Syllabus of Plane Geometry: (corresponding to Euclid, Books I-VI) ...Macmillan & Company, 1876 - 58 sider |
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Side 14
... pair of equal angles equal , then the triangles are identically equal , and of the sides those are equal which are opposite to equal angles . [ By Superposition and Theor . 9.1 THEOR . 18. Any two angles of a triangle are together less ...
... pair of equal angles equal , then the triangles are identically equal , and of the sides those are equal which are opposite to equal angles . [ By Superposition and Theor . 9.1 THEOR . 18. Any two angles of a triangle are together less ...
Side 15
... pair of opposite sides parallel . This figure is sometimes called a trapezoid . DEF . 37. A parallelogram is a quadrilateral whose opposite sides are parallel . DEF . 38. When a straight line intersects two other straight lines it makes ...
... pair of opposite sides parallel . This figure is sometimes called a trapezoid . DEF . 37. A parallelogram is a quadrilateral whose opposite sides are parallel . DEF . 38. When a straight line intersects two other straight lines it makes ...
Side 16
... pair of alternate angles equal , or a pair of corresponding angles equal , or a pair of interior angles on the same side supplementary ; then , in each case , the two pairs of alternate angles are equal , and the four pairs of ...
... pair of alternate angles equal , or a pair of corresponding angles equal , or a pair of interior angles on the same side supplementary ; then , in each case , the two pairs of alternate angles are equal , and the four pairs of ...
Side 20
... pair of straight lines parallel to the given line , at the given distance from it and on opposite sides of it . iii . The locus of a point equidistant from two given points is the straight line that bisects , at right angles , the line ...
... pair of straight lines parallel to the given line , at the given distance from it and on opposite sides of it . iii . The locus of a point equidistant from two given points is the straight line that bisects , at right angles , the line ...
Side 38
... pairs of magnitudes compared are both of the same kind they are denoted by letters taken from the early part of the alphabet , as A , B compared with C , D ; but where they are or may be of different kinds , from different parts of the ...
... pairs of magnitudes compared are both of the same kind they are denoted by letters taken from the early part of the alphabet , as A , B compared with C , D ; but where they are or may be of different kinds , from different parts of the ...
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Syllabus of Plane Geometry: (corresponding to Euclid, Books I-VI) ... Association for the improvement of geometrical teaching Uten tilgangsbegrensning - 1876 |
Vanlige uttrykk og setninger
adjacent angles adjoining sides angles are equal angles equal angles opposite antecedent bisects Book called centre circle a regular circumscribe conjugate angles consequent construct a triangle contrapositive diagonal distance divided internally equal altitude equal angles equal arcs equal circles equimultiples given angle given circle given point given ratio given rectilineal figure given straight line greater angle hypotenuse identically equal inscribe interior angles intersect lines are proportional locus middle point minor arcs multiple obtuse angle opposite angles parallel straight lines parallelogram perpendicular PLANE GEOMETRY point of contact point of division polygon PROB quadrilateral radii radius ratio compounded ratios are equal rectangle contained regular figures right angles Rule of Conversion Rule of Identity SECTION sector segments side opposite Similar rectilineal figures square straight angle straight line drawn straight line joining subtended Superposition SYLLABUS OF PLANE tangent THEOR Theorem triangles are identically vertex whence whole numbers
Populære avsnitt
Side 14 - If two triangles have two angles of the one equal to two angles of the other, each to each, and one side equal to one side, viz.
Side 17 - Assuming that 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...
Side 14 - Of all the straight lines that can be drawn to a given straight line from a given point outside it, the perpendicular is the shortest.
Side 13 - Any two sides of a triangle are together greater than the third side.
Side 23 - Iff a straight line be divided into any two parts, four times the rectangle contained by the whole line, and one of the parts, together with the square of the other part, is equal to the square of the straight line which is made up of the whole and that part.
Side 13 - If two triangles have the three sides of the one equal to the three sides of the other, each to each, the triangles are congruent.
Side 34 - If the distance between the centres of two circles is equal to the difference of their radii, the two circles will touch each other internally.
Side 56 - If three straight lines be proportionals, the rectangle contained by the extremes is equal to the square on the mean ; and conversely, if the rectangle contained by the extremes be equal to the square on the mean, the three straight lines are proportionals.
Side 28 - In the same circle, or in equal circles, equal arcs are subtended by equal chords : and conversely, equal chords subtend equal arcs.
Side 4 - The enunciation of a Theorem consists of two parts, — the hypothesis, or that which is assumed, and the conclusion, or that which is asserted to follow therefrom. Thus in the typical Theorem, If A is B, then C is D, (i), the hypothesis is that A is B, and the conclusion, that C is D.