The Harpur Euclid: An Edition of Euclid's ElementsRivingtons, 1890 - 515 σελίδες |
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Σελίδα 63
... . Ex . 61. If we omitted the words ' towards the same parts ' from the hypothesis of I. 33 , what modification should we have to make in the conclusion ? DEF . - A parallelogram is a quadrilateral which has Book I. Prop . 33 . 63.
... . Ex . 61. If we omitted the words ' towards the same parts ' from the hypothesis of I. 33 , what modification should we have to make in the conclusion ? DEF . - A parallelogram is a quadrilateral which has Book I. Prop . 33 . 63.
Σελίδα 64
... parallelogram is || gm . PROPOSITION 34. THEOREM . The opposite sides and angles of a parallelogram are equal to one another , and the diameter bisects the parallelogram , i.e. divides it into two equal parts . Let ACDB be a || gm of ...
... parallelogram is || gm . PROPOSITION 34. THEOREM . The opposite sides and angles of a parallelogram are equal to one another , and the diameter bisects the parallelogram , i.e. divides it into two equal parts . Let ACDB be a || gm of ...
Σελίδα 65
... parallelogram . Ex . 63. The diagonals of a parallelogram bisect each other . Ex . 64. If the diagonals of a quadrilateral bisect each other it must be a parallelogram . Ex . 65. The join of the mid - points of two sides of a triangle ...
... parallelogram . Ex . 63. The diagonals of a parallelogram bisect each other . Ex . 64. If the diagonals of a quadrilateral bisect each other it must be a parallelogram . Ex . 65. The join of the mid - points of two sides of a triangle ...
Σελίδα 66
... Parallelograms on the same base and between the same parallels are equal to one another . Let || gms ABCD , EBCF be on the same base and between the same || s AF , BC , ABCD shall be equal to EBCF . F A DE B B Fig . 1 . Fig . 2 ...
... Parallelograms on the same base and between the same parallels are equal to one another . Let || gms ABCD , EBCF be on the same base and between the same || s AF , BC , ABCD shall be equal to EBCF . F A DE B B Fig . 1 . Fig . 2 ...
Σελίδα 67
... , is the Lr distance between the base and the opposite side or vertex . Ex . 70. - State and prove a converse of this Proposition . PROPOSITION 36. THeorem . Parallelograms on equal bases and between Book I. Prop . 35 . 67.
... , is the Lr distance between the base and the opposite side or vertex . Ex . 70. - State and prove a converse of this Proposition . PROPOSITION 36. THeorem . Parallelograms on equal bases and between Book I. Prop . 35 . 67.
Άλλες εκδόσεις - Προβολή όλων
The Harpur Euclid: An Edition of Euclid's Elements, Revised in Accordance ... Edward Mann Langley,Euclid,W. Seys Phillips Δεν υπάρχει διαθέσιμη προεπισκόπηση - 2015 |
Συχνά εμφανιζόμενοι όροι και φράσεις
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
Δημοφιλή αποσπάσματα
Σελίδα 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.
Σελίδα 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.
Σελίδα 390 - ... figures are to one another in the duplicate ratio of their homologous sides.
Σελίδα 97 - Let it be granted that a straight line may be drawn from any one point to any other point.
Σελίδα 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.
Σελίδα 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.
Σελίδα 40 - Any two sides of a triangle are together greater than the third side.
Σελίδα 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.
Σελίδα 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.
Σελίδα 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...