Elements of Geometry and Trigonometry |
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Page 18
THEOREM . The sum of any two sides of a triangle , is greater than the third side . Let ABC be a triangle : then will the sum of two of its sides , as AC , CB , be greater than the third side AB . For the straight line AB is the ...
THEOREM . The sum of any two sides of a triangle , is greater than the third side . Let ABC be a triangle : then will the sum of two of its sides , as AC , CB , be greater than the third side AB . For the straight line AB is the ...
Page 19
... it is evident that GC , or its equal EF , will be shorter than BC ( Ax . 8. ) . B Ꮐ Third Case . Lastly , if the point G fall within the triangle BAC , we shall have , by the preceding theorem , AG + GC < AB + BC ...
... it is evident that GC , or its equal EF , will be shorter than BC ( Ax . 8. ) . B Ꮐ Third Case . Lastly , if the point G fall within the triangle BAC , we shall have , by the preceding theorem , AG + GC < AB + BC ...
Page 21
THEOREM . Conversely , if two angles of a triangle are equal , the sides opposite them are also equal , and the triangle is isosceles . Let the angle ABC be equal to the angle ACB ; then will the side AC be equal to the side AB .
THEOREM . Conversely , if two angles of a triangle are equal , the sides opposite them are also equal , and the triangle is isosceles . Let the angle ABC be equal to the angle ACB ; then will the side AC be equal to the side AB .
Page 22
THEOREM . From a given point , without a straight line , only one perpendicular can be drawn to that line . Let A be the point , and DE the given line . A Let us suppose that we can draw two perpendiculars , AB , AC .
THEOREM . From a given point , without a straight line , only one perpendicular can be drawn to that line . Let A be the point , and DE the given line . A Let us suppose that we can draw two perpendiculars , AB , AC .
Page 24
If a straight line have two points D and F , equally distant from the extremities A and B , it will be perpendicular to AB at the middle point C. PROPOSITION XVII . THEOREM . If two right angled triangles have the hypothenuse and a side ...
If a straight line have two points D and F , equally distant from the extremities A and B , it will be perpendicular to AB at the middle point C. PROPOSITION XVII . THEOREM . If two right angled triangles have the hypothenuse and a side ...
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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
Bibliographic information
| Title | Elements of Geometry and Trigonometry DAVIES' COURSE OF MATHEMATICS |
| Author | Adrien Marie Legendre |
| Editor | Charles Davies |
| Translated by | David Brewster |
| Publisher | A.S. Barnes and Company, 1839 |
| Original from | Harvard University |
| Digitized | 14 Jan 2008 |
| Length | 359 pages |
| Export Citation | BiBTeX EndNote RefMan |