| 1852 - 316 pages
...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,...by the two parts, together with the square of the** aforesaid part. following sentence, shewing the variou» clauses, &c. :— " Not to do your best when... | |
| Euclides - 1852 - 152 pages
...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,...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 rectangle AB,... | |
| Royal Military Academy, Woolwich - Mathematics - 1853 - 400 pages
...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 - 146 pages
...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 - Geometry - 1853 - 176 pages
...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 - Geometry - 1853 - 334 pages
...into any two parts : then the rectangle contained by the whole line and one of the parts, shall be **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 any two parts in c. Then. the rectangle AB,... | |
| William Somerville Orr - Science - 1854 - 534 pages
...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«. . .... | |
| Euclides - 1855 - 270 pages
...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... | |
| John Playfair - Euclid's Elements - 1855 - 340 pages
...PROP. III. THEOR. If a straight line be divided into any two parts, the rectangle contained by ttie **whole and one of the parts, is equal to the rectangle contained by** the twtt parts, together with the square of the aforesaid part. Let the straight line AB be divided... | |
| Euclides - 1856 - 168 pages
...and each of the parts. Cor. 2. — In like manner making A equal to one of the parts, it appears that **if a straight line be divided into any two parts,...contained by the two parts together with the square of the** first mentioned part. XLIX.— EUCLID II. 4. If a straight line be divided into any two parts the square... | |
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