A Text-book of Euclid's Elements for the Use of Schools, Βιβλίο 1Macmillan, 1904 - 456 σελίδες |
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Σελίδα vi
... whole , we have employed all such signs and abbreviations as we believe to add to the clearness of the reasoning , care being taken that the symbols chosen are com- patible with a rigorous geometrical method , and are recognised by the ...
... whole , we have employed all such signs and abbreviations as we believe to add to the clearness of the reasoning , care being taken that the symbols chosen are com- patible with a rigorous geometrical method , and are recognised by the ...
Σελίδα ix
... whole of a proposition at one view , or of bringing notes and exercises into closer connection with the text to which they refer . Further , the symbols " . " for therefore , " for is equal to are now introduced from the 35th ...
... whole of a proposition at one view , or of bringing notes and exercises into closer connection with the text to which they refer . Further , the symbols " . " for therefore , " for is equal to are now introduced from the 35th ...
Σελίδα 8
... whole is greater than its part . * To preserve the classification of general and geometrical axioms , we have placed Euclid's ninth axiom before the eighth . GEOMETRICAL AXIOMS . 8. Magnitudes which can be made to coincide with one ...
... whole is greater than its part . * To preserve the classification of general and geometrical axioms , we have placed Euclid's ninth axiom before the eighth . GEOMETRICAL AXIOMS . 8. Magnitudes which can be made to coincide with one ...
Σελίδα 20
... whole ; which is absurd . Ax . 9 . Therefore AB is not unequal to AC ; that is , AB is equal to AC . Q.E.D. COROLLARY . Hence if a triangle is equiangular it is also equilateral . NOTE ON PROPOSITIONS 5 AND 6 . The enunciation of 20 ...
... whole ; which is absurd . Ax . 9 . Therefore AB is not unequal to AC ; that is , AB is equal to AC . Q.E.D. COROLLARY . Hence if a triangle is equiangular it is also equilateral . NOTE ON PROPOSITIONS 5 AND 6 . The enunciation of 20 ...
Σελίδα 22
... whole angle ACD is greater than its part , the angle BCD ; therefore also the angle ADC is greater than the angle BCD ; still more then is the angle BDC greater than the angle BCD . Again , in the triangle BCD , because BC is equal to ...
... whole angle ACD is greater than its part , the angle BCD ; therefore also the angle ADC is greater than the angle BCD ; still more then is the angle BDC greater than the angle BCD . Again , in the triangle BCD , because BC is equal to ...
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Συχνά εμφανιζόμενοι όροι και φράσεις
ABCD AC is equal adjacent angles Algebra angle BAC angle equal base BC bisected bisectors centre chord circumference circumscribed circle concyclic Constr Describe a circle diagonal diameter divided equal angles equiangular Euclid Euclid's exterior angle find the locus given circle given point given straight line given triangle greater Hence hypotenuse inscribed circle isosceles triangle Let ABC line which joins magnitudes meet middle point nine-points circle opposite sides orthocentre par¹ parallelogram parm pass pedal triangle perp perpendiculars drawn plane XY polygon produced Proof proportional PROPOSITION PROPOSITION 13 prove quadrilateral radical axis radius rectangle contained rectilineal figure regular polygon right angles segment shew shewn side BC Similarly square straight line drawn tangent THEOREM triangle ABC twice the rect vertex vertical angle
Δημοφιλή αποσπάσματα
Σελίδα 353 - Pythagoras' theorem states that the square of the length of the hypotenuse of a right-angled triangle is equal to the sum of the squares of the lengths of the other two sides.
Σελίδα 340 - If two triangles have one angle of the one equal to one angle of the other and the sides about these equal angles proportional, the triangles are similar.
Σελίδα 65 - If two triangles have two angles of the one equal to two angles of the other, each to each, and also one side of the one equal to the corresponding side of the other, the triangles are congruent.
Σελίδα 162 - AB into two parts, so that the rectangle contained by the whole line and one of the parts, shall be equal to the square on the other part.
Σελίδα 326 - From this it is manifest that prisms upon triangular bases, of the same altitude, are to one another as their bases. Let the...
Σελίδα 162 - If a straight line be bisected and produced to any point, the rectangle contained by the whole line thus produced and the part of it produced, together •with the square...
Σελίδα 291 - The side of a regular hexagon inscribed in a circle is equal to the radius of the circle.
Σελίδα 79 - The straight line joining the middle points of two sides of a triangle is parallel to the third side and equal to half of it 46 INTERCEPTS BY PARALLEL LINES.
Σελίδα 18 - THE angles at the base of an isosceles triangle are equal to one another : and, if the equal sides be produced, the angles upon the other side of the base shall be equal.
Σελίδα 242 - We may here notice that the perpendiculars from the vertices of a triangle to the opposite sides are concurrent ; their meet is called the orthocentre, and the triangle obtained by joining the feet of the perpendiculars is called the pedal triangle.