Syllabus of Plane Geometry: (corresponding to Euclid, Books I-VI) ...Macmillan & Company, 1876 - 58 σελίδες |
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Σελίδα 38
... 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 alphabet , as A , B compared with P , Q or X , Y ...
... 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 alphabet , as A , B compared with P , Q or X , Y ...
Σελίδα 39
... kind is the relation of the former to the latter in respect of quantuplicity . The ratio of A to B is denoted thus A : B , and A is called the antecedent of the ratio , B the consequent . The quantuplicity of A with respect to B may be ...
... kind is the relation of the former to the latter in respect of quantuplicity . The ratio of A to B is denoted thus A : B , and A is called the antecedent of the ratio , B the consequent . The quantuplicity of A with respect to B may be ...
Σελίδα 41
... kind are said to be proportionals , when the ratio of the first to the second is equal to that of the second to the third that is when A : B :: B : C. In this case C is said to be the third proportional to A and B , and B the mean ...
... kind are said to be proportionals , when the ratio of the first to the second is equal to that of the second to the third that is when A : B :: B : C. In this case C is said to be the third proportional to A and B , and B the mean ...
Σελίδα 42
... kind , then A : C > or < B : C , as A > = = or < B and C : A > or < C : B , as A < = or > B. If A = B , it follows directly from Def . 4 that A : C :: B : C and C : A :: B : A. If A > B , m can be found such that mB is less than mA by a ...
... kind , then A : C > or < B : C , as A > = = or < B and C : A > or < C : B , as A < = or > B. If A = B , it follows directly from Def . 4 that A : C :: B : C and C : A :: B : A. If A > B , m can be found such that mB is less than mA by a ...
Σελίδα 43
... kind be proportionals , the first will be greater than , equal to , or less than the third , according as the second is greater than , equal to , or less than the fourth . [ Let A B C : D. : Then if A = C , A : B :: C : B , and ...
... kind be proportionals , the first will be greater than , equal to , or less than the third , according as the second is greater than , equal to , or less than the fourth . [ Let A B C : D. : Then if A = C , A : B :: C : B , and ...
Άλλες εκδόσεις - Προβολή όλων
Συχνά εμφανιζόμενοι όροι και φράσεις
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
Δημοφιλή αποσπάσματα
Σελίδα 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.
Σελίδα 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...
Σελίδα 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.
Σελίδα 13 - Any two sides of a triangle are together greater than the third side.
Σελίδα 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.
Σελίδα 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.
Σελίδα 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.
Σελίδα 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.
Σελίδα 28 - In the same circle, or in equal circles, equal arcs are subtended by equal chords : and conversely, equal chords subtend equal arcs.
Σελίδα 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.