| Euclid - 1845 - 199 sider
...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 - 1845
...is equal to the squares of the two parts, together with twice the rectangle contained by the parts. **Let the straight line AB be divided into any two parts in** C. Then the square of AB shall be equal to the squares of AC, and CB, together with twice the rectangle... | |
| Euclid, John Playfair - 1846 - 317 sider
...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,...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.... | |
| Great Britain. Admiralty - 1846
...A.BC = A.BD+A.DE+A.EC. Wherefore, if there be two str. lines, &c. PROP. XLII. THEOR. 3. 2 En. angle **contained by the two parts, together with the square of the aforesaid part. Let the** str. line AB be divided into two parts in the pt. C ; then AB . BC = AC. BC + BC 8 . Prop. 38 . On... | |
| Great Britain. Admiralty - 1846
...there be two str. lines, &c. PROP. XLII. THEOR. 3 . 2E u. Prop. 10. Prop. 3. Prop. 30. Piop. 33. angle **contained by the two parts, together with the square of the aforesaid part. Let the** str. line AB be divided into two parts in the pt. C ; then AB. BC = AC. BC + BC". Prop 38 On BC descr.... | |
| Euclides - 1846
...to twice the rectangle contained by the whole and that part, together with the square of the other **part. Let the straight line AB be divided into any two parts** at the point C : the squares of AB, BC shall be equal to twice the rectangle AB, BC, together with... | |
| John Playfair - 1847 - 317 sider
...the rectangle contained by the whole and that part, together with the square of the other part. L et **the straight line AB be divided into any two parts in the point C ; the** squares of AB, BC, ar.e equal to twice the rectangle AB.BC, together with the square of AC, or AB2+BC2... | |
| J. Goodall, W. Hammond - 1848
...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,...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, the squares... | |
| Euclides - 1848
...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,...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 the whole line is... | |
| Euclid, Thomas Tate - 1849 - 108 sider
...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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