Elements of Geometry |
From inside the book
Results 1-5 of 63
Page x
... but which cannot be exactly assigned . Algebra furnishes methods for approximating , as nearly as we please , the roots of numbers which are not perfect powers . III . 1. When two proportions have a common ratio X Introduction .
... but which cannot be exactly assigned . Algebra furnishes methods for approximating , as nearly as we please , the roots of numbers which are not perfect powers . III . 1. When two proportions have a common ratio X Introduction .
Page xi
... ratio then will be equal to the primitive ratio increased by unity . If the same operation be performed upon the two ratios of a proportion , there will evidently result from it two new ratios equal to each other , and consequently a ...
... ratio then will be equal to the primitive ratio increased by unity . If the same operation be performed upon the two ratios of a proportion , there will evidently result from it two new ratios equal to each other , and consequently a ...
Page xii
... ratios A : C , B : D , being common to the two proportions above obtained , it follows that the other ratios of the same proportions are equal , and that consequently B + A : D + C :: B - A : D - C , or , by changing the place of the ...
... ratios A : C , B : D , being common to the two proportions above obtained , it follows that the other ratios of the same proportions are equal , and that consequently B + A : D + C :: B - A : D - C , or , by changing the place of the ...
Page xiii
... ratios A : B :: C : D :: E : F , by considering only the two first , which form the proportion A : B :: C : D , we obtain by what precedes + C : B + D : : A : B ; and , since the third ratio E : F is equal to the first A : B , we have A ...
... ratios A : B :: C : D :: E : F , by considering only the two first , which form the proportion A : B :: C : D , we obtain by what precedes + C : B + D : : A : B ; and , since the third ratio E : F is equal to the first A : B , we have A ...
Page 14
... ratio between AM and AG , that there is between AL and AF . From this proportion it follows , not only that the right line AE , must meet BD , if the two lines are pro- duced sufficiently far , but also that we may even assign upon AE ...
... ratio between AM and AG , that there is between AL and AF . From this proportion it follows , not only that the right line AE , must meet BD , if the two lines are pro- duced sufficiently far , but also that we may even assign upon AE ...
Other editions - View all
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...