 | 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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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. 
