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A Text-book of Geometrical Deductions: Corresponding to Euclid, book ..., Boek 2
Volledige weergave - 1892
AB=AC ABCD adjacent altitude angle angle is equal Apply Ex base base BC BC produced bisected bisector Book Bookwork College Compare concurrent Consider constant Construct Construct a rectangle DEDUCTIONS described diagonals difference distances drawn Enunciations equal to twice EUCLID externally falls figure find the locus four points geometrical construction given points given square given straight line hence hypotenuse internally isosceles triangle length line be divided lines is equal Loci means medians mid-point of AB mid-points of BC Observe obtuse angle opposite sides parallel straight lines parallelogram perimeter point in BC point of intersection points in order Problems projection proof Propositions prove rectangle contained right-angled triangle School segments square on half Standard Theorem taken twice the rectangle twice the square vertex vertices whole line
Pagina 180 - If a straight line be divided into two equal parts, and also into two unequal parts; the rectangle contained by the unequal parts, together with the square of the line between the points of section, is equal to the square of half the line.
Pagina 181 - 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 of half the line bisected, is equal to the square of the straight line which is made up of the half and the part produced.
Pagina 181 - If a straight line be divided into any two parts, four times the rectangle contained by the whole line, and one of the parts, together with the square of the other part, is equal to the square of the straight line which is made up of the whole and that part.
Pagina 180 - 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 169 - In every triangle, the square on the side subtending either of the acute angles, is less than the squares on the sides containing that angle, by twice the rectangle contained by either of these sides, and the straight line intercepted between the...
Pagina 181 - 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 181 - In obtuse-angled triangles, if a perpendicular be drawn from either of the acute angles to the opposite side produced, the square on the side subtending the obtuse angle is greater than the squares on the sides containing the obtuse angle, by twice the rectangle contained by the side...
Pagina 168 - In any obtuse triangle, the square of the side opposite the obtuse angle is equal to the sum of the squares of the other two sides, increased by twice the product of one of these sides and the projection of the other side upon it.
Pagina 171 - AB into two parts, so that the rectangle contained by the whole line and one of the parts, shall be equal to the square on the other part.