Syllabus of Plane Geometry: (corresponding to Euclid, Books I-VI) ...Macmillan & Company, 1876 - 58 sider |
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Side 21
... altitude are equal to those of the parallelogram . COR . 2. Parallelograms on equal bases and of equal altitude . are equal ; and of parallelograms of equal altitudes , that is the greater which has the greater base ; and also of ...
... altitude are equal to those of the parallelogram . COR . 2. Parallelograms on equal bases and of equal altitude . are equal ; and of parallelograms of equal altitudes , that is the greater which has the greater base ; and also of ...
Side 22
... altitude are equal to those of the triangle . COR . 1. Triangles on the same or equal bases and of equal altitude are equal . COR . 2. Equal triangles on the same or equal bases have equal altitudes . COR . 3. If two equal triangles ...
... altitude are equal to those of the triangle . COR . 1. Triangles on the same or equal bases and of equal altitude are equal . COR . 2. Equal triangles on the same or equal bases have equal altitudes . COR . 3. If two equal triangles ...
Side 48
... is parallel to the base of the triangle . [ From Theor . I by the Rule of Identity , since by Theor . 2 there is only one point of division of a given line in a given ratio . ] THEOR . 4. Rectangles of equal altitude are to one.
... is parallel to the base of the triangle . [ From Theor . I by the Rule of Identity , since by Theor . 2 there is only one point of division of a given line in a given ratio . ] THEOR . 4. Rectangles of equal altitude are to one.
Side 49
... altitude are to one another in the same ratio as their bases . [ Let AC , BC be two rectangles having the common side OC and their bases OA , OB on the same side of OC . In the line OAB indefinitely produced , take OM = m.OA and ON = n ...
... altitude are to one another in the same ratio as their bases . [ Let AC , BC be two rectangles having the common side OC and their bases OA , OB on the same side of OC . In the line OAB indefinitely produced , take OM = m.OA and ON = n ...
Side 57
... altitudes . THEOR . 15. Similar triangles are to one another in the duplicate ratio of their homologous sides . THEOR . 16. The areas of similar rectilineal figures are to one another in the duplicate ratio of their homologous sides ...
... altitudes . THEOR . 15. Similar triangles are to one another in the duplicate ratio of their homologous sides . THEOR . 16. The areas of similar rectilineal figures are to one another in the duplicate ratio of their homologous sides ...
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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.