 | William Trail - Algebra - 1796 - 334 pages
...place of that conftruction. PROP. PROP. I. To divide a given Jlraight line AB into two parts, fo that the rectangle contained by the -whole line, and one of the parts, may be equal to thefquare of the other part. This is Prop. i ith II. B. of Euclid. e ~-~ ACB Let C... | |
 | Alexander Ingram - Trigonometry - 1799 - 374 pages
...a PROP. BOOK IT, See N. I. « 34- 1• bCoi. 4. 2 PROP. VIII. TIIEOR. F a ftraight line be divided into any two parts, four times the rectangle contained...whole line, and one of the parts, together with the Iquare of the other part, is equal to the fquare of the ftraight line which is made up of the whole... | |
 | John Bonnycastle - 1803 - 306 pages
...AS, Bg, CD and DA. Q..ED PROP. XXII, PROBLEM. To divide a given right line into two parts, fo that the rectangle contained by the whole line and one of the parts, fhall be equal to the fquare of the other part. Let AB be the given right line ; it is required to... | |
 | Robert Simson - Trigonometry - 1804 - 530 pages
...fquare of AC. Wherefore if a ftraight line, &c. Q^ED PROP. VIII. THE OR. IF a ftraight line be divided into any two parts, four times the rectangle contained...whole line, and one of the parts, together with the fquare of the other part, is equal to the fquare of the ftraight line which is made up of the whole... | |
 | John Playfair - Mathematics - 1806 - 320 pages
...the square of the difference of the lines." ,, PROP. VIII. THEOR. .• IF a straight line be divided into any two parts, four times the rectangle contained...parts, together with the square of the other part, are equal to the square of the straight line which is made up of the whole and the firstmentioned part.... | |
 | Robert Simson - Trigonometry - 1806 - 546 pages
...line thus produced, and the part of it produced, together with the square of half the line bisected, is equal to the square of the straight line which is made up of the half and the part produced. Let the straight line AB be bisected in C, and produced to the point D... | |
 | John Mason Good - 1813 - 714 pages
...part, together with the square of the other part. Prop. VIII. Theor. If a straight line be divided into any two parts, four times the rectangle contained...line which is made up of the whole and that part. Prop. IX. Theor. If a straight line be divided into two equal, and also into two unequal parts; the... | |
 | Euclides - 1814 - 560 pages
...square of AC. Wherefore, if a straight line, &c. QED PROP. VIII. THEOR. IF a straight line be divided into any two parts, four times the rectangle contained...is equal to the square of the straight line, which is'made up of the whole and that part. Let the straight line AB be divided into any two parts in the... | |
 | Euclides - 1816 - 588 pages
...line thus produced, and the part of it produced, together with the square of half the line bisected, is equal to the square of the straight line which is made up of the half and the part produced. Let the straight line AB be bisected in C, and produced to the point D... | |
 | Daniel Cresswell - Euclid's Elements - 1817 - 454 pages
...circle DPE. PROP. XXIV. 114. Problem. To divide a given finite straight line into two parts, such that the rectangle, contained by the whole line and one of the parts, shall most exceed the square of that part. Let AB be the given finite straight line ; it is required... | |
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If a straight line be divided into any two parts, four times the rectangle contained by the whole line and one of the parts, together with the square of the other part, is equal to the square of the straight line which is made up of the whole and that... 
