^nbj}iiics,cr 

 ir^pet.ium, 



1. In rhombo ^ rhomhoide area producttur. ex duBu perpen- 

 diciilaris in latus, in qiiod cadit perpendicularis ; vt in rhombo 

 & rhomboide A B , C D. producccur arca ex multiplicationc 

 • perpendicularis AE.in latus B C. 





B 



Alicer inueftigatur area rhombi & rhomboidis.fi diagona- 

 Jis (quam in hoc fchcmate cxhibec D A ) figutas illas fccct in 

 duo triangula. Si cnim vnius duntaxat trianguh perpendicu- 

 latis menfuretur , Sc in incegram diagonalem mulciphcctur. 

 co<»nofceturateaparallclograrami D B A C daci. 



Si in agro a.h c d llnea ab eft fundamemalis. 



C 



Ou6d fi in agri circuitu portio aliqua fucrit curua, P"<:ur- 

 uamina ducctui rea.i.qua: lineam iftam cutuam iquahtetd.- 

 uidat : vt in figuia AB G D l.nca refta A C pcr curt,am du- 

 aa,vndiquaqu"c ab agro. partes hk toUit.ilhc addit.ad ccnlu- 



am agrimenforis xquales. 



■ - Sttrapez.itimdt{o habeatlateraparaUela.areaprodticitur, 



'^{i^perpendiculara tnter dtio latera paratlela demijfi dimidiiim 



multtplwtur tn fummam additorum parallelorum. Rcs codem 



''"ledic fi femitr.sadditotum parallelotum in integram perpen- 



'dicularcra ducatut.V.gr. in crapezio CD EF.perpendicularis 



AB fit i4.pedum,lacirsCD fit li.alterura latus eidemparal- 



"' lclura E F fit !<:. pcdum. Summa laterum add.torum erit 2.8. 



'%uius femifTis , vcpote 14. multiplicata in AB i^.ped. notam 



'; efficict ateara trapezij dati,videlicet pc(J.i96. 



A 



Si lacus , fylua vel agct fit inacceffibilis , conftitucs circa 

 ao-rum vel oblongum vel crapezium reaangulum , atquc cx 

 iSeribusillis ad omnes & fingulos agri menfurandi angulos 

 duces pcrpendiculatcs lincas , qux cxccfrum, quo c.rcumfcn- 

 otum quadiangulum maius cft , quam campi arca , in tr.an- 

 Lla & trapezia reaangula fecabunt : qiiorum finguloium 

 atca: fi vnam in fummam rcdigamur , & lumma collcfla ab 

 eodem obloneo vel trapczio teaangulo auteratur , rehquus 

 erit arca campi def.derata : vt in cicmplo BCDE vidcre 

 habes. 



E B * 



Poteft etiam ttapezium rcfolui in fua ttiangula & qua- 

 'diangula. 



yiL ArU 



