## 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 square - root of the product of A and B. 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**. 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 . For , from the first proportion we have MxQ = N × P , or NxP = MxQ But the products Nx P and MxQ are the products of the extremes and

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

**means**of the four quantities N , M , Q , P , and these ...### What people are saying - Write a review

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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 produced 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