## Elements of Geometry and Trigonometry |

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Page 12

A theorem is a truth , which becomes evident by

A theorem is a truth , which becomes evident by

**means**of a train of reasoning called a demonstration . A problem is a question proposed , which requires a solution . A lemma is a subsidiary truth , employed for the demonstration of a ... Page 13

The sign indicates a root to be extracted ; thus √2

The sign indicates a root to be extracted ; thus √2

**means**the square - root of 2 ; √A × B**means**the the product of A and B. square - root of Axioms . 1. Things which are equal to the same thing , are equal to each other . 2. Page 35

The first and last terms are called the two extremes , and the second and third terms , the two

The first and last terms are called the two extremes , and the second and third terms , the two

**means**. 3. ... that the second has to the third ; and then the middle term is said to be a**mean**proportional between the other two . 5. Page 36

When four quantities are in proportion , the product of the two extremes is equal to the product of the two

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

M : N :: P : Q ; then will N : M :: Q : P . Let For , from the first proportion we have MxQ = Nx P , or NxP = MxQ But the products Nx P and M × Q are the products of the extremes and

M : N :: P : Q ; then will N : M :: Q : P . Let For , from the first proportion we have MxQ = Nx P , or NxP = MxQ But the products Nx P and M × Q are the products of the extremes and

**means**of the four quantities N , M , Q , P , and ...### 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