## Elements of Geometry and Trigonometry |

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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 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

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

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

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

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

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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