## Elements of Geometry and Trigonometry |

### From inside the book

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Page 35

Of four

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

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

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

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

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**.### What people are saying - Write a review

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### Other editions - View all

Elements of Geometry and Trigonometry from the Works of A. M. Legendre A. M. Legendre No preview available - 2017 |

### 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