Elementary Geometry: PlaneAmerican Book Company, 1903 - 358 σελίδες |
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Αποτελέσματα 1 - 5 από τα 40.
Σελίδα vi
... measures until he has learned that geometry can be developed independently of it altogether . For this notion is ... measure- numbers are introduced as a natural outgrowth from the general notion of ratio , and the irrational numbers ...
... measures until he has learned that geometry can be developed independently of it altogether . For this notion is ... measure- numbers are introduced as a natural outgrowth from the general notion of ratio , and the irrational numbers ...
Σελίδα vii
... measurement of the circle is based on the cor- rect definition of the length of a curved line ( in terms of a straight measuring - unit ) given by the best continental writers . Here the idea of a limit is imbedded in the defi- nition ...
... measurement of the circle is based on the cor- rect definition of the length of a curved line ( in terms of a straight measuring - unit ) given by the best continental writers . Here the idea of a limit is imbedded in the defi- nition ...
Σελίδα x
... Measures 242 Scale of Relation . 251 On the Notion of Ratio 252 Properties of Ratios 255 Properties of a Proportion 264 Two or ... Measure - number 332 334 Measurement of Rectangles . Directed Lines 337 339 • Measurement of Triangles 341 ...
... Measures 242 Scale of Relation . 251 On the Notion of Ratio 252 Properties of Ratios 255 Properties of a Proportion 264 Two or ... Measure - number 332 334 Measurement of Rectangles . Directed Lines 337 339 • Measurement of Triangles 341 ...
Σελίδα 242
... MEASURES DEFINITIONS 2. Multiples . If any number of equivalent magnitudes are added together , then their sum is called a multiple of any one of them . If any magnitude P is equivalent to the sum of n magni- tudes each equivalent to 4 ...
... MEASURES DEFINITIONS 2. Multiples . If any number of equivalent magnitudes are added together , then their sum is called a multiple of any one of them . If any magnitude P is equivalent to the sum of n magni- tudes each equivalent to 4 ...
Σελίδα 243
... , ... , pn , .... Any two natural numbers are magnitudes of the same kind , since they , or any of their multiples , are directly comparable . When any two magnitudes are mentioned together , they are MULTIPLES AND MEASURES 243.
... , ... , pn , .... Any two natural numbers are magnitudes of the same kind , since they , or any of their multiples , are directly comparable . When any two magnitudes are mentioned together , they are MULTIPLES AND MEASURES 243.
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Συχνά εμφανιζόμενοι όροι και φράσεις
ABCD adjacent sides angle AOB angle equal angles are equal antecedents apothem base bisector bisects called central angle central line chord circumscribed circles coincide contraposite corresponding sides Definition diagonal difference divided Draw drawn equal angles equal circles equal ratios equiangular equilateral polygon equivalent figure geometry given angle given circle given line given point given polygon given ratio greater half Hence hypotenuse hypothesis inscribed interior angles intersect isosceles triangle less Let ABC line joining line-segment magnitudes measure-number mid-point mth multiple n-gon number of sides number-correspondent opposite sides parallel parallelogram perigon perimeter perpendicular PROBLEM prolonged prove quadrangle radii radius ratio compounded ratio of similitude regular polygons respectively equal rhombus right angle right triangle segments Show similar polygons similar triangles Similarly solution statement straight angle straight line subtended superposable 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.