| Robert Potts - 1868 - 434 pages
...DA is equal to AB : and CE is contained by AB, BC, for BE is equal to AK : PROPOSITION III. THEOREM. **If a straight line be divided into any two parts, the rectangle contained** ky the whole and one of the parts, is equal to the rectangle contained by the twa parts, together with... | |
| Edinburgh univ - 1871 - 392 pages
...triangles, what things must be equal, in order that the triangles may be equal in every respect ? 3. **If a straight line be divided into any two parts,...parts, together with the square of the foresaid part.** 4. Equal straight lines in a circle are equally distant from the centre; and those which are equally... | |
| Euclides - 1871 - 136 pages
...CB. QED • Ex. The square on a straight line is equal to four times tlie square on half the line. **If a straight line be divided into any two parts,...contained by the two parts together with the square** on the aforesaid part. Let the st. line AB be divided into any two parts in C. Then must rect. AB,... | |
| Henry William Watson - Geometry - 1871 - 320 pages
...of the parts AE and EB, and the rectangle of CD and EB would be equal to the square of EB, therefore **If a straight line be divided into any two parts, the rectangle** of the whole line and one of the parts will be equal to the rectangle of the two parts, together with... | |
| Euclides, James Hamblin Smith - Geometry - 1872 - 376 pages
...square on a straight line is equal to forr times the square on half the line. PROPOSITION III. THEOREM. **If a straight line be divided into any two parts,...contained by the two parts together with the square** on the aforesaid part. Let the st. line AB be divided into any two parts in C. Then must rect. AB,... | |
| Euclid, Charles Peter Mason - Geometry - 1872 - 216 pages
...the same as the rectangles under the whole line BC and each of its parts. PBOPOSITION III. If a right **line be divided into any two parts, the rectangle contained by the whole** line and one of the parts is equal to the square on that part together with the rectangle contained... | |
| Henry Major - Student teachers - 1873 - 588 pages
...AC, together with the rectangle AB, BC, is equal to the square of AB. III. — If a straight line lie **divided into any two parts, the rectangle contained...by the two parts, together with the square of the** aforesaid part. Let AB be divided into any two parts in the point C; then the rectangle AB, BC, is... | |
| Euclides - 1874 - 120 pages
...this, and ifm=a + b, shew that its symbolical expression is m? = am + bin. PROPOSITION 3. THEOREM. **If a straight line be divided into any two parts,...contained by the two parts, together with the square** on the aforesaid part. Let the straight line AB be divided into any two parts at the point C: the rectangle... | |
| Edward Atkins - 1874 - 428 pages
...parts AF+ CE. And;.= AB-AC+ AB-BC. AB-BC= BCa+ AC • BC. For AE=AD +CE. Proposition 3.— Theorem. **If a straight line be divided into any two parts,...by the whole and one of the parts is equal to the** square on t/tnt part, together with the rectangle contained liy the two parts. Let the straight line... | |
| Euclides - 1874 - 342 pages
...&c. QED PROPOSITION 3. — Theorem. If a straight line be divided into any two parts, the rectangU **contained by the whole and one of the parts is equal...contained by the two parts, together with the square** on the aforesaid part. Let the straight line AB be divided into any two parts in the point C. AC ..... | |
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