Elements of Plane and Solid GeometryGinn and Heath, 1877 - 398 σελίδες |
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Σελίδα 128
George Albert Wentworth. BOOK III . PROPORTIONAL LINES AND SIMILAR POLYGONS . ON THE THEORY OF PROPORTION . 245. DEF . The Terms of a ratio are the quantities com- pared . 246. DEF . The Antecedent of ... SIMILAR POLYGONS THEORY OF ...
George Albert Wentworth. BOOK III . PROPORTIONAL LINES AND SIMILAR POLYGONS . ON THE THEORY OF PROPORTION . 245. DEF . The Terms of a ratio are the quantities com- pared . 246. DEF . The Antecedent of ... SIMILAR POLYGONS THEORY OF ...
Σελίδα 142
... Similar Polygons are polygons which have their homologous angles equal and their homologous sides proportional . Homologous points , lines , and angles , in similar polygons , are points , lines , and angles similarly situated . ON SIMILAR ...
... Similar Polygons are polygons which have their homologous angles equal and their homologous sides proportional . Homologous points , lines , and angles , in similar polygons , are points , lines , and angles similarly situated . ON SIMILAR ...
Σελίδα 143
... similar . A ' A B ' CI E B H C In the ABC and A'B'C ' let & A , B , C be equal to A ' , B ' , C ' respectively . We are to prove AB : A'B ' = AC : A'C ' : = BC : B'C ' . Apply the △ A ... similar when SIMILAR POLYGONS . 143 SIMILAR POLYGONS.
... similar . A ' A B ' CI E B H C In the ABC and A'B'C ' let & A , B , C be equal to A ' , B ' , C ' respectively . We are to prove AB : A'B ' = AC : A'C ' : = BC : B'C ' . Apply the △ A ... similar when SIMILAR POLYGONS . 143 SIMILAR POLYGONS.
Σελίδα 144
... similar , ( two mutually equiangular are similar ) . = BC A B A E EH ' ( homologous sides of similar △ are proportional ) . § 70 § 70 Iden . $ 279 § 278 But Since A B BC A E EH = = 144 BOOK III . GEOMETRY .
... similar , ( two mutually equiangular are similar ) . = BC A B A E EH ' ( homologous sides of similar △ are proportional ) . § 70 § 70 Iden . $ 279 § 278 But Since A B BC A E EH = = 144 BOOK III . GEOMETRY .
Σελίδα 145
... similar to △ ABC . Q. E. D. 283. SCHOLIUM . The primary idea of similarity is likeness of form ; and the two ... similar . In the quadrilaterals R and R ' , the homologous angles are equal , but the sides are not proportional , and the ...
... similar to △ ABC . Q. E. D. 283. SCHOLIUM . The primary idea of similarity is likeness of form ; and the two ... similar . In the quadrilaterals R and R ' , the homologous angles are equal , but the sides are not proportional , and the ...
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Συχνά εμφανιζόμενοι όροι και φράσεις
AABC ABCD altitude arc A B axis base and altitude centre circle circumference circumscribed coincide conical surface COROLLARY cylinder denote diagonals diameter dihedral angle distance divided draw equal arcs equal respectively equally distant equiangular polygon equilateral equivalent frustum given point greater Hence homologous sides hypotenuse intersection isosceles lateral area lateral edges lateral faces Let A B line A B measured by arc middle point mutually equiangular number of sides parallelogram parallelopiped perimeter perpendicular plane MN prism prove pyramid Q. E. D. PROPOSITION quadrilateral radii radius equal ratio rectangles regular polygon right angles right triangle SCHOLIUM segment sides of equal similar polygons slant height sphere spherical angle spherical polygon spherical triangle square straight line drawn subtend surface symmetrical tangent tetrahedron THEOREM third side trihedral vertex vertices volume
Δημοφιλή αποσπάσματα
Σελίδα 40 - If two triangles have two angles of the one equal to two angles of the other, each to each, and one side equal to one side, viz.
Σελίδα 126 - To describe an isosceles triangle having each of the angles at the base double of the third angle.
Σελίδα 175 - Any two rectangles are to each other as the products of their bases by their altitudes.
Σελίδα 38 - Any side of a triangle is less than the sum of the other two sides.
Σελίδα 349 - A sphere is a solid bounded by a surface all points of which are equally distant from a point within called the centre.
Σελίδα 83 - A straight line perpendicular to a radius at its extremity is a tangent to the circle. Let MB be perpendicular to the radius OA at A.
Σελίδα 207 - To construct a parallelogram equivalent to a given square, and having the difference of its base and altitude equal to a given line.
Σελίδα 188 - In any triangle, the square of the side opposite an acute angle is equal to the sum of the squares of the other two sides diminished by twice the product of one of those sides and the projection of the other upon that side.
Σελίδα 146 - The areas of two triangles which have 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. A D A' Hyp. In triangles ABC and A'B'C', To prove AABC A A'B'C' A'B' x A'C ' Proof. Draw the altitudes BD and B'D'.
Σελίδα 134 - In a series of equal ratios, the sum of the antecedents is to the sum of the consequents as any antecedent is to its consequent. Let a: b = c: d — e :/= g: h.