(. 27 ) 



'v/s fefkper r'efoli>i poterit ift du^s atiai-, irt 

 quacunque directione agentes. 



IXi Sic A B C P (Fig. 6.) parflllelogrammum ; 

 O punctum qnoddam extra vel intra parallelo- 

 grammum , pro libitu fumtum; fi ex hoc punc- 

 to demittantur pcrpcndicula O D , O E , O F , 

 in latera adjacentia AP et BP, ec in diagona- 

 lem GP, erit fempcr: 

 ' PC X OF =PB X OD -i-PAXOE, 



fi punctum O extra parallelogrammum cadit , 



(iiti in Fig. -6. N°. i.) fed 'fipHnctum illud , 



("uti in Fig. 6. N^. 2.) intra parallelogram- 



ma pofitum est erit : ''^ -^^ ''* 



PCXOF = .PBXOD-PAXOE. 



Quoniam produCta PCXOF,PBXOD; 

 PA' X OE ^ifiint duplae areae trian^guloruni 

 OPC, OPB ct OPA, facile demonflrar^ 

 posfumus proprietates indicatas : namque , pro- 

 ductis AC et DO, crit: ' ' ' 



i^. (Fig. 6. N*. I.) A PAC-A CXO 

 = i AC X (DQ - OQ) =: i AC X DO 

 = PB X 1 DO = A POB; 



ergo A PAC - A OAC =J A POB, 



fed A PAO = A PAO; 



ergo aPAC + aPAO -a0AC=::aPB0 

 - + A PAO; 



-- id csc aPOC^aOPA 



4- A OPB, 

 fi- 



