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" THEOR. //' 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. "
Elements of Geometry: Containing the First Six Books of Euclid, with a ... - Σελίδα 74
των John Playfair - 1836 - 311 σελίδες
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The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ...

Euclid - 1810 - 554 σελίδες
...straight line. WhereforCi if a straight line, &c. QED A CB G s / M / N 9 u X / • 'E F PROP. IX. THEOR. IF a straight 'line be divided into two equal, and...half the line, and of the square of the line between tlie points, of section. Let the straight line AB be divided at the point C into two equal, and at...

Pantologia. A new (cabinet) cyclopædia, by J.M. Good, O. Gregory ..., Τόμος 5

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 square...

The Elements of Euclid; viz. the first six books, together with the eleventh ...

Euclides - 1814 - 560 σελίδες
...times the rectangle AB, BC, is equal to the gnomon AOH. To G P / K / EHJ / R N 0 , F PROP. IX. THEOR. IF a straight line be divided into two equal, and...square of the line between the points of section. From the point C draw3 CE at right angles to AB, and • 11. i. make it equal to AC or CB, and join...

Geometrical Problems Deducible from the First Six Books of Euclid, Arranged ...

Miles Bland - 1819 - 444 σελίδες
....-. EB : GI :: EH . HG, whence (Eucl. v. 15.) EF : FG :: EH : HG and alt. EF . EH . FG . HG. (23.) If a straight line be divided into two equal, and also into two unequal parts, and be produced, so that the part produced may have to the whole line so produced the same ratio that...

Geometrical Problems Deducible from the First Six Books of Euclid, Arranged ...

Miles Bland - 1819 - 442 σελίδες
....: EB : GI :: EH : HG, whence (Eucl. v. 15.) EF : FG :: EH : HG and alt. EF . EH :: FG : HG. (23.) If a straight line be divided into two equal, and also into two unequal parts, and be produced, so that the part produced may have to the whole line so produced the same ratio that...

The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ...

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...square of the line between the points of section. • •M Let the straight line AB be divided at the point C into two equal, and at D into two unequal...

Solutions of the Cambridge Problems: From 1800 to 1820, Τόμος 2

John Martin Frederick Wright - 1825 - 798 σελίδες
...given rectilinear figure, having an angle equal to a given rectilinear angle. 2. If a straight Hue be divided into two equal, and also into two unequal,...square of half the line, and of the square of the Une between the points of section. 3. If two straight lines within a circle cut one another, the rectangle...

Elements of Arithmetic, Algebra, and Geometry

George Lees - 1826 - 276 σελίδες
...a straight line AB be divided into two equal parts AC, CB, and also into two unequal parts AD, DB ; the squares of the two unequal parts are together...square of half the line, and of the square of the tine CD, between the points of section. • . ; Or, AD2 + DB2 = 2AC2 .+ 2CD2. From the point C, draw...

Elements of Geometry, Containing the First Six Books of Euclid

Euclid - 1826 - 234 σελίδες
...PROPOSITION IX. ТНЕОПЕМ. J/1 a rzgAf Kne ie any how cut into two equal and two unequal parts, then the squares of the two unequal parts are, together, double of the square of the half line, and the square of the intermediate part. Let any right line AB be cut into two equal...

Euclid's Elements of geometry, transl. To which are added, algebraic ...

Euclides - 1826 - 226 σελίδες
...PROPOSITION IX. THEOREM. If a right line be any how cut info two equal and two unequal parts, then the squares of the two unequal parts are, together, double of the square of the half line, and the square oftJie intermediate part. Let any right line AB be cut into two equal...




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