The Harpur Euclid: An Edition of Euclid's ElementsRivingtons, 1890 - 515 páginas |
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Página 21
... prove that the angles CAB , DAB are equal to each other . Ex . 4. - In the figure of Prop .. I join CD and prove that the angles ACD , BCD are equal to each other . Ex . 5. - In the figure of Prop . I let E be the point where CD cuts AB ...
... prove that the angles CAB , DAB are equal to each other . Ex . 4. - In the figure of Prop .. I join CD and prove that the angles ACD , BCD are equal to each other . Ex . 5. - In the figure of Prop . I let E be the point where CD cuts AB ...
Página 36
... . Ex . 23. - Not more than two straight lines equal to one another can be drawn from a given point to a given straight line . ( Prove indirectly . ) PROPOSITION 18. THEOREM . The greater side of every triangle 36 Euclid's Elements .
... . Ex . 23. - Not more than two straight lines equal to one another can be drawn from a given point to a given straight line . ( Prove indirectly . ) PROPOSITION 18. THEOREM . The greater side of every triangle 36 Euclid's Elements .
Página 39
... proving a converse ( see Prop . 6 ) . It should be carefully remembered that this proposition is merely equivalent to the following : — ' If two angles of a triangle are unequal , the side which sub- tends the greater is greater than ...
... proving a converse ( see Prop . 6 ) . It should be carefully remembered that this proposition is merely equivalent to the following : — ' If two angles of a triangle are unequal , the side which sub- tends the greater is greater than ...
Página 40
... the other two sides . Prove this ( 1 ) independently , ( 2 ) as a deduction from Prop . 20 . Ex . 26. Any three sides of a quadrilateral are together greater than the fourth . Ex . 27. - Any two sides of a triangle 40 Euclid's Elements .
... the other two sides . Prove this ( 1 ) independently , ( 2 ) as a deduction from Prop . 20 . Ex . 26. Any three sides of a quadrilateral are together greater than the fourth . Ex . 27. - Any two sides of a triangle 40 Euclid's Elements .
Página 41
... prove a similar theorem as regards a quadri- lateral . Can it be extended to other polygons ( figures with more sides than three ) ? The four sides of a quadrilateral are together greater than the diagonals . Are the five sides of a ...
... prove a similar theorem as regards a quadri- lateral . Can it be extended to other polygons ( figures with more sides than three ) ? The four sides of a quadrilateral are together greater than the diagonals . Are the five sides of a ...
Otras ediciones - Ver todas
The Harpur Euclid: An Edition of Euclid's Elements, Revised in Accordance ... Edward Mann Langley,Euclid,W. Seys Phillips Sin vista previa disponible - 2015 |
Términos y frases comunes
bisect bisector Brocard point chord circum-circle of triangle circumference coincide common concyclic congruent cyclic quadrilateral demonstration described diagonals diameter diamr divided draw equal angles equiangr equiangular equidistant equilateral triangle equimultiples Euclid exterior angle Geometry given circle given point given ratio given st given straight line given triangle greater Hence inscribed intersect isosceles isosceles triangle Join Let ABC locus magnitude meet mid-point opposite sides parallel parallelogram pass pentagon perpendicular plane produced Prop PROPOSITION PROPOSITION 13 radical axis radius rect rectangle contained reqd rhombus right angles segment Show sides BC similar Similarly Simson's line square straight line drawn student subtended symmedian symmedian point tangent THEOREM touch triangle ABC vertex vertices
Pasajes populares
Página 21 - 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.
Página 369 - 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.
Página 390 - ... figures are to one another in the duplicate ratio of their homologous sides.
Página 97 - Let it be granted that a straight line may be drawn from any one point to any other point.
Página 370 - IN a right-angled triangle, if a perpendicular be drawn from the right angle to the base, the triangles on each side of it are similar to the whole triangle, and to one another.
Página 96 - 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.
Página 40 - Any two sides of a triangle are together greater than the third side.
Página 143 - Three times the sum of the squares on the sides of a triangle is equal to four times the sum of the squares of the lines joining the middle point of each side with the opposite angles.
Página 407 - 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.
Página 156 - 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...