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" If a straight line be divided into any two parts, the squares of the whole line, and of one of the parts, are equal to twice the rectangle contained by the whole and that part, together with the square of the other part. Let the straight line AB be divided... "
The figures of Euclid with the enunciations, as printed in Euclid's Elements ... - Page 26
by Euclides - 1840
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The Teacher's Assistant in the "Course of Mathematics Adapted to the Method ...

Mathematics - 1836 - 488 pages
...is equal to the square of the straight line which is made up of the half and the part produced. VII. If a straight line be divided into any two parts,...equal to twice the rectangle contained by the whole and that part, together with the square of the other part. Сон. Hence the sum of the squares of...
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A companion to Euclid: being a help to the understanding and remembering of ...

Euclides - Euclid's Elements - 1837 - 112 pages
...these = AL + CM + LG, which = AM + LG, and that these last = AD X DB + CB*. PROPOSITION VII. Theorem. If a straight line be divided into any two parts,...part, together with the square of the other part. i> K Proved by showing that AB* + uc* = figs. AG + GE + 2 CH + KF, and that these = 2 AH + KF ; ;and...
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The First Six and the Eleventh and Twelfth Books of Euclid's Elements: With ...

Euclid, James Thomson - Geometry - 1837 - 410 pages
...figure, as there will remain the rectangle AM and the square LG, together equal to tb« square CF. IF a straight line be divided into any two parts,...equal to twice the rectangle contained by the whole and that part, together with the square of the other part. Let the straight line AB be divided into...
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Elements of Geometry: Containing the First Six Books of Euclid : with a ...

John Playfair - Euclid's Elements - 1837 - 332 pages
...to each member of the equality, we shall have, PROP. VII. THEOR. If a straight line be divided into two parts, the squares of the whole line, and of one....equal to twice the rectangle contained by the whole and that part, together with the square of the other part. L et the straight line AB be divided into...
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Euclid's Elements [book 1-6] with corrections, by J.R. Young

Euclides - 1838 - 264 pages
...together with the square of CB, is equal to the square of CD. Wherefore, if a straight line, Ac. «,in D. PROP. VII. THEOR. If a straight line be divided into...equal to twice the rectangle contained by the whole and that part, together with the square of the other part. Let the straight line AB be divided into...
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The Elements of Euclid

Euclid - Geometry - 1838 - 470 pages
...of CB, is equal to the square of CD. Wherefore, if a straight line, &c. a. ED PROP. VII. THEOR. Ir a straight line be divided into any two parts, the...equal to twice the rectangle contained by the whole and that part, together with the square of the other part. Let the straight line AB be divided into...
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Euclid's Elements of plane geometry [book 1-6] with explanatory appendix ...

Euclides - 1840 - 192 pages
...square of the sum of the whole line AB and one of its parts CB, is equal to 4 AB'CB, or four times the rectangle contained by the whole line and that part, together with AC2 or the square of the other part. PROP. IX. THEOR. If a straight line (AB) be divided equally (in...
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The Elements of Euclid; viz. the first six books,together with the eleventh ...

Euclides - Geometry - 1841 - 378 pages
...equal to the square of CD. Wherefore, if a straight line, &c. QED PROP. VII. THEOR. *36. 1. a * 43. 1. If a straight line be divided into any two parts,...equal to twice the rectangle contained by the whole and that part, together with the square of the otherpart. Let the straight line AB be divided into...
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Elements of Geometry: Containing the First Six Books of Euclid, with a ...

John Playfair - Euclid's Elements - 1842 - 332 pages
...to each member of the equality, we shall have, PROP. VII. THEOR. If a straight line be divided into two parts, the squares of the whole line, and of one...equal to twice the rectangle contained by the whole and that part, together with the square of the other part. L et the straight line AB be divided into...
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The British Annals of Education for ...: Being The Scholastic ..., Volumes 1-2

Education - 1844 - 688 pages
...equal to the rectangles contained by the undivided line and the several parts of the divided line. 7. If a straight line be divided into any two parts,...equal to twice the rectangle contained by the whole and that part, together with the square of the other part. 8. If two circles touch one another internally,...
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