 | James Maurice Wilson - 1869 - 260 pages
...rectangle AB x .#.#'; and FH is the square on AH; therefore AB x BH= AH*. EXERCISES. 1. If a straight line be divided into any two parts, the square on the whole line will be equal to the sum of the rectangles contained by the whole line and each of the parts. 2. Construct... | |
 | Euclid, Charles Peter Mason - Geometry - 1872 - 216 pages
...preceding proposition is usually incorporated in the proof of the Fourth Proposition. PBOPOSITION IV. If a right line be divided into any two parts, the square on the whole line is equal to the sum of the squares on the parts together with twice the rectangle under the parts. For the construction... | |
 | Euclides, James Hamblin Smith - Geometry - 1872 - 376 pages
...produced to B, AB and CB are called the external sesrments of AC. PROPOSITION IV. THEOREM. If a straight line be divided into any two parts, the square on the whole line is equal to the squares on the two parti together with tucice the rectangle contained by the parts. A cr B X Tt... | |
 | Francis Cuthbertson - Euclid's Elements - 1874 - 400 pages
...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 by the parts. If Let the straight... | |
 | Euclides - 1874 - 120 pages
...equal to the rectangle AC, CB together with the square on AC. PROPOSITION 4. THEOREM. 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 by the rts. Let the straight... | |
 | Euclides - 1874 - 342 pages
...square on BC. If therefore a straight line be divided, &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 squares on the two parts, together with twice the rectangle contained by the parts. Let the straight... | |
 | Edward Atkins - 1874 - 426 pages
...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 contained by the parts.... | |
 | Euclid, James Bryce, David Munn (F.R.S.E.) - Geometry - 1874 - 236 pages
...square on CB, is equal to the square on CD. QED PROP. VII.— THEOKEM. (Euc. II. 7.) If a, straight line be divided into any two parts, the square on the whole line, together with the square on one of the parts, is equal to twice the rcctangle contained by the whole... | |
 | 1876 - 710 pages
...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 by the two parts. FIRST DIVISION.... | |
 | Education Department,London - 1876 - 1010 pages
...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 by the two parts. The rectangle... | |
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If a straight line be divided into any two parts, the square on the whole line is... 
