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" IF a straight line be divided into two equal, and also into two unequal parts; the squares of the two unequal parts are together double of the square of half the line, and of the square of the line between the points of section. "
The Elements of Euclid; viz. the first six books,together with the eleventh ... - Side 58
av Euclides - 1841 - 351 sider
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Mathematical Questions and Solutions, from the "Educational Times.", Volum 3

1865
...geometrically, in the following form, which is analogous to that of Euclid II. 5. If a circular arc be divided into two equal and also into two unequal parts, the rectangle contained by the chords of the two unequal arcs, together with the square on the chord of...
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Examination papers collected by A. Clark as a student and as an examiner

1867
...to three given straight lines, but any two whatever of these must be greater than the third. 5. 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...
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The Elements of Euclid for the Use of Schools and Colleges: Comprising the ...

Euclid, Isaac Todhunter - 1867 - 400 sider
...the line made 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 unequal parts, the squares on the two unequal parts are t 'gather double of the square on half the line and of the square on the...
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Elementary Geometry, Volum 1

James Maurice Wilson - 1868
...difference of any two lines is equivalent to the difference of the squares on those lines 61 THEOREM 28. If a straight line be divided into two equal and also...parts are together double of the square of half the Hue bisected, and the square on the line made up of the half and the part produced ........ 62 THEOREM...
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Euclid's Elements of Geometry: Chiefly from the Text of Dr. Simson, with ...

Robert Potts - 1868 - 410 sider
...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. Let the straight line AB be divided into two equal parts in the point C, and into two unequal parts in the point D. Then the squares on AD, DB together, shall...
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Elementary geometry

James Maurice Wilson - 1869
...theorems may be used to demonstrate other properties of divided lines. For example, THEOREM 28. If a straight line be divided into two equal and also into two unequal segments, the squares of the two unequal segments are together double of the square of half the line...
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Examination for women. Examination papers, with lists of syndics and examiners

Cambridge univ, exam. papers - 1870
...two equal parts. If the diagonals of a quadrilateral bisect one another, it is a parallelogram. 2. 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...
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Gradations in Euclid : books i. and ii., with an explanatory preface [&c ...

Euclides - 1870
...the extraction of the Square root. PROP. 9. — THBOB. If a st. line be divided into two equal parts, and also into two •unequal parts, the squares of the two unequal parts are togetJier double of the square of the half line and of the square of the line between the points of...
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Elements of geometry, containing the first two (third and fourth ..., Del 1

Euclides - 1871
...and sq. on AC =sum of the eight rectangles and XH =AEFD = sq. on AD. X X 0 K Tf -U -XZ~ F p -R 0 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 an half the line and of the square on the...
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The Edinburgh university calendar

Edinburgh univ - 1871
...the greater angle is greater than the base of the other. A complete demonstration is required. 4. 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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