Plane Geometry: With Problems and ApplicationsAllyn and Bacon, 1910 - 280 páginas |
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Página vii
... CHAPTER III . Measurement of Straight Line - segments . Approximate Measurement Ratios of Line - segments Theorems on Proportional Segments . 112 114 116 Similar Polygons Computations by Means of Sines of Angles Problems vii.
... CHAPTER III . Measurement of Straight Line - segments . Approximate Measurement Ratios of Line - segments Theorems on Proportional Segments . 112 114 116 Similar Polygons Computations by Means of Sines of Angles Problems vii.
Página 114
... RATIOS OF LINE - SEGMENTS . 238. The ratio of two commensurable line - segments is the quotient of their numerical measures taken with respect to the same unit . E.g. if two segments are respectively 3 ft . and 4 ft . in length , the ratio ...
... RATIOS OF LINE - SEGMENTS . 238. The ratio of two commensurable line - segments is the quotient of their numerical measures taken with respect to the same unit . E.g. if two segments are respectively 3 ft . and 4 ft . in length , the ratio ...
Página 115
... ratio of two incommensurable line- segments is the quotient of their approximate numerical measures . It will be seen that this approximate ratio depends upon the length of the smallest measuring unit available , and that the ...
... ratio of two incommensurable line- segments is the quotient of their approximate numerical measures . It will be seen that this approximate ratio depends upon the length of the smallest measuring unit available , and that the ...
Página 116
... ratio . Four numbers , a , b , c , and d , are said to be in a C proportion , in the order given , if the ratios and are d equal . In this case a and care called the antecedents and b and d the consequents . Also a and d are called the ...
... ratio . Four numbers , a , b , c , and d , are said to be in a C proportion , in the order given , if the ratios and are d equal . In this case a and care called the antecedents and b and d the consequents . Also a and d are called the ...
Página 120
... ratio , it is parallel to the third side . Given the points D and E on the sides of the ABC such AD AE that DB EC To prove that DE || BC . Proof : Suppose DE ' is drawn paral- lel to BC . It is proposed to prove that the point E ...
... ratio , it is parallel to the third side . Given the points D and E on the sides of the ABC such AD AE that DB EC To prove that DE || BC . Proof : Suppose DE ' is drawn paral- lel to BC . It is proposed to prove that the point E ...
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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,