344 Encyclop^db ^^^- ^V 



4. P/»M trinnguli v»rio,cuius fngitU lat$ya funt cognita.angt^ 

 hoc modo tnucfiigttntur. S*cut latus maximum fe habet ad 3' 

 gregatura duorum reliquorum : fic difFcrcntia latcruin mi°" 

 rum inarqualium ad fegraentum lateris maximi ; quod fu'''^." 

 dum a toto lateie rclinquit lineam , in cuius mcdiur""" 

 perpendiCulum.vnde exiftunt duo triangula rcftang.i'^' 1"^ 

 foluunturgemina pragmatia,qu6d omncs anguli fi,- '"^1"*' 

 lcs. Vc cfto triangulum varium j e i,cuius latus ^^ '"^ *■ ' P^"^" 

 tium,<it 10, Ae I j. qusritur de amplitudine at?"'^''""'- J??" 

 Cre?atum ex;»« &<»e cft 35: diffeientia ir''^ 10 & i j elt 7. 

 ItaqV vt II ad } j,fic 7 ad fcgmentum li-'*f -,■ <l"°'l P". ^^" 

 gulam proportionura erit i ■. Subtia.?'^ " ^ '»'"^ """""^ 

 «i, rclinquunturio. Decerpe itaqiv 1° P^.^^.f.'' '«"= ^ '• 

 eifquc diuidc in duas partes a!qu"«.Tum in oilegmcntum 

 «det perpendiculum ^<».Hinc '«"'ft""' ^^° "'anS"'^ '««^tan- 

 gula,in quibus fempcr tria fu^^^ aoHr 



m triangulo reBilineo qutritntur anguli,r»diui femftrotcUf 

 lit medtum locum reguU detri^numerui minor homogeneui ra- 

 to primum, minor hetero^eneu^ fecundiim. 'iluotus tndicM ji- 

 num , tangentem, 'velfccantcm anguli ijuifiti. Vt in rriangulo 

 A B C, A C eft 10 ped. B C 8 ped. -Q.ujeritur de amplitudine 

 an^uli A C B.qucm fuhtcndit cathctus. Hk tria funt nota, vi- 

 dclicet hypotcnufa, bafis , Sc. angulus cacheti ; & hypotenufa 

 c(l fecans,bafis rad^us totus,vtefeq.tabula patct. Dico itaquc 

 Vt B C. ad A C. ita radius torus ad fdcantcm anguli A C B 



8— 10 iooojo.i ^ 115000. 



Secantem iflam qua;ro in Canone,& deprchendo ipfi rcfpon- 

 dcre grad,6 5. 



B 



e.Si in triangulo rcclangido.cognitis angulis ^ vno latere, qui- 

 rantur reliqua larera , lattis dntn») femper occupabit tertium lo- 

 cumin reguld dctri,^' numcrus ij>fi homogeneus ex ftnubus pri- 

 mum numcrtu mator alter fecundum. Vc in pra^ced. triangulo 

 notum cft lacus EC 8 pcd. Quxritur dc catheto A B.'Cum 

 vero ■quilibet cathetus pro bafi poflitlumi , dico B C cflcca- 

 thetum,&c C effe angulum bafcos.63.graduum.Tum bafis AB 

 hoc inodo inuenitur. 

 Vt ladius totus ad tangentem ang, jy.ita B C.ad B A, 



iQOOOB 75355 5* (•■rJ^^s^- 



7. Vt triangula reHangula co e.vpeditias foluantur ( cumjiat 

 valde vfitata)fequens tabellafitin confpecin. 



fCatheto &^ 

 bafi 



f Anguli cx datis j Catheto & 



In folutione triangulo- 

 rum q4jiruatur 



& cognitis la-y 

 tcribus • vc ex 



hypotc- 



nusa 



> 



Hypote- 

 nusa & 

 L bafi 



Quacruntur 

 ignoti an- 

 guliiquf^s^ 

 fubicndit 



CBafis efl fangcDS. 

 I Cathetus. rad.totus» 

 f Bafis.Eius angulus ) Hypntenufa, ndms. 

 inuenitur ciim "^. Bafis, linus rcftus, 

 1 Hypoteaufa, fecans. 

 ^Cathetus, rad.totuf. 



Cathetus.Eius an- 

 gulus inuenitur ,' 



rCathetus eft tangens. 



I hafis, rad us. 

 Hvpotenufa, radius, 

 C<»f^ft«/, finus reduS/ 



I Hvpoten.iQCMS. 



^.£<i/(.r,radius. 



f Cathetus.quo 



inuelli^racur 



fCatheti 



rCathetM eft finus reftus. 

 f Bafis; fl , B.ifis eft finus complementi. 

 I I Citrhefus eft tangens, 



, l.£«/;; citradius totus. 



angulo 



I fCathetus eft finus redus. 



I Hypotenu-s ii;j/;i,efl finus totus. 

 L fa;li I C<»r/;m^,clt tangens. 



^Ba(is, eft fecans. 

 fCathetM eft radius. 

 Balis ; fi /;;t/(j,tangcns. 



Cathctus,i\n\M complcmcnti. 

 LBafcoi -^ li5-T/7i,linus rcftus. 



fCathetused radius. 

 Hvpoccnufa; fl ,' Hypoieni<fa,Ct:Cim. 



; C.uhetiis,Cinns complcmenti, 

 ^Hypore>!:ifa,iAi.\'ms. 

 Latera cx ang-jlis & vno^J Bafis. Vbi non opus cft fubdiiiifionc : quia q',iilibcc cachecus potcll fufti- 

 latere cognito , cjuod 'isc'^ victiu bafcos. 

 l. cllvcl f H.potentifaed rsdhis. 



fB.;lIs;G ', Eitfis.Unus complemcnci. 

 1 ~i Hypotnnufit.Cccins. 



fCachcti^^ l.B>ij7/, raaius. 



f Hypotcnufa,c[i'ml\\is. 



Hypotcnufa ; ex qua-^ 

 inucrtigatur vna | 



LCathetus; fi { Cathciui,U\-\as reclus. 

 I Hypotcnufi fccans. 

 \.Ci-ithetM, tansrens. 



cura angulo 



I f Hypotenufi cft radius. 



I fBafis;(i l iJ.t/»{,(inus rcflus. 



I I ' Hvpotcnufa,Ct:c3.ns. 



»-Bafcos / Litij/ii.tangens. 



"j fHypoicnufa cft radius. 



I I C/ir/jff/^ eftfinus comple- 



i Cathetus i fi"^ mcnti. 



1 Hypotimtfa,Ceczns. 

 V. Cathetus, tadius totus. 



Hic 



