Elementary Geometry: PlaneAmerican Book Company, 1903 - 358 σελίδες |
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Αποτελέσματα 1 - 5 από τα 25.
Σελίδα 8
... contain implied agreements that the thing defined shall be regarded as existing . These implied agreements are called postulates of existence . Thus by means of the definitions we have postulated the existence of points , lines , and ...
... contain implied agreements that the thing defined shall be regarded as existing . These implied agreements are called postulates of existence . Thus by means of the definitions we have postulated the existence of points , lines , and ...
Σελίδα 87
... contain an angle equal to 4 . Construct the triangle ABD having AB equal to a , AD equal to d , and the included angle DAB equal to △ ( 133 ) . Next on BD construct the triangle BCD having BC equal to b , and CD equal to c ( 132 ) . -7 ...
... contain an angle equal to 4 . Construct the triangle ABD having AB equal to a , AD equal to d , and the included angle DAB equal to △ ( 133 ) . Next on BD construct the triangle BCD having BC equal to b , and CD equal to c ( 132 ) . -7 ...
Σελίδα 115
... contained by the two given intersecting lines . Synthesis . It has now been proved that every point which satisfies the prescribed condition lies on one or other of the two angle - bisectors . It will next be proved conversely that ...
... contained by the two given intersecting lines . Synthesis . It has now been proved that every point which satisfies the prescribed condition lies on one or other of the two angle - bisectors . It will next be proved conversely that ...
Σελίδα 122
... contain an angle equal to an exterior angle of the triangle . 6. The lines joining the adjacent extremities of unequal and paral- lel lines will meet if prolonged through the extremities of the shorter parallel ( 124 ) . 7. Construct a ...
... contain an angle equal to an exterior angle of the triangle . 6. The lines joining the adjacent extremities of unequal and paral- lel lines will meet if prolonged through the extremities of the shorter parallel ( 124 ) . 7. Construct a ...
Σελίδα 138
... contained by the whole lines is equiv- alent to the sum of all the rectangles contained by each part of one and each part of the other . [ Prove by repeated applications of 39 ; or else by an independent figure . ] NOTE . This important ...
... contained by the whole lines is equiv- alent to the sum of all the rectangles contained by each part of one and each part of the other . [ Prove by repeated applications of 39 ; or else by an independent figure . ] NOTE . This important ...
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.