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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. "
Elements of Geometry: Containing the First Six Books of Euclid, with a ... - Σελίδα 55
των Euclid, John Playfair - 1826 - 320 σελίδες
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Euclid's Elements of Geometry: Chiefly from the Text of Dr. Simson, with ...

Robert Potts - 1876 - 403 σελίδες
...added together in one straight line. Wherefore, if a straight line, &c, QED .1 PROPOSITION IX. THEOREM. If a straight line be divided into two equal, and also into two unequal parti; the squares on the two unequal parts are together double of the square on half the line, and...

Examination Papers for Science Schools and Classes

Great Britain. Education Department. Department of Science and Art - 1877
...Given that a : b '.'. b : c, show that :— a'+6'+c'=(a+6+c) (a-6+c) (20.) Section B.—Geometry. 27. If a straight line be divided into two equal and also into t\ro unequal parts, show that the rectangle contained by the unequal parts, together with the square...

Civil Service of India: Open Competition for the Regulations, Examinations ...

1878
...parallelogram with the middle points of either pair of opposite sides will trisect the other diagonal. 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...

Moffatt's pupil teachers' course (ed. by T. Page). Candidates, 2nd (-4th) year

Moffatt and Paige - 1879
...added together 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 parts, the squares on the two unequal parts are together double of the square on half the line and of the square on the...

Moffatt's scholarship answers, by T.J. Livesey (T. Page).

Moffatt and Paige - 1879
...E. That is, 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 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...

Euclid, books i. & ii., with notes, examples, and explanations, by a late ...

Euclides - 1879
...Now BC 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 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...

First Public Examination in Literis Graecis Et Latinis

University of Oxford - 1879
...their other angles 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 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...

Queen's scholarship examination. Amner's eight years' scholarship questions ...

Joseph Wollman - 1879
...square on BC is 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...

A complete set of male pupil teachers' examination questions in Euclid [book ...

W J. Dickinson - 1879 - 36 σελίδες
...14. Show how 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...

The Elements of Plane and Solid Geometry: With Chapters on Mensuration and ...

Isaac Sharpless - 1879 - 266 σελίδες
...joining the 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...




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