Elementary Geometry: PlaneAmerican Book Company, 1903 - 358 σελίδες |
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Σελίδα 1
... extremity of two adjoining parts of a line is a fourth kind of space element , called a point . A point is not divisible into parts ; hence , the point is the simplest space element . 6. A fine tracing point , or a dot on a sheet of ...
... extremity of two adjoining parts of a line is a fourth kind of space element , called a point . A point is not divisible into parts ; hence , the point is the simplest space element . 6. A fine tracing point , or a dot on a sheet of ...
Σελίδα 4
... extremities of the two portions coincide . 17. It follows from this definition that if two straight lines pass through the same two points , the lines coincide , and may then be regarded as the same line . This may be conveniently ...
... extremities of the two portions coincide . 17. It follows from this definition that if two straight lines pass through the same two points , the lines coincide , and may then be regarded as the same line . This may be conveniently ...
Σελίδα 10
... extremity . Any two segments of the same straight line are called collinear segments . If two collinear segments have a common extremity , and are at opposite sides of this common point , they are called adjacent collinear segments ...
... extremity . Any two segments of the same straight line are called collinear segments . If two collinear segments have a common extremity , and are at opposite sides of this common point , they are called adjacent collinear segments ...
Σελίδα 11
... extremity . P E.g. , to compare the segments PQ and RS , take an indefinite line , and transfer PQ to the position AC , and RS to the posi- tion AB . Then they have a com- mon extremity 4. If the other two extremities B and C happen to ...
... extremity . P E.g. , to compare the segments PQ and RS , take an indefinite line , and transfer PQ to the position AC , and RS to the posi- tion AB . Then they have a com- mon extremity 4. If the other two extremities B and C happen to ...
Σελίδα 21
... extremity o from the position 04 through a perigon into the position OA again . Similarly let a line revolve about o ' from the position ' A ' through a perigon into the position ' A ' again . To prove that these perigons are equal ...
... extremity o from the position 04 through a perigon into the position OA again . Similarly let a line revolve about o ' from the position ' A ' through a perigon into the position ' A ' again . To prove that these perigons are equal ...
Άλλες εκδόσεις - Προβολή όλων
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.