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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 geometry of the three first books of Euclid, by direct proof from ... - Página 64
por Euclides - 1856
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The College Euclid: Comprising the First Six and the Parts of the Eleventh ...

Euclides - 1865 - 402 páginas
...added together in one straight line. Wherefore, if a straight line, &c. QED PROP. IX. — THEOREM. If a, straight line be divided into two equal and also into two unequal parts; then the squares of the two unequal parts are together double of the •quare of half the line, and...
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Mathematical Questions and Solutions, from the "Educational Times.", Volumen3

1865 - 128 páginas
...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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Mathematical Questions and Solutions, Volumen3

1865 - 132 páginas
...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 - 224 páginas
...equal 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 - 426 páginas
...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, Volumen1

James Maurice Wilson - 1868 - 132 páginas
...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 - 434 páginas
...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...
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Elementary geometry

James Maurice Wilson - 1869 - 260 páginas
...lines is equivalent to the difference of the squares tin those lines 6l One Corollary. 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 - 272 páginas
...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 - 270 páginas
...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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