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 ## Elementary geometry

James Maurice Wilson - 1869 - 260 pages
...by addition that AB* + BC* = 2AD* + 2DB*. Ex. 3. To divide a straight line into two parts such that the rectangle contained by the whole line and one of the parts is equal to the square of the other part. Let AB be the given line. Construction. Draw a square ACDB... ## Elements of geometry, containing the first two (third and fourth ..., Part 1

Euclides - 1871 - 136 pages
...lines be drawn from G to B and from G to Z>, shew that BGD is a straight line. /i as a If. a straight line be divided into any two parts, four times the...line and one of the parts, together with the square on the other part, is equal to the square on the straight line which is made up of the whole and the... ## Elements of geometry, containing books i. to vi.and portions of books xi ...

Euclides, James Hamblin Smith - Geometry - 1872 - 376 pages
...G to B and from G to D, show that BGD is a straight line. PROPOSITION VIII. THEOREM. If a straight line be divided into any two parts, four times the...line and one of the parts, together with the square on the otJter part, is equal to the square on the straight line which is made up of the \ and the first... ## The first and second books of Euclid explained to beginners, by C.P. Mason

Euclid, Charles Peter MASON - Geometry - 1872 - 216 pages
...whole line BC and each of its parts. PBOPOSITION III. If a right line be divided into any two parts, the rectangle contained by the whole line and one of the parts is equal to the square on that part together with the rectangle contained by the two parts. The propositions... ## The Acting Teacher's and Student's in Training Guide and Text Book for ...

Henry Major - Student teachers - 1873 - 592 pages
...BC are equal to twice the rectangle AB, BC. together with the square of AC. VIII. — If a straight line be divided into any two parts four times the rectangle contained by the wJwle line, and one of the parts, together with the square oftha other part, is equal to the square... ## A School Euclid. Being Books I.&II. of Euclid's Elements. With Notes ...

Euclides - 1874 - 120 pages
...Algebra is similarly expressed, and is thus represented in symbols, PROPOSITION 8. THEOREM. If a straight line be divided into any two parts, four times the...line and one of the parts together with the square on the other part, is equal to the square on the straight line which is made up of the whole and that... ## Pure mathematics, Volume 1

Edward Atkins - 1874 - 424 pages
...the square on AC. Therefore, if a straight line, &c. QED Proposition 8. — Theorem. If a straight line be divided into any two parts, four times the...line and one of the parts, together with the square on the other part, is equal to the square on the straight line which is made up of the whole line and... ## Pure mathematics, Volume 1

Edward Atkins - 1874 - 428 pages
...the square on AC. Therefore, if a straight line, &c. QED Proposition 8. — Theorem. If a straight line be divided into any two parts, four times the...contained by the whole line and one of the parts, toget/ier with the square on the other part, is equal to the square on tlie straight line which is... ## Elements of Euclid [selections from book 1-6] adapted to modern methods in ...

Euclides - 1874 - 234 pages
...BC. <^. E. D, PROP. III. — THEOREM. (Euc. II. 3.) If a straight line be divided into any two parts, the rectangle contained by the whole line and one of the parts, is equal to the square of that part, together with the rectangle contained by the two parts. Let AB... 