Elements of Geometry and Trigonometry |
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Page 35
Of four proportional quantities , the first and third are called the antecedents , and the second and fourth the consequents ; and the last is said to be a fourth proportional to the other three taken in order . 4.
Of four proportional quantities , the first and third are called the antecedents , and the second and fourth the consequents ; and the last is said to be a fourth proportional to the other three taken in order . 4.
Page 36
If there are three proportional quantities ( Def . 4. ) , the product of the extremes will be equal to the square of the mean . PROPOSITION II . THEOREM . If the product of two quantities be equal to the product of two other quantities ...
If there are three proportional quantities ( Def . 4. ) , the product of the extremes will be equal to the square of the mean . PROPOSITION II . THEOREM . If the product of two quantities be equal to the product of two other quantities ...
Page 37
Let and then will For , by alternation If there be four proportional quantities , and four other proportional quantities , having the antecedents the same in both , the consequents will be proportional . and M : N :: P : Q M : R :: P ...
Let and then will For , by alternation If there be four proportional quantities , and four other proportional quantities , having the antecedents the same in both , the consequents will be proportional . and M : N :: P : Q M : R :: P ...
Page 38
Let M and N be any two quantities , and m any integral number ; then will m . M : m . N :: M : N. For m . MxN = m . NxM , since the quantities in each member are the same ; therefore , the quantities are proportional ( Prop . II . ) ...
Let M and N be any two quantities , and m any integral number ; then will m . M : m . N :: M : N. For m . MxN = m . NxM , since the quantities in each member are the same ; therefore , the quantities are proportional ( Prop . II . ) ...
Page 39
Let For , since And since Therefore , Of four proportional quantities , if the two consequents be either augmented or diminished by quantities which have the same ratio as the antecedents , the resulting quantities and the antecedents ...
Let For , since And since Therefore , Of four proportional quantities , if the two consequents be either augmented or diminished by quantities which have the same ratio as the antecedents , the resulting quantities and the antecedents ...
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Common terms and phrases
ABCD adjacent altitude base become Book called centre chord circle circumference circumscribed common cone consequently contained Cosine Cotang cylinder described determine diameter difference distance divided draw drawn equal equations equivalent expressed extremities faces feet figure follows formed four frustum give given gles greater half hence homologous hypothenuse included inscribed intersection less let fall logarithm manner means measured meet middle multiplied number of sides opposite parallel parallelogram pass perpendicular plane polygon prism PROBLEM Prop proportional PROPOSITION pyramid quadrant quantities radii radius ratio reason rectangle regular remaining right angles Scholium segment sides similar Sine solid solid angle sphere spherical triangle square straight line suppose taken Tang tangent THEOREM third triangle triangle ABC unit vertex whole
Bibliographic information
| Title | Elements of Geometry and Trigonometry DAVIES' COURSE OF MATHEMATICS |
| Author | Adrien Marie Legendre |
| Editor | Charles Davies |
| Translated by | David Brewster |
| Publisher | A.S. Barnes and Company, 1839 |
| Original from | Harvard University |
| Digitized | 14 Jan 2008 |
| Length | 359 pages |
| Export Citation | BiBTeX EndNote RefMan |