An Introduction to Algebra: Being the First Part of a Course of Mathematics, Adapted to the Method of Instruction in the American CollegesH. Howe, 1827 - 332 σελίδες |
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Σελίδα 2
... triangle is defined , by saying , that it is a figure bounded by three equal sides . It is essential to a complete definition , that it perfectly dis- tinguish the thing defined , from every thing else . On many subjects , it is ...
... triangle is defined , by saying , that it is a figure bounded by three equal sides . It is essential to a complete definition , that it perfectly dis- tinguish the thing defined , from every thing else . On many subjects , it is ...
Σελίδα 4
... triangle are equal , the an- gles are equal ; and secondly , that if the angles are equal , the sides are equal . Here , in the first proposition , the equal- ity of the sides is given ; and the equality of the angles in- ferred : in ...
... triangle are equal , the an- gles are equal ; and secondly , that if the angles are equal , the sides are equal . Here , in the first proposition , the equal- ity of the sides is given ; and the equality of the angles in- ferred : in ...
Σελίδα 292
... triangle is equal to two right angles , ( Euc . 32. 1. ) may be demonstrated , either in common language , or by means of the signs used in algebra . Let the side AB , of the triangle ABC , ( Fig . 1. ) be contin- ued to D ; let the ...
... triangle is equal to two right angles , ( Euc . 32. 1. ) may be demonstrated , either in common language , or by means of the signs used in algebra . Let the side AB , of the triangle ABC , ( Fig . 1. ) be contin- ued to D ; let the ...
Σελίδα 298
... triangle is equal to half the product of the base and height . Thus the area of the triangle ABG , ( Fig . 7. ) is equal to half AB into GH or its equal BC , that is , a = ABXBC . For the area of the parallelogram ABCD is AB × BC ...
... triangle is equal to half the product of the base and height . Thus the area of the triangle ABG , ( Fig . 7. ) is equal to half AB into GH or its equal BC , that is , a = ABXBC . For the area of the parallelogram ABCD is AB × BC ...
Σελίδα 299
... triangles ABC , ACE , and ECD . The area of the triangle That of the triangle That of the triangle ABC ACXBL , ACE ACEH , ECDECX DG . The area of the whole figure is , therefore equal to ( ¦AC × BL ) + ( ¦AC × EH ) + ( ÷ EC × DG ) . The ...
... triangles ABC , ACE , and ECD . The area of the triangle That of the triangle That of the triangle ABC ACXBL , ACE ACEH , ECDECX DG . The area of the whole figure is , therefore equal to ( ¦AC × BL ) + ( ¦AC × EH ) + ( ÷ EC × DG ) . The ...
Συχνά εμφανιζόμενοι όροι και φράσεις
12 rods abscissa added algebraic antecedent applied arithmetical become binomial calculation called co-efficients common difference Completing the square compound quantity consequent contained cube root cubic equation curve diminished Divide the number dividend division divisor dollars equa Euclid exponents expression extracting factors fourth fraction gallons geometrical geometrical progression given quantity greater greatest common measure Hence inches infinite series inverted last term length less letters manner mathematics Mult multiplicand multiplied or divided negative quantity notation nth power nth root number of terms ordinate parallelogram perpendicular positive preceding prefixed principle Prob proportion proposition quadratic equation quan quotient radical quantities radical sign ratio reciprocal Reduce the equation remainder rule sides square root substituted subtracted subtrahend supposed supposition third tion tities Transposing triangle twice unit unknown quantity varies
Δημοφιλή αποσπάσματα
Σελίδα 190 - But it is commonly necessary that this first proportion should pass through a number of transformations before it brings out distinctly the unknown quantity, or the proposition which we wish to demonstrate. It may undergo any change which will not affect the equality of the ratios ; or which will leave the product of the means equal to the product of the extremes.
Σελίδα 124 - ... the product of the two, plus the square of the second. In the third case, we have (a + b) (a — 6) = a2 — b2. (3) That is, the product of the sum and difference of two quantities is equal to the difference of their squares.
Σελίδα 31 - MULTIPLYING BY A WHOLE NUMBER is TAKING THE MULTIPLICAND AS MANY TIMES, AS THERE ARE UNITS IN THE MULTIPLIER.
Σελίδα 188 - : b : : mx : y, For the product of the means is, in both cases, the same. And if na : b : : x : y, then a : b : : x :ny. 375. On the other hand, if the product of two quantities is equal to the product of two others, the four quantities...
Σελίδα 87 - MULTIPLY THE QUANTITY INTO ITSELF, TILL IT is TAKEN AS A FACTOR, AS MANY TIMES AS THERE ARE UNITS IN THE INDEX OF THE POWER TO WHICH THE QUANTITY IS TO BE RAISED.
Σελίδα 137 - In the same manner, it may be proved, that the last term of the square of any binomial quantity, is equal to the square of half the co-elficient of the root of the first term.
Σελίδα 295 - The operation consists in repeating the multiplicand, as many times as there are units in the multiplier.
Σελίδα 292 - After remarking that the mathematician positively knows that the sum of the three angles of a triangle is equal to two right angles...
Σελίδα 49 - As the value of a fraction is the quotient of the numerator divided by the denominator, it is evident, from Art.
Σελίδα 233 - Divide the first term of the dividend by the first term of the divisor, and write the result as the first term of the quotient. Multiply the whole divisor by the first term of the quotient, and subtract the product from the dividend.