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" If a straight line be divided into any two parts, the rectangle contained by the whole and one of the parts, is equal to the rectangle contained by the two parts, together with the square of the aforesaid part. "
The Elements of Euclid: Viz, the First Six Books, Together with the Eleventh ... - Side 49
av Euclid, Robert Simson - 1829 - 516 sider
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The Edinburgh university calendar

Edinburgh univ - 1871
...triangles, what things must be equal, in order that the triangles may be equal in every respect ? 3. If a straight line be divided into any two parts,...parts, together with the square of the foresaid part. 4. Equal straight lines in a circle are equally distant from the centre; and those which are equally...
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Elements of geometry, containing the first two (third and fourth ..., Del 1

Euclides - 1871
...CB. QED • Ex. The square on a straight line is equal to four times tlie square on half the line. If a straight line be divided into any two parts,...contained by the two parts together with the square on the aforesaid part. Let the st. line AB be divided into any two parts in C. Then must rect. AB,...
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The Elements of Plane and Solid Geometry

Henry William Watson - 1871 - 285 sider
...of the parts AE and EB, and the rectangle of CD and EB would be equal to the square of EB, therefore If a straight line be divided into any two parts, the rectangle of the whole line and one of the parts will be equal to the rectangle of the two parts, together with...
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Elements of geometry, containing books i. to vi.and portions of books xi ...

Euclides, James Hamblin Smith - 1872 - 349 sider
...square on a straight line is equal to forr times the square on half the line. PROPOSITION III. THEOREM. If a straight line be divided into any two parts,...contained by the two parts together with the square on the aforesaid part. Let the st. line AB be divided into any two parts in C. Then must rect. AB,...
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The first and second books of Euclid explained to beginners, by C.P. Mason

Euclid, Charles Peter Mason - 1872
...the same as the rectangles under the 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...
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The Acting Teacher's and Student's in Training Guide and Text Book for ...

Henry Major - 1873
...AC, together with the rectangle AB, BC, is equal to the square of AB. III. — If a straight line lie divided into any two parts, the rectangle contained...by the two parts, together with the square of the aforesaid part. Let AB be divided into any two parts in the point C; then the rectangle AB, BC, is...
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A school Euclid, being books i. & ii. of Euclid's Elements, with notes by C ...

Euclides - 1874
...this, and ifm=a + b, shew that its symbolical expression is m? = am + bin. PROPOSITION 3. THEOREM. If a straight line be divided into any two parts,...contained by the two parts, together with the square on the aforesaid part. Let the straight line AB be divided into any two parts at the point C: the rectangle...
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Pure Mathematics, Volum 1

Edward Atkins - 1874
...parts AF+ CE. And;.= AB-AC+ AB-BC. AB-BC= BCa+ AC • BC. For AE=AD +CE. Proposition 3.— Theorem. If a straight line be divided into any two parts,...by the whole and one of the parts is equal to the square on t/tnt part, together with the rectangle contained liy the two parts. Let the straight line...
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The Elements of Euclid, containing the first six books, with a selection of ...

Euclides - 1874
...&c. QED PROPOSITION 3. — Theorem. If a straight line be divided into any two parts, the rectangU contained by the whole and one of the parts is equal...contained by the two parts, together with the square on the aforesaid part. Let the straight line AB be divided into any two parts in the point C. AC .....
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Elements of Euclid [selections from book 1-6] adapted to modern methods in ...

Euclides - 1874
...BAandAC, together with that contained by AB and 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...
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