Elements of Geometry and Trigonometry |
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Page 12
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 solu- tion . A lemma is a subsidiary truth , employed for the demonstra- tion of ...
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 solu- tion . A lemma is a subsidiary truth , employed for the demonstra- tion of ...
Page 13
The sign indicates a root to be extracted ; thus √2 means the square - root of 2 ; √Ax B means the square - root of the product of A and B. 1 Axioms . 1. Things which are equal to the same thing , are equal to each other . 2.
The sign indicates a root to be extracted ; thus √2 means the square - root of 2 ; √Ax B means the square - root of the product of A and B. 1 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 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.
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 means . Let A , B , C , D , be four quantities in proportion , and M : N :: P : Q be their numerical representatives ; then will ...
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 = Nx 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 ...
M : N :: P : Q ; then will N : M :: Q : P . For , from the first proportion we have MxQ = Nx 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 ...
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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
Bibliographic information
| Title | Elements of Geometry and Trigonometry |
| Author | Adrien Marie Legendre |
| Editor | Charles Davies |
| Translated by | David Brewster |
| Edition | 4 |
| Publisher | A.S. Barnes and Company, 1834 |
| Original from | the University of California |
| Digitized | 14 Oct 2010 |
| Length | 359 pages |
| Export Citation | BiBTeX EndNote RefMan |