Elements of Geometry |
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Page 213
... denominators in an equation to disappear To write a question in the form of an equation Examples · Methods for performing , as far as is possible , the operations in- dicated upon quantities , that are represented by letters Explanation ...
... denominators in an equation to disappear To write a question in the form of an equation Examples · Methods for performing , as far as is possible , the operations in- dicated upon quantities , that are represented by letters Explanation ...
Page 16
... denominators ; but it is often more simple to reduce all the terms to the same denomi- nator which may then be ... denominator , beginning with the fractions , which are 2x 4x 5x 5 ' 5 ' 7 ' I convert them by the first of the rules ...
... denominators ; but it is often more simple to reduce all the terms to the same denomi- nator which may then be ... denominator , beginning with the fractions , which are 2x 4x 5x 5 ' 5 ' 7 ' I convert them by the first of the rules ...
Page 17
... denominator may now be cancelled , since by doing it we only multiply all the parts of the equation by this denominator , ( Arith . 54 ) , which does not destroy the equality of the members . It will become then or 5 × 7 × 2x + 3 × 5 ...
... denominator may now be cancelled , since by doing it we only multiply all the parts of the equation by this denominator , ( Arith . 54 ) , which does not destroy the equality of the members . It will become then or 5 × 7 × 2x + 3 × 5 ...
Page 20
... denominator m , it becomes mx + nx + px = am , and we deduce from this am x = m + n + p This result is nothing more nor less than an algebraic expres- sion of the rule of Fellowship , ( Arith . 124 ) ; for by regarding the numbers m , n ...
... denominator m , it becomes mx + nx + px = am , and we deduce from this am x = m + n + p This result is nothing more nor less than an algebraic expres- sion of the rule of Fellowship , ( Arith . 124 ) ; for by regarding the numbers m , n ...
Page 41
... denominator , if we divide it by c2 we shall decompose it into c2 x c2 ; and by suppressing the factor c2 common to the two terms , this letter disappears from the numerator , but will remain in the denominator with the exponent 2 ...
... denominator , if we divide it by c2 we shall decompose it into c2 x c2 ; and by suppressing the factor c2 common to the two terms , this letter disappears from the numerator , but will remain in the denominator with the exponent 2 ...
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Common terms and phrases
ABCD adjacent angles algebraic algebraic quantities altitude angle ACB base centre chord circ circle circular sector circumference coefficient common divisor cone consequently contains Corollary cube cylinder Demonstration denominator denoted diameter divided dividend division equal equivalent evident example exponent expression factors figure fraction frustum given gives greater greatest common divisor homologous sides inscribed less letters logarithm manner measure multiplied obtain parallel parallelogram parallelopiped perpendicular plane MN polyedron preceding prism proportion proposed equation proposition quotient radical sign radii radius ratio rectangle reduced regular polygon remainder result right angles Scholium side BC similar solid angle sphere spherical square root straight line substitute subtract suppose term THEOREM third tion triangle ABC triangular pyramids unity unknown quantity vertex whence
Popular passages
Page 63 - The square of the hypothenuse is equal to the sum of the squares of the other two sides ; as, 5033 402+302.
Page 7 - If two triangles have the three sides of the one equal to the three sides of the other, each to each, the triangles are congruent.
Page 151 - THE sphere is a solid terminated by a curve surface, all the points of which are equally distant from a point within, called the centre.
Page 76 - The perimeters of two regular polygons of the same number of sides, are to each other as their homologous sides, and their areas are to each other as the squares of those sides (Prop.
Page 25 - Two equal chords are equally distant from the centre ; and of two unequal chords, the less is at the greater distance from the centre.
Page 52 - The sum of the squares on the sides of a parallelogram is equal to the sum of the squares on the diagonals.
Page 160 - If two triangles have two sides and the inchtded angle of the one respectively equal to two sides and the included angle of the other, the two triangles are equal in all respects.
Page 203 - In every triangle the sum of the three angles is equal to two right angles.
Page 162 - In any spherical triangle, the greater side is opposite the greater angle ; and conversely, the greater angle is opposite the greater side.
Page 141 - If a pyramid is cut by a plane parallel to its base, the...