The Harpur Euclid: An Edition of Euclid's ElementsRivingtons, 1890 - 515 σελίδες |
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Σελίδα 9
... side of that base ; ( c ) The other two sides of the equilateral triangle may be produced either both through the vertex , or , as in the diagram , both in the opposite direction ; so that with BC and A given there are eight ways in ...
... side of that base ; ( c ) The other two sides of the equilateral triangle may be produced either both through the vertex , or , as in the diagram , both in the opposite direction ; so that with BC and A given there are eight ways in ...
Σελίδα 12
... angles shall be equal , each to each , namely those to which the equal sides are opposite . Let ABC , DEF be two triangles which have the two sides AB , AC equal to the two sides DE , DF , each to each , namely AB to DE , and AC to DF ...
... angles shall be equal , each to each , namely those to which the equal sides are opposite . Let ABC , DEF be two triangles which have the two sides AB , AC equal to the two sides DE , DF , each to each , namely AB to DE , and AC to DF ...
Σελίδα 21
... sides of the other , each to each , then the triangles are identically equal , and of the angles , those are equal which are opposite to equal sides . ( Syllabus . ) Ex . 3. - In the figure of Prop . I join AD , BD , and prove that the ...
... sides of the other , each to each , then the triangles are identically equal , and of the angles , those are equal which are opposite to equal sides . ( Syllabus . ) Ex . 3. - In the figure of Prop . I join AD , BD , and prove that the ...
Σελίδα 23
... side remote from A. 2. The demonstration would be just as easy if the △ DFE were merely an isosceles △ having DE ... opposite sides of a common base , AF , and such that superposition could be effected by turning either of them about ...
... side remote from A. 2. The demonstration would be just as easy if the △ DFE were merely an isosceles △ having DE ... opposite sides of a common base , AF , and such that superposition could be effected by turning either of them about ...
Σελίδα 27
... opposite sides of AB , when they cut , are joined , then the join of CE bisects AB . We do not join AC , CB , AE , EB because we are not concerned with demonstrating the correctness of our method ; on the other hand Euclid does not draw ...
... opposite sides of AB , when they cut , are joined , then the join of CE bisects AB . We do not join AC , CB , AE , EB because we are not concerned with demonstrating the correctness of our method ; on the other hand Euclid does not draw ...
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...