| Elias Loomis - 1849 - 226 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... | |
| 1852
...the right angle, is equal to the squares described upon the sides which contain the right angle. III. **If a straight line be divided into any two parts,...parts, together with the square of the aforesaid part.** following sentence, shewing the variou» clauses, &c. :— " Not to do your best when you are told... | |
| Euclides - 1852
...equal to the two numbers multiplied together.] 90 BOOK II. • xlvi. 1. THE ELEMENTS 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 rectangle AB, BC is equal to the rectangle AC, CB, together with the... | |
| Royal Military Academy, Woolwich - 1853
...AB, BC, is equal to the square of AB. If therefore a straight line, etc. QED PROPOSITION III. THEOR. **If a straight line be divided into any two parts,...the rectangle contained by the two parts, together** loith the square of the aforesaid part. Let the straight line AB be divided into any two parts in the... | |
| Euclides - 1853
...AB, BC, is equal to the square of AB. If, therefore, a straight line, &c. QED PROP. III. — THEOREM. **If a straight line be divided into any two parts,...the rectangle contained by the two parts, together** mill the square of the aforesaid part. Let the straight line AB be divided into any two parts in the... | |
| Euclides - 1853 - 147 sider
...the square of ab. If QED df therefore a straight line, &c. PROPOSITION III. — THEOREM. If a slraigM **line be divided into any two parts, the rectangle...rectangle contained by the two parts, together with** tlie square of the aforesaid part. LET the straight line ab be divided into any two parts in the point... | |
| Euclides - 1853
...the other part shall be equal to the square of the line which is made up of the whole line and that **part. Let the straight line AB be divided into any two parts** AC, CB in c. Then four times the rectangle AB, BC together with the square of AC shall be equal to... | |
| William Somerville Orr - 1854
...PROPOSITION III.— ТНЕОЕБИ. . ., If a straight line (AB) be divided into any two parts (AC, CB), **the rectangle contained ,by the whole and one of the parts is equal to the rectangle contained by** the twoparts% together with the square of the aforesaid part : that is, AB-BC = AOCB + :вс«. . .... | |
| John Playfair - 1855 - 318 sider
...rectangle contained by tht whole ami one of the parts, is equal to the rectangle contained by the tw» **parts, together with the square of the aforesaid part. Let the straight line AB be divided into** two parts, in the point C ; the rectangle AB.BC is equal to the rectangle AC.BC, together with BC 2... | |
| Euclides - 1855
...lines mentioned in its enunciation are equal, their rectangle is в square. PROP. III. THEO КЕМ. **If a straight line be divided into any two parts, the rectangle contained by the** inhale and one of the parts is equal to the rectangle contained by the two parts, together toith the... | |
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