Elementary Geometry: PlaneAmerican Book Company, 1903 - 358 σελίδες |
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Σελίδα 32
... Outline . On an indefinite line lay off OA , OB , OC , equal tively to the given lines . Then by hypothesis AB and BC are Take CD equal to OA . Prove OD equal to double OB . Bisection of angle . 73. PROBLEM 4. To bisect a given angle ...
... Outline . On an indefinite line lay off OA , OB , OC , equal tively to the given lines . Then by hypothesis AB and BC are Take CD equal to OA . Prove OD equal to double OB . Bisection of angle . 73. PROBLEM 4. To bisect a given angle ...
Σελίδα 33
... Outline proof . Suppose , if possible , that OQ is a second perpendicular . Prolong OP , making PN equal to OP . Join NQ . Prove that the angles OQP and NQP are equal ; and that OQN is a straight line ( 52 ) . Show the absurdity from ...
... Outline proof . Suppose , if possible , that OQ is a second perpendicular . Prolong OP , making PN equal to OP . Join NQ . Prove that the angles OQP and NQP are equal ; and that OQN is a straight line ( 52 ) . Show the absurdity from ...
Σελίδα 35
... greater than BAC ; hence the vertically opposite angle CBD is also greater than BAC . Therefore the exterior angle CBD is greater than either of the interior and opposite angles . 80. Cor . straight angle . Outline . The sum TRIANGLES 35.
... greater than BAC ; hence the vertically opposite angle CBD is also greater than BAC . Therefore the exterior angle CBD is greater than either of the interior and opposite angles . 80. Cor . straight angle . Outline . The sum TRIANGLES 35.
Σελίδα 36
Plane James McMahon. 80. Cor . straight angle . Outline . The sum of two angles of a triangle is less than a Prove the sum of CAB and CBA less than the sum of CBD and CBA . Ex . If a triangle has one right angle or obtuse angle , its ...
Plane James McMahon. 80. Cor . straight angle . Outline . The sum of two angles of a triangle is less than a Prove the sum of CAB and CBA less than the sum of CBD and CBA . Ex . If a triangle has one right angle or obtuse angle , its ...
Σελίδα 55
... Outline . Use problem 7 ( Art . 77 ) , and prove by theorem 21 ( Art . 112 ) . 115. NOTE . This solution establishes the actual existence of parallel straight lines . It shows that there is at least one line pass- ing through a given ...
... Outline . Use problem 7 ( Art . 77 ) , and prove by theorem 21 ( Art . 112 ) . 115. NOTE . This solution establishes the actual existence of parallel straight lines . It shows that there is at least one line pass- ing through a given ...
Άλλες εκδόσεις - Προβολή όλων
Συχνά εμφανιζόμενοι όροι και φράσεις
ABCD adjacent sides altitude angle AOB angle equal angles are equal antecedents apothem base bisector bisects called central angle central line chord circumscribed circles coincide common point construct Definition diagonal difference divided Draw drawn equal angles equal circles equiangular equilateral polygon equivalent figure given angle given circle given line given number given point given ratio greater half Hence hypotenuse included angle inscribe a regular interior angles intersect isosceles triangle less Let ABC line joining magnitudes measure-number meet the circle mid-point minor arc mth multiple n-gon number of sides number-correspondent opposite sides pair parallel parallelogram perigon perimeter perpendicular PROBLEM prolonged prove quadrangle radii radius ratio compounded rectangle regular polygon respectively equal rhombus right angle right triangle segments Show similar polygons Similarly solution statement straight angle straight line subtended surface symmetric tangent THEOREM triangle ABC unequal vertex vertical angle
Δημοφιλή αποσπάσματα
Σελίδα 148 - In every triangle, the square on the side subtending an acute angle is less than the sum of the squares on the sides containing that angle, by twice the rectangle contained by either of these sides, and the straight line intercepted between the perpendicular let fall on it from the opposite angle, and the acute angle.
Σελίδα 147 - In an obtuse-angled triangle the square on the side opposite the obtuse angle is greater than the sum of the squares on the other two sides by twice the rectangle contained by either side and the projection on it of the other side.
Σελίδα 5 - LET it be granted that a straight line may be drawn from any one point to any other point.
Σελίδα 38 - When two triangles have two sides of the one respectively equal to two sides of the other, and the included angles unequal, the third side in that triangle which has the greater angle, is greater than in the other.
Σελίδα 136 - If a straight line be divided into any two parts, the square on the whole line is...
Σελίδα 195 - UPON a given straight line to describe a segment of a circle containing an angle equal to a given rectilineal angle.
Σελίδα 80 - The straight line joining the middle points of two sides of a triangle is parallel to the third side and equal to half of it 46 INTERCEPTS BY PARALLEL LINES.
Σελίδα 263 - If four magnitudes of the same kind be proportionals, they shall also be proportionals when taken alternately. Let A, B, C, D be four magnitudes of the same kind, which are proportionals, viz.
Σελίδα 307 - 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. D c A' D' Hyp. In triangles ABC and A'B'C', ZA = ZA'. To prove AABC = ABxAC. A A'B'C' A'B'xA'C' Proof. Draw the altitudes BD and B'D'.
Σελίδα 287 - ... they have an angle of one equal to an angle of the other and the including sides are proportional; (c) their sides are respectively proportional.