 In isosceles triangles, the angles at the base are equal to one another, and, if the equal straight lines be produced further, the angles under the base will be equal to one another.  此零非彼O - Σελίδα 216των 洪萬生 - 2006 - 353 σελίδεςΠεριορισμένη προεπισκόπηση - Σχετικά με αυτό το βιβλίο
 | Euclides - 1833 - 304 σελίδες
...respectively = , the whole triangles must coincide and be e=. PROP. 5, THEOR. In an isosceles triangle the angles at the base are equal to one another ; and, if the equal sides be produced, the angles below the base shall be also equal. Assume points in the legs below the... | |
 | 1835 - 684 σελίδες
...likewise equal to the angle opposite to the other ; and conversely . . 6 (e) lu au isosceles triangle, 1. The angles at the base are equal to one another ; and if the equal sides are produced, the angles upon the other side of the base are likewise equal . cor, 6 2. The following... | |
 | Euclid - 1908 - 550 σελίδες
...throughout so far as both extend; and Savile's argument then proves that B coincides with E. PROPOSITION 5. In isosceles triangles the angles at the base are...angles under the base will be equal to one another. Let ABC be an isosceles triangle having the side AB 5 equal to the side AC; and let the straight lines... | |
 | Euclid - 1908 - 456 σελίδες
...is equilateral ; and therefore its three angles EGD, GDE, DEG are equal to one another, inasmuch as, in isosceles triangles, the angles at the base are equal to one another. [i. 5] And the three angles of the triangle are equal to two right angles ; [i. 32] therefore the angle... | |
 | David Eugene Smith - 1911 - 360 σελίδες
...the equal sides are equal. This is Euclid's Proposition 5, the second of his theorems, but he adds, "and if the equal straight lines be produced further,...angles under the base will be equal to one another." Since, however, he does not use this second part, its genuineness is doubted. He would not admit the... | |
 | Mathematical Association - 1923 - 88 σελίδες
...will be equal to the remaining angles respectively, namely those which the equal sides subtend. 1.5: In isosceles triangles the angles at the base are...angles under the base will be equal to one another. I. 8 : If two triangles have the two sides equal to two sides respectively, and have also the base... | |
 | David E. Smith - 1958 - 756 σελίδες
...be considered, the first being Proposition 5 of Book I. As given by Euclid, this reads as follows: In isosceles triangles the angles at the base are...angles under the base will be equal to one another. Proclus states that Thales (c. 600 BC) was the first to prove this proposition. At any rate it was... | |
 | G.E. Martin - 1997 - 536 σελίδες
...17, we shall discuss this as well as an alternative method. Euclid's Propositions 1.5 through 1.7 5. In isosceles triangles the angles at the base are...angles under the base will be equal to one another. (Theorem 17.5) 6. If in a triangle two angles be equal to one another, the sides which subtend the... | |
 | Daniel Pedoe - 1983 - 338 σελίδες
...Postulates, the fifth, and what the search led to. We have already made use of Euclid's Proposition 5 : In isosceles triangles the angles at the base are equal to one another. An isosceles triangle ABC is one in which, say, the side AB is equal to the side AC (Figure 58). If... | |
 | Daniel Pedoe - 1988 - 468 σελίδες
...angles will be equal to the remaining angles respectively, namely those which the equal sides subtend. 5 In isosceles triangles the angles at the base are...angles under the base will be equal to one another. 6 If in a triangle two angles be equal to one another, the sides which subtend the equal angles will... | |
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