Elements of GeometryGinn and Heath, 1881 - 250 σελίδες |
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Σελίδα 9
... included between two straight lines which meet each other so that the two adjacent angles formed by producing one of the lines through the vertex are equal . Thus if the straight line AB meet the straight line CD so that the adjacent ...
... included between two straight lines which meet each other so that the two adjacent angles formed by producing one of the lines through the vertex are equal . Thus if the straight line AB meet the straight line CD so that the adjacent ...
Σελίδα 19
... included by them . C E A B Let CA and C B be two lines drawn from the point C to the extremities of the straight line A B. Let O A and O B be two lines similarly drawn , but included by CA and C B. We are to prove CA + C B > O A + O B ...
... included by them . C E A B Let CA and C B be two lines drawn from the point C to the extremities of the straight line A B. Let O A and O B be two lines similarly drawn , but included by CA and C B. We are to prove CA + C B > O A + O B ...
Σελίδα 20
... included by them ) ; ..2 CH 2 CK ; ..CH > CK . Q. E. D. 56. COROLLARY . Only two equal straight lines can be drawn from a point to a straight line ; and of two unequal lines , the greater cuts off the greater distance from the foot of ...
... included by them ) ; ..2 CH 2 CK ; ..CH > CK . Q. E. D. 56. COROLLARY . Only two equal straight lines can be drawn from a point to a straight line ; and of two unequal lines , the greater cuts off the greater distance from the foot of ...
Σελίδα 42
... included angle of the one are equal respectively to two sides and the included angle of the other . C C ' A B A In the triangles A B C and A'B'C ' , let A B = A CA ' C ' , ZA ZA ' . We are to prove AABC = · Δ Α ' Β ' Γ ' . B = A ' B ...
... included angle of the one are equal respectively to two sides and the included angle of the other . C C ' A B A In the triangles A B C and A'B'C ' , let A B = A CA ' C ' , ZA ZA ' . We are to prove AABC = · Δ Α ' Β ' Γ ' . B = A ' B ...
Σελίδα 47
... included respectively to two sides and the included = .. LA LB , ( being homologous △ of equal △ ) . Hyp . Iden . Cons . § 106 of the one are equal of the other ) . Q. E. D. Ex . If the equal sides of an isosceles triangle be produced ...
... included respectively to two sides and the included = .. LA LB , ( being homologous △ of equal △ ) . Hyp . Iden . Cons . § 106 of the one are equal of the other ) . Q. E. D. Ex . If the equal sides of an isosceles triangle be produced ...
Άλλες εκδόσεις - Προβολή όλων
Συχνά εμφανιζόμενοι όροι και φράσεις
A B C D AABC AACB AB² ABCD adjacent angles apothem arc A B base and altitude BC² centre centre of symmetry circumference circumscribed construct a square COROLLARY decagon diagonals diameter divided Draw equal arcs equal distances equal respectively equiangular equiangular polygon equilateral equilateral polygon exterior angles figure given circle given line given polygon given square homologous sides hypotenuse intersecting isosceles Let A B Let ABC line A B measured by arc middle point number of sides parallelogram perpendicular plane polygon ABC polygon similar PROBLEM prove Q. E. D. PROPOSITION quadrilateral radii radius equal ratio rect rectangles regular inscribed regular polygon required to construct right angles right triangle SCHOLIUM segment semicircle similar polygons subtend symmetrical with respect tangent THEOREM triangle ABC vertex vertices
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 136 - The first of four magnitudes is said to have the same ratio to the second which the third has to the fourth, when...
Σελίδα 207 - Construct a rectangle having the difference of its base and altitude equal to a given line, and its area equivalent to the sum of a given triangle and a given pentagon.
Σελίδα 202 - In any proportion, the product of the means is equal to the product of the extremes.
Σελίδα 142 - If a line divides two sides of a triangle proportionally, it is parallel to the third side.
Σελίδα 175 - Any two rectangles are to each other as the products of their bases by their altitudes.
Σελίδα 72 - Every point in the bisector of an angle is equally distant from the sides of the angle ; and every point not in the bisector, but within the angle, is unequally distant from the sides of the angle.
Σελίδα 73 - A 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.
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'.