Plane Geometry: With Problems and ApplicationsAllyn and Bacon, 1910 - 280 páginas |
Dentro del libro
Resultados 1-5 de 24
Página 30
... hypothesis and conclusion . In a geometrical theorem , the hypothesis specifies cer- tain properties which the figures in question are assumed to possess . The conclusion asserts that certain other prop- erties belong to the figures ...
... hypothesis and conclusion . In a geometrical theorem , the hypothesis specifies cer- tain properties which the figures in question are assumed to possess . The conclusion asserts that certain other prop- erties belong to the figures ...
Página 31
... . ax . , axiom . th . , theorem . def . , definition . cor . , corollary . alt . , alternate . ext . , exterior . int . , interior . hyp . , by hypothesis . INEQUALITIES OF PARTS OF TRIANGLES . 81. Definition . If RECTILINEAR FIGURES . 31.
... . ax . , axiom . th . , theorem . def . , definition . cor . , corollary . alt . , alternate . ext . , exterior . int . , interior . hyp . , by hypothesis . INEQUALITIES OF PARTS OF TRIANGLES . 81. Definition . If RECTILINEAR FIGURES . 31.
Página 34
... hypothesis that ∠ B > ∠ A. And it cannot be true that b < a , for in that case ∠ B < ∠A , contrary to the hypothesis . Hence it follows that b > a . ( § 84 ) 86. The above argument is called proof by exclusion . 34 PLANE GEOMETRY .
... hypothesis that ∠ B > ∠ A. And it cannot be true that b < a , for in that case ∠ B < ∠A , contrary to the hypothesis . Hence it follows that b > a . ( § 84 ) 86. The above argument is called proof by exclusion . 34 PLANE GEOMETRY .
Página 38
... hypothesis 12 || 11 and thus we have through P two lines parallel to 11 , which is contrary to Ax . VIII . Therefore , the supposition that 2 is not equal to 21 leads to a contradiction , and hence ∠1 = ∠ 2 . 98. Compare this theorem ...
... hypothesis 12 || 11 and thus we have through P two lines parallel to 11 , which is contrary to Ax . VIII . Therefore , the supposition that 2 is not equal to 21 leads to a contradiction , and hence ∠1 = ∠ 2 . 98. Compare this theorem ...
Página 45
... hypothesis that AC > A'C ' , show that two of the three following statements are impossible : ( 1 ) ∠B = ∠B ' ; ( 2 ) ∠B < ∠B ' ; ( 3 ) ∠ B > ∠B ' . See § 86 . 119. Axiom IX . If a , b , c RECTILINEAR FIGURES . 45.
... hypothesis that AC > A'C ' , show that two of the three following statements are impossible : ( 1 ) ∠B = ∠B ' ; ( 2 ) ∠B < ∠B ' ; ( 3 ) ∠ B > ∠B ' . See § 86 . 119. Axiom IX . If a , b , c RECTILINEAR FIGURES . 45.
Otras ediciones - Ver todas
Términos y frases comunes
ABCD acute angle adjacent angles altitude angle formed angles are equal apothem axes of symmetry axioms base bisects called central angle chord circle tangent circumscribed coincide congruent corresponding sides Definition diagonal diameter distance divided dodecagon Draw drawn equal angles equal circles equiangular equilateral triangle EXERCISES exterior angle figure Find the area Find the locus Find the radius fixed point geometric Give the proof given point given segment given triangle Hence hypotenuse hypothesis inches inscribed intersection isosceles trapezoid isosceles triangle l₁ length line-segment measure meet middle points number of sides Outline of Proof parallel lines parallelogram perigon perimeter plane proof in full quadrilateral radii ratio rectangle regular hexagon regular octagon regular polygon rhombus right angles right triangle secant semicircle Show shown square straight angle straight line subtend SUGGESTION THEOREM trapezoid triangle ABC vertex vertices width
Pasajes populares
Página 223 - If two triangles have two sides of the one equal to two sides of the other...
Página 41 - An exterior angle of a triangle is equal to the sum of the two opposite interior angles.
Página 121 - Sines that the bisector of an angle of a triangle divides the opposite side into parts proportional to the adjacent sides.
Página 60 - 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.
Página 182 - 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.
Página 161 - The formula states that the square of the hypotenuse of a right triangle is equal to the sum of the squares of the base and altitude.
Página 227 - Find the locus of a point such that the difference of the squares of its distances from two fixed points is a constant.
Página 210 - The area of a rectangle is equal to the product of its base and altitude.
Página 31 - Kuclid divided unproved propositions into two classes: axioms, or "common notions," which are true of all things, such as, " If things are equal to the same thing they are equal to each other"; and postulates, which apply only to geometry, such as,