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" If a straight line be divided into any two parts, the squares of the whole line, and of one of the parts, are equal to twice the rectangle contained by the whole and that part, together with the square of the other part. Let the straight line AB be divided... "
The Elements of Euclid: The Errors, by which Theon, Or Others, Have Long Ago ... - Side 48
av Robert Simson - 1762 - 466 sider
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The synoptical Euclid; being the first four books of Euclid's Elements of ...

Euclides - 1853
...straight line, &c. QED PROP. VII. THEOREM. If a straight line be divided into any two parts, the squares of the whole line and of one of the parts, are equal to twice the rectangle contained by tke whole and that part, together with the square of the other part. Let the straight line AB be divided...
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Orr's Circle of the Sciences: The mathematical sciences

William Somerville Orr - 1854
...THEOREM. If a straight line (AB) be divided into any two parts (in C), the squares of the whole lint, and of one of the parts, are equal to twice the rectangle contained by the whole and Hunt part, together with the square of the other part: that is, AB2 + BC2=twice AB'BC + AC!. [See Diagram,...
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Elements of geometry and mensuration

Thomas Lund - 1854 - 192 sider
...line be divided into any two parts, the squares of the whole line and one of the parts are together equal to twice the rectangle contained by the whole and that part, together with the square of the other part. With the same construction as in (44), and in the same manner it may be shewn,...
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The Elements of geometry; or, The first six books, with the eleventh and ...

Euclides - 1855
...square of СD. Р B, O P. VII. THEOREM. If a straight line be divided into any two parts, the squares of the whole line, and of one of the parts, are equal...contained by the whole and that part, together with the square of the other part. Let the straight line AB be divided into any two parts at the point С. The...
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Cambridge examination papers: a suppl. to the University calendar, 1856-59

Cambridge univ, exam. papers - 1856
...parallelogram will also be a square. 4. If a straight line be divided into any two parts, the squares of the whole line and of one of the parts, are equal...contained by the whole and that part, together with the square of the other part. State this result algebraically. 5. One circle cannot touch another in more...
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Manual of Method for the use of teachers in elementary schools

W. F. RICHARDS - 1856 - 184 sider
...rectangle contained by the parts. 2. If a straight line be divided into any two parts, the squares of the whole line, and of one of the parts, are equal...contained by the whole and that part, together with the square of the other part. 3. Divide a straight line so that the rectangle contained by the whole line...
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National Society's Monthly Paper

1856
...to a given rectilineal angle. and 2. If a straight line be divided into any two parts, the squares of the whole line, and of one of the parts, are equal...contained by the whole and that part, together with the square of the other part. 3. Divide a straight line so that the rectangle contained by the whole line...
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Elements of Geometry: Containing the First Six Books of Euclid with a ...

John Playfair - 1856 - 318 sider
...VII. THEOR. If a straight line be divided into two parts, the squares of the whole line, and . ^jgfone of the parts, are equal to twice the rectangle contained by the whole and that part, together with the square of the other part. Let the straight line AB be divided into any two parts in the point C ; the...
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The geometry of the three first books of Euclid, by direct proof from ...

Euclides - 1856
...straight line be divided into any two parts, the squares of the whole line and of one of the parts is equal to twice the rectangle contained by the whole and that part together with the square of the other part. Let AB (Fig. 39) be divided into any two parts in the point C, the squares...
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Middle-class education. 2, Volum 18

Middle-class education - 1857
...answer. 32. Prove geometrically that, if a straight line be divided into any two parts, the squares of the whole line and of one of the parts are equal...contained by the whole, and that part, together with the square of the other part. 33. Prove the last proposition algebraically also. 34. If a straight line...
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