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acres acting Algebra Apply ARITHMETIC Assuming axes axis base bisected body cent centre centre of gravity chords circle coefficient common condition contained cubic curve cuts Define Describe determine diameter differential direction distance Divide Draw drawn equal equation Euclid expansion Explain expression feet Find Find the equation force four fraction Geometry given given straight line greater greatest half heavy horizontal hour inches inclination inscribed intersection length logarithms mean measure meet miles Multiply opposite origin parabola parallel parallelogram particle pass perpendicular plane positive pound pressure produced proportional prove Pure Mathematics radius ratio rectangle rectangular Reduce referred respectively resultant right angles roots shew sides spherical triangle square straight line string Subtract surface taken tangent tension touches triangle vertical weight whole yards
Side 83 - If two triangles have one angle of the one equal to one angle of the other and the sides about these equal angles proportional, the triangles are similar.
Side 72 - IF a side of any triangle be produced, the exterior angle is equal to the two interior and opposite angles ; and the three interior angles of every triangle are equal to two right angles.
Side 17 - Parallelograms on the same base, and between the same parallels, are equal to one another.
Side 54 - If a straight line touch a circle, and from the point of contact a straight line be drawn cutting the circle ; the angles which this line makes with the line touching the circle, shall be equal to the angles which are in the alternate segments of the circle.
Side 12 - AB be the given straight line ; it is required to divide it into two parts, so that the rectangle contained by the whole, and one of the parts, shall be equal to the square of the other part.
Side 82 - IF from any point without a circle two straight lines be drawn, one of which cuts the circle, and the other touches it ; the rectangle contained by the whole line which cuts the circle, and the part of it without the circle, shall be equal to the square of the line which touches it.
Side 44 - 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.
Side 82 - In any right-angled triangle, the square which is described upon the side subtending the right angle, is equal to the squares described upon the sides which contain the right angle.