Elements of Geometry, After Legendre, with a Selection of Geometrical Exercises, and Hints for the Solution of the Same |
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Página 97
... homologous sides proportional . By homologous sides are meant those which have a corresponding position in the two figures , or which are adjacent to equal angles . These angles themselves are called homologous angles . Two equal ...
... homologous sides proportional . By homologous sides are meant those which have a corresponding position in the two figures , or which are adjacent to equal angles . These angles themselves are called homologous angles . Two equal ...
Página 115
... homologous sides are propor- tional ; for DE being parallel to BC , we have ( Prop . XVI . ) : AD AB AE : AC , and , drawing EF parallel to AB , we have : AE AC : BF : BC . D E B F And since the parallels DE , BF , intercepted between ...
... homologous sides are propor- tional ; for DE being parallel to BC , we have ( Prop . XVI . ) : AD AB AE : AC , and , drawing EF parallel to AB , we have : AE AC : BF : BC . D E B F And since the parallels DE , BF , intercepted between ...
Página 116
... homologous to DE , take AG = DE , and draw GH parallel to BC . The triangle AGH thus formed is simi- lar to ABC ... homologous sides are opposite to the equal angles . PROPOSITION XXI , THEOREM . Two triangles which have their homologous ...
... homologous to DE , take AG = DE , and draw GH parallel to BC . The triangle AGH thus formed is simi- lar to ABC ... homologous sides are opposite to the equal angles . PROPOSITION XXI , THEOREM . Two triangles which have their homologous ...
Página 117
... homologous sides give the proportion , AB : AG : AC : AH ; or , since AG = DE , AB : DE : AC : AH . But we have by hypothesis , AB : DE : AC : DF . A B D H E F Hence , AH = DF . In like manner we can prove GH = EF . Hence , the triangle ...
... homologous sides give the proportion , AB : AG : AC : AH ; or , since AG = DE , AB : DE : AC : AH . But we have by hypothesis , AB : DE : AC : DF . A B D H E F Hence , AH = DF . In like manner we can prove GH = EF . Hence , the triangle ...
Página 118
... homologous sides of the other . PROPOSITION XXIII . THEOREM . Two triangles which have their homologous sides parallel , or perpendicu- lar to each other , are similar . For , First , if the side AB is parallel to DE , and BC to EF ...
... homologous sides of the other . PROPOSITION XXIII . THEOREM . Two triangles which have their homologous sides parallel , or perpendicu- lar to each other , are similar . For , First , if the side AB is parallel to DE , and BC to EF ...
Otras ediciones - Ver todas
Elements of Geometry, After Legendre: With a Selection of Geometrical ... Charles Scott Venable Vista de fragmentos - 1890 |
Elements of Geometry, After Legendre: With a Selection of Geometrical ... Adrien Marie Legendre,Charles Scott Venable Sin vista previa disponible - 2014 |
Términos y frases comunes
ABCD altitude angle ACB angles equal apothem base bisect bisectrix Book centre chord circ circumference circumscribed circle common cone Construct convex surface cylinder decagon described diagonals diameter dicular diedral distance divided draw drawn edges equally distant equilateral triangle equivalent Exercises exterior angles Find the locus frustum Geometric given circle given line given point given straight line greater Hence homologous homologous sides hypothenuse isosceles join let fall line parallel loci measure median meet middle point number of sides opposite parallelogram parallelopipedon perimeter perpen perpendicular plane angles plane MN point of contact point of intersection polyedron prism problem Prop proportional PROPOSITION pyramid quadrilateral radii ratio rectangle regular polygon right angled triangle S-ABC SCHOLIUM segment similar solid angle sphere spherical triangle square tangent tetraedron THEOREM triangle ABC triangular prism triedral vertex vertices volume
Pasajes populares
Página 255 - THE sphere is a solid terminated by a curve surface, all the points of which are equally distant from a point within, called the centre.
Página 49 - The straight line joining the middle points of two sides of a triangle is parallel to the third side and equal to half of it 46 INTERCEPTS BY PARALLEL LINES.
Página 20 - Parallel straight lines are such as are in the same plane, and which, being produced ever so far both ways, do not meet.
Página 54 - CIRCLE is a plane figure bounded by a curved line, all the points of which are equally distant from a point within called the centre; as the figure ADB E.
Página 45 - If two triangles have the three sides of the one equal to the three sides of the other, each to each, the triangles are congruent.
Página 67 - The circumference of every circle is supposed to be divided into 360 equal parts, called degrees ; each degree into 60 equal parts, called minutes ; and each minute into 60 equal parts, called seconds.
Página 107 - 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.
Página 300 - The volume of a frustum of a cone is equivalent to the sum of the volumes of three cones whose common altitude is the altitude of the frustum and whose bases are the lower base, the upper base, and a mean proportional between the bases of the frustum.
Página 276 - Scholium. The spherical ungula, bounded by the planes AMB, ANB, is to the whole solid sphere, as the angle A is to four right angles. For, the lunes being equal, the spherical ungulas will also be equal ; hence two spherical ungulas are to each other, as the angles formed by the planes which bound them. PROPOSITION XVIII.
Página 9 - Ratio is the relation which one quantity bears to another in respect of magnitude, the comparison being made by considering what multiple, part, or parts, one is of the other.