Elements of Geometry and Trigonometry |
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Page 1
REVISED AND ABRIDGED BY CHARLES DAVIES , PROFESSOR OF MATHEMATICS IN THE MILITARY ACADEMY , AND AUTHOR OF THE COMMON SCHOOL ARITHMETIC , DESCRIPTIVE GEOMETRY , ELEMENTS OF SURVEYING , AND A TREATISE ON SHADOWS AND PERSPECTIVE .
REVISED AND ABRIDGED BY CHARLES DAVIES , PROFESSOR OF MATHEMATICS IN THE MILITARY ACADEMY , AND AUTHOR OF THE COMMON SCHOOL ARITHMETIC , DESCRIPTIVE GEOMETRY , ELEMENTS OF SURVEYING , AND A TREATISE ON SHADOWS AND PERSPECTIVE .
Page 12
The common name , proposition , is applied indifferently , to theorems , problems , and lemmas . A corollary is an obvious consequence , deduced from one or several propositions . A scholium is a remark on one or several preceding ...
The common name , proposition , is applied indifferently , to theorems , problems , and lemmas . A corollary is an obvious consequence , deduced from one or several propositions . A scholium is a remark on one or several preceding ...
Page 14
THEOREM .. straight lines , which have two points common , coincide with each other throughout their whole extent , and form one and the same straight line . Let A and B be the two common points . In the first place it is evident that ...
THEOREM .. straight lines , which have two points common , coincide with each other throughout their whole extent , and form one and the same straight line . Let A and B be the two common points . In the first place it is evident that ...
Page 15
If a straight line meet two other straight lines at a common point , making the sum of the two adjacent angles equal to twó right angles , the two straight lines which are met , will form one and the same straight line .
If a straight line meet two other straight lines at a common point , making the sum of the two adjacent angles equal to twó right angles , the two straight lines which are met , will form one and the same straight line .
Page 20
Then , the triangles BAD , DAC , will have all the sides of the one equal to those of the other , each to each ; for BA is equal to AC , by hypothesis ; AD is common , and BD is equal to DC by construction : therefore , by the last ...
Then , the triangles BAD , DAC , will have all the sides of the one equal to those of the other , each to each ; for BA is equal to AC , by hypothesis ; AD is common , and BD is equal to DC by construction : therefore , by the last ...
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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 |