...is understood to be positive, ie it is the angle through which OX would have to be turned about O, in a direction opposite to the motion of the hands of a clock in order to make its direction the same as that of the vector. The angle expressing the direction is...

...it follows : ADVANCED ALGEBRA 431. The multiplication of a real number by — 1, is représentée, graphically by a rotation through an angle of 180°....represent the multiplication by an unknown number x. Then OA2 = ax, and OAS = OA2 • x = a • x • x. Or — a — a • x2. Therefore x = V— 1, and...

...— 1 as an operator which turns the line which represents the first factor through two right angles, in a direction opposite to the motion of the hands of a clock. 487. Graphical Representation of the Imaginary Unit i (§ 276). By the definition of §¿75, — 1...

...1 is represented by turning the line OA which represents the number + a, through two right angles, in a direction opposite to the motion of the hands of a clock. Then, in the product of any real number by — 1, we may regard —1 as an operator which turns the...

...clock — if the eye is at the vertex O'; but if he follows around AD alphabetically, he is moving in a direction opposite to the motion of the hands of a clock — if the eye is at the vertex O. 557. A trihedral angle is a polyhedral angle having three and only...

...— 1 as an operator which turns the line which represents the first factor through two right angles, in a direction opposite to the motion of the hands of a clock. 202. Graphical Representation of the Imaginary Unit i (§ 196). Y By the definition of § 198, - 1...

...electromagnet (such as the field spool of a motor), a pole will be north if the current is flowing around it in a direction opposite to the motion of the hands of a watch," Fig. 3, and south if in CURRENT FIG. 3. DIRECTION OF CURRENT AND MAGNETISM IN POLE PIECE. the...

...t/ava Qi. AM B FIG. 98 = - fyndx - C Jb i/o = - f yfa, •AC*) the last integral being taken around C in a direction opposite to the motion of the hands of a clock. Similarly, if the line NQ^ intersects C in Qi and Q2, where NQi = xi and = x,, we have A = C x^dy -...

...Earth around the Sun. — The earth not only turns on its axis every day, but it travels around the sun in a direction opposite to the motion of the hands of a watch. It moves with the tremendous average velocity of about 19 miles a second. It is this revolution...

...Çby2dx- СЬ, •>u va XO. л| *f а • - С yd. J(Ci dx, the last integral being taken around С in a direction opposite to the motion of the hands of a clock. л> f J а X D О AM В л Fio. 209 Similarly, if the line NQ.2 intersects 67 in Qj and Q2, where NQl...