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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 39
av Euclides - 1834
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The College Euclid: Comprising the First Six and the Parts of the Eleventh ...

Euclides - 1865 - 402 sider
...equal to the rectangles under the whole and each of the parts . . . . . II. 2. 2. The rectangle under the whole and one of the parts, is equal to the rectangle under the two parts, together with the square on the aforesaid part . . . . . . . n. 3. 3. The square...
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Elements of Geometry: Containing the First Six Books of Euclid: With a ...

John Playfair - 1855 - 360 sider
...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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Examination papers collected by A. Clark as a student and as an examiner

1867 - 224 sider
...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,...contained by the two parts, together with the square on the aforesaid part. 4. Make a triangle of which the sides shall be equal to three given straight...
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The Elements of Euclid for the Use of Schools and Colleges: Comprising the ...

Euclid, Isaac Todhunter - 1867 - 424 sider
...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,...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 (7: the...
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The Elements of Euclid for the Use of Schools and Colleges: Comprising the ...

Euclid, Isaac Todhunter - 1867 - 426 sider
...the other part, is equal to the square on the straight line which is made up of the whole and that part. Let the straight line AB be divided into any two parts at the point C: lour times the rectangle AB, BC, together with the square on AC, shall be equal to...
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Euclid's Elements of Geometry: Chiefly from the Text of Dr. Simson, with ...

Robert Potts - 1868 - 434 sider
...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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The Edinburgh university calendar

Edinburgh univ - 1871 - 392 sider
...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,...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 those which...
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Elements of geometry, containing the first two (third and fourth ..., Del 1

Euclides - 1871 - 136 sider
...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 - 320 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, Conic Sections, and Plane Trigonometry

Elias Loomis - 1871 - 302 sider
...equivalent to the squares of the two parts, together with twice the rectangle contained by 'the parts. Let the straight line AB be divided into any two parts in C ; the square on AB is equivalent to the squares on AC CB, together with twice the rectangle contained...
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