Elements of Geometry and Trigonometry from the Works of A.M. Legendre: Adapted to the Course of Mathematical Instruction in the United States |
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Page iii
... corresponds more exactly to the idea intended . Many other departures have been made from the original text , the value and utility of which have been made manifest in the practical tests to which the work has been subjected . In the ...
... corresponds more exactly to the idea intended . Many other departures have been made from the original text , the value and utility of which have been made manifest in the practical tests to which the work has been subjected . In the ...
Page 12
... are equal in all their parts when each part of one is equal to the corresponding part of the other , when taken either in the same or in the reverse order . ELEMENTS OF GEOMETRY . BOOK I. ELEMENTARY PRINCIPLES . DEFINITIONS 12 GEOMETRY .
... are equal in all their parts when each part of one is equal to the corresponding part of the other , when taken either in the same or in the reverse order . ELEMENTS OF GEOMETRY . BOOK I. ELEMENTARY PRINCIPLES . DEFINITIONS 12 GEOMETRY .
Page 46
... corresponding exterior angle , is equal as B Co to two right angles ( P. I. ) ; hence , the sum of all the inte- rior and exterior angles is equal to two right angles taker . But the sum of as many times as the polygon 46 GEOMETRY .
... corresponding exterior angle , is equal as B Co to two right angles ( P. I. ) ; hence , the sum of all the inte- rior and exterior angles is equal to two right angles taker . But the sum of as many times as the polygon 46 GEOMETRY .
Page 49
... corresponding sides of the other ; they are , therefore , equal in all respects : hence , the angles AEB , BEC , are equal , and therefore , the two diagonals bisect each other at right angles . 11 EXERCISES . 1. Show that the lines ...
... corresponding sides of the other ; they are , therefore , equal in all respects : hence , the angles AEB , BEC , are equal , and therefore , the two diagonals bisect each other at right angles . 11 EXERCISES . 1. Show that the lines ...
Page 59
... corresponding consequent . From the definition of a continued proportion ( D. 3 ) , A : B : C D E : F :: hence , :: GH , & c .; BA Α = BA А = ᄋᄋ ᄋ whence , BA = AB ; whence , BC = AD ; F = whence , BE = AF ; E H = whence , BG = AH ...
... corresponding consequent . From the definition of a continued proportion ( D. 3 ) , A : B : C D E : F :: hence , :: GH , & c .; BA Α = BA А = ᄋᄋ ᄋ whence , BA = AB ; whence , BC = AD ; F = whence , BE = AF ; E H = whence , BG = AH ...
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Common terms and phrases
ABē ACē altitude angle is equal apothem Applying logarithms axis base and altitude base multiplied bisects centre chord circumference cone consequently convex surface corresponding cosec cosine cotangent cylinder denote diagonals diameter distance divided draw drawn edges equal altitudes equal in volume equilateral feet find the area formula frustum given line given point greater hence homologous hypothenuse included angle inscribed circle inscribed polygon intersection less Let ABC logarithm lower base mantissa mean proportional measured by half number of sides opposite parallelogram parallelopipedon perimeter perpendicular plane angles plane MN polyedral angle polyedron prism PROBLEM.-To PROPOSITION proved pyramid quadrant radii radius rectangle regular polygons right angles right-angled triangle Scholium segment similar sine slant height sphere spherical angle spherical polygon spherical triangle square straight line tangent THEOREM triangle ABC triangular prisms triedral angle upper base vertex vertices whence
Popular passages
Page 28 - If two triangles have two sides of the one equal to two sides of the...
Page 90 - A cos 6 = cos a cos c + sin a sin c cos B cos c = cos a cos 6 + sin a sin 6 cos C Law of Cosines for Angles cos A = — cos B...
Page 18 - Things which are equal to the same thing, are equal to each other. 2. If equals are added to equals, the sums are equal. 3. If equals are subtracted from equals, the remainders are equal. 4. If equals are added to unequals, the sums are unequal.
Page 4 - The logarithm of any power of a number is equal to the logarithm of the number multiplied by the exponent of the power.
Page 253 - For, the point A being the pole of the arc EF, the distance AE is a 'quadrant ; the point C being the pole of the arc DE, the distance CE is likewise a quadrant : hence the point E is...
Page 61 - A Circle is a plane figure bounded by a curved line every point of which is equally distant from a point within called the center.
Page 94 - 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 126 - If two polygons are composed of the same number of triangles, similar each to each and similarly placed, the polygons are similar.
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 125 - THEOREM. Similar triangles are to each other as the squares of their homologous sides.