Elements of GeometryGinn, Heath, & Company, 1882 - 250 σελίδες |
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Σελίδα 8
... common . Conversely Two straight lines lying in the same plane which do not meet have the same direction ; for if they had different directions they would meet , which is contrary to the hypothesis that they do not meet . Two straight ...
... common . Conversely Two straight lines lying in the same plane which do not meet have the same direction ; for if they had different directions they would meet , which is contrary to the hypothesis that they do not meet . Two straight ...
Σελίδα 9
... common vertex and a common side between them . Thus the angles CDE and CDF are adjacent angles . E D A B C -F 25. DEF . A Right Angle is an angle included between two straight lines which meet each other so that the two adjacent angles ...
... common vertex and a common side between them . Thus the angles CDE and CDF are adjacent angles . E D A B C -F 25. DEF . A Right Angle is an angle included between two straight lines which meet each other so that the two adjacent angles ...
Σελίδα 15
... common ≤ OC A. Then LOCB = LACP . In like manner we may prove = LACO L P C B. Q. E. D. 50. COROLLARY . If two straight lines cut one another , the four angles which they make at the point of intersection are together equal to four ...
... common ≤ OC A. Then LOCB = LACP . In like manner we may prove = LACO L P C B. Q. E. D. 50. COROLLARY . If two straight lines cut one another , the four angles which they make at the point of intersection are together equal to four ...
Σελίδα 16
... common Z O CA. Then = LOCF LOC B. .. CB and C F coincide , and cannot form two lines as rep- resented in the figure . .. A C and C B are in the same straight line . Q. E. D. PROPOSITION III . THEOREM . 52. A perpendicular measures the ...
... common Z O CA. Then = LOCF LOC B. .. CB and C F coincide , and cannot form two lines as rep- resented in the figure . .. A C and C B are in the same straight line . Q. E. D. PROPOSITION III . THEOREM . 52. A perpendicular measures the ...
Σελίδα 23
... common property . Thus , the perpendicular erected at the middle of a straight line is the locus of all points equally distant from the extremi- ties of that straight line . 60. SCHOLIUM . Since two points determine the position of a ...
... common property . Thus , the perpendicular erected at the middle of a straight line is the locus of all points equally distant from the extremi- ties of that straight line . 60. SCHOLIUM . Since two points determine the position of a ...
Άλλες εκδόσεις - Προβολή όλων
Συχνά εμφανιζόμενοι όροι και φράσεις
A B C D AABC AACB ABCD adjacent angles apothem arc A B base and altitude centre centre of symmetry chord circumscribed coincide construct a square COROLLARY decagon describe an arc 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 hexagon homologous sides hypotenuse 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 square equivalent 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 124 - To describe an isosceles triangle having each of the angles at the base double of the third angle.
Σελίδα 201 - In any proportion, the product of the means is equal to the product of the extremes.
Σελίδα 173 - Any two rectangles are to each other as the products of their bases by their altitudes.
Σελίδα 185 - In any obtuse triangle, the square of the side opposite the obtuse angle is equal to the sum of the squares of the other...
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 41 - The exterior angle of a triangle is equal to the sum of the two opposite interior angles.
Σελίδα 140 - If a line divides two sides of a triangle proportionally, it is parallel to the third side.
Σελίδα 113 - From A as a centre, with a radius equal to o, describe an arc ; and from B as a centre, with a radius equal to m, describe an arc intersecting the former arc at С.
Σελίδα 155 - 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.