 | Education - 1844 - 688 pages
...squares described upon the other two sides of it, the angle contained by these two is a right angle. 6. If a straight line be divided into any two parts,...by the two parts, together with the square of the aforesaid part. 7. Describe a square equal to a given rectilineal figure. 8. Find the centre of a circle.... | |
 | Euclides - 1845 - 546 pages
...AB, BC is equal to the square of AB. If therefore a straight line, &c. QED PROPOSITION III. THEOREM. If a straight line be divided into any two parts,...by the two parts, together with the square of the aforesaid part. Let the straight line AB be divided into any two parts in the point C. Then the rectangle... | |
 | Euclid, James Thomson - Geometry - 1845 - 382 pages
...them, instead of being established by continual appeals to original principles. PROP. III. THEOR. — If a straight line be divided into any two parts,...by the whole and one of the parts, is equal to the square of that part, together with the rectangle contained by the two parts. Let the straight line... | |
 | Euclid - Geometry - 1845 - 218 pages
...straight line, &c. QED CB FE BOOK II. PROP. m. IV. • 46. 1. t 31. 1. PROPOSITION III. THEOK. — If a straight line be divided into any two parts,...rectangle contained by the whole and one of the parts, w equal to the rectangle contained by the two parts, together with the square of the aforesaid part.... | |
 | Euclides - 1846 - 292 pages
...rectangle AB, BC, is equal to the square of AB. Wherefore, If a straight line Sjc. QED PROP. III. THEOR. If a straight line be divided into any two parts,...by the two parts, together with the square of the aforesaid part, Let the straight line AB be divided into any two parts in the point C : the rectangle... | |
 | Euclid, John Playfair - Euclid's Elements - 1846 - 334 pages
...multiplying both members of this equality by a, we shall have as=ab+ad FE K JL H PROP. III. THEOR. If a straight line be divided into any two parts,...by the two parts, together with the square of the aforesaid part. Let the straight line AB be divided into two parts, in the point C ; the B rectangle... | |
 | John Playfair - Euclid's Elements - 1847 - 340 pages
...parts, is equal to the rectangle contained by. the two parts, together with the square of the aforesaid part. Let the straight line AB be divided into two parts, in the point C ; the B rectangle AB.BC is equal to the rectangle AC.BC, together with BC2. Upon BC describe (Prop. 46. 1.)... | |
 | J. Goodall, W. Hammond - 1848 - 390 pages
...two sides of it, the angle contained by these two sides is a right angle. Section 3. 1. Prove that if a straight line be divided into any two parts,...by the two parts, together with the square of the aforesaid part. 2. Prove that if a straight line be divided into two equal and also two unequal parts,... | |
 | Euclides - 1848 - 52 pages
...whole and each of the parts, are together equal to the square of the whole line. PROP. III. THEOREM. If a straight line be divided into any two parts,...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 square of... | |
 | Euclid, Thomas Tate - 1849 - 120 pages
...contained by two straight lines AB, AC is sometimes simply called the rectangle AB, AC. PROP. III. THEOR. If a straight line be divided into any two parts,...contained by the whole and one of the parts is equal with the rectangle contained by the two parts, together with the square of the aforesaid part. Let... | |
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If a straight line be divided into any two parts, the rectangle contained by the whole and one of the parts, is equal to the rectangle contained by the two parts, together with the square of the aforesaid part. 
