Elements of Geometry |
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Page vi
... line and angle named . He should be encouraged , in reviewing each Book , to do the original exercises ; to state ... a b as a limit ; if , however , x decrease and approach zero as a limit , the area of the rectangle decreases and ...
... line and angle named . He should be encouraged , in reviewing each Book , to do the original exercises ; to state ... a b as a limit ; if , however , x decrease and approach zero as a limit , the area of the rectangle decreases and ...
Page 4
... lines as having position , but no extent . DEFINITIONS . 1. DEF . Space or ... line may be conceived as traced or generated by a point in motion . 4. DEF ... A B , BD , DC , and AC will generate the sur- faces AF , BH , DK , and AK ...
... lines as having position , but no extent . DEFINITIONS . 1. DEF . Space or ... line may be conceived as traced or generated by a point in motion . 4. DEF ... A B , BD , DC , and AC will generate the sur- faces AF , BH , DK , and AK ...
Page 7
... line , as A B , A B , has two opposite directions , namely from A toward B , which is expressed by say- ing line AB , and from B toward A , which is expressed by saying line B A. В с 20. If a straight line change its magnitude , it must ...
... line , as A B , A B , has two opposite directions , namely from A toward B , which is expressed by say- ing line AB , and from B toward A , which is expressed by saying line B A. В с 20. If a straight line change its magnitude , it must ...
Page 9
... 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 angles ABC and ABD are equal to ...
... 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 angles ABC and ABD are equal to ...
Page 12
... AB , we shall have one continuous straight line AD equal to the sum of the lines A B and C D. : Again if we have the angles ABC and DEF , by placing the vertex B on E and the side BC in the direction of ED , the angle ABC will take the ...
... AB , we shall have one continuous straight line AD equal to the sum of the lines A B and C D. : Again if we have the angles ABC and DEF , by placing the vertex B on E and the side BC in the direction of ED , the angle ABC will take the ...
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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'.