Books Books If a straight line be divided into two equal parts, and also into two unequal parts, the rectangle contained by the unequal parts, together with the square on the line between the points of section, is equal to the square on half the line. The first and second books of Euclid explained to beginners, by C.P. Mason - Page 144
by Euclid, Charles Peter MASON - 1872 ## Elements of Geometry: Containing the First Six Books of Euclid, with a ...

John Playfair - Euclid's Elements - 1860 - 332 pages
...is divided be denoted by a and l; then, (a+6) 1 =o 2 +2a6+6 2 . PROP. V. THEOR. If a straight linele divided into two equal parts, and also into two unequal...contained by the unequal parts, together with the square of the line between the points of section, is equal to the square of half the line. Let the straight... ## Elements of Geometry, and Plane and Spherical Trigonometry: With Numerous ...

Horatio Nelson Robinson - Geometry - 1860 - 472 pages
...equation AD x D£-\- CB*= CD , which i* the algehraic proof of the theorem. THEOREM XLV. If a straight line be divided into two equal parts, and also into...two unequal parts, the rectangle contained by the two unequal parts together with the square of the line between the points of division, will be equivalent... ## Euclid's Elements of Geometry: Chiefly from the Text of Dr. Simson, with ...

Robert Potts - Geometry, Plane - 1860 - 380 pages
...= <*'— m', to each of these equals add m' ; .'. (a + m) (a — m) + m' = a'. That is, if a number be divided into two equal parts, and also into two unequal parts, the product of the unequal parts together with the square 1 of half their difference, is equal to the square... ## Guide to the army - competitive examinations

Alexander Hadden Hutchinson - 1861 - 128 pages
...described upon the sides which contain the right angle. 2. 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 cf the line between the points of section is equal to the square of half the line. VOLUNTARY PORTION.... ## Examination papers used at the examination of candidates for appointment to ...

War office - 1861 - 260 pages
...between the same parallels are equal to one another. 2. 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 section is equal to the square of half the line. State and explain... ## Euclid's Elements of geometry, books i. ii. iii. iv

Euclides - 1862 - 140 pages
...parallelograms about the diagonal of a square are likewise squares. PROPOSITION 5.— THEOREM. If a straight line be divided into two equal parts, and also into...square on the line between the points of section, ^s equal to the square on half the line. (References— Prop. I. 31, 34, 36, 43, 46; II. 4, cor.) Hypothesis.... ## The school Euclid: comprising the first four books, by A.K. Isbister

Euclides - 1862 - 172 pages
...parallelograms about the diameter of a square are likewise squares. PROP. V.— THEOREM. //' a straight line be divided into two equal parts, and also into two unequal parts ; then the rectangle contained by the unequal parts, together with the square of the line between the... ## Responsions

University of Oxford - Education, Higher - 1863 - 328 pages
...rectangles contained by the undivided line and the several parts of the divided line. 8 If a straight line be divided into two equal parts, and also into...contained by the unequal parts, together with the square of the line between the points of section, is equal to the square of half the line. 9. Divide a given... ## Report on the examination for admission to the Royal military academy at ...

Woolwich roy. military acad - 1864 - 588 pages
...arranged, under the restriction that the tvco vowels e shall never stand together 1 10. If a straight line be divided into two equal parts, and also into...of section is equal to the square on half the line. Hence show that a square is the greatest rectangle of given perimeter. 11. Describe a circle about... 