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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... "
The Elements of Euclid for the Use of Schools and Colleges: Comprising the ... - Σελίδα 60
των Euclid, Isaac Todhunter - 1883 - 400 σελίδες
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Papers for the schoolmaster, Τόμος 3

1867
...sum of the squares of two lines cannot be less than twice their rectangle. 3. If a straight line be divided into any two parts, four times the rectangle...line and one of the parts, together with the square of the other part, is equal to the square of the straight liue which is made up of the whole and that...

The First Two Books of the Elements of Euclid ... with Additional Figures ...

Euclides - 1852
...Proposition are equal to the two squares AE and kc added together.] PROP. VIII. THEOR. If a straight line be divided into any two parts, four times the rectangle...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...

The first six books of the Elements of Euclid, with numerous exercises

Euclides - 1853 - 147 σελίδες
...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 rectangle...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...

The synoptical Euclid; being the first four books of Euclid's Elements of ...

Euclides - 1853
...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 rectangle...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...

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

Royal Military Academy, Woolwich - 1853
...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 rectangle...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 of the whole and that...

The Elements of Euclid: With Many Additional Propositions ..., Μέρος 1

Euclid - 1853 - 136 σελίδες
...and the produced part, to• gether with the square on <• half the line bisected, is equal in area to the square on the straight line which is made up of the half and the produced part. 11.10.. . II. 11, cor. II. 4, cor. 2.. . II. 1. . II. l.cor. II. 5, schol....

The Elements of Euclid. Books I.-VI.; XI. 1-21 XII. 1-2. A New ..., Βιβλίο 1

Euclides - 1853
...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 - 1853
...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 ...

William Walton, Charles Frederick Mackenzie - 1854 - 225 σελίδες
...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...

Solutions of the problems and riders proposed in the Senate-house ...

Cambridge univ, exam. papers - 1854
...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...




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