Plane GeometryGinn, 1899 - 256 sider |
Inni boken
Resultat 1-5 av 29
Side 20
... external point . A B D C Let AB be the given line , P the given external point , PC a perpen- dicular to AB from P , and PD any other line from P to AB . To prove that PD is not 1 to AB . Proof . Produce PC to P ' , making CP ' equal to ...
... external point . A B D C Let AB be the given line , P the given external point , PC a perpen- dicular to AB from P , and PD any other line from P to AB . To prove that PD is not 1 to AB . Proof . Produce PC to P ' , making CP ' equal to ...
Side 21
... external point . P -B Let AB be the given straight line , P the given point , PC the per- pendicular , and PD any other line drawn from P to AB . To prove that PC < PD . Proof . Produce PC to P ' , making CP ' = PC . Then Draw DP ' . PD ...
... external point . P -B Let AB be the given straight line , P the given point , PC the per- pendicular , and PD any other line drawn from P to AB . To prove that PC < PD . Proof . Produce PC to P ' , making CP ' = PC . Then Draw DP ' . PD ...
Side 24
... external point ) . .. AB and CD are parallel . $ 96 Q. E. D. 105. Axiom . Through a given point only one straight line can be drawn parallel to a given straight line . 106. COR . Two straight lines in the same plane parallel to a third ...
... external point ) . .. AB and CD are parallel . $ 96 Q. E. D. 105. Axiom . Through a given point only one straight line can be drawn parallel to a given straight line . 106. COR . Two straight lines in the same plane parallel to a third ...
Side 26
... external point ) . .. ZOCD coincides with ZOBA , and is equal to it , § 60 ( two angles are equal , if their vertices coincide and their sides coincide , each with each ) . 0. E. D. PROPOSITION XIII . THEOREM . 111. CONVERSELY : When ...
... external point ) . .. ZOCD coincides with ZOBA , and is equal to it , § 60 ( two angles are equal , if their vertices coincide and their sides coincide , each with each ) . 0. E. D. PROPOSITION XIII . THEOREM . 111. CONVERSELY : When ...
Side 69
... external segments are equal , the extremities of these segments will be equally distant from the extremities of the base , respectively . Α Ex . 46. If through any point in the bisector of an angle a line is drawn parallel to either of ...
... external segments are equal , the extremities of these segments will be equally distant from the extremities of the base , respectively . Α Ex . 46. If through any point in the bisector of an angle a line is drawn parallel to either of ...
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Vanlige uttrykk og setninger
AB² ABCD AC² acute angle adjacent angles altitude angles are equal apothem arc A'B base bisector bisects called centre chord circumference circumscribed circle coincide decagon diagonals diameter divide Draw equal circles equiangular equiangular polygon equidistant equilateral triangle exterior angle feet Find the area Find the locus given angle given circle given line given point given straight line given triangle greater Hence homologous sides hypotenuse inches inscribed regular intercepted intersecting isosceles trapezoid isosceles triangle legs limit line drawn median middle point number of sides parallelogram perimeter perpendicular plane PROBLEM Proof prove Q. E. D. PROPOSITION quadrilateral radii radius ratio rectangle regular hexagon regular inscribed regular polygon rhombus right angle right triangle secant segments straight angle supplementary tangent THEOREM third side trapezoid triangle ABC triangle is equal variable vertex
Populære avsnitt
Side 33 - The sum of two sides of a triangle is greater than the third side, and their difference is less than the third side.
Side 150 - If two triangles have an angle of the one equal to an angle of the other, and the including sides proportional, they are similar. In the triangles ABC and A'B'C', let ZA = Z A', and let AB : A'B' = AC : A'C'. To prove that the A ABC and A'B'C
Side 66 - If two triangles have two sides of the one equal respectively to two sides of the other, but the included angle of the first greater than the included angle of the second, then the third side of the first is greater than the third side of the second. Given A ABC and A'B'C...
Side 191 - 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. To prove that Proof. A Let the triangles ABC and ADE have the common angle A. A ABC -AB X AC Now and A ADE AD X AE Draw BE.
Side 169 - In any triangle the product of two sides is equal to the product of the diameter of the circumscribed circle by the altitude upon the third side.
Side 32 - After remarking that the mathematician positively knows that the sum of the three angles of a triangle is equal to two right angles...
Side 71 - The sum of the perpendiculars dropped from any point within an equilateral triangle to the three sides is constant, and equal to the altitude.
Side 156 - 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.
Side 75 - PERIPHERY of a circle is its entire bounding line ; or it is a curved line, all points of which are equally distant from a point within called the centre.
Side 162 - The sum of the squares of the two legs of a right triangle is equal to the square of the hypotenuse.