The elements of plane geometry, Τόμος 1 |
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Αποτελέσματα 1 - 5 από τα 14.
Σελίδα 7
... Definitions . Axioms . Postulates BOOK II . Equality of Areas . Section I. Theorems Section II . Problems Definitions . PAGE 9 11 16 24 49 69 84 94 • ΙΟΙ 126 138 SYLLABUS OF GEOMETRICAL CONSTRUCTIONS . [ NOTE . - The.
... Definitions . Axioms . Postulates BOOK II . Equality of Areas . Section I. Theorems Section II . Problems Definitions . PAGE 9 11 16 24 49 69 84 94 • ΙΟΙ 126 138 SYLLABUS OF GEOMETRICAL CONSTRUCTIONS . [ NOTE . - The.
Σελίδα 11
... theorems . The Associ- ation think that at first all the steps by which any theorem is demonstrated should be carefully gone through by the student , rather than that its truth should be inferred from the logical rules here laid down ...
... theorems . The Associ- ation think that at first all the steps by which any theorem is demonstrated should be carefully gone through by the student , rather than that its truth should be inferred from the logical rules here laid down ...
Σελίδα 12
... Theorem , If A is B , then C is D , ( i ) , the hypothesis is that A is B , and the conclusion , that C is D. From this Theorem it necessarily follows that : If C is not D , then A is not B , ( ii ) . Two such Theorems as ( i ) and ( ii ) ...
... Theorem , If A is B , then C is D , ( i ) , the hypothesis is that A is B , and the conclusion , that C is D. From this Theorem it necessarily follows that : If C is not D , then A is not B , ( ii ) . Two such Theorems as ( i ) and ( ii ) ...
Σελίδα 13
... Theorem ( i ) . 6. Sometimes the hypothesis of a Theorem is complex , i.e. , consists of several distinct hypotheses ; in this case every Theorem formed by interchanging the con- clusion and one of the hypotheses is a converse of the ...
... Theorem ( i ) . 6. Sometimes the hypothesis of a Theorem is complex , i.e. , consists of several distinct hypotheses ; in this case every Theorem formed by interchanging the con- clusion and one of the hypotheses is a converse of the ...
Σελίδα 14
... Theorems having been demonstrated the converse of each is necessarily true . 10. Rule of Identity . If there is but one A , and but one B ; then from the ... Theorem . THE ELEMENTS OF PLANE GEOMETRY . BOOK I. THE STRAIGHT 14 INTRODUCTION .
... Theorems having been demonstrated the converse of each is necessarily true . 10. Rule of Identity . If there is but one A , and but one B ; then from the ... Theorem . THE ELEMENTS OF PLANE GEOMETRY . BOOK I. THE STRAIGHT 14 INTRODUCTION .
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Συχνά εμφανιζόμενοι όροι και φράσεις
AB is equal ABCD AC is equal adjacent angles adjoining sides alternate angle angle ABC angle ACB angle AFG angle BAC angle CAB angle DEF angle EDF angle FGD angles are equal angles equal BA and AC base BC bisector bisects centre circle cutting Constr construct a triangle contrapositive diagonal distance draw a circle equal angles equal to AC equal to CD exterior angle find the locus Geometry given angle given point given straight line greater Hence hypotenuse identically equal interior opposite angle isosceles triangle less Let ABC meet middle point obtuse angle opposite sides parallel straight lines parallelogram perpendicular point equidistant Prob produced quadrilateral rectangle contained rectangle whose base right angles right-angled triangle shew side AB side AC sides equal square on AC squares on AB straight line drawn Theorem trapezium triangle ABC triangles are identically twice the rectangle vertex
Δημοφιλή αποσπάσματα
Σελίδα 27 - 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. either the sides adjacent to the equal...
Σελίδα 98 - A circle is a plane figure contained by one line, which is called the circumference, and is such that all straight lines drawn from a certain point within the figure to the circumference, are equal to one another.
Σελίδα 56 - ... is equal to twice as many right angles as the polygon
Σελίδα 35 - Any two sides of a triangle are together greater than the third side.
Σελίδα 26 - The straight lines drawn from the extremities of the base of an isosceles triangle to the middle points of the opposite sides are equal to one another.
Σελίδα 37 - 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 70 - A diameter of a circle is a straight line drawn through the centre, and terminated both ways by the circumference.
Σελίδα 110 - 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 31 - Any two angles of a triangle are together less than two right angles.
Σελίδα 115 - In a right.angled triangle, the square on the hypotenuse is equal to the sum of the squares on the sides containing the right angle . . . . 130 Applications of Pythagoras' theorem . . . . 132 THEOREM 6.