Elements of Geometry |
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Page 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 ...
Page 9
... common vertex and a common side between them . Thus the angles CDE and CDF are adjacent angles . E Ꭰ C 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 Ꭰ C 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 ...
Page 15
... common ≤ O C A. Then - LOCB LACP . In like manner we may prove = LACO L P CB . 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 ≤ O C A. Then - LOCB LACP . In like manner we may prove = LACO L P CB . 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 ...
Page 16
... common ZOC A. Then = LOCF ZOC B. .. C B 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 ZOC A. Then = LOCF ZOC B. .. C B 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 ...
Page 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 ...
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Common terms and phrases
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
Popular passages
Page 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.
Page 126 - To describe an isosceles triangle having each of the angles at the base double of the third angle.
Page 136 - The first of four magnitudes is said to have the same ratio to the second which the third has to the fourth, when...
Page 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.
Page 202 - In any proportion, the product of the means is equal to the product of the extremes.
Page 142 - If a line divides two sides of a triangle proportionally, it is parallel to the third side.
Page 175 - Any two rectangles are to each other as the products of their bases by their altitudes.
Page 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.
Page 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.
Page 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'.