Elements of Geometry and Trigonometry from the Works of A.M. Legendre: Revised and Adapted to the Course of Mathematical Instruction in the United StatesA.S. Barnes & Company, 1854 - 432 Seiten |
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Seite 24
... fall on C , and the third side EF , will coincide with the third side BC ( A. 11 ) : consequent- ly , the triangle EDF is equal to the triangle BAC ( A. 14 ) . Cor . When two triangles have these three things equal , viz . , the side ED ...
... fall on C , and the third side EF , will coincide with the third side BC ( A. 11 ) : consequent- ly , the triangle EDF is equal to the triangle BAC ( A. 14 ) . Cor . When two triangles have these three things equal , viz . , the side ED ...
Seite 25
... falling at the same time in the two straight lines BA and CA , must fall at their intersection A : hence , the two triangles EDF , BAC , coincide with each other , and consequently , are equal ( a . 14 ) . Cor . Whenever , in two ...
... falling at the same time in the two straight lines BA and CA , must fall at their intersection A : hence , the two triangles EDF , BAC , coincide with each other , and consequently , are equal ( a . 14 ) . Cor . Whenever , in two ...
Seite 27
... falls without the triangle BAC . 2d . When it falls on the side BC ; and 3d . When it falls within the triangle . Case I. In the triangles AGC and ABC , we have , GI + IC > GC ; and AI + IB > AB ; therefore AG ÷ BC GC + AB . B4 A D ...
... falls without the triangle BAC . 2d . When it falls on the side BC ; and 3d . When it falls within the triangle . Case I. In the triangles AGC and ABC , we have , GI + IC > GC ; and AI + IB > AB ; therefore AG ÷ BC GC + AB . B4 A D ...
Seite 28
... fall on the side BC , it is evident that GC , or its equal EF , will be shorter than BC ( A. 8 ) . B A Case III . Lastly , if the point G fall within the triangle BAC , we shall have AG + GC < AB + BC , taking AG from the one , and its ...
... fall on the side BC , it is evident that GC , or its equal EF , will be shorter than BC ( A. 8 ) . B A Case III . Lastly , if the point G fall within the triangle BAC , we shall have AG + GC < AB + BC , taking AG from the one , and its ...
Seite 32
... fall on the line , and oblique lines be drawn to different points : 1st . The perpendicular will be shorter than any oblique line . 2d . Any two oblique lines which intersect the given line at points equally distant from the foot of the ...
... fall on the line , and oblique lines be drawn to different points : 1st . The perpendicular will be shorter than any oblique line . 2d . Any two oblique lines which intersect the given line at points equally distant from the foot of the ...
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Häufige Begriffe und Wortgruppen
adjacent angles altitude angle ACB angle BAD base ABCD bisect centre chord circ circumference circumscribed common comp cone consequently convex surface cosine Cotang cylinder diagonal diameter distance divided draw drawn edges equations equivalent feet figure find the area frustum given angle given line given point gles greater hence homologous homologous sides hypothenuse included angle inscribed circle intersect less Let ABC let fall logarithm magnitudes measured by half middle point number of sides oblique lines opposite parallelogram parallelopipedon pendicular perimeter perpendicular plane MN polyedral angle polyedron PROBLEM PROPOSITION pyramid quadrant radii radius ratio rectangle regular polygon right angles right-angled triangle Scholium secant segment side BC similar sine slant height solidity sphere spherical polygon spherical triangle square described straight line Tang tangent THEOREM triangle ABC triangular prism triedral angles vertex vertices
Beliebte Passagen
Seite 27 - If two triangles have two sides of the one equal to two sides of the...
Seite 227 - A spherical triangle is a portion of the surface of a sphere, bounded by three arcs of great circles.
Seite 256 - The logarithm of . the quotient of two numbers, is equal to the logarithm of the dividend diminished by the logarithm of the divisor.
Seite 97 - The square described on the hypothenuse of a right-angled triangle is equivalent to the sum of the squares described on the other two sides.
Seite 26 - The sum of any two sides of a triangle is greater than the third side.
Seite 271 - The circumference of every circle is supposed to be divided into 360 equal parts, called degrees...
Seite 93 - The area of a parallelogram is equal to the product of its base and altitude.
Seite 358 - CUBIC MEASURE 1728 cubic inches = 1 cubic foot 27 cubic feet = 1 cubic yard...
Seite 323 - 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.
Seite 64 - Two equal chords are equally distant from the centre ; and of two unequal chords, the less is at the greater distance from the centre.