## Elements of Geometry and Trigonometry |

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Page 32

Taking from each the sum of the interior angles , and there remains the exterior angles , equal to

Taking from each the sum of the interior angles , and there remains the exterior angles , equal to

**four**right angles . In every parallelogram , the opposite sides and angles are equal . Let ABCD be a parallelogram : then will AB = DC ... Page 35

If there be

If there be

**four**magnitudes A , B , C , and D , having such B. D values that is equal to- then A is said to have the same ratio A to B , that C has to D , or the ratio of A to B is equal to the ratio of C to D. When**four**quantities have ... Page 36

When

When

**four**quantities are in proportion , the product of the two extremes is equal to the product of the two means X Let A , B , C , D , be**four**quantities in proportion , and M : N :: P : Q be their numerical representatives ; then will ... Page 37

Let and then will For , by alternation If there be

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 , as before , M , N , P , Q , be the numerical representatives of the

Let , as before , M , N , P , Q , be the numerical representatives of the

**four**quantities , so that M : N :: P : Q ; then will M ± N : M :: P ± Q : P . For , from the first proportion , we have MxQ = NxP , or Nx P = M × Q ; Add each of ...### 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