Plane Geometry: With Problems and ApplicationsAllyn and Bacon, 1910 - 280 páginas |
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Página iv
... the content of the defini- tions and theorems . It is well known that pupils often study and recite definitions and theorems without really comprehending their meaning . It is sought to check this tendency iv PREFACE .
... the content of the defini- tions and theorems . It is well known that pupils often study and recite definitions and theorems without really comprehending their meaning . It is sought to check this tendency iv PREFACE .
Página v
... definitions only when they are to be used , and by imme- diately verifying both definitions and theorems in concrete cases . The figure on page 4 is the basis for a large number of questions of this type . For example , see § 25 , Ex ...
... definitions only when they are to be used , and by imme- diately verifying both definitions and theorems in concrete cases . The figure on page 4 is the basis for a large number of questions of this type . For example , see § 25 , Ex ...
Página viii
... Definitions and Proofs . 220 Loci Considerations 226 Problems and Applications 226 Further Data concerning Triangles 230 Problems and Applications 233 The Incommensurable Cases 238 Problems and Applications 245 Further Applications of ...
... Definitions and Proofs . 220 Loci Considerations 226 Problems and Applications 226 Further Data concerning Triangles 230 Problems and Applications 233 The Incommensurable Cases 238 Problems and Applications 245 Further Applications of ...
Página 1
... defined in a strictly logical sense . Their meaning is made clear by description and by con- crete illustrations like the following . 2. Certain portions of space are occupied by objects which we call physical solids , as , for instance ...
... defined in a strictly logical sense . Their meaning is made clear by description and by con- crete illustrations like the following . 2. Certain portions of space are occupied by objects which we call physical solids , as , for instance ...
Página 12
... definition see §§ 255 , 256 . Two figures are said to be equivalent or simply equal if they have the same size or magnitude . This is denoted by the symbol = , read is equivalent to or is equal to . Two figures are said to be congruent ...
... definition see §§ 255 , 256 . Two figures are said to be equivalent or simply equal if they have the same size or magnitude . This is denoted by the symbol = , read is equivalent to or is equal to . Two figures are said to be congruent ...
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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,