| John Playfair - 1855 - 317 sider
...multiplying both members of this equality by a, we shall have a2=«A + a</ PE Q KLD PROP. III. THEOR. tf **a straight line be divided into any two parts, the...the parts, is equal to the rectangle contained by** the tttm parts, together with the square of the aforesaid part. Let the straight line AB be divided... | |
| 1867
...one another, and likewise those which are terminated at the other extremity equal to one another. 3. **If a straight line be divided into any two parts,...contained by the two parts, together with the square** on the aforesaid part. 4. Make a triangle of which the sides shall be equal to three given straight... | |
| Euclid, Isaac Todhunter - 1867 - 400 sider
...AB, BC, is equal to the square on AB. Wherefore, if a straight line &c. QED PROPOSITION 3. THEOREM. **If a straight line be divided into any two parts,...contained by the two parts, together with the square** on the aforesaid part. Let the straight line AB be divided into any two parts at the point (7: the... | |
| Euclid, Isaac Todhunter - 1867 - 400 sider
...the other part, is equal to the square on the straight line which is made up of the whole and that **part. Let the straight line AB be divided into any two parts** at the point C: lour times the rectangle AB, BC, together with the square on AC, shall be equal to... | |
| Robert Potts - 1868 - 410 sider
...DA is equal to AB : and CE is contained by AB, BC, for BE is equal to AK : PROPOSITION III. THEOREM. **If a straight line be divided into any two parts, the rectangle contained** ky the whole and one of the parts, is equal to the rectangle contained by the twa parts, together with... | |
| Edinburgh univ - 1871
...triangles, what things must be equal, in order that the triangles may be equal in every respect ? 3. **If a straight line be divided into any two parts,...by the two parts, together with the square of the** foresaid part. 4. Equal straight lines in a circle are equally distant from the centre; and those which... | |
| Euclides - 1871
...CB. QED • Ex. The square on a straight line is equal to four times tlie square on half the line. **If a straight line be divided into any two parts,...contained by the two parts together with the square** on the aforesaid part. Let the st. line AB be divided into any two parts in C. Then must rect. AB,... | |
| Henry William Watson - 1871 - 285 sider
...of the parts AE and EB, and the rectangle of CD and EB would be equal to the square of EB, therefore **If a straight line be divided into any two parts, the rectangle** of the whole line and one of the parts will be equal to the rectangle of the two parts, together with... | |
| Elias Loomis - 1871 - 58 sider
...equivalent 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 ; the square on AB is equivalent to the squares on AC CB, together with twice the rectangle contained... | |
| Euclides, James Hamblin Smith - 1872 - 349 sider
...square on a straight line is equal to forr times the square on half the line. PROPOSITION III. THEOREM. **If a straight line be divided into any two parts,...contained by the two parts together with the square** on the aforesaid part. Let the st. line AB be divided into any two parts in C. Then must rect. AB,... | |
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