...a flraight line be divided into any two parts, the fquare of the whole line is equal to the fquares of the two parts, together with twice the rectangle contained by the parts. Let the ftraight line AB be divided into any two parts in C; the fquare of AB is equal to the fquares of AC,...

...are at the oppofite Angles of the Parallelograms which make the Gnomon. Pl.zF14. 119. THEOREM i. If a Line AB be divided into any two Parts in C, the Square of the whole Line AB, viz. ABED, is equal to the Squares of the two Parts AC, CB, together with twice...

...ftraight line be divided into any two parts, the •*• fquare of the whole line is equal to the fquares of the two parts, together with twice the rectangle contained by the parts. Let the ftraight line AB be divided into any two parts in C i ike fquire of AB is equal to the fquares of AC,...

...ftraight line be divided into any two parts, the fquare of the whole line is equal to trie fquares of the two parts, together with twice the rectangle contained by the parts. Let the ftraight line AB be divided into any two parts in C ; the fquare of AB is equal to the fquares of AC,...

...equal to the square of the straight line which is made up of the whole and the firstmentioned part. Let the straight line AB be divided into any two parts in the point C ; four times the rectangle AB.BC, together with the square of AC, are equal to the square...

...rectangle contained by the two parts, together with the aquarc of the foresaid part. Prop. IV. Theor. If a straight line be divided into any two parts,...•with twice the rectangle contained by the parts. Prop. V. Theor. If a straight line be divided into two equal parts, and also into two unequal parts)...

...than in ordinary language. The proposition, (Euc. 4. 2.)] that when a straight line is divided into two parts, the square of the whole line is equal to the squares of the two parts, togedier with twice die product of the parts, is demonstrated, by involving a binomial. Let the side...

...other part, is equal to the square of the straight line, which is made up of the whole and that part. Let the straight line AB be divided into any two parts in the point C; four times the rectangle AB, BC, together with the square of AC, is equal to the square...

...if a straight If D -E line, &c. Q, ED PROP. IV. THEOR. If a straight line be divided into any tiio parts, the square, of the whole line is equal to the...straight line AB be divided into any two parts in C ; Uie square of AB is equal to the squares of AC, CB, and to twice the rectangle contained by AC, CB,...

...rectangle contained by the two parts, together with tiie square of the furesaicl part. Prop. IV. Theor. If a straight line be divided into any two parts, the square of the whole line n equal to the squares of the two parts, together with twice the rectangle contained by the parts....