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Skeleton propositions &c. of Euclid, books i and ii, with ..., Volume 1
Volledige weergave - 1868
acute Algebra already Applications Area Arith ARITHMETIC ascertain base Book II Conc Concl Cone cut in extreme Definitions difference double established EUCLID examination EXERCISES extreme and mean frith GEOMETRICAL GEOMETRICAL REASONING given half the line half the square Ilyp knowledge Learner Let a line line A B line be bisected line be divided line in extreme lines is equal live magnitudes margin mean ratio measure method miles mind object obtuse angle opposite perp practical PRICE Principles printed PROB proceed produced progression PROP Pror Recap Recap Alg recapitulatory recommended rectangle contained references REMARKS respecting Series side SKELETON PROPOSITIONS square of half THEOR triangle truths twice the rect twice the rectangle unequal uniformity VIII whole line write written
Pagina 95 - If a straight line be divided into any two parts, the squares of the whole line, and of one of the parts, are equal to twice the rectangle contained by the whole and that part, together with the square of the other part. Let the straight line AB be divided into any two parts in the point C ; the squares of AB, BC are equal to twice the rectangle AB, BC, together with the square of AC.
Pagina 107 - To divide a given straight line into two parts, so that the rectangle contained by the whole and one of the parts, shall be equal to the square on the other part.
Pagina 93 - 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...
Pagina 101 - 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 of the square of half the line bisected, and of the square of the line made up of the half and the part produced.
Pagina 81 - If there be two straight lines, one of which is divided into any number of parts, the rectangle contained by the two straight lines is equal to the rectangles contained by the undivided line, and the several parts of the divided line. Let...
Pagina 109 - IN obtuse angled triangles, if a perpendicular be drawn from any of the acute angles to the opposite side produced, the square of the side subtending the obtuse angle is greater than the squares of the sides containing the obtuse angle, by twice the rectangle contained by the side upon which, when produced, the perpendicular falls, and the straight line intercepted without the triangle between the perpendicular and the obtuse angle.