Elements of Geometry: Plane geometryAmerican Book Company, 1896 |
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Side 18
... centres describe arcs with equal radii intersecting at Z. Join PZ . This will be the required per- pendicular . [ This can be proved correct after reaching § 104. ] PROPOSITION VII . THEOREM 36. If two straight lines are 18 PLANE GEOMETRY.
... centres describe arcs with equal radii intersecting at Z. Join PZ . This will be the required per- pendicular . [ This can be proved correct after reaching § 104. ] PROPOSITION VII . THEOREM 36. If two straight lines are 18 PLANE GEOMETRY.
Side 73
... radii and the intercepted arc . SECTOR The angle between the radii is called the angle of the sector . These definitions are repeated from § 20 . 156. Def . - Concentric circles are circles which have BOOK II THE CIRCLE.
... radii and the intercepted arc . SECTOR The angle between the radii is called the angle of the sector . These definitions are repeated from § 20 . 156. Def . - Concentric circles are circles which have BOOK II THE CIRCLE.
Side 74
... radii are equal , and if their centres be made to coincide they will coincide throughout ; conversely , equal circles have equal radii . C ' I. GIVEN ― any two circles , C and C 74 PLANE GEOMETRY.
... radii are equal , and if their centres be made to coincide they will coincide throughout ; conversely , equal circles have equal radii . C ' I. GIVEN ― any two circles , C and C 74 PLANE GEOMETRY.
Side 75
... radii would be unequal , which is con- trary to the hypothesis . Ax . 10 Therefore , the circumferences coincide , and the circles coincide and are equal . Q. E. D. II . CONVERSELY : GIVEN TO PROVE two equal circles . their radii equal ...
... radii would be unequal , which is con- trary to the hypothesis . Ax . 10 Therefore , the circumferences coincide , and the circles coincide and are equal . Q. E. D. II . CONVERSELY : GIVEN TO PROVE two equal circles . their radii equal ...
Side 76
... radii of equal circles . ] Then the arc AB will coincide with the arc A'B ' , and is equal to it . II . CONVERSELY : GIVEN equal circles having equal arcs AB and A'B ' . TO PROVE the subtended angles O and O ' equal . $ 150 Q. E. D. ...
... radii of equal circles . ] Then the arc AB will coincide with the arc A'B ' , and is equal to it . II . CONVERSELY : GIVEN equal circles having equal arcs AB and A'B ' . TO PROVE the subtended angles O and O ' equal . $ 150 Q. E. D. ...
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Vanlige uttrykk og setninger
AC AC adjacent angles altitude angles of parallel apothem base and altitude bisector bisects centre chord circumference circumscribed circle coincide construct a square decagon Def.-The diagonals diameter distance divided draw drawn equally distant equilateral triangle Exercise.-If exterior angle external tangents figure Find the area given circle given line given point given square given straight line GIVEN TO PROVE given triangle Hence homologous sides hypotenuse included angle intersection isosceles triangle locus mean proportional middle points number of sides opposite sides parallel to BC parallelogram perpendicular Q. E. D. PROPOSITION quadrilateral radii ratio of similitude rect rectangle regular inscribed regular polygon respectively equal right angles right triangle secant segments similar polygons similar triangles square equivalent straight line joining tangent THEOREM third side triangle ABC triangle is equal triangle whose sides vertex vertices
Populære avsnitt
Side 248 - The area of a regular inscribed hexagon is a mean proportional between the areas of the inscribed and circumscribed equilateral triangles.
Side 215 - The areas of two regular polygons of the same number of sides are to each other as the squares of their radii or as the squares of their apothems.
Side 63 - To draw a straight line through a given point parallel to a given straight line. Let A be the given point, and BC the given straight line ; it is required to draw a straight line through the point A, parallel to the straight hue BC. In BC take any point D, and join AD; and at the point A, in the straight line AD, make (I.
Side 49 - If, from a point within a triangle, two straight lines are drawn to the extremities of either side, their sum will be less than the sum of the other two sides of the triangle.
Side 148 - In any obtuse triangle, the square of the side opposite the obtuse angle is equal to the sum of the squares of the other two sides, increased by twice the product of one of these sides and the projection of the other side upon it.
Side 47 - ... the third side of the first is greater than the third side of the second.
Side 149 - Sines that the bisector of an angle of a triangle divides the opposite side into parts proportional to the adjacent sides.
Side 47 - If two triangles have two sides of one equal respectively to two sides of the other...
Side 100 - At a given point in a straight line to erect a perpendicular to that line. Let AB be the straight line, and let c D be a given point in it.
Side 140 - If in a right triangle a perpendicular is drawn from the vertex of the right angle to the hypotenuse : I.