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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 student's guide to the University of Durham, with information respecting ... - Página 136
1880 - 144 páginas
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Elements of Geometry: Containing the First Six Books of Euclid: With a ...

John Playfair - 1855 - 317 páginas
...multiplying both members of this equality by a, we shall have a2=«A + a</ PE Q KLD PROP. III. THEOR. tf a straight line be divided into any two parts, the...the parts, is equal to the rectangle contained by the tttm parts, together with the square of the aforesaid part. Let the straight line AB be divided...
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The Elements of Euclid for the Use of Schools and Colleges: Comprising the ...

Euclid, Isaac Todhunter - 1867 - 400 páginas
...AB, BC, is equal to the square on AB. Wherefore, if a straight line &c. QED PROPOSITION 3. THEOREM. If a straight line be divided into any two parts,...parts, together with the square on the aforesaid part. Let the straight line AB be divided into any two parts at the point (7: the rectangle AB, BC shall...
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Examination papers collected by A. Clark as a student and as an examiner

1867
...one another, and likewise those which are terminated at the other extremity equal to one another. 3. If a straight line be divided into any two parts,...parts, together with the square on the aforesaid part. 4. Make a triangle of which the sides shall be equal to three given straight lines, but any two whatever...
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Euclid's Elements of Geometry: Chiefly from the Text of Dr. Simson, with ...

Robert Potts - 1868 - 410 páginas
...DA is equal to AB : and CE is contained by AB, BC, for BE is equal to AK : PROPOSITION III. THEOREM. If a straight line be divided into any two parts, the rectangle contained ky the whole and one of the parts, is equal to the rectangle contained by the twa parts, together with...
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Elements of geometry, containing the first two (third and fourth ..., Parte1

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,...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, CB = sum of rect. AC, CB...
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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,...contained by the two parts, together with the square of the foresaid part. 4. Equal straight lines in a circle are equally distant from the centre; and...
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The Elements of Plane and Solid Geometry

Henry William Watson - 1871 - 285 páginas
...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 páginas
...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,...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, CB = sum of rect. AC, CB...
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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...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,...
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