Books Books 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. First Steps in Geometry: A Series of Hints for the Solution of Geometrical ... - Page 175
by Richard Anthony Proctor - 1887 - 180 pages ## Dialogues on the First Principles of the Newtonian System, Volume 4

Walter Henry Burton - Astronomy - 1828 - 84 pages
...understand this proposi-Prop. xix. tion, which is necessary for our further progress: that if a straight line be divided into two equal, and also into two unequal parts, the square of either of the equal parts (or the rectangle under both) is equal to the rectangle under the... ## Elements of Geometry: Containing the First Six Books of Euclid : with a ...

John Playfair - Euclid's Elements - 1832 - 358 pages
...Now BC' + BC.AC = AB.BC "(3. 2.) and therefore AD = AC +4 AB.BC. 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 purls are together double of the square of half the line, and of the square of the line between the... ## The Elements of Euclid; viz. the first six books, together with the eleventh ...

Euclides - 1834 - 518 pages
.../ K / / lt 2 HL 1 PROPOSITION IX. THEOR. — If a straight line be divided into two equal, andalso 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.... ## The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ...

Euclid - 1835 - 540 pages
...Wherefore, " if a straight line" &c. QED HL A. M X CB D / G K M 0 P / R / PROP. IX. THEOR. If a straight line be divided into two equal, and also into two...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.... ## Solutions of the Cambridge Problems, from 1800 to 1820, Volume 2

John Martin Frederick Wright - Mathematics - 1836 - 776 pages
...to a given rectilinear figure, having an angle equal to a given rectilinear angle. 2. If a straight line be divided into two equal, and also into two...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.... ## The Teacher's Assistant in the "Course of Mathematics Adapted to the Method ...

Mathematics - 1836 - 488 pages
...manifest, that the square of any line is quadruple of the square of half that line. IX. If a straight line be divided into two equal, and also into two...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 Plane Geometry According to Euclid

Andrew Bell - Euclid's Elements - 1837 - 290 pages
...square of any line is quadruple of the square of half that line. PROPOSITION IX. THEOREM. If a straight line be divided into two equal, and also into two...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.... ## A companion to Euclid: being a help to the understanding and remembering of ...

Euclides - Euclid's Elements - 1837 - 112 pages
...that these = 4 AK + XH, and that these last = 4 AB x BC + AC*. PROPOSITION IX. Theorem. If a straight line be divided into two equal and also into two unequal parts, the squares of the two un- ^ equal parts are together double / GJ.^J? of the square of half the line, and /'^..^ \ \ \ of... ## The First Six and the Eleventh and Twelfth Books of Euclid's Elements: With ...

Euclid, James Thomson - Geometry - 1837 - 410 pages
...together in one straight line. * Wherefore, if a straight line, &c. PROP. IX. THEOR. IF a straight line be divided into two equal, and also into two unequal parts ; the squares of the unequal parts are together double of the square of half the line, and of the square of the line between... 