...called the rectangle ab, ac. Я PROPOSITION IV. — THEOREM. If a straight line be divided into any two parts, the square of the whole line is equal to the squares oftíie two parts, togetlwr with twice the rectangle contained by the parts. LET the straight...

...opposite, .-. / ACS = / BCD = a right angle. 44. PROP. XXII. If a straight line be divided into any two parts, the square of the whole line is equal to the sum of the squares of the two parts together with twice the rectangle* contained by the parts. QDEF. A rectangle...

...represent the parts into which any right line is divided, it follows from the example sec. II, 45, that the square of the whole line is equal to the sum of the squares of the parts, plus twice the rectangle under each two of them, &c. 24. If the sum of the equal...

...out the part of your demonstration in which it is evaded. 3. If a straight line be divided into any two parts, the square of the whole line is equal to the squares of the two parts, together with twice the rectangle contained by the parts. A modification...

...7th, 27th, 32nd and 48th prop, of the 1st book of Euclid. . 3. If a straight line be divided into any two parts, the square of the whole line is equal to the squares of the two parts, together with twice their rectangle. 4. If a straight line be divided into...

...and concise than in ordinary language. The proposition, (Euclid 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, together with twice the product of the parts, is demonstrated, by squaring...

...two sides of a triangle will be parallel to the third side' 5. If a straight line be divided into any two parts, the square of the whole line is equal to the squares of the two parts, together with twice the rectangle contained by the parts. 6. In every triangle,...

...its angles equal to a given rectilineal angle. Section 2. 1. If a straight line be divided into any two parts, the square of the whole line is equal to the squares of the two parts, together with twice the rectangle contained by the two parts. 2. If a straight...

...straight line, their rectangle becomes a square. PROP. IV. THEOREM. If a straight line be divided into any two parts, the square of the whole line is equal to the squares of the two parts, together with twice the rectangle contained by the parts. Let the straig-ht...

...base and between the same parallels, are .equal to each other. 7. If a right line be divided into any two parts, the square of the whole line is equal to the squares of the two parts, together with twice the rectangle contained by the parts. 8. Describe a square...