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" IF a straight line be divided into any two parts, the square of the whole line is equal to the squares of the two parts, together with twice the rectangle contained by the parts. "
The Elements of Euclid; viz. the first six books, together with the eleventh ... - Página 43
por Euclides - 1814
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Euclidian Geometry

Francis Cuthbertson - 1874 - 349 páginas
...CAQ. The Theorems in Proposition II. may be established independently as follows :— THEOREM (a). If a straight line be divided into any two parts, the square on the whole line is' equal to the squares on the parts together with twice the rectangle contained...
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Pure mathematics, Volumen1

Edward Atkins - 1874
...together with the rectangle AC, CB. Therefore, if a straight line, <fec. QED Proposition 4. — Theorem. If a straight line be divided into any two parts, the square on the whole line is equal to the sum of the squares on the two parts, together with twice the rectangle...
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Pure Mathematics, Volumen1

Edward Atkins - 1874
...twice the rectangle contained by the whole and that part, together with the square on the other part. Let the straight line AB be divided into any two parts in the point C; PROPOSITIONS. CONSTRUCTION. — Upon AB describe the square ADEB (I. 46), and join BD....
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Elements of Euclid [selections from book 1-6] adapted to modern methods in ...

Euclides - 1874
...on BC, together with the rectangle contained by AC and CB. QED PKOP. IV.— THEOREM. (Euc. II. 4.) If a straight line be divided into any two parts, the square on the whole line is equal to the squares on the two parts, together with twice the rectangle contained...
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Primer of geometry

Francis Cuthbertson (geometer.) - 1876
...= A PQR. Wherefore a rectangle has been described equal to the given triangle. QEF PROPOSITION III. If a straight line be divided into any two parts, the square on the whole line will be equal to the squares on the two parts, together with twice the rectangle...
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Examination Christmas,1875

Education Department,London - 1876
...four right angled trianglc.-s of equal area can be drawn having the same hypotenuse. SECTION III. 1. If a straight line be divided into any two parts, the square on the whole line is equal to the squares on the two parts together with twice the rectangle contained...
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Annual Report

1876
...to the squares described upon the sides which contain the right angle. 4. Proposition IV, Book II. If a straight line be divided into any two parts, the square on the whole line is equal to the squares on the two parts, together with twice the rectangle contained...
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Euclid's Elements of Geometry: Chiefly from the Text of Dr. Simson, with ...

Robert Potts - 1876 - 403 páginas
...straight line, which joins the middle points of two sides of a triangle, is parallel to the base. 9. If a straight line be divided into any two parts, the square on the whole line is equal to the squares on the two parts, together with twice the rectangle contained...
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Elements of geometry, based on Euclid, books i-iii

Edward Atkins - 1876 - 119 páginas
...together with the rectangle AC, CB. Therefore, if a straight line, &c. QED Proposition 4.— Theorem. If a straight line be divided into any two parts, the square on the whole line is equal to the sum of the squares on the two parts, together with twice the rectangle...
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Modern geometry [ed.] with an appendix by W.B. Jack

Richard Wormell - 1876
...rectangles contained by the first and second, first and third, and second and third parts respectively. 103. If a straight line be divided into any two parts, the square on the whole line and one of the parts is equivalent to twice the rectangle contained by the whole...
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