a2 N.IL TRIGONOSCOPLE CVJVSDAM NOVE 
ex A & B norm>%&s-AH, BG ; tum ob angulum in femicirculo ECF re=_ 
&um, erit CZ ipfis AH, BG parallela, & vb has parallelas AE, EB: : 
HC. CC; fed ob fimilia Triangula FBG & FAH, erit AF, FB:: AH. 
BG: cumgue fit ex hypothefi AE. EB: : AF.BF, erit ergo ex quo HC, 
©u:: AH.BG. Unde per 6tam Gti fimilia erunt Triangula Rettangula 
CAH & CBG, proindeque etiam erit HC.CG :: AC.BC. Sed erat fu- 
pra HC. CG :: AE.EB::M.N; ergo etiam eft AC, BC:: AE.EB:: 
M.N. QE.D. 
X, Propofitio. Problema 7. Fig. 19, 
Si tria [mt pofitione data pına, feilicet, D, E, G, quorum G defignet 
medium lateris cujusdam Tringuli pundlum; E fit ejusdem lateris punötum 
u 
bi ipfi oceurrit veta oppofitum fibi angulum bifecans ‚ID fit punökum ejus= 
dem lateris, ubi ipfi oceurrit perpendicularis ab oppofita angulo demifa z 
conftruere iflud Triangulum, 4 
Conftruktio. 
Hocce Problema eft indeterminatum; enimverd dufta per data punfta 
lineä re&ta, bafis jam dabit pofitionem, Imhanc ad lubitum & G ponantur 
trinque zquales GA & GB, ur fir AB bafıs; tum ere&ta indefinita per- 
pendiculari in D; angulus fiat quilibet BAI, & fir AH zqualis GE feu 
AE-EB,atque HI zqualis EB, huic per I ducatur parallela, occurrens 
AB inF;; tum fi centro L, ınedio ipfius EF pun&to, & intervallo LE de- 
feriptus arcus normalı in D occutrat in C, duttis CA & CB: dico fattuın, 
& Trianpgulum ACB propofitis omnibus gaudere conditionibus, “ 
Demontftratio, oh 
Evidens jam eft G effe pun&tum bafıs medium , & D effe punftum, 
ubi perpendicularis ipfi occurrit ab oppofito angulo demiffa. Porro autem 
jungatur refta EC ; cum .ex conftruftione fa&ta fir AH vel AE-EB. HI 
V 
3 
el EB:: AB. BF, ergo componendo erit AE.EB: : AF. BF, arque fü- 
ra EF tanquam diametro defcriptus eft circulus EC, & ab arcus illius 
pun&to C dultz fünt CA & CB; ergo per przcedentem erit in Triangus 
gulo ACB, AC. CB: AE. EB, unde per ztiam gti CE eft rekta bife-. 
cans angulum ACB bafı AB oppofitim, Q.F.E. D. E D> 
XI, Propofstio, Problema 8, Fg2o. ve 
Confiruere Triangulumy eujus perpendicularis ab uno angulo in oppofi= 
sum Tarus equetur da rehe Id; ejw, anem reciaseundem angulum bife= 
+, DD 
