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Sivu 125 - Again ; the mathematical postulate, that " things which are equal to the same are equal to one another," is similar to the form of the syllogism in logic, which unites things agreeing in the middle term.
Sivu 303 - How quick they wheel'd, and flying behind them shot Sharp sleet of arrowy showers against the face Of their pursuers, and overcame by flight...
Sivu 263 - The sum of the angles of a spherical triangle is greater than two and less than six right angles. Hyp. ABC is a spherical triangle. To prove ZA + ZB + ZG> 180°, and ZA + ZB + ZC<5±0°. Proof. Construct the polar triangle A'B'C', and denote the number of degrees in B'C', C'A', and A'B', respectively, by a, b, and c.
Sivu 147 - FC; then, because each of the angles BAC, BAG is a right angle (Def. 30.), the two straight lines AC, AG upon the opposite sides of AB, make with it at the point A the adjacent angles equal to two right angles; therefore CA is in the same straight line (i.
Sivu 261 - From the same demonstration it likewise follows that the arc which a body, uniformly revolving in a circle by means of a given centripetal force, describes in any time is a mean proportional between the diameter of the circle and the space which the same body falling by the same given force would descend through in the same given time.
Sivu 147 - ... described upon the side subtending the right angle, is equal to the squares described upon the sides which contain the right angle. Let ABC be a right-angled triangle, having the right angle BAC : the square described upon the side BC shall be equal to the squares described upon BA, AC.
Sivu 311 - Having given the radius of an arc of any colour in the secondary rainbow, find the ratio of the sine of incidence to the sine of refraction when rays of that colour pass out of air into water.
Sivu 315 - What must be the magnitude and point of application of a single force that will support a sluice-gate in the shape of an inverted parabola ? 4. Find the specific gravity of a body which is lighter than the fluid in which it is weighed. 5. If the specific gravity of air...