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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. "
The student's guide to the University of Durham, with information respecting ... - Página 136
1880 - 144 páginas
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Moffatt's pupil teachers' course (ed. by T. Page). Candidates, 2nd (-4th) year

Moffatt and Paige - 1879
...AC is equal to the square on A B. Therefore, if a straight line, etc. QED Proposition III. Theorem. If a straight line be divided into any two parts,...parts, together with the square on the aforesaid part. Let the straight line AB be divided into any two parts in the point C. Then the rectangle AB, BC shall...
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A complete set of male pupil teachers' examination questions in Euclid [book ...

W J. Dickinson - 1879 - 36 páginas
...Deduce from this that a square on a straight line is equal to four times the square on half the line. 3. If a straight line be divided into any two parts,...parts, together with the square on the aforesaid part 1G Same proposition. Divide a given line so that the rectangle contained by the whole line and one...
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Euclid, books i. & ii., with notes, examples, and explanations, by a late ...

Euclides - 1879
...this formula in terms corresponding to the enunciation of the proposition.] PROPOSITION III. THEOREM. If a straight line be divided into any two parts,...parts, together with the square on the aforesaid part. Let AB be divided into any two parts at C. Then rect. AB, BC == rect. AC, BC, together with sq. on...
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Mathews' Euclid examination papers ... on Euc. i.-iv

Edward Harri Mathews - 1879
...sides is a right angle. Find a square equal to the difference of two given squares. Section III. 1. If a straight line be divided into any two parts,...parts together with the square on the aforesaid part. 2. If a straight line be divided into any two parts, the squares on the whole line and on one of the...
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First Public Examination in Literis Graecis Et Latinis

University of Oxford - 1879
...the line, and the two interior angles on the same side of it together equal to two right angles. 3. If a straight line be divided into any two parts,...contained by the two parts, together with the square of the aforesaid part. 4. From a given point, either without or in the circumference of a circle, draw...
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The Elements of Plane and Solid Geometry: With Chapters on Mensuration and ...

Isaac Sharpless - 1879 - 266 páginas
...AF+CE=AE; AF=AD.AC=AB.AC, CE=CF.CB = AB. CB, AE-AB * ; AB.AC+AB.CB=AB\ Proposition 3. Theorem.—If a straight line be divided into any two parts, the...contained by the two parts, together with the square of the aforesaid part. Let the straight line AB be divided in two parts in the point C, then AB.BC=AC.CB+BC\...
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Euclid for beginners, books i. and ii., with simple exercises by F.B. Harvey

Euclid, F. B. Harvey - 1880 - 119 páginas
...rectangles contained by MN and MO, and by MN and NO, together = the square on MN. PBOP. III. THEOREM. If a straight line be divided into any two parts,...parts, together with the square on the aforesaid part. Let AB be a straight line divided into any two parts in C. Then it is to be proved that The rectangle}...
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The Elements of Euclid for the Use of Schools and Colleges: With Notes, an ...

Isaac Todhunter - 1880 - 400 páginas
...line lie divided into any ttco parts, the rectangle contained by tlie whole and one of the parts, u equal to the rectangle contained by the two parts, together with the square on the aforesaid part. Let the straight line AB be divided into any two parts at the point C: the rectangle AB, BC shall be...
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The Elements of geometry; or, The first six books, with the eleventh and ...

Euclides - 1881
...when the two straight lines mentioned in Us enunciation are equal, their rectangle is a square. FK If a straight line be divided into any two parts,...contained by the two parts, together with the square of the foresaid part. Let the straight line AB be divided into any two parts at the point C. The rectangle...
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Class lessons on Euclid

Marianne Nops - 1882
...AC, and AB, CB = sq. on AB. Wherefore if a straight line, &c. — QED *2 PROPOSITION III., THEOREM 3. If a straight line be divided into any two parts the...parts, together with the square on the aforesaid part. Let the straight line AB be divided into any two parts at C. The rect. AB, BC = the rect. AC, CB, and...
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