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 conse- quents ; 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 conse- quents ; 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 ...
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 ...
Page 37
If there be four proportional quantities , and four other propor- tional quantities , having the antecedents the same in both , the consequents will be proportional . Let and M : N :: P : Q M : R :: P : S then will N : Q :: R : S For ...
If there be four proportional quantities , and four other propor- tional quantities , having the antecedents the same in both , the consequents will be proportional . Let and M : N :: P : Q M : R :: P : S then will N : Q :: R : S For ...
Page 38
Of four proportional quantities , if there be taken any equimul- tiples of the two antecedents , and any equimultiples of the two consequents , the four resulting quantities will be proportional . Let M , N , P , Q , be the numerical ...
Of four proportional quantities , if there be taken any equimul- tiples of the two antecedents , and any equimultiples of the two consequents , the four resulting quantities will be proportional . Let M , N , P , Q , be the numerical ...
Page 39
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 ante- cedents will be proportional .
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 ante- cedents will be proportional .
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Common terms and phrases
ABCD adjacent altitude base become Book called centre chord circle circumference circumscribed common cone consequently construction contained corresponding cosine Cotang cylinder described diameter difference distance divided draw drawn equal equation equivalent evident expressed extremities fall figure follows formed formulas four frustum give given gles greater half hence homologous included inscribed intersection less likewise logarithm manner means measured meet middle multiplied opposite parallel parallelogram parallelopipedon pass perpendicular plane polygon prism PROBLEM Prop proportional PROPOSITION pyramid quantities radii radius ratio reason rectangle regular remaining right angles Scholium segment shown sides similar sine solid solid angle sphere spherical triangle square straight line Suppose surface taken tang tangent THEOREM third triangle triangle ABC vertex whole
Bibliographic information
| Title | Elements of Geometry and Trigonometry |
| Author | Adrien Marie Legendre |
| Editor | Charles Davies |
| Translated by | David Brewster |
| Edition | 4 |
| Publisher | A.S. Barnes and Company, 1834 |
| Original from | the University of California |
| Digitized | 14 Oct 2010 |
| Length | 359 pages |
| Export Citation | BiBTeX EndNote RefMan |