Syllabus of Plane Geometry: (corresponding to Euclid, Books I-VI) ...Macmillan & Company, 1876 - 58 sider |
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Side 5
... true , and of the conclusions that no two can be true at the same time , then the converse of every Theorem of the group will necessarily be true . OBS . The simplest example of such a group is presented when a Theorem and its obverse ...
... true , and of the conclusions that no two can be true at the same time , then the converse of every Theorem of the group will necessarily be true . OBS . The simplest example of such a group is presented when a Theorem and its obverse ...
Side 6
... true . Rule of Identity . If there is but one A , and but one B ; then from the fact that A is B it necessarily follows that B is A. OBS . This rule may be frequently applied with great ad- vantage in the demonstration of the converse ...
... true . Rule of Identity . If there is but one A , and but one B ; then from the fact that A is B it necessarily follows that B is A. OBS . This rule may be frequently applied with great ad- vantage in the demonstration of the converse ...
Side 41
... true of the multiples of X and Y , the multiples of A are distributed among those of B as the multiples of X among those of Y. ] THEOR . 2. If two ratios are equal , as the antecedent of the first is greater than , equal to , or less ...
... true of the multiples of X and Y , the multiples of A are distributed among those of B as the multiples of X among those of Y. ] THEOR . 2. If two ratios are equal , as the antecedent of the first is greater than , equal to , or less ...
Side 42
... , and so also C : A > C : B. Hence the proposition is proved . ] COR . The converses of both parts of the proposition are true , since the " Rule of Conversion " is applicable . THEOR . 5. The ratio of equimultiples of two magnitudes.
... , and so also C : A > C : B. Hence the proposition is proved . ] COR . The converses of both parts of the proposition are true , since the " Rule of Conversion " is applicable . THEOR . 5. The ratio of equimultiples of two magnitudes.
Side 44
... true for all values of m and n , AC B D. ] THEOR . 9. If any number of magnitudes of the same kind be proportionals , as one of the antecedents is to its consequent , so shall the sum of the antecedents be to the sum of the consequents ...
... true for all values of m and n , AC B D. ] THEOR . 9. If any number of magnitudes of the same kind be proportionals , as one of the antecedents is to its consequent , so shall the sum of the antecedents be to the sum of the consequents ...
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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.