 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 - 1860 - 288 pages
...unequal segments is equal to the difference between the squares on half the line and the mean distance. If a straight line be divided into any two parts, the squares on the whole line, and on one of the parts, are equal to twice the rectangle contained by the whole... | |
 | Royal college of surgeons of England - 1860 - 332 pages
...angles. 5. Parallelograms upon equal bases and between the same parallels are equal to one another. 6. If a straight line be divided into any two parts, the squares on the whole line and one of the parts are equal to twice the rectangle contained by the whole and... | |
 | Robert Potts - Geometry, Plane - 1860 - 380 pages
...CB, is equal to the square on QD. Wherefore, if a straight line, &c. QED PROPOSITION VII. THEOREM. If a straight line be divided into any two parts, the squares on the whole line, and on one of the parts, are equal to twice the rectangle contained by the whole... | |
 | Woolwich roy. military acad - 1861 - 572 pages
...expect to find the " differences " largest at the early part of the table and gradually decreasing. 14. If a straight line be divided into any two parts, the squares on the whole line and on one of the parts are equal to twice the rectangle contained by the whole and... | |
 | War office - 1861 - 714 pages
...to it. 2. Triangles upon the same base, and between the same parallels, are equal to one another. 3. If a straight line be divided into any two parts, the squares on the whole line and on one of the parts are equal to twice the rectangle contained by the whole and... | |
 | Euclides - 1862 - 172 pages
...straight line, &c. QED PROP. VII.— THEOREM. If a straight line be divided into any two parts ; tlien the squares of the whole line and of one of the parts, are equal to twice tjie rectangle contained by the whole and that part, together wM the square of the other part. (References... | |
 | Euclides - 1862 - 140 pages
...to the square on CD. Conclusion. — Therefore, if a straight line, &c. QED PROPOSITION 7. -THEOREM. If a straight line be divided into any two parts, the squares on the wlutle line) and on one of the parts, are equal to twice the rectangle contained by the whole... | |
 | Architecture - 1863 - 300 pages
...9. Divide an equilateral trianglo into four equal triangles. Book 2. 10. Proposition 7, Theorem ; It a straight line be divided into any two parts the squares of the whole line, and one of the parts, are equal to twice the rectangle contained by the whole and that part, together with... | |
 | Euclides - 1863 - 122 pages
...whole line (AB), and of one of the parts (BC) are equal to twice the rectangle (AB, BC) contained bg the whole and that part, together with the square of the other part (AC). Upon AB describe the square AE (I. 46) and join BD. Through through G draw HGK parallel to AB... | |
 | University of Oxford - Education, Higher - 1863 - 316 pages
...with the square on the line between the points of section, is equal to the square on half the line. 9. If a straight line be divided into any two parts, the squares on the whole line and on one of the parts are equal to twice the rectangle contained by the whole and... | |
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