Elements of Geometry and Trigonometry: From the Works of A.M. Legendre |
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Page 18
... drawn joining two given points . 12. The shortest distance from one point to another is measured on the straight line which joins them . 13. Through the same point , only one straight line can be drawn parallel to a given straight line ...
... drawn joining two given points . 12. The shortest distance from one point to another is measured on the straight line which joins them . 13. Through the same point , only one straight line can be drawn parallel to a given straight line ...
Page 28
... drawn , making the angle CAG equal to the angle D ( Post . 7 ) ; make AG equal to DE , and draw GC . Then will the triangles AGC and DEF have two sides and the included angle of the one equal to two sides and the included angle of the ...
... drawn , making the angle CAG equal to the angle D ( Post . 7 ) ; make AG equal to DE , and draw GC . Then will the triangles AGC and DEF have two sides and the included angle of the one equal to two sides and the included angle of the ...
Page 31
... drawn from the vertex of an isosceles triangle to the middle of the base , bisects the angle at the vertex , and is ... draw DC . Then , in the triangles ABC , DBC , we have the side BD equal to AC , by construction , the side BC common ...
... drawn from the vertex of an isosceles triangle to the middle of the base , bisects the angle at the vertex , and is ... draw DC . Then , in the triangles ABC , DBC , we have the side BD equal to AC , by construction , the side BC common ...
Page 32
... draw CD , making the angle BCD equal to the angle B ( Post . 7 ) : then , in the triangle DCB , we have the angles DCB and DBC equal : hence , the opposite sides DB and DC are equal ( P. XII . ) . In the triangle ACD , we have ( P. VII ...
... draw CD , making the angle BCD equal to the angle B ( Post . 7 ) : then , in the triangle DCB , we have the angles DCB and DBC equal : hence , the opposite sides DB and DC are equal ( P. XII . ) . In the triangle ACD , we have ( P. VII ...
Page 33
... drawn from A. A D- BE F For , suppose a second perpendicular AC to be drawn . Prolong AB till BF is equal to AB , and draw CF. Then , the triangles ABC and FBC will have AB equal to BF , by construction , CB common , and the included ...
... drawn from A. A D- BE F For , suppose a second perpendicular AC to be drawn . Prolong AB till BF is equal to AB , and draw CF. Then , the triangles ABC and FBC will have AB equal to BF , by construction , CB common , and the included ...
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Common terms and phrases
AB² ABCD AC² adjacent angles altitude apothem Applying logarithms base and altitude bisect centre chord circle circumference circumscribed coincide cone consequently convex surface corresponding cosec cosine Cotang cylinder denote diagonals diameter difference distance divided draw drawn edges equally distant feet find the area Formula frustum given angle given straight line greater hence homologous hypothenuse included angle interior angles intersection less Let ABC log sin lower base mantissa measured by half number of sides opposite parallel parallelogram parallelopipedon perimeter perpendicular plane MN polyedral angle polyedron prism PROPOSITION proved pyramid quadrant radii radius rectangle regular polygons right angles right-angled triangle Scholium secant segment semi-circumference side BC similar sine slant height sphere spherical polygon spherical triangle square subtracted Tang tangent THEOREM triangle ABC triangular prisms triedral angle upper base vertex vertices whence
Popular passages
Page 126 - The square of the hypothenuse is equal to the sum of the squares of the other two sides ; as, 5033 402+302.
Page 59 - A'B'C', and applying the law of cosines, we have cos a' = cos b' cos c' + sin b' sin c' cos A'. Remembering the relations a' = 180° -A, b' = 180° - B, etc. (this expression becomes cos A = — cos B cos C + sin B sin C cos a.
Page 18 - The circumference of every circle is supposed to be divided into 360 equal parts called degrees, and each degree into 60 equal parts called minutes, and each minute into 60 equal parts called seconds, and these into thirds, fourths, &c.
Page 104 - The square described on the hypothenuse of a rightangled triangle is equal to the sum of the squares described on the other two sides.
Page 6 - The logarithm of any power of a number is equal to the logarithm of the number multiplied by the exponent of the power.
Page 28 - If two triangles have two sides of the one equal to two sides of the...
Page 46 - All the interior angles of any rectilineal figure, together with four right angles, are equal to twice as many right angles as the figure has sides.
Page 99 - The area of a parallelogram is equal to the product of its base and altitude.
Page 172 - If two planes are perpendicular to 'each other, a straight line drawn in one of them, perpendicular to their intersection, will be perpendicular to the other.
Page 214 - A sphere is a solid bounded by a curved surface, every point of which is equally distant from a point within called the center.