 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 Elements of Geometry, Symbolically Arranged - Page 63by Great Britain. Admiralty - 1846Full view - About this book
 | Euclides - 1853 - 146 pages
...square of CB, is equal to the square of CD. Wherefore, if a straight line, &c. QED PROP. VII. THEOREM. If a straight line be divided into any two parts,...parts, are equal to twice the rectangle contained by tke whole and that part, together with the square of the other part. Let the straight line AB be divided... | |
 | Euclides - Geometry - 1853 - 334 pages
...CD. Which was to be proved. PEOP. VII. THEOE. If a straight line be divided into any two parts: then the squares of the whole line and of one of the parts shall be, equal to twice the rectangle contained by the whole line and that part, together with the... | |
 | William Somerville Orr - Science - 1854 - 534 pages
...THEOREM. If a straight line (AB) be divided into any two parts (in C), the squares of the whole lint, and of one of the parts, are equal to twice the rectangle contained by the whole and Hunt part, together with the square of the other part: that is, AB2 + BC2=twice AB'BC + AC!. [See Diagram,... | |
 | Thomas Lund - Geometry - 1854 - 520 pages
...very elegant proof of the important Theorem in (43) may be given as follows :— 45. PROP. XXIII. Jf a straight line be divided into any two parts, the squares of the whole line and one of the parts are together equal to twice the rectangle contained by the whole and that part, together... | |
 | Euclides - 1855 - 270 pages
...the rectangle AD.DB, and the square of С В is equal to the square of СD. Р B, O P. VII. THEOREM. If a straight line be divided into any two parts,...together with the square of the other part. Let the straight line AB be divided into any two parts at the point С. The squares of AB and B С are equal... | |
 | Great Britain. Committee on Education - School buildings - 1855 - 976 pages
...equal to the squares of the two other sides, the angles contained by those sides is a right angle. 4. If a straight line be divided into any two parts,...squares of the whole line and of one of the parts are together equal to twice the rectangle contained by the whole line and one of the parts, together with... | |
 | Robert Potts - 1855 - 1050 pages
...from D, the middle point of BC, DE is drawn perpendicular to AS: shew that BE is, one-fourth of AB. 5. If a straight line be divided into any two parts, the squares on the whole line and one of the parts, shall be together equal to twice the rectangle contained by... | |
 | 1856 - 376 pages
...anle. . o rag ne o appy a paraeogra have one of its angles equal to a given rectilineal angle. and 2. If a straight line be divided into any two parts,...part, together with the square of the other part. 3. Divide a straight line so that the rectangle contained by the whole line and one part shall be equal... | |
 | Cambridge univ, exam. papers - 1856 - 200 pages
...to one anoiher. If one of the complements be a square, the parallelogram will also be a square. 4. If a straight line be divided into any two parts,...part, together with the square of the other part. State this result algebraically. 5. One circle cannot touch another in more points than one, whether... | |
 | W F. Richards - Elementary school teaching - 1856 - 198 pages
...to the sum of the squares of the parts, together with twice the rectangle contained by the parts. 2. If a straight line be divided into any two parts,...part, together with the square of the other part. 3. Divide a straight line so that the rectangle contained by the whole line and one part, shall be... | |
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