Plane and Solid GeometryLongmans, Green and Company, 1898 - 210 sider |
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Side 90
... homologous sides propor- tional . But in the case of triangles we learn , from Proposi- tions XIII . and XIV ... homologous altitudes of two similar triangles have the same ratio as any two homologous sides . 6. If in any triangle a ...
... homologous sides propor- tional . But in the case of triangles we learn , from Proposi- tions XIII . and XIV ... homologous altitudes of two similar triangles have the same ratio as any two homologous sides . 6. If in any triangle a ...
Side 91
... homologous sides are proportional . Since the triangles AEB and A'E'B ' are similar by hypoth- esis , they are ( by 223 ) equiangular ; that gives ZA = ZA ' , and ≤ ABE = △ A'B'E ' . Likewise , in the triangles EBC and E'B'C ' , LEBC ...
... homologous sides are proportional . Since the triangles AEB and A'E'B ' are similar by hypoth- esis , they are ( by 223 ) equiangular ; that gives ZA = ZA ' , and ≤ ABE = △ A'B'E ' . Likewise , in the triangles EBC and E'B'C ' , LEBC ...
Side 92
... homologous sides . E A A ' E ' B C B ' Let the two similar polygons be ABCDE and A'B'C'D'E ' , and let P and P ' represent their perimeters . To prove P : P ' :: AB : A'B ' . Since the polygons are similar ( by 223 ) , AE A'E ' = ED E'D ...
... homologous sides . E A A ' E ' B C B ' Let the two similar polygons be ABCDE and A'B'C'D'E ' , and let P and P ' represent their perimeters . To prove P : P ' :: AB : A'B ' . Since the polygons are similar ( by 223 ) , AE A'E ' = ED E'D ...
Side 109
... homologous sides . A C B AL C ' B ' Let AB and A'B ' be homologous sides of the similar tri- angles ABC and A'B'C ' . To prove that ABC AB2 = A'B'C ' A'B2 The triangles being similar , they are ( by 223 ) equiangular , therefore ( by ...
... homologous sides . A C B AL C ' B ' Let AB and A'B ' be homologous sides of the similar tri- angles ABC and A'B'C ' . To prove that ABC AB2 = A'B'C ' A'B2 The triangles being similar , they are ( by 223 ) equiangular , therefore ( by ...
Side 110
... homologous sides . Therefore the sums of the triangles or polygons are to each other as the squares of their homologous sides . PROPOSITION IX . THE PYTHAGOREAN THEOREM . * 265. In any right triangle the square described upon the ...
... homologous sides . Therefore the sums of the triangles or polygons are to each other as the squares of their homologous sides . PROPOSITION IX . THE PYTHAGOREAN THEOREM . * 265. In any right triangle the square described upon the ...
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Vanlige uttrykk og setninger
ABCD AC² acute angle AD² adjacent adjacent angles altitude angle formed angles are equal apothem arc BC base and altitude bisect bisector called centre chord circumference circumscribed cone cylinder diagonals diameter diedral angles distance divided draw drawn ECDH equally distant equilateral equivalent EXERCISES faces four right angles frustum given point given straight line hence homologous homologous sides hypotenuse inscribed polygon interior angles intersection isosceles triangle join lateral area lateral edges Let ABC lune mean proportional measured by one-half middle point number of sides parallelogram parallelopiped perimeter perpendicular polyedral angle polyedron PROPOSITION XI prove pyramid Q.E.D. PROPOSITION quadrilateral radii radius ratio rectangle rectangular parallelopiped regular polygon right triangle SCHOLIUM segments semiperimeter sphere spherical angle spherical polygon spherical triangle surface tangent THEOREM triangle ABC triangles are equal triangular triangular prism V-ABC vertex vertical angle
Populære avsnitt
Side 46 - PERIPHERY of a circle is its entire bounding line ; or it is a curved line, all points of which are equally distant from a point within called the centre.
Side 105 - ... any two parallelograms are to each other as the products of their bases by their altitudes. PROPOSITION V. THEOREM. 403. The area of a triangle is equal to half the product of its base by its altitude.
Side 82 - If any number of quantities are proportional, any antecedent is to its consequent as the sum of all the antecedents is to the sum of all the consequents. Let a : b = c : d = e :f Now ab = ab (1) and by Theorem I.
Side 192 - A sphere is a solid bounded by a surface all points of which are equally distant from a point within called the centre.
Side 108 - Two triangles having an angle of the one equal to an angle of the other are to each other as the products of the sides including the equal angles.
Side 146 - A STRAIGHT line is perpendicular to a plane, when it is perpendicular to every straight line which it meets in that plane.
Side 30 - In an isosceles triangle, the angles opposite the equal sides are equal.
Side 80 - In any proportion the terms are in proportion by Composition ; that is, the sum of the first two terms is to the first term as the sum of the last two terms is to the third term.
Side 79 - If the product of two quantities is equal to the product of two others, one pair may be made the extremes, and the other pair the means, of a proportion. Let ad = ос.
Side 148 - Equal oblique lines from a point to a plane meet the plane at equal distances from the foot of the perpendicular ; and of two unequal oblique lines the greater meets the plane at the greater distance from the foot of the perpendicular.