 | University of Oxford - Greek language - 1879 - 414 pages
...shall be equal, each to each, namely those to which the equal sides are opposite. 3. If a straight line be divided into two equal, and also into two...the squares on the two unequal parts are together double of the square on half the line and of the square on the line between the points of section.... | |
 | Moffatt and Paige - 1879 - 378 pages
...square on semi-diameter is half of the whole square. SECTION IV. (Three Questions.) 1. If a straight line be divided into two equal, and also into two...the squares on the two unequal parts are together double of the square on half the line, and of the square on the line between the points of section.... | |
 | Moffatt and Paige - 1879 - 506 pages
...in one straight line. Therefore, if a straight line, etc. QED Proposition IX. Theorem. If a straight line be divided into two equal and also into two unequal...the squares on the two unequal parts are together double of the square on half the line and of the square on the line between the points of section.... | |
 | Euclides - 1879 - 146 pages
...contains a — x units, hence the analogous result is established.] PROPOSITION IX. THEOREM. If a straight line be divided into two equal, and also into two...the squares on the two unequal parts are together double of the square on half the line, and of the square on the line between the points of section.... | |
 | Euclides, James Hamblin Smith - 1879 - 376 pages
...BC and sq. on AC _sum of the eight rectangles and XH II. II. PROPOSITION IX. THEOREM. If a straight line be divided into two equal, and also into two unequal parts, the squares on the tu'o unequal parts ore together double of the square on half the line and of th, square on the line... | |
 | Isaac Sharpless - Geometry - 1879 - 282 pages
...middle points the diagonals. From (II. 9) Add and apply (II. 4, Cor. 2) and (II. 9). 6. If a straight line be divided into two equal, and also into two unequal, parts, the rectangle contained by the unequal parts, together with the square of the line between the points of... | |
 | Edward Harri Mathews - 1879 - 94 pages
...in order ; show that a, b, c, d, are the angular points of another parallelogram. 2. If a straight line be divided into two equal, and also into two unequal parts, the rectangle contained by the two unequal parts, together with the square of the line between the points... | |
 | Joseph Wollman - 1879 - 120 pages
...less than four times the square on AD, the triangle ABC is an acute-angled triangle. 3. If a straight line be divided into two equal and also into two unequal parts, the rectangle contained by the unequal parts together with the square on the line between the points of... | |
 | W J. Dickinson - Geometry - 1879 - 44 pages
...to describe a square that shall be equal to a given rectilineal figure. Deductions. 1. If a straight line be divided into two equal, and also into two unequal parts, the part between the points of section is •equal to half the difference of the unequal parts. 2. If the... | |
 | Isaac Todhunter - Euclid's Elements - 1880 - 426 pages
...of AB and BC together. Wherefore, if a, straight line &c. QED PROPOSITION 9. THEOREM. If a straight line be divided into two equal, and also into two...the squares on the two unequal parts are together double of the square on half the line and of the square on the line between the pointt of section.... | |
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If a straight line be divided into two equal, and also into two unequal parts, the squares on the two unequal parts are together double of the square on half the line and of the square on the line between the points of section. 
