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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... "
Elements of Geometry: Containing the First Six Books of Euclid : with a ... - Σελίδα 52
των John Playfair - 1837 - 318 σελίδες
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The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ...

Euclid - 1835 - 513 σελίδες
...CD. Wherefore, " if a straigtd line" &c. QED PROP. VII. THEOR. If a straight line be divided into any two parts, the squares of the whole line, and of one...part, together with the square of the other part. Let the straight line AB be divided into any two parts in Book i i- the point C ; the squares of AB,...

The Element of Geometry

John Playfair - 1836 - 114 σελίδες
...the square of AH. Which was to be done. E PROP. XXV. THEOR. If a straight line be divided into any two parts, the squares of the whole line, and of one...part, together with the square of the other part. Let the straight line AB be divided into any two parts in the point C ; the squares of AB, BC are equal...

The Teacher's Assistant in the "Course of Mathematics Adapted to the Method ...

1836 - 472 σελίδες
...line which is made up of the half and the part produced. VII. If a straight line be divided into any two parts, the squares of the whole line, and of one...part, together with the square of the other part. Сон. Hence the sum of the squares of any two lines is equal to twice the rectangle contained by...

The First Six and the Eleventh and Twelfth Books of Euclid's Elements: With ...

Euclid - 1837 - 390 σελίδες
...rectangle AM and the square LG, together equal to tb« square CF. IF a straight line be divided into any two parts, the squares of the whole line, and of one...part, together with the square of the other part. Let the straight line AB be divided into any two parts in the point C ; the squares of AB, BC are equal...

A companion to Euclid: being a help to the understanding and remembering of ...

Euclides - 1837 - 88 σελίδες
...and that these last = AD X DB + CB*. PROPOSITION VII. Theorem. If a straight line be divided into any two parts, the squares of the whole line and of one...equal to twice the rectangle contained by the whole line and that part, together with the square of the other part. i> K Proved by showing that AB* + uc*...

Elements of Plane Geometry According to Euclid

Andrew Bell - 1837 - 240 σελίδες
...the diiferencc between the squares of half the line and the mean distance. PROPOSITION TIL THEOREM. to twice the rectangle contained by the whole and...part, together with the square of the other part. Let the straight line AB be divided into any two parts in the point C ; the squares of AB, BO, are...

Euclid's Elements [book 1-6] with corrections, by J.R. Young

Euclides - 1838
...Wherefore, if a straight line, Ac. «,in D. PROP. VII. THEOR. If a straight line be divided into any two parts, the squares of the whole line, and of one...part, together with the square of the other part. Let the straight line AB be divided into any two parts in the point C : the squares of AB, BC shall...

The figures of Euclid with the enunciations, as printed in Euclid's Elements ...

Euclides - 1840
...made up of the half and the produced part. DA PROP. VII. THEOR. If a straight line be divided into any two parts, the squares of the whole line and of one...equal to twice the rectangle contained by the whole line and that part, together with the square of the other part. PROP. VIII. THEOR. If a straight line...

Euclid's Elements of plane geometry [book 1-6] with explanatory appendix ...

Euclides - 1840
...the produced part. PROP. VII. THEOR. If a straight line (AB) be divided into any two parts (AF, FB), the squares of the whole line and of one of the parts,...equal to twice the rectangle contained by the whole line and that part, together with the square of the other part. Upon AB construct the square ACDB ;...

The Elements of Euclid; viz. the first six books,together with the eleventh ...

Euclides - 1841 - 351 σελίδες
...straight line, &c. QED PROP. VII. THEOR. *36. 1. a * 43. 1. If a straight line be divided into any two parts, the squares of the whole line, and of one...whole and that part, together with the square of the otherpart. Let the straight line AB be divided into any two parts in the point C; the squares of AB,...




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