 | Robert Simson - 1806 - 546 σελίδες
...and BC added together in one straight line. Wherefore, if a straight line, &c. QED PROP. IX. THEOR. IF a straight line be divided into two equal, and also into two unequal parts ; the squares of the two unequal parts are together double of the square of half the line, and of the... | |
 | John Playfair - 1806 - 320 σελίδες
...AD2=AC2+4BC2+4BC.AC. Now BC* + BC.AC = AB.BCb ; therefore AD2=AC2+ U3.2. 4AB.BC. QED" Book II. PROP. IX. THEOR. IF a straight line be divided into two equal, and also into two unequal parts, the squares of the two unequal parts are together double of the square of half the line, and of the... | |
 | John Mason Good - 1813 - 714 σελίδες
...equal to the square of the straight 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 tqniMN of the two unequal parts arc together double of the square of half the line, and of the... | |
 | Euclides - 1816 - 588 σελίδες
...straight line. Wherefore, if a straight line, &c. QED TIL F ACBT z .... 6 K / P R / PROP. IX. THEOR. IF a straight line be divided into two equal, and also into two unequal parts; the squares of the two unequal parts are together double of the square of half the line, and of the... | |
 | Miles Bland - 1819 - 442 σελίδες
...DE is parallel to GK, (Eucl. vi. 2.) DE : KG :: EF : FG and EB being parallel to GI, .: EB : GI :: EH : HG, whence (Eucl. v. 15.) EF : FG :: EH : HG...of unequal section from one extremity of the given Une, from its middle point, from the extremity of the part produced, and from the other extremity of... | |
 | John Playfair - 1819 - 354 σελίδες
...AD3=AC3+4BC3-HBC.AC. Now BC3-f BC.AC=AB.BC(3. 2); " and therefore ADs=AC3+4AB.BC. q. ED" PROP. IX. THEOR. 'If /a straight line be divided into two equal, and also into too untquai parts ; the squares of the two unequal parts are together double of the square of half... | |
 | Euclid, Robert Simson - 1821 - 514 σελίδες
...together in one straight line. Wherefore, if a straight line, &c. Q. ED. PROP. IX. THEOR. • . | IP a straight line be divided into two equal, and also .into two unequal parts; the squares of the two unequal parts are together double of the square of half the line, and of the... | |
 | Peter Nicholson - 1825 - 1046 σελίδες
...added together in one straight line. ^herefore, if a straight line, &c. QED Proposition IX. Theorem, If a straight line be divided into two equal, and also into two unequal parts ; the squares of the two unequal parts are together double of the square of half the line, and of the... | |
 | Euclid, John Playfair - 1826 - 326 σελίδες
.../ P R C. Now BO+RC.AC=\B.BC (3.2.) and therefore AD3==AC + 4\B.BC. Q, E, D," -V PROP. IX. THEOR. ., If a straight line be divided into two equal, and also into two unequal parts; the squares of the two, unequal parts are together double of the square of half the line, and of the... | |
 | Robert Simson - 1827 - 546 σελίδες
...and BC added together in one straight line. Wherefore, if a straight line, &c. GED PROP. IX. THEOR. If a straight line be divided into two equal, and also into two unequal parts; the squares of the two unequal parts arc together double of the square of half the line, and of the... | |
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IF a straight line be divided into two equal, and also into two unequal parts ; the squares of the two unequal parts are together double of the square of half the line, and of the square of the line between the points of section. 
