 | Euclides - 1865 - 402 pages
...equal to the square of the straight line which is made up of the half and the part prodnced. Prop. 7 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... | |
 | Euclid, Isaac Todhunter - Euclid's Elements - 1867 - 426 pages
...is that which is half of the given square. 504. Divide a given straight line into two parts so that the squares on the whole line and on one of the parts jnay be together double of the square on the other part. 505. Two rectangles have equal areas and equal... | |
 | Woolwich roy. military acad - 1868 - 426 pages
...without taking the same three children together more than once. How often will each child go ? 11. If a straight line be divided into any two parts,...part, together with the square on the other part. Where does Euclid afterwards use this proposition? 12. To inscribe a square in a given circle. 13.... | |
 | Robert Potts - 1868 - 434 pages
...CB, is equal to the square on CD. 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 Uie parts, are equal to twice the rectangle contained by the whole and that part, together with the... | |
 | 1868 - 344 pages
...line be divided into an; two parts, the squares of the whole line and one of the parti are together equal to twice the rectangle contained by the whole and that part, together with the square of the other part. 3. In an obtuse angled triangle, if a perpendicular be drawn from either of the... | |
 | Schools inquiry commission - Education - 1868 - 532 pages
...line be divided into any two parts : then the squares of the whole line and one of the parts shall be equal to twice the rectangle contained by the whole and that part together with the square of the other part. 4. The square of the difference of two numbers is equal to the sum of the squares... | |
 | Edinburgh univ - 1868 - 336 pages
...Parallelograms upon equal bases and between the same parallels are equal. 4. Prove Prop. 47, BI 5. 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 line... | |
 | Euclides - 1870 - 270 pages
...PBOP. 7. — THEOB. If a st. 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 a square of the other part. Cons.— 46. I., Pst. 1 and 31. I. DEM. — 43. I., AM. 2 and 6, Def. 30.... | |
 | Euclides - 1871 - 136 pages
...Shew that Propositions V. and VI. might be deduced from this Proposition. PROPOSITION VII. THEOREM. If a straight line be divided into any two parts,...that part together with the square on the other part. s Let AB be divided into any two parts in C. Then must sqq. on AB, BC— twice rect. AB, BC together... | |
 | Euclid, Charles Peter Mason - Geometry - 1872 - 216 pages
...fifth proposition the former of these two Qs is the larger, in the sixth, the latter. PBOPOSITION VTI. If a straight line be divided into any two parts,...squares on the whole line and on one of the parts are together equal to twice the rectangle contained by the whole and that part together with the square... | |
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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... 
