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Skeleton propositions &c. of Euclid, books i and ii, with ..., Volum 1
Visualització completa - 1868
9 Ax acute Algebra already Applications Area Arith ARITHMETIC ascertain base Conc Concl Cone Construction Definitions Demonstration difference double drawn equal to twice established examination EXERCISES extreme and mean GEOMETRICAL given Gradations half the line half the square knowledge Learner Let a line line A B line be bisected line be divided line thus produced lines is equal magnitudes margin mean ratio measure method miles mind obtuse angle opposite perp Phop Pºop practical PRICE Principles printed PROB proceed produced progression Prop Recap rect rectangle contained references REMARKs respecting rith Series side SKELETON PROPOSITIONS square of half squares ºf Theon THEoR triangle truths twice the rectangle unequal uniformity VIII whole line write written
Pàgina 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.
Pàgina 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.
Pàgina 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...
Pàgina 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.
Pàgina 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...
Pàgina 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.