Elementary Geometry: PlaneAmerican Book Company, 1903 - 358 σελίδες |
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Σελίδα x
... Multiples and Measures 242 Scale of Relation . 251 On the Notion of Ratio 252 Properties of Ratios 255 Properties of a Proportion 264 Two or More Proportions 267 BOOK V. - RATIOS OF LINES , POLYGONS , ETC. Similarly Divided Lines ...
... Multiples and Measures 242 Scale of Relation . 251 On the Notion of Ratio 252 Properties of Ratios 255 Properties of a Proportion 264 Two or More Proportions 267 BOOK V. - RATIOS OF LINES , POLYGONS , ETC. Similarly Divided Lines ...
Σελίδα 242
... multiple of 4. We may regard A itself as once A , and call it the first multiple of a . 3. Series of multiples . The magnitudes denoted by the symbols A , 2A , 3A , 4 A , ... NA , 242 ... may be thought of as formed by beginning with ...
... multiple of 4. We may regard A itself as once A , and call it the first multiple of a . 3. Series of multiples . The magnitudes denoted by the symbols A , 2A , 3A , 4 A , ... NA , 242 ... may be thought of as formed by beginning with ...
Σελίδα 243
... multiples of A. In considering the mutual relations of certain magnitudes , their series of mutiples will play an ... multiple , etc. , have definite meanings when applied to them . Thus , the number 3 has its series . of multiples ...
... multiples of A. In considering the mutual relations of certain magnitudes , their series of mutiples will play an ... multiple , etc. , have definite meanings when applied to them . Thus , the number 3 has its series . of multiples ...
Σελίδα 244
... multiple . If it should happen that some mul- tiple of A is also a multiple of B , then this is said to be a common multiple of A and B. It rarely happens that two geometrical magnitudes taken at random have a common multiple ; but if ...
... multiple . If it should happen that some mul- tiple of A is also a multiple of B , then this is said to be a common multiple of A and B. It rarely happens that two geometrical magnitudes taken at random have a common multiple ; but if ...
Σελίδα 245
... multiples and like measures . If there are any two given magnitudes ( not necessarily of the same kind ) , and if two multiples of them are formed by taking each of them the same number of times , then the two resulting magni- tudes are ...
... multiples and like measures . If there are any two given magnitudes ( not necessarily of the same kind ) , and if two multiples of them are formed by taking each of them the same number of times , then the two resulting magni- tudes are ...
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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.