Books Books 11 - 20 of 189 on Prove it. 6.If a straight line be bisected and produced to any point, the rectangle.... Prove it. 6.If a straight line be bisected and produced to any point, the rectangle contained by the whole line thus produced, and the part of it produced together with the -square on half the line bisected, is equal to the square on the straight line... Government examinations, a companion to 'Under government' and a key to the ... - Page 88
by Joseph Charles Parkinson - 1860 ## Elements of Geometry, Geometrical Analysis, and Plane Trigonometry: With an ...

Sir John Leslie - Geometry, Analytic - 1809 - 493 pages
...another problem of the same nature; in which it is required to produce a straight line AB, such that the rectangle contained by the whole line thus produced and the part produced, shall be equivalent to the square of the line AB itself. Divide AB in C, so that the rectangle... ## Pantologia. A new (cabinet) cyclopædia, by J.M. Good, O. Gregory, and N ...

...square of half the line, and of the square of the line between the points of section. Prop. X. Theor. If a straight line be bisected, and produced to any point, the square of tht; whole line thus produced, and the square of the part of it produced, are together double... ## An Easy Introduction to the Mathematics: In which the Theory and ..., Volume 2

Charles Butler - Mathematics - 1814
...<•! a + xx + aa=(aa + %ax+xx=) a+xf; that is, the rectangle contained by the line produced and part produced, together with the square of half the line bisected, is equal to the square of the line made up of the half, and part produced. QKD Cor. Hence, if three lines ,r, a 4 ,r, and 2rt + ,r... ## The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ...

Euclides - Euclid's Elements - 1816 - 528 pages
...of AD, DB are double of the squares of AC, CD. If therefore a straight line, &c. QED PROP. X. THEOR. IF a straight line be bisected, and produced to any point, the square of the whole line thus produced, and the square of the part of it produced, are together double... ## An Elementary Treatise on the Geometrical and Algebraical Investigation of ...

Daniel Cresswell - Euclid's Elements - 1817 - 436 pages
...subtend equal angles, at the center of the circle. (LXVII.) To produce a given straight line, so that the rectangle contained by the whole line thus produced, and the part of it produced, shall be equal to a given square. (LXVII i.) If, from the bisection of any given arch of a circle,... ## Elements of Geometry: Containing the First Six Books of Euclid, with a ...

John Playfair - Circle-squaring - 1819 - 333 pages
...rectangle " contained by their sum and difference, or that AC2 - CD2 = (AC+ CD)(AC_CD)." PROP. VI. THEOR. if a straight line be bisected, and produced to any...the part of it produced, together with the square nf half the. line bisected, is equal to the square of the straight line which is made up of the half... ## A Supplement to the Elements of Euclid

Daniel Cresswell - Geometry - 1819 - 410 pages
...itself also touches the circle. PROP. LXXIII. 93. PROBLEM. To produce a given straight line, so that the rectangle contained by the whole line thus produced, and the part of it produced, shall be equal to a given square. Let AB be a given straight line, and L the side D EX of a given square... ## A Popular Course of Pure and Mixed Mathematics ...: With Tables of ...

Peter Nicholson - Mathematics - 1825 - 372 pages
...AC, CD, is equal to the rectangle contained by their sum and difference. Proposition VI. Theoretn. If a straight line be bisected, and produced .to any point : the recangle contained by the whole line thus produced, and the part of it produced, together with the... ## The Elements of Euclid: The Errors by which Theon, Or Others, Have Long ...

Robert Simson - Trigonometry - 1827 - 513 pages
...AD, DB, are double of the squares of AC, CD. If therefore a straight line, &c. QED PROP. X. THEOR. If a, straight line be bisected, and produced to any point, the square of the whole line thus produced, and the square of the part of it produced, are together double... 