### Popular passages

Page 18 - Suppose a* = n, then x is called the logarithm ofnto the base a; thus the logarithm of a number to a given base is the index of the power to which the base must be raised to be equal to the number. The logarithm of n to the base a is written logaw; thus logaw = x expresses the same relation as a* = n.
Page 10 - The areas of two triangles which have an angle of the one equal to an angle of the other are to each other as the products of the sides including the equal angles. D c A' D' Hyp. In triangles ABC and A'B'C', ZA = ZA'. To prove AABC = ABxAC. A A'B'C' A'B'xA'C' Proof. Draw the altitudes BD and B'D'.
Page 10 - Since the area of a rectangle is equal to the product of the number of units of length in the length and...
Page 190 - If 6+e=24.8 cm., nr=11.89 cm., ^=39�, find B and C. 10. A lighthouse is observed from a ship which is steaming due N. to bear 62� W. of N. ; after the ship has sailed 10 miles, the lighthouse is observed to bear 40� W. of S. Calculate the distance of the ship from the lighthouse when it was nearest to it. STATICS AND DYNAMICS. ( Two and a holf1umn.) [Assume g=32 for foot-second unitt.] 1.
Page 12 - Proposition 3. The ratio of the circumference of any circle to its diameter is less than 3...
Page 11 - The opposite angles of a quadrilateral inscribed in a circle are together equal to two right angles, with converse.
Page 92 - Two observers on the same side of a balloon, and in the same vertical plane with it, are a mile apart, and find the angles of elevation to be 17� and 68� 25' respectively : what is its height ? [1836 feet.
Page 92 - ... and 63� 41'. Find the distance of each ship from the fort. 235. From the summit of a tower, whose height is 108 feet, the angles of depression of the top and bottom of a vertical column, standing in the horizontal plane, are found to be 30� and 60� respectively.
Page 9 - ... the three angles of a triangle are together equal to two right angles, although it is not known to all.
Page 9 - Any two sides of a triangle are together greater than the third side.