...figures HF, CK, AG, GE, are equal to the squares on AC, CB, and twice the rectangle AC, CB; but HF, CK, AG, GE make up the whole figure ADEB, which is the square on AB ; therefore 16. The square on AB is equal to the squares on AC, CB, and twice the rectangle AC,...

...CB. ifj^CB Therefore, if a straight line, &c. QED COROLLARY. — From this demonstration it follows that the parallelograms about the diameter of a square are likewise squares. Proposition 5. — Theorem. If a straight line be divided into two equal parts, and also into two unequal...

...squares on AC, CB,and twice the rectangle AC, CB. Wherefore, if a straight line be divided, &c Q..ED COE. From the demonstration, it is manifest, that the parallelograms...about the diameter of a square, are likewise squares • -i •• PROPOSITION V. THEOREM. :.,.t If a straight line be divided into two equal parts, and...

...AG, GE are equal to the squares on AC and CB, together with twice the rectangle AC, CB. But HF, CK, AG, GE, make up the whole figure ADEB, which is the square on AB ; j-'\^hole Therefore the square on AB is equal to the squares on A~B'/lor AC and CB and twice...

...CK, AG, GE are together equal to the squares on AC, CB and twice the rectangle AC, CB. But HF, CK, AG, GE make up the whole figure ADEB, which is the square on A B. Therefore the square on AB is equal to the squares on AC, CB and twice the rectangle AC, C...

...CK, AG, GE&ro equal to the squares on AC, CB, together with twice the rectangle AC, CB. But HF, CK, AG, GE make up the whole figure ADEB, which is the square on AB. Therefore the square on AB is equal to the squares on AC, CB, together with twice the rectangle...

...CB, with twice the rectangle AC.CB. But the figures HF, CK, AG and GE make up the whole figure AE, which is the square of AB. Therefore the square of AB is equal to the squares of AC and CB, and twice the rectangle 4 C. CB. Wherefore, if a straight line be divided, &c. QED Con. 1....

...CK, AG, GEsate equal to the squares on AC, CB, together with twice the rectangle AC, CB. But HF, CK, AG, GE make up the whole figure ADEB, which is the square on AB. Therefore the square on AB is equal to the squares on AC, CB, together with twice the rectangle...

...Saturday, ЗШ June, 1883, 2 PM to 5 PM (Great importance will be attached to accuracy.) 1, — Prove that the parallelograms about the diameter of a square are likewise squares. Sol. This is proved in Eue. II. 4, and is stated as a corollary to that proposition. g. — (1) Divide...

...the triangle ABC. Then, because D is a right angle, the angle ACB is greater than aright angle; and the square of AB is equal to the squares of AC, CB, and twice the, rectangle uci, BC, CD ; to each add the square of BC ; therefore the squares of AB, BC are equal to the square...