...than in ordinary language. The proposition, (Euc. 4. 2.) that when a straight line is divided into two par.ts, the square of the whole line is equal...squares of the two parts, together with twice the product of the parts, is demonBtrated, by involving a binomial Let the side of a square be represented...

...triangle. 3. A straight line being divided into two parts, prove the square of the whole line to be equal to the squares of the two parts, together with twice the rectangle contained by the parts. 4. Prove the angle in a semicircle to be a right angle. 518 mities 36° 201 and 60° 10* ; required...

...rectangle contained by the two parts, together with the square of the aforesaid part. PROP. IV. THEOREM. If a straight line be divided into any two parts, the...together with twice the rectangle contained by the parts. COR. From the demonstration, it is manifest, that the parallelograms about the diameter of a square...

...concise, 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...squares of the two parts, together with twice the product of the parts, is demonstrated, by involving a binomial. Let the side of a square be represented...

...parts, the square of the whole line is equal to the squares of the two parts, together with tvtice the rectangle contained by the parts. Let the straight...CB, and to twice the rectangle contained by AC, CB, that is, AB2=AC2+CB2+2AC.CB. Upon AB describe (Prop. 46. 1.) the square ADEB, and join BD, and through...

...rectangle AC, CB together with the square of BC. If therefore a straight, &c. QED PROP. IV. THEOR. If a straight line be divided into any two parts, the...together with twice the rectangle contained by the parts. Upon AB describe (i. 46.) the square ADEB, and join BD, and through c draw (i. 31.) CGF parallel to...

...middle points of the sides which are not parallel. PROPOSITION VIII. THEOREM. If a straight line is divided into any two parts, the square of the whole line is equivalent to the squares of the two parts, together with twice the rectangle contained by 'the parts....

...sides which contain the right angle. Section 3. 1. If a straight line be divided into any two part» the square of the whole line is equal to the squares...parts, together with twice the rectangle contained hy the parts. 2. Show that if a straight line be divided into any two parts, the squares of the whole...

...language. The proposition, (Euc, 4. 2.) that when a straight line is divided into two parts, tilesquare of the whole line is equal to the squares of the two parts, together with twice the product of the parts, is demonstrated, Ijy involving a binomial. Let the side of a square be represented...

...makes the alternate angles equal. — Define parallel lines, and alternate angles. 3. If a line be cut into any two parts, the square of the whole line is equal to the squares of the parts, and twice the rectangle contained by the parts. — Show the same Algebraically. 4. Prove tluit...