Elements of Geometry and Trigonometry |
From inside the book
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Page 21
... B and the side BC common : therefore , the two triangles , BDC , BAC , have two sides and the included angle in the one , equal to two sides and the included angle in the other , each to each : hence they are equal ( Prop . V. ) .
... B and the side BC common : therefore , the two triangles , BDC , BAC , have two sides and the included angle in the one , equal to two sides and the included angle in the other , each to each : hence they are equal ( Prop . V. ) .
Page 22
CBF are right angles , the side CB is common , and the side AB equal to BF , by construction ; therefore , the triangles are equal , and the angle ACB = BCF ( Prop . V. Cor . ) . But the angle ACB is a right angle , by hypothesis ...
CBF are right angles , the side CB is common , and the side AB equal to BF , by construction ; therefore , the triangles are equal , and the angle ACB = BCF ( Prop . V. Cor . ) . But the angle ACB is a right angle , by hypothesis ...
Page 23
The triangle BCF , is equal to the triangle BCA , for they have the right angle CBF CBA , the side CB common , and the side BF - BA ; hence the third sides , CF and CA are equal ( Prop . V. Cor . ) . But ABF , being a straight line ...
The triangle BCF , is equal to the triangle BCA , for they have the right angle CBF CBA , the side CB common , and the side BF - BA ; hence the third sides , CF and CA are equal ( Prop . V. Cor . ) . But ABF , being a straight line ...
Page 28
Hence the two triangles EFG , FGH , have a common side , and two adjacent angles in each equal ; hence these triangles are equal ( Prop . VI . ) ; therefore , the side EG , which measures the distance of the parallels AB and CD at the ...
Hence the two triangles EFG , FGH , have a common side , and two adjacent angles in each equal ; hence these triangles are equal ( Prop . VI . ) ; therefore , the side EG , which measures the distance of the parallels AB and CD at the ...
Page 30
... into as many triangles , less two , as the polygon has sides ; for , these triangles may be considered as having the point A for a common vertex , and for bases , the several sides of the polygon , excepting the two sides which form ...
... into as many triangles , less two , as the polygon has sides ; for , these triangles may be considered as having the point A for a common vertex , and for bases , the several sides of the polygon , excepting the two sides which form ...
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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 |