First-year Mathematics for Secondary Schools

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Página 152 - In any proportion, the product of the means equals the product of the extremes.
Página 136 - Then any trinomial, in which two terms are squares (and positive) and the other term is plus or minus twice the product of the square roots of those two terms, is the square of the sum or difference of those two square roots according as the third term is plus or minus. 23. Factor k'+бkl+gl'.
Página 95 - A person engaged to work a days on these conditions: for each day he worked he was to receive b cents, and for each day he was idle he was to forfeit с cents. At the end of a days he received d cents. How many days was he idle?
Página 30 - The area of a triangle is equal to % the product of its base and altitude.
Página 162 - A bar of iron, of uniform thickness, 10 ft. long, and weighing 1 5 cwt., is supported at its extremities in a horizontal position, and carries a weight of 4 cwt. suspended from a point distant 3 ft. from one extremity. Find the pressures on the points of support.
Página 41 - I label the two new points e and/.' With the help of this figure he then proceeds to the usual proof of the theorem that the area of a parallelogram is equal to the product of the base by the altitude, establishing the equality of certain lines and angles and the congruence of the pair of triangles.
Página 94 - At what time between 3 and 4 o'clock are the hands of a watch opposite to each other ? Let x = the number of minute-spaces passed over by the minutehand from 3 o'clock to the required time.
Página 177 - The logarithm of a quotient is the logarithm of the dividend minus the logarithm of the divisor.
Página 36 - Euclid, eg first asserts and proves, that the exterior angle of a triangle is greater than either of the interior opposite angles...
Página 92 - If 1 pound of lead loses /7 of a pound, and 1 pound of iron loses ^ of a pound when weighed in water, how many pounds of lead and of iron are there in a mass of lead and iron that weighs 159 pounds in air and 143 pounds in water ? 78.

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