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Algebra angle-bisector arcs axes axis bisects center of gravity circle co-initial coincide collinear commutative complanar cos0 cosc curve cyclic permutation cyclical order denotes diagonals direction of rotation directrix divisor ellipse equal esin expression extremities factor find the locus formula function given lines given point Hence hyperbola initial point length Let Fig Let oa line joining mean point medial middle point multiplication notation obtain opposite origin parabola parallelogram plane aob plane curve quadrilateral quaternion quotient radius ratio reciprocal represented rhombus right angles right line Sa/Jy scalar second member sides sin0 sinb sine sphere squares straight line Substituting subtracting symbol tangent line tensor tetraedron tion triangle unit vectors vector areas vector perpendicular versor vertex vertices whence write zero
Page 91 - ... by four times the square of the line joining the middle points of the diagonals.
Page 9 - If two triangles which have two sides of the one proportional to two sides of the other, be joined at one angle, so as to have their homologous sides parallel to one another! the remaining sides shall be in a straight line. Let ABC, DCE be two triangles which have the two sides BA, AC proportional to the two CD, DE, viz.
Page 83 - In any triangle, the square of a side opposite an acute angle is equal to...
Page 90 - Show that the sum of the squares of the diagonals of any quadrilateral is twice the sum of the squares of the lines joining the middle points of the opposite sides.
Page 31 - The bisector of an angle of a triangle divides the opposite side into segments proportional to the adjacent sides. 144. Theorem. The bisector of an exterior angle of a triangle divides the opposite side produced into segments proportional to the other two sides.
Page iii - The chief aim has been to meet the wants of beginners in the class-room. The Elements and Lectures of Sir WR Hamilton are mines of wealth, and may be said to contain the suggestion of all that will be done in the way of Quaternion research and application : for this reason, as also on account of their diffuseness of style, they are not suitable for the purposes of elementary instruction. The same may be...
Page 88 - Prove that parallelograms on the same base and between the same parallels are equal in area.
Page 175 - The locus of a point, the ratio of whose distances from two given points is constant, is a circle*.
Page 97 - The angles at the base of an isosceles triangle are equal to each other ; and if the equal sides be produced, the angles on the other side of the base shall be equal.
Page 169 - ... foci of conies, in the original figure, and illustrate your theory by stating in a form true for all conies the property that the angle at the center of a circle is double that at the circumference. 2. Prove that if m is prime to a the least positive remainders of the series of...