Books Books 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 ## The geometry, by T. S. Davies. Conic sections, by Stephen Fenwick

Royal Military Academy, Woolwich - Mathematics - 1853 - 400 pages
...with the square of AC. Wherefore, if a straight line, etc. QED PROPOSITION VIII. THEOR. 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 of the whole and that part. Let the straight line AB be divided into any... ## The first six books of the Elements of Euclid, with numerous exercises

Euclides - Geometry - 1853 - 176 pages
...square of a С. Wherefore, if a straight line, &c. QED PROPOSITION VIII. — THEOREM. 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, LET the straight line ab be divided into... ## The synoptical Euclid; being the first four books of Euclid's Elements of ...

Euclides - 1853 - 146 pages
...together with the square of AC. Wherefore, if a straight line, &c. QED PROP. VIII. THEOREM. 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. Let the straight line AB be divided into... ## The Elements of Euclid. Books I.-VI.; XI. 1-21 XII. 1-2. A New Text ..., Book 1

Euclides - Geometry - 1853 - 334 pages
...other part. Let AB be the given straight line. It is required to divide it into two such parts, that the rectangle contained by the whole line and one of the parts shall be equal to the square of the other part. On AB describe (i. 46) the square ACDB ; and supposing... ## Arithmetic, algebra, differential and integral calculus, by W. Rutherford ...

Royal Military Academy, Woolwich - Mathematics - 1853 - 472 pages
...question in its literal meaning. 2. To divide a line of 20 inches in length into two parts such that the rectangle contained by the whole line and one of the parts shall be equal to the square of the other part. Let x = the greater part ; then 20 — x = the less... ## Solutions of the problems and riders proposed in the Senate-house ...

Cambridge univ, exam. papers - 1854 - 282 pages
...parallelograms GF, EH is equal to twice the triangle KBD. 2. Divide a given straight line into two parts so that the rectangle contained by the whole line and one of the parts shall be equal to the square of the other part. Produce a given straight line to a point such that... ## Solutions of the Problems and Riders Proposed in the Senate-house ...

William Walton, Charles Frederick Mackenzie - Mathematics - 1854 - 266 pages
...parallelograms is equal to twice the triangle BSD. 2. Divide a given straight line into two parts so that the rectangle contained by the whole line and one of the parts shall be equal to the square of the other part. Produce a given straight line to a point such that... ## Elements of Geometry: Containing the First Six Books of Euclid with a ...

John Playfair - Geometry - 1855 - 336 pages
...derived from the above algebraical equality, by transposition. PROP. VIII. THEOR. If a straight line lie divided into any two parts, four times the rectangle...square of the other part, is equal to the square of the straight line which is made vp of the whole and thefirst-mentioned part. Let the straight line AB be... ## Minutes of the Committee of Council on Education

Great Britain. Committee on Education - School buildings - 1855 - 976 pages
...into any two parts, the squares of the whole line and of one of the parts are together equal to twice the rectangle contained by the whole line and one...parts, together with the square of the other part. 5. To construct a square equal to a given rectangle. 6. If a straight line passing through the centre... 