Elements of Geometry and Trigonometry |
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Page 1
BY CHARLES DAVIES , PROFESSOR OF MATHEMATICS IN THE MILITARY ACADEMY , AND AUTHOR OF THE COMMON SCHOOL ARITHMETIC , ELEMENTS OF DESCRIPTIVE GEOMETRY , ANALYTICAL GEOMETRY , DIFFERENTIAL AND INTEGRAL CALCULUS , AND A TREATISE ON SHADOWS ...
BY CHARLES DAVIES , PROFESSOR OF MATHEMATICS IN THE MILITARY ACADEMY , AND AUTHOR OF THE COMMON SCHOOL ARITHMETIC , ELEMENTS OF DESCRIPTIVE GEOMETRY , ANALYTICAL GEOMETRY , DIFFERENTIAL AND INTEGRAL CALCULUS , AND A TREATISE ON SHADOWS ...
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
Two 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 the two ...
Two 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 the two ...
Page 15
which can only be the case when the lines Tu anů CE coincide : therefore , the straight lines which have two points A and B common , cannot separate at any point , when produced ; hence they form one and the same straight line .
which can only be the case when the lines Tu anů CE coincide : therefore , the straight lines which have two points A and B common , cannot separate at any point , when produced ; hence they form one and the same straight line .
Page 16
Take away from both , the common angle ACE , there remains the angle ACD , equal to its opposite or vertical angle ECB ( Ax . 3. ) . Scholium . The four angles formed about a point by two straight lines , which intersect each other ...
Take away from both , the common angle ACE , there remains the angle ACD , equal to its opposite or vertical angle ECB ( Ax . 3. ) . Scholium . The four angles formed about a point by two straight lines , which intersect each other ...
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Common terms and phrases
ABCD adjacent altitude angled triangle base become Book called centre chord circle circumference circumscribed common cone consequently contained corresponding 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 logarithm manner means measured meet middle multiplied number of sides 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 sides similar sine solid solid angle sphere spherical triangle square straight line suppose taken tang tangent THEOREM third triangle triangle ABC unit vertex whole
Popular passages
Page 18 - If two triangles have two sides of the one equal to two sides of the...
Page 232 - ... the logarithm of a fraction is equal to the logarithm of the numerator minus the logarithm of the denominator.
Page 168 - The radius of a sphere is a straight line drawn from the centre to any point of the surface ; the diameter or axis is a line passing through this centre, and terminated on both sides by the surface.
Page 31 - Hence, the interior angles plus four right angles, is equal to twice as many right angles as the polygon...
Page 18 - America, but know that we are alive, that two and two make four, and that the sum of any two sides of a triangle is greater than the third side.
Page 241 - In every plane triangle, the sum of two sides is to their difference as the tangent of half the sum of the angles opposite those sides is to the tangent of half their difference.
Page 86 - The areas of two triangles which have an angle of the one equal to an angle of the other are to each other as the products of the sides including the equal angles. A D A' Hyp. In triangles ABC and A'B'C', To prove AABC A A'B'C' A'B' x A'C ' Proof. Draw the altitudes BD and B'D'.
Page 168 - CIRCLE is a plane figure bounded by a curved line, all the points of which are equally distant from a point within called the centre; as the figure ADB E.
Page 287 - How many square feet are there in the convex surface of the frustum of a square pyramid, whose slant height is 10 feet, each side of the lower base 3 feet 4 inches, and each side of the upper base 2 feet 2 inches ? Ans.
Page 64 - To inscribe a circle in a given triangle. Let ABC be the given triangle. Bisect the angles A and B by the lines AO and BO, meeting at the point 0.
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, 1837 |
| Original from | the University of Michigan |
| Digitized | 9 Jun 2007 |
| Length | 359 pages |
| Export Citation | BiBTeX EndNote RefMan |