Syllabus of Plane Geometry: (corresponding to Euclid, Books I-VI) ...Macmillan & Company, 1876 - 58 sider |
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Side 5
... former are true ; consequently it will never be necessary to demon- strate geometrically more than two of the four Theorems , care being taken that the two selected are not contrapositive each of the other . Rule of Conversion . If of ...
... former are true ; consequently it will never be necessary to demon- strate geometrically more than two of the four Theorems , care being taken that the two selected are not contrapositive each of the other . Rule of Conversion . If of ...
Side 15
... former case the triangles are identically equal . [ By Superposition . ] COR . Two such triangles are identically equal ( 1 ) If the two angles given equal are right angles or obtuse angles . ( 2 ) If the angles opposite to the other ...
... former case the triangles are identically equal . [ By Superposition . ] COR . Two such triangles are identically equal ( 1 ) If the two angles given equal are right angles or obtuse angles . ( 2 ) If the angles opposite to the other ...
Side 16
... former . THEOR . 21. If a straight line intersects two other straight lines and makes the alternate angles equal , the straight lines are parallel . [ Contrapositive of Theor . 9. ] THEOR . 22. If two straight lines are parallel , and ...
... former . THEOR . 21. If a straight line intersects two other straight lines and makes the alternate angles equal , the straight lines are parallel . [ Contrapositive of Theor . 9. ] THEOR . 22. If two straight lines are parallel , and ...
Side 28
... former are called semicircles ; and the latter are called quadrants . THEOR . 3. In the same circle , or in equal circles , equal arcs subtend equal angles at the centre , and of two un- equal arcs the greater subtends the greater angle ...
... former are called semicircles ; and the latter are called quadrants . THEOR . 3. In the same circle , or in equal circles , equal arcs subtend equal angles at the centre , and of two un- equal arcs the greater subtends the greater angle ...
Side 38
... former contains the latter an exact number of times . According as the number of times is 1 , 2 , 3 ... m , so is the multiple said to be the 1st , 2nd , 3rd , ... mth . A SYLLABUS OF PLANE GEOMETRY . 39 DEF . 2. Of Ratio and Proportion.
... former contains the latter an exact number of times . According as the number of times is 1 , 2 , 3 ... m , so is the multiple said to be the 1st , 2nd , 3rd , ... mth . A SYLLABUS OF PLANE GEOMETRY . 39 DEF . 2. Of Ratio and Proportion.
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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.