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" If a straight line be divided into any two parts, four times the rectangle contained by the whole line, and one of the parts, together with the square of the other part, is equal to the square of the straight line which is made up of the whole and that... "
Gradations in Euclid : books i. and ii., with an explanatory preface [&c ... - Page 161
by Euclides - 1858
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The papers set at the professional preliminary examination

College of preceptors - 1882 - 528 pages
...(without proof) a converse of this proposition. 4. To divide a given straight line into two parts, so that the rectangle contained by the whole line and one of the parts may be equal to the square on the other part. Give the enunciation (without the proof) of a subsequent...
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The Competitor, Volumes 1-2

1882 - 480 pages
...twice the rectangle contained by the two parts. 5. Divide a given straight lite into two parts so that the rectangle contained by the whole line and one of the parts may be equal to the square on the other part. Divide a given ttraight line into two parts so that the...
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The Elements of Euclid for the Use of Schools and Colleges: Comprising the ...

Euclid, Isaac Todhunter - Euclid's Elements - 1883 - 428 pages
...BC, together with the square on AC. EUCLID'S ELEMENTS. PROPOSITION 8. THEOREM. If a straight line lie divided into any two parts, four times the rectangle...line and one of the parts, together with the square on the other part, is equal to the square on the straight line which is made up of the whole and that...
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Glasgow University Calendar

University of Glasgow - 1883 - 438 pages
...action. HIGHER MATHEMATICS. Uth Oc'ober, 1882. 1. Divide a given straight lino into two parts, such that the rectangle contained by the whole line and one of the parts shall be equal to the square on the other part. Where does Euclid afterwards make use of this proposition...
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Syllabus of plane geometry, books 1-3, corresponding to Euclid, books 1-4 ...

Mathematical association - 1883 - 86 pages
...several parts into which the other is divided. COR. 1. If a straight line is divided into two parts, the rectangle contained by the whole line and one of the parts is equal to the sum of the square on that part and the rectangle contained by the two parts. COR. 2....
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Geometry for schools, comprising books i. and ii. of Euclid, with some ...

Euclides - 1883 - 176 pages
...(ie, AB2) = AB . AC + AB . CB. QED PROP. 3. THEOR. If a straight line be divided into any two parts, the rectangle contained by the whole line and one of the parts will be equal to the square on that part together with the rectangle contained by the two parts. Let...
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Stewart's specific subjects. Euclid. [1st] (-3rd stage). [With 2 issues of ...

Stewart W. and co - 1884 - 272 pages
...BC are equal to twice the rectangle AB, BC, together with the square of AC. VIII. — If a straight line be divided into any two parts four times the...square of the other part, is equal to the square of the straight line, which is made up of the whole and that part, This proposition is generally omitted by...
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The Elements of Plane Geometry ...

Association for the improvement of geometrical teaching - Geometry, Modern - 1884 - 150 pages
...contained by AB and CE, AB and EF, AB and FD. QED vj COR. 1. If a straight line is divided into two parts, the rectangle contained by the whole line and one of the parts is equal to the sum of the square on that part and the rectangle contained by the two parts. This follows...
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The elements of plane geometry, Volume 1

Mathematical association - 1884 - 146 pages
...contained by AB and CE, AB and EF, AB and FD. QED COR. 1. If a straight line is divided into two parts, the rectangle contained by the whole line and one of the parts is equal to the sum of the square on that part and the rectangle contained by the two parts. This follows...
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The Practical Teacher, Volume 4

Education - 1885 - 630 pages
...learnt the proposition given to him in the form of—' If a straight line be divided into any two pans, four times the rectangle contained by the whole line and one of the parts, together with the square on the other part, is equivalent to the square of the straight line, which is made up of the whole...
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